%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW302+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:05:44 AM UTC 2026
% Result : Theorem 33.35s 33.60s
% Output : Proof 33.56s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
! [V_g_2,V_f_2] :
( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
=> V_f_2 = V_g_2 ),
file('theBenchmark.p',fact_ext) ).
fof(fact_equal__triple__def,axiom,
! [V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(T_b)),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_equal__triple__def) ).
fof(fact_Rep__triple__inject,axiom,
! [V_y_2,V_x_2,T_b] :
( hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2) = hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_Rep__triple__inject) ).
fof(fact_equal,axiom,
! [T_b] :
( class_HOL_Oequal(T_b)
=> c_HOL_Oequal__class_Oequal(T_b) = c_fequal ),
file('theBenchmark.p',fact_equal) ).
fof(fact_equal__refl,axiom,
! [V_x,T_a] :
( class_HOL_Oequal(T_a)
=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ),
file('theBenchmark.p',fact_equal__refl) ).
fof(fact_equal__eq,axiom,
! [V_y_2,V_x_2,T_b] :
( class_HOL_Oequal(T_b)
=> ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_equal__eq) ).
fof(fact_eq__equal,axiom,
! [T_b] :
( class_HOL_Oequal(T_b)
=> c_fequal = c_HOL_Oequal__class_Oequal(T_b) ),
file('theBenchmark.p',fact_eq__equal) ).
fof(fact_Rep__triple__inverse,axiom,
! [V_x_2,T_b] : hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2)) = V_x_2,
file('theBenchmark.p',fact_Rep__triple__inverse) ).
fof(fact_Rep__triple,axiom,
! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))),
file('theBenchmark.p',fact_Rep__triple) ).
fof(fact_type__definition__triple,axiom,
! [T_b] : c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(T_b),tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool),c_Hoare__Mirabelle_ORep__triple(T_b),c_Hoare__Mirabelle_OAbs__triple(T_b),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))),
file('theBenchmark.p',fact_type__definition__triple) ).
fof(fact_Abs__triple__inverse,axiom,
! [V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
=> hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_Abs__triple__inverse) ).
fof(fact_Abs__triple__inject,axiom,
! [V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_x_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
=> ( hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_x_2) = hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_Abs__triple__inject) ).
fof(fact_equalityCE,axiom,
! [V_ca_2,T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_equalityCE) ).
fof(fact_type__definition_OAbs__inject,axiom,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
=> ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_type__definition_OAbs__inject) ).
fof(fact_type__definition_OAbs__inverse,axiom,
! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
=> hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ),
file('theBenchmark.p',fact_type__definition_OAbs__inverse) ).
fof(fact_type__definition_ORep,axiom,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ),
file('theBenchmark.p',fact_type__definition_ORep) ).
fof(fact_Abs__triple__induct,axiom,
! [V_x_2,V_Pa_2,T_b] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),B_y),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
=> hBOOL(hAPP(V_Pa_2,hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),B_y))) )
=> hBOOL(hAPP(V_Pa_2,V_x_2)) ),
file('theBenchmark.p',fact_Abs__triple__induct) ).
fof(fact_Abs__triple__cases,axiom,
! [T_b,V_x_2] :
~ ! [B_y] :
( V_x_2 = hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),B_y)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),B_y),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ),
file('theBenchmark.p',fact_Abs__triple__cases) ).
fof(fact_Rep__triple__induct,axiom,
! [V_Pa_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
=> ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),B_x)))
=> hBOOL(hAPP(V_Pa_2,V_y_2)) ) ),
file('theBenchmark.p',fact_Rep__triple__induct) ).
fof(fact_Rep__triple__cases,axiom,
! [V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
=> ~ ! [B_x] : V_y_2 != hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),B_x) ),
file('theBenchmark.p',fact_Rep__triple__cases) ).
fof(fact_type__definition_ORep__inject,axiom,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_type__definition_ORep__inject) ).
fof(fact_type__definition_ORep__inverse,axiom,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ),
file('theBenchmark.p',fact_type__definition_ORep__inverse) ).
fof(fact_Collect__def,axiom,
! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2,
file('theBenchmark.p',fact_Collect__def) ).
fof(fact_eq__mem__trans,axiom,
! [V_A_2,T_b,V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eq__mem__trans) ).
fof(fact_mem__def,axiom,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_mem__def) ).
fof(fact_eqset__imp__iff,axiom,
! [V_x_2,T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_eqset__imp__iff) ).
fof(fact_eqelem__imp__iff,axiom,
! [V_A_2,T_b,V_y_2,V_x_2] :
( V_x_2 = V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eqelem__imp__iff) ).
fof(fact_eq__mem,axiom,
! [V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_eq__mem) ).
fof(fact_type__definition_OAbs__cases,axiom,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ~ ! [B_y] :
( V_x_2 = hAPP(V_Abs_2,B_y)
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) ) ),
file('theBenchmark.p',fact_type__definition_OAbs__cases) ).
fof(fact_type__definition_OAbs__induct,axiom,
! [V_x_2,V_Pa_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2))
=> hBOOL(hAPP(V_Pa_2,hAPP(V_Abs_2,B_y))) )
=> hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
file('theBenchmark.p',fact_type__definition_OAbs__induct) ).
fof(fact_type__definition_ORep__induct,axiom,
! [V_Pa_2,V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
=> ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(V_Rep_2,B_x)))
=> hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ),
file('theBenchmark.p',fact_type__definition_ORep__induct) ).
fof(fact_type__definition_ORep__cases,axiom,
! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
=> ~ ! [B_x] : V_y_2 != hAPP(V_Rep_2,B_x) ) ),
file('theBenchmark.p',fact_type__definition_ORep__cases) ).
fof(fact_induct__false__def,axiom,
~ c_HOL_Oinduct__false,
file('theBenchmark.p',fact_induct__false__def) ).
fof(fact_ord_OatMost__iff,axiom,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ),
file('theBenchmark.p',fact_ord_OatMost__iff) ).
fof(fact_ord_OatLeast__iff,axiom,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ),
file('theBenchmark.p',fact_ord_OatLeast__iff) ).
fof(fact_ord_OlessThan__iff,axiom,
! [V_k_2,V_less_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ),
file('theBenchmark.p',fact_ord_OlessThan__iff) ).
fof(fact_ord_OgreaterThan__iff,axiom,
! [V_k_2,V_less_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ),
file('theBenchmark.p',fact_ord_OgreaterThan__iff) ).
fof(fact_ord_OatLeastAtMost__iff,axiom,
! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
fof(fact_ord_OgreaterThanLessThan__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
fof(fact_ord_OgreaterThanAtMost__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
fof(fact_ord_OatLeastLessThan__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
fof(fact_ballE,axiom,
! [V_x_2,V_Pa_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
=> ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_ballE) ).
fof(fact_bexE,axiom,
! [V_Pa_2,V_A_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_bexE) ).
fof(fact_bexI,axiom,
! [V_A_2,T_b,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_bexI) ).
fof(fact_InterE,axiom,
! [V_X_2,V_C_2,V_A_2,T_b] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
file('theBenchmark.p',fact_InterE) ).
fof(fact_InterD,axiom,
! [V_X_2,V_C_2,V_A_2,T_b] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
file('theBenchmark.p',fact_InterD) ).
fof(fact_UnionI,axiom,
! [V_A_2,V_C_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
=> 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))) ) ),
file('theBenchmark.p',fact_UnionI) ).
fof(fact_emptyE,axiom,
! [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)))),
file('theBenchmark.p',fact_emptyE) ).
fof(fact_UNIV__I,axiom,
! [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)))),
file('theBenchmark.p',fact_UNIV__I) ).
fof(fact_subsetD,axiom,
! [V_ca_2,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),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subsetD) ).
fof(fact_equalityI,axiom,
! [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),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_equalityI) ).
fof(fact_top1I,axiom,
! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)),
file('theBenchmark.p',fact_top1I) ).
fof(fact_empty__subsetI,axiom,
! [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)),
file('theBenchmark.p',fact_empty__subsetI) ).
fof(fact_predicate1D,axiom,
! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> hBOOL(hAPP(V_Qa_2,V_x_2)) ) ),
file('theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
=> hBOOL(hAPP(V_Qa_2,V_x_2)) ) ),
file('theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_Inf__empty,axiom,
! [T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Inf__empty) ).
fof(fact_Inter__empty,axiom,
! [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)),
file('theBenchmark.p',fact_Inter__empty) ).
fof(fact_Inf__UNIV,axiom,
! [T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Inf__UNIV) ).
fof(fact_Inter__UNIV,axiom,
! [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)),
file('theBenchmark.p',fact_Inter__UNIV) ).
fof(fact_Sup__empty,axiom,
! [T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Sup__empty) ).
fof(fact_Union__empty,axiom,
! [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)),
file('theBenchmark.p',fact_Union__empty) ).
fof(fact_Sup__UNIV,axiom,
! [T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Sup__UNIV) ).
fof(fact_Union__UNIV,axiom,
! [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)),
file('theBenchmark.p',fact_Union__UNIV) ).
fof(fact_le__Inf__iff,axiom,
! [V_A_2,V_b_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( 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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ),
file('theBenchmark.p',fact_le__Inf__iff) ).
fof(fact_Sup__le__iff,axiom,
! [V_b_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( 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))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ),
file('theBenchmark.p',fact_Sup__le__iff) ).
fof(fact_Union__mono,axiom,
! [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)),V_A_2),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_Union__mono) ).
fof(fact_Inter__anti__mono,axiom,
! [V_A_2,V_B_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_B_2),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_Inter__anti__mono) ).
fof(fact_equalityE,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ),
file('theBenchmark.p',fact_equalityE) ).
fof(fact_subset__trans,axiom,
! [V_C_2,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),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_subset__trans) ).
fof(fact_equalityD2,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
file('theBenchmark.p',fact_equalityD2) ).
fof(fact_equalityD1,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_equalityD1) ).
fof(fact_set__eq__subset,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__eq__subset) ).
fof(fact_subset__empty,axiom,
! [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_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)) ),
file('theBenchmark.p',fact_subset__empty) ).
fof(fact_subset__refl,axiom,
! [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)),
file('theBenchmark.p',fact_subset__refl) ).
fof(fact_subset__UNIV,axiom,
! [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)))),
file('theBenchmark.p',fact_subset__UNIV) ).
fof(fact_UNIV__not__empty,axiom,
! [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)),
file('theBenchmark.p',fact_UNIV__not__empty) ).
fof(fact_Union__upper,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_Union__upper) ).
fof(fact_Sup__upper,axiom,
! [V_A_2,V_x_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Sup__upper) ).
fof(fact_Inter__lower,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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)) ),
file('theBenchmark.p',fact_Inter__lower) ).
fof(fact_Inf__lower,axiom,
! [V_A_2,V_x_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_Inf__lower) ).
fof(fact_in__mono,axiom,
! [V_x_2,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),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__mono) ).
fof(fact_set__rev__mp,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__rev__mp) ).
fof(fact_set__mp,axiom,
! [V_x_2,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),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__mp) ).
fof(fact_all__not__in__conv,axiom,
! [V_A_2,T_b] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_ex__in__conv,axiom,
! [V_A_2,T_b] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
<=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ex__in__conv) ).
fof(fact_empty__iff,axiom,
! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_empty__iff) ).
fof(fact_equals0D,axiom,
! [V_a_2,T_b,V_A_2] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
file('theBenchmark.p',fact_equals0D) ).
fof(fact_empty__Collect__eq,axiom,
! [V_Pa_2,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
<=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
file('theBenchmark.p',fact_empty__Collect__eq) ).
fof(fact_Collect__empty__eq,axiom,
! [V_Pa_2,T_b] :
( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
file('theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_order__refl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ),
file('theBenchmark.p',fact_order__refl) ).
fof(fact_top__apply,axiom,
! [V_x_2,T_c,T_b] :
( class_Orderings_Otop(T_b)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ),
file('theBenchmark.p',fact_top__apply) ).
fof(fact_bot__apply,axiom,
! [V_x_2,T_c,T_b] :
( class_Orderings_Obot(T_b)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
file('theBenchmark.p',fact_bot__apply) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [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)))),
file('theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_top__greatest,axiom,
! [V_x,T_a] :
( class_Orderings_Otop(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ),
file('theBenchmark.p',fact_top__greatest) ).
fof(fact_le__fun__def,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> ! [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))) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
fof(fact_le__funD,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
=> 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))) ) ),
file('theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
=> 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))) ) ),
file('theBenchmark.p',fact_le__funE) ).
fof(fact_bot__least,axiom,
! [V_x,T_a] :
( class_Orderings_Obot(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ),
file('theBenchmark.p',fact_bot__least) ).
fof(fact_InterI,axiom,
! [V_A_2,V_C_2,T_b] :
( ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
=> 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))) ),
file('theBenchmark.p',fact_InterI) ).
fof(fact_UnionE,axiom,
! [V_C_2,V_A_2,T_b] :
( 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)))
=> ~ ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ),
file('theBenchmark.p',fact_UnionE) ).
fof(fact_Inter__greatest,axiom,
! [V_C_2,V_A_2,T_b] :
( ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),B_X)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
file('theBenchmark.p',fact_Inter__greatest) ).
fof(fact_linorder__le__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_xt1_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_xt1_I5_J,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__trans) ).
fof(fact_order__antisym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I4_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I4_J) ).
fof(fact_ord__le__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__le__eq__trans) ).
fof(fact_xt1_I3_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I3_J) ).
fof(fact_ord__eq__le__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__eq__le__trans) ).
fof(fact_order__antisym__conv,axiom,
! [V_x_2,V_y_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__refl,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( V_x = V_y
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_order__eq__refl) ).
fof(fact_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( V_x_2 = V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__eq__iff) ).
fof(fact_linorder__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_linorder__linear) ).
fof(fact_Powp__mono,axiom,
! [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),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_Powp__mono) ).
fof(fact_Inter__subset,axiom,
! [V_B_2,V_A_2,T_b] :
( ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_Inter__subset) ).
fof(fact_Union__least,axiom,
! [V_C_2,V_A_2,T_b] :
( ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) )
=> 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)),V_C_2)) ),
file('theBenchmark.p',fact_Union__least) ).
fof(fact_Inf__greatest,axiom,
! [V_z_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) ) ),
file('theBenchmark.p',fact_Inf__greatest) ).
fof(fact_Sup__least,axiom,
! [V_z_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_z_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_z_2)) ) ),
file('theBenchmark.p',fact_Sup__least) ).
fof(fact_subsetI,axiom,
! [V_B_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_subsetI) ).
fof(fact_greaterThan__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_greaterThan__subset__iff) ).
fof(fact_Pow__UNIV,axiom,
! [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)),
file('theBenchmark.p',fact_Pow__UNIV) ).
fof(fact_PowI,axiom,
! [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),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
file('theBenchmark.p',fact_PowI) ).
fof(fact_atMost__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_atMost__subset__iff) ).
fof(fact_atLeast__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_atLeast__subset__iff) ).
fof(fact_greaterThan__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_greaterThan__eq__iff) ).
fof(fact_atLeast__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_atLeast__eq__iff) ).
fof(fact_atMost__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_atMost__eq__iff) ).
fof(fact_Pow__top,axiom,
! [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))),
file('theBenchmark.p',fact_Pow__top) ).
fof(fact_Union__Pow__eq,axiom,
! [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,
file('theBenchmark.p',fact_Union__Pow__eq) ).
fof(fact_Pow__not__empty,axiom,
! [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)),
file('theBenchmark.p',fact_Pow__not__empty) ).
fof(fact_Pow__bottom,axiom,
! [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))),
file('theBenchmark.p',fact_Pow__bottom) ).
fof(fact_PowD,axiom,
! [V_B_2,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_B_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_PowD) ).
fof(fact_Pow__iff,axiom,
! [V_B_2,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_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_Pow__iff) ).
fof(fact_Pow__mono,axiom,
! [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),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_Pow__mono) ).
fof(fact_atMost__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_atMost__iff) ).
fof(fact_atLeast__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_atLeast__iff) ).
fof(fact_subset__Pow__Union,axiom,
! [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)))),
file('theBenchmark.p',fact_subset__Pow__Union) ).
fof(fact_Pow__empty,axiom,
! [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))),
file('theBenchmark.p',fact_Pow__empty) ).
fof(fact_lessThan__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_lessThan__subset__iff) ).
fof(fact_INF__subset,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> 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))) ) ),
file('theBenchmark.p',fact_INF__subset) ).
fof(fact_SUP__subset,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> 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))) ) ),
file('theBenchmark.p',fact_SUP__subset) ).
fof(fact_greaterThanLessThan__empty,axiom,
! [V_k_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
=> 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)) ) ),
file('theBenchmark.p',fact_greaterThanLessThan__empty) ).
fof(fact_greaterThanAtMost__empty,axiom,
! [V_k_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
=> 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)) ) ),
file('theBenchmark.p',fact_greaterThanAtMost__empty) ).
fof(fact_Collect__mono,axiom,
! [T_b,V_Qa_2,V_Pa_2] :
( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> hBOOL(hAPP(V_Qa_2,B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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))) ),
file('theBenchmark.p',fact_Collect__mono) ).
fof(fact_UNIV__eq__I,axiom,
! [V_A_2,T_b] :
( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = V_A_2 ),
file('theBenchmark.p',fact_UNIV__eq__I) ).
fof(fact_UNIV__witness,axiom,
! [T_b] :
? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_UNIV__witness) ).
fof(fact_le__funI,axiom,
! [T_b,V_g_2,V_f_2,T_c] :
( class_Orderings_Oord(T_c)
=> ( ! [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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ),
file('theBenchmark.p',fact_le__funI) ).
fof(fact_equals0I,axiom,
! [V_A_2,T_b] :
( ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_equals0I) ).
fof(fact_insertCI,axiom,
! [V_b_2,V_B_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
=> V_a_2 = V_b_2 )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_insertCI) ).
fof(fact_insertE,axiom,
! [V_A_2,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_b_2),V_A_2)))
=> ( V_a_2 != V_b_2
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_insertE) ).
fof(fact_insert__absorb2,axiom,
! [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),
file('theBenchmark.p',fact_insert__absorb2) ).
fof(fact_insert__commute,axiom,
! [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)),
file('theBenchmark.p',fact_insert__commute) ).
fof(fact_insert__code,axiom,
! [V_x_2,V_A_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
<=> ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2 ) ),
file('theBenchmark.p',fact_insert__code) ).
fof(fact_lessThan__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_lessThan__eq__iff) ).
fof(fact_insert__absorb,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
file('theBenchmark.p',fact_insert__absorb) ).
fof(fact_insertI2,axiom,
! [V_b_2,V_B_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_insertI2) ).
fof(fact_insert__ident,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_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_B_2)
<=> V_A_2 = V_B_2 ) ) ),
file('theBenchmark.p',fact_insert__ident) ).
fof(fact_insert__iff,axiom,
! [V_A_2,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_b_2),V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_insert__iff) ).
fof(fact_insertI1,axiom,
! [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))),
file('theBenchmark.p',fact_insertI1) ).
fof(fact_empty__not__insert,axiom,
! [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),
file('theBenchmark.p',fact_empty__not__insert) ).
fof(fact_insert__not__empty,axiom,
! [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)),
file('theBenchmark.p',fact_insert__not__empty) ).
fof(fact_doubleton__eq__iff,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,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_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
<=> ( ( V_b_2 = V_ca_2
& V_a_2 = V_d_2 )
| ( V_b_2 = V_d_2
& V_a_2 = V_ca_2 ) ) ),
file('theBenchmark.p',fact_doubleton__eq__iff) ).
fof(fact_singleton__inject,axiom,
! [V_b_2,V_a_2,T_b] :
( 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)))
=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_singleton__inject) ).
fof(fact_subset__insertI,axiom,
! [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))),
file('theBenchmark.p',fact_subset__insertI) ).
fof(fact_subset__insertI2,axiom,
! [V_b_2,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),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_subset__insertI2) ).
fof(fact_insert__mono,axiom,
! [V_a_2,V_D_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
=> 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))) ),
file('theBenchmark.p',fact_insert__mono) ).
fof(fact_singleton__iff,axiom,
! [V_a_2,V_b_2,T_b] :
( 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)))))
<=> V_b_2 = V_a_2 ),
file('theBenchmark.p',fact_singleton__iff) ).
fof(fact_singletonE,axiom,
! [V_a_2,V_b_2,T_b] :
( 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)))))
=> V_b_2 = V_a_2 ),
file('theBenchmark.p',fact_singletonE) ).
fof(fact_insert__subset,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( 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))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_insert__subset) ).
fof(fact_subset__insert,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subset__insert) ).
fof(fact_subset__singletonD,axiom,
! [V_x_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_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(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_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_subset__singletonD) ).
fof(fact_Sup__singleton,axiom,
! [V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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 ),
file('theBenchmark.p',fact_Sup__singleton) ).
fof(fact_Inf__singleton,axiom,
! [V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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 ),
file('theBenchmark.p',fact_Inf__singleton) ).
fof(fact_the__elem__eq,axiom,
! [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,
file('theBenchmark.p',fact_the__elem__eq) ).
fof(fact_ivl__disj__un_I1_J,axiom,
! [V_l_2,T_b] :
( class_Orderings_Olinorder(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_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) ),
file('theBenchmark.p',fact_ivl__disj__un_I1_J) ).
fof(fact_atMost__Int__atLeast,axiom,
! [V_n_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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))) ),
file('theBenchmark.p',fact_atMost__Int__atLeast) ).
fof(fact_ivl__disj__un_I2_J,axiom,
! [V_u_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_ivl__disj__un_I2_J) ).
fof(fact_diff__single__insert,axiom,
! [V_B_2,V_x_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),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))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_diff__single__insert) ).
fof(fact_subset__insert__iff,axiom,
! [V_B_2,V_x_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_Set_Oinsert(T_b),V_x_2),V_B_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_subset__insert__iff) ).
fof(fact_Int__eq__Inter,axiom,
! [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))))),
file('theBenchmark.p',fact_Int__eq__Inter) ).
fof(fact_Un__eq__Union,axiom,
! [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))))),
file('theBenchmark.p',fact_Un__eq__Union) ).
fof(fact_ivl__disj__int_I5_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I5_J) ).
fof(fact_ivl__disj__int_I6_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I6_J) ).
fof(fact_ivl__disj__un_I11_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I11_J) ).
fof(fact_sup1CI,axiom,
! [T_b,V_A_2,V_x_2,V_B_2] :
( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
=> hBOOL(hAPP(V_A_2,V_x_2)) )
=> 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)) ),
file('theBenchmark.p',fact_sup1CI) ).
fof(fact_sup1E,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( 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))
=> ( ~ hBOOL(hAPP(V_A_2,V_x_2))
=> hBOOL(hAPP(V_B_2,V_x_2)) ) ),
file('theBenchmark.p',fact_sup1E) ).
fof(fact_inf1E,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( 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))
=> ~ ( hBOOL(hAPP(V_A_2,V_x_2))
=> ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
file('theBenchmark.p',fact_inf1E) ).
fof(fact_inf1I,axiom,
! [T_b,V_B_2,V_x_2,V_A_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
=> ( hBOOL(hAPP(V_B_2,V_x_2))
=> 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)) ) ),
file('theBenchmark.p',fact_inf1I) ).
fof(fact_UnE,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
file('theBenchmark.p',fact_UnE) ).
fof(fact_UnCI,axiom,
! [V_A_2,V_B_2,V_ca_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnCI) ).
fof(fact_IntI,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_IntI) ).
fof(fact_IntE,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
file('theBenchmark.p',fact_IntE) ).
fof(fact_DiffI,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_DiffI) ).
fof(fact_DiffE,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
file('theBenchmark.p',fact_DiffE) ).
fof(fact_inf1D2,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( 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))
=> hBOOL(hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_inf1D2) ).
fof(fact_inf1D1,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( 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))
=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_inf1D1) ).
fof(fact_sup1I2,axiom,
! [V_A_2,T_b,V_x_2,V_B_2] :
( hBOOL(hAPP(V_B_2,V_x_2))
=> 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)) ),
file('theBenchmark.p',fact_sup1I2) ).
fof(fact_sup1I1,axiom,
! [V_B_2,T_b,V_x_2,V_A_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
=> 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)) ),
file('theBenchmark.p',fact_sup1I1) ).
fof(fact_Un__Int__crazy,axiom,
! [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)),
file('theBenchmark.p',fact_Un__Int__crazy) ).
fof(fact_Diff__Int2,axiom,
! [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),
file('theBenchmark.p',fact_Diff__Int2) ).
fof(fact_Un__Diff__Int,axiom,
! [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,
file('theBenchmark.p',fact_Un__Diff__Int) ).
fof(fact_ball__Un,axiom,
! [V_Pa_2,V_B_2,V_A_2,T_b] :
( ! [B_x] :
( 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)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ) ),
file('theBenchmark.p',fact_ball__Un) ).
fof(fact_bex__Un,axiom,
! [V_Pa_2,V_B_2,V_A_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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))) )
<=> ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_bex__Un) ).
fof(fact_Un__Int__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_Un__Int__distrib2) ).
fof(fact_Int__Un__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_Int__Un__distrib2) ).
fof(fact_Diff__Int__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__Int__distrib2) ).
fof(fact_Un__Diff,axiom,
! [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)),
file('theBenchmark.p',fact_Un__Diff) ).
fof(fact_Un__assoc,axiom,
! [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)),
file('theBenchmark.p',fact_Un__assoc) ).
fof(fact_Int__assoc,axiom,
! [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)),
file('theBenchmark.p',fact_Int__assoc) ).
fof(fact_Int__Diff,axiom,
! [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)),
file('theBenchmark.p',fact_Int__Diff) ).
fof(fact_Un__Diff__cancel2,axiom,
! [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),
file('theBenchmark.p',fact_Un__Diff__cancel2) ).
fof(fact_Diff__idemp,axiom,
! [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),
file('theBenchmark.p',fact_Diff__idemp) ).
fof(fact_Un__Int__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_Un__Int__distrib) ).
fof(fact_Diff__Int__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__Int__distrib) ).
fof(fact_Int__Un__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_Int__Un__distrib) ).
fof(fact_Diff__Un,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__Un) ).
fof(fact_Diff__Int,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__Int) ).
fof(fact_Un__left__commute,axiom,
! [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)),
file('theBenchmark.p',fact_Un__left__commute) ).
fof(fact_Int__left__commute,axiom,
! [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)),
file('theBenchmark.p',fact_Int__left__commute) ).
fof(fact_Un__left__absorb,axiom,
! [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),
file('theBenchmark.p',fact_Un__left__absorb) ).
fof(fact_Un__Diff__cancel,axiom,
! [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),
file('theBenchmark.p',fact_Un__Diff__cancel) ).
fof(fact_Int__left__absorb,axiom,
! [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),
file('theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_Un__commute,axiom,
! [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),
file('theBenchmark.p',fact_Un__commute) ).
fof(fact_Int__commute,axiom,
! [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),
file('theBenchmark.p',fact_Int__commute) ).
fof(fact_Un__absorb,axiom,
! [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,
file('theBenchmark.p',fact_Un__absorb) ).
fof(fact_Int__absorb,axiom,
! [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,
file('theBenchmark.p',fact_Int__absorb) ).
fof(fact_Diff__triv,axiom,
! [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_Orderings_Obot__class_Obot(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 ),
file('theBenchmark.p',fact_Diff__triv) ).
fof(fact_Diff__disjoint,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__disjoint) ).
fof(fact_Diff__partition,axiom,
! [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),V_B_2))
=> 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 ),
file('theBenchmark.p',fact_Diff__partition) ).
fof(fact_Diff__subset__conv,axiom,
! [V_C_2,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_C_2))
<=> 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))) ),
file('theBenchmark.p',fact_Diff__subset__conv) ).
fof(fact_Un__Int__assoc__eq,axiom,
! [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__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))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ),
file('theBenchmark.p',fact_Un__Int__assoc__eq) ).
fof(fact_Union__Un__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_Union__Un__distrib) ).
fof(fact_Pow__Int__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Pow__Int__eq) ).
fof(fact_Inter__Un__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_Inter__Un__distrib) ).
fof(fact_Union__Int__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Union__Int__subset) ).
fof(fact_Inter__Un__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Inter__Un__subset) ).
fof(fact_Diff__iff,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Diff__iff) ).
fof(fact_DiffD1,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
file('theBenchmark.p',fact_DiffD1) ).
fof(fact_DiffD2,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ),
file('theBenchmark.p',fact_DiffD2) ).
fof(fact_Un__iff,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Un__iff) ).
fof(fact_UnI1,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnI1) ).
fof(fact_UnI2,axiom,
! [V_A_2,V_B_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnI2) ).
fof(fact_Int__iff,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD1,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
file('theBenchmark.p',fact_IntD1) ).
fof(fact_IntD2,axiom,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ),
file('theBenchmark.p',fact_IntD2) ).
fof(fact_Diff__cancel,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__cancel) ).
fof(fact_Diff__empty,axiom,
! [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,
file('theBenchmark.p',fact_Diff__empty) ).
fof(fact_empty__Diff,axiom,
! [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)),
file('theBenchmark.p',fact_empty__Diff) ).
fof(fact_Un__empty,axiom,
! [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_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))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Un__empty) ).
fof(fact_Un__empty__right,axiom,
! [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,
file('theBenchmark.p',fact_Un__empty__right) ).
fof(fact_Un__empty__left,axiom,
! [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,
file('theBenchmark.p',fact_Un__empty__left) ).
fof(fact_disjoint__iff__not__equal,axiom,
! [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_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
=> B_x != B_xa ) ) ),
file('theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(fact_Int__empty__right,axiom,
! [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)),
file('theBenchmark.p',fact_Int__empty__right) ).
fof(fact_Int__empty__left,axiom,
! [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)),
file('theBenchmark.p',fact_Int__empty__left) ).
fof(fact_double__diff,axiom,
! [V_C_2,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),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)),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 ) ),
file('theBenchmark.p',fact_double__diff) ).
fof(fact_Diff__mono,axiom,
! [V_B_2,V_D_2,V_C_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),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Diff__mono) ).
fof(fact_Diff__subset,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__subset) ).
fof(fact_Un__insert__left,axiom,
! [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)),
file('theBenchmark.p',fact_Un__insert__left) ).
fof(fact_Un__insert__right,axiom,
! [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)),
file('theBenchmark.p',fact_Un__insert__right) ).
fof(fact_insert__inter__insert,axiom,
! [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)),
file('theBenchmark.p',fact_insert__inter__insert) ).
fof(fact_Un__mono,axiom,
! [V_D_2,V_B_2,V_C_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),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Un__mono) ).
fof(fact_Un__least,axiom,
! [V_B_2,V_C_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),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> 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)) ) ),
file('theBenchmark.p',fact_Un__least) ).
fof(fact_Un__absorb2,axiom,
! [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),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
file('theBenchmark.p',fact_Un__absorb2) ).
fof(fact_Un__absorb1,axiom,
! [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),V_B_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_Un__absorb1) ).
fof(fact_subset__Un__eq,axiom,
! [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),V_B_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_subset__Un__eq) ).
fof(fact_Un__upper2,axiom,
! [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))),
file('theBenchmark.p',fact_Un__upper2) ).
fof(fact_Un__upper1,axiom,
! [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))),
file('theBenchmark.p',fact_Un__upper1) ).
fof(fact_Un__UNIV__right,axiom,
! [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)),
file('theBenchmark.p',fact_Un__UNIV__right) ).
fof(fact_Un__UNIV__left,axiom,
! [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)),
file('theBenchmark.p',fact_Un__UNIV__left) ).
fof(fact_Int__mono,axiom,
! [V_D_2,V_B_2,V_C_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),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Int__mono) ).
fof(fact_Int__greatest,axiom,
! [V_B_2,V_A_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Int__greatest) ).
fof(fact_Int__absorb1,axiom,
! [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),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_Int__absorb1) ).
fof(fact_Int__absorb2,axiom,
! [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),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 ),
file('theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__lower2,axiom,
! [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)),
file('theBenchmark.p',fact_Int__lower2) ).
fof(fact_Int__lower1,axiom,
! [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)),
file('theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__UNIV__right,axiom,
! [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,
file('theBenchmark.p',fact_Int__UNIV__right) ).
fof(fact_Int__UNIV__left,axiom,
! [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,
file('theBenchmark.p',fact_Int__UNIV__left) ).
fof(fact_Un__Pow__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Un__Pow__subset) ).
fof(fact_insert__Diff1,axiom,
! [V_A_2,V_B_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> 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) ),
file('theBenchmark.p',fact_insert__Diff1) ).
fof(fact_insert__Diff__if,axiom,
! [V_A_2,V_B_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> 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) ) ),
file('theBenchmark.p',fact_insert__Diff__if) ).
fof(fact_insert__Diff__single,axiom,
! [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),
file('theBenchmark.p',fact_insert__Diff__single) ).
fof(fact_Diff__insert2,axiom,
! [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),
file('theBenchmark.p',fact_Diff__insert2) ).
fof(fact_Diff__insert,axiom,
! [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)))),
file('theBenchmark.p',fact_Diff__insert) ).
fof(fact_Int__insert__left__if1,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> 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)) ),
file('theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_Int__insert__right__if1,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ),
file('theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_Int__insert__left__if0,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> 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) ),
file('theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_Int__insert__right__if0,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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) ),
file('theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_Int__insert__left,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> 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)) ) ),
file('theBenchmark.p',fact_Int__insert__left) ).
fof(fact_Int__insert__right,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_Int__insert__right) ).
fof(fact_Diff__UNIV,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__UNIV) ).
fof(fact_Sup__insert,axiom,
! [V_A_2,V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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)) ),
file('theBenchmark.p',fact_Sup__insert) ).
fof(fact_insert__is__Un,axiom,
! [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),
file('theBenchmark.p',fact_insert__is__Un) ).
fof(fact_Inf__insert,axiom,
! [V_A_2,V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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)) ),
file('theBenchmark.p',fact_Inf__insert) ).
fof(fact_Union__disjoint,axiom,
! [V_A_2,V_C_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_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
=> 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)) ) ),
file('theBenchmark.p',fact_Union__disjoint) ).
fof(fact_ivl__disj__un_I20_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I20_J) ).
fof(fact_ivl__disj__int_I14_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I14_J) ).
fof(fact_Union__insert,axiom,
! [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)),
file('theBenchmark.p',fact_Union__insert) ).
fof(fact_Inter__insert,axiom,
! [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)),
file('theBenchmark.p',fact_Inter__insert) ).
fof(fact_Diff__insert__absorb,axiom,
! [V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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 ),
file('theBenchmark.p',fact_Diff__insert__absorb) ).
fof(fact_insert__Diff,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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 ),
file('theBenchmark.p',fact_insert__Diff) ).
fof(fact_Sup__binary,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Sup__binary) ).
fof(fact_Inf__binary,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Inf__binary) ).
fof(fact_single__Diff__lessThan,axiom,
! [V_k_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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))) ),
file('theBenchmark.p',fact_single__Diff__lessThan) ).
fof(fact_ivl__disj__un_I9_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I9_J) ).
fof(fact_ivl__disj__int_I3_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I3_J) ).
fof(fact_ivl__disj__int_I1_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I1_J) ).
fof(fact_ivl__disj__int_I10_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I10_J) ).
fof(fact_distrib__sup__le,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_distrib__sup__le) ).
fof(fact_distrib__inf__le,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_distrib__inf__le) ).
fof(fact_minus__apply,axiom,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( class_Groups_Ominus(T_b)
=> 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)) ),
file('theBenchmark.p',fact_minus__apply) ).
fof(fact_inf__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( class_Lattices_Olattice(T_b)
=> 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)) ),
file('theBenchmark.p',fact_inf__apply) ).
fof(fact_sup__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( class_Lattices_Olattice(T_b)
=> 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)) ),
file('theBenchmark.p',fact_sup__apply) ).
fof(fact_inf__top__left,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__top(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ),
file('theBenchmark.p',fact_inf__top__left) ).
fof(fact_inf__top__right,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__top(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ),
file('theBenchmark.p',fact_inf__top__right) ).
fof(fact_inf__eq__top__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Obounded__lattice__top(T_b)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
<=> ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
& V_x_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ),
file('theBenchmark.p',fact_inf__eq__top__iff) ).
fof(fact_sup__top__left,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__top(T_a)
=> 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) ),
file('theBenchmark.p',fact_sup__top__left) ).
fof(fact_sup__top__right,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__top(T_a)
=> 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) ),
file('theBenchmark.p',fact_sup__top__right) ).
fof(fact_inf__sup__absorb,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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 ),
file('theBenchmark.p',fact_inf__sup__absorb) ).
fof(fact_sup__assoc,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> 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)) ),
file('theBenchmark.p',fact_sup__assoc) ).
fof(fact_inf__sup__aci_I6_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__sup__aci_I6_J) ).
fof(fact_sup_Oassoc,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> 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)) ),
file('theBenchmark.p',fact_sup_Oassoc) ).
fof(fact_sup__left__commute,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> 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)) ),
file('theBenchmark.p',fact_sup__left__commute) ).
fof(fact_inf__sup__aci_I7_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__sup__aci_I7_J) ).
fof(fact_sup_Oleft__commute,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> 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)) ),
file('theBenchmark.p',fact_sup_Oleft__commute) ).
fof(fact_sup__left__idem,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> 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) ),
file('theBenchmark.p',fact_sup__left__idem) ).
fof(fact_inf__sup__aci_I8_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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) ),
file('theBenchmark.p',fact_inf__sup__aci_I8_J) ).
fof(fact_sup_Oleft__idem,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> 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) ),
file('theBenchmark.p',fact_sup_Oleft__idem) ).
fof(fact_sup__commute,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__sup(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_y),V_x) ),
file('theBenchmark.p',fact_sup__commute) ).
fof(fact_inf__sup__aci_I5_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(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_y),V_x) ),
file('theBenchmark.p',fact_inf__sup__aci_I5_J) ).
fof(fact_sup_Ocommute,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Osemilattice__sup(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_b),V_a) ),
file('theBenchmark.p',fact_sup_Ocommute) ).
fof(fact_sup__idem,axiom,
! [V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_sup__idem) ).
fof(fact_sup_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_sup_Oidem) ).
fof(fact_inf__assoc,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_inf_Oassoc,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__left__commute,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__sup__aci_I3_J) ).
fof(fact_inf_Oleft__commute,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__left__idem,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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) ),
file('theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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) ),
file('theBenchmark.p',fact_inf__sup__aci_I4_J) ).
fof(fact_inf_Oleft__idem,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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) ),
file('theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__commute,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(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_y),V_x) ),
file('theBenchmark.p',fact_inf__commute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(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_y),V_x) ),
file('theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_inf_Ocommute,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Osemilattice__inf(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_b),V_a) ),
file('theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__idem,axiom,
! [V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_inf__idem) ).
fof(fact_inf_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_inf_Oidem) ).
fof(fact_le__supE,axiom,
! [V_x,V_b,V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( 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))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
file('theBenchmark.p',fact_le__supE) ).
fof(fact_sup__mono,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_sup__mono) ).
fof(fact_sup__least,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
=> 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)) ) ) ),
file('theBenchmark.p',fact_sup__least) ).
fof(fact_le__supI,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
=> 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)) ) ) ),
file('theBenchmark.p',fact_le__supI) ).
fof(fact_sup__absorb1,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ),
file('theBenchmark.p',fact_sup__absorb1) ).
fof(fact_sup__absorb2,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ),
file('theBenchmark.p',fact_sup__absorb2) ).
fof(fact_le__supI2,axiom,
! [V_a,V_b,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_le__supI2) ).
fof(fact_le__supI1,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> 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))) ) ),
file('theBenchmark.p',fact_le__supI1) ).
fof(fact_le__sup__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( 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))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_le__sup__iff) ).
fof(fact_le__iff__sup,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ),
file('theBenchmark.p',fact_le__iff__sup) ).
fof(fact_sup__ge2,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> 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))) ),
file('theBenchmark.p',fact_sup__ge2) ).
fof(fact_inf__sup__ord_I4_J,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Olattice(T_a)
=> 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))) ),
file('theBenchmark.p',fact_inf__sup__ord_I4_J) ).
fof(fact_sup__ge1,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> 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))) ),
file('theBenchmark.p',fact_sup__ge1) ).
fof(fact_inf__sup__ord_I3_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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))) ),
file('theBenchmark.p',fact_inf__sup__ord_I3_J) ).
fof(fact_le__infE,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( 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)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ),
file('theBenchmark.p',fact_le__infE) ).
fof(fact_inf__mono,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_inf__mono) ).
fof(fact_inf__greatest,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
=> 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))) ) ) ),
file('theBenchmark.p',fact_inf__greatest) ).
fof(fact_le__infI,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_le__infI) ).
fof(fact_inf__absorb2,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ),
file('theBenchmark.p',fact_inf__absorb2) ).
fof(fact_inf__absorb1,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ),
file('theBenchmark.p',fact_inf__absorb1) ).
fof(fact_le__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_le__infI2) ).
fof(fact_le__infI1,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_le__infI1) ).
fof(fact_le__inf__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_le__inf__iff) ).
fof(fact_le__iff__inf,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ),
file('theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__le2,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_inf__le1,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_sup__eq__bot__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Obounded__lattice__bot(T_b)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
<=> ( V_y_2 = c_Orderings_Obot__class_Obot(T_b)
& V_x_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ),
file('theBenchmark.p',fact_sup__eq__bot__iff) ).
fof(fact_sup__bot__right,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__bot(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ),
file('theBenchmark.p',fact_sup__bot__right) ).
fof(fact_sup__bot__left,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__bot(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ),
file('theBenchmark.p',fact_sup__bot__left) ).
fof(fact_inf__bot__right,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__bot(T_a)
=> 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) ),
file('theBenchmark.p',fact_inf__bot__right) ).
fof(fact_inf__bot__left,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__bot(T_a)
=> 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) ),
file('theBenchmark.p',fact_inf__bot__left) ).
fof(fact_sup__inf__distrib2,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Lattices_Odistrib__lattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_sup__inf__distrib2) ).
fof(fact_inf__sup__distrib2,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Lattices_Odistrib__lattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__sup__distrib2) ).
fof(fact_sup__inf__distrib1,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Odistrib__lattice(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)) ),
file('theBenchmark.p',fact_sup__inf__distrib1) ).
fof(fact_inf__sup__distrib1,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Odistrib__lattice(T_a)
=> 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)) ),
file('theBenchmark.p',fact_inf__sup__distrib1) ).
fof(fact_sup__inf__absorb,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(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_x),V_y)) = V_x ),
file('theBenchmark.p',fact_sup__inf__absorb) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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_ca_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_ivl__disj__un_I5_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I5_J) ).
fof(fact_ivl__disj__un_I4_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I4_J) ).
fof(fact_ivl__disj__un_I13_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I13_J) ).
fof(fact_psubset__insert__iff,axiom,
! [V_B_2,V_x_2,V_A_2,T_b] :
( 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)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_psubset__insert__iff) ).
fof(fact_ivl__disj__un_I10_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I10_J) ).
fof(fact_Int__Collect__mono,axiom,
! [V_Qa_2,V_Pa_2,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),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ( hBOOL(hAPP(V_Pa_2,B_x))
=> hBOOL(hAPP(V_Qa_2,B_x)) ) )
=> 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)))) ) ),
file('theBenchmark.p',fact_Int__Collect__mono) ).
fof(fact_fold__graph_H_Ointros_I2_J,axiom,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( 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)
=> 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)) ) ),
file('theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
fof(fact_ivl__disj__un_I12_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I12_J) ).
fof(fact_insert__partition,axiom,
! [V_F_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
=> ( ! [B_x] :
( 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)))
=> ! [B_xa] :
( 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)))
=> ( B_x != B_xa
=> 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)) ) ) )
=> 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)) ) ),
file('theBenchmark.p',fact_insert__partition) ).
fof(fact_atLeastatMost__psubset__iff,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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_ca_2,V_d_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(fact_linorder__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ( V_x != V_y
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
file('theBenchmark.p',fact_linorder__cases) ).
fof(fact_order__less__asym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__asym) ).
fof(fact_xt1_I10_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_order__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I2_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I2_J) ).
fof(fact_ord__less__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__less__eq__trans) ).
fof(fact_xt1_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I1_J) ).
fof(fact_ord__eq__less__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__eq__less__trans) ).
fof(fact_xt1_I9_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_order__less__asym_H,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ),
file('theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> V_y != V_x ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> V_x != V_y ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__less,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_less__imp__neq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> V_x != V_y ) ),
file('theBenchmark.p',fact_less__imp__neq) ).
fof(fact_linorder__neqE,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x != V_y
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
file('theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__neq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( V_x_2 != V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_order__less__irrefl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ),
file('theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_psubset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_psubset__trans) ).
fof(fact_atLeastatMost__empty,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
=> 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)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty) ).
fof(fact_lessThan__strict__subset__iff,axiom,
! [V_n_2,V_m_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_lessThan__strict__subset__iff) ).
fof(fact_diff__eq__diff__less,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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_ca_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_fold__graph_H_Oequations_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(fact_fold__graph_H_Ointros_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
fof(fact_less__fun__def,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__le__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Opreorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__le__less,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_leI,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_not__leE) ).
fof(fact_linorder__antisym__conv1,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_order__neq__le__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_xt1_I12_J,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_leD,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_leD) ).
fof(fact_order__less__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( V_a != V_b
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> ( V_a != V_b
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__less__le__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I7_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__le__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_xt1_I8_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_psubsetD,axiom,
! [V_ca_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubsetD) ).
fof(fact_not__psubset__empty,axiom,
! [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)))),
file('theBenchmark.p',fact_not__psubset__empty) ).
fof(fact_less__supI1,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
=> 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))) ) ),
file('theBenchmark.p',fact_less__supI1) ).
fof(fact_less__supI2,axiom,
! [V_a,V_b,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_less__supI2) ).
fof(fact_less__infI1,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_less__infI1) ).
fof(fact_less__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_less__infI2) ).
fof(fact_subset__psubset__trans,axiom,
! [V_C_2,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),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_psubset__imp__subset,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [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),V_B_2))
<=> ( V_A_2 = V_B_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__eq,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> ( V_A_2 != V_B_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubset__eq) ).
fof(fact_less__Sup__iff,axiom,
! [V_S_2,V_a_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
file('theBenchmark.p',fact_less__Sup__iff) ).
fof(fact_Inf__less__iff,axiom,
! [V_a_2,V_S_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
file('theBenchmark.p',fact_Inf__less__iff) ).
fof(fact_lessThan__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_lessThan__iff) ).
fof(fact_ivl__disj__un_I19_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I19_J) ).
fof(fact_greaterThanAtMost__empty__iff,axiom,
! [V_l_2,V_k_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
file('theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).
fof(fact_greaterThanAtMost__empty__iff2,axiom,
! [V_l_2,V_k_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
file('theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).
fof(fact_greaterThan__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_atLeastatMost__empty__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty__iff) ).
fof(fact_atLeastatMost__empty__iff2,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty__iff2) ).
fof(fact_atLeastatMost__subset__iff,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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_ca_2,V_d_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_atLeastatMost__subset__iff) ).
fof(fact_atLeastAtMost__singleton_H,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( V_a_2 = V_b_2
=> 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))) ) ),
file('theBenchmark.p',fact_atLeastAtMost__singleton_H) ).
fof(fact_atLeastAtMost__singleton__iff,axiom,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
<=> ( V_b_2 = V_ca_2
& V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
fof(fact_atLeastAtMost__singleton,axiom,
! [V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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))) ),
file('theBenchmark.p',fact_atLeastAtMost__singleton) ).
fof(fact_diff__eq__diff__eq,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( 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_ca_2),V_d_2)
=> ( V_a_2 = V_b_2
<=> V_ca_2 = V_d_2 ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_ivl__disj__un_I22_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I22_J) ).
fof(fact_ivl__disj__int_I4_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I4_J) ).
fof(fact_ivl__disj__int_I16_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I16_J) ).
fof(fact_ivl__disj__int_I13_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I13_J) ).
fof(fact_ivl__disj__int_I12_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I12_J) ).
fof(fact_ivl__disj__int_I7_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I7_J) ).
fof(fact_ivl__disj__un_I16_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I16_J) ).
fof(fact_ivl__disj__un_I7_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I7_J) ).
fof(fact_fold__graph_H_Oequations_I2_J,axiom,
! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
( 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))
<=> ( ? [B_x,B_y] :
( 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)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
& hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) )
| ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2
& V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ),
file('theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
fof(fact_ivl__disj__un_I18_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I18_J) ).
fof(fact_ivl__disj__un_I3_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I3_J) ).
fof(fact_ivl__disj__un_I6_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I6_J) ).
fof(fact_ivl__disj__un_I15_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I15_J) ).
fof(fact_Diff1__fold__graph,axiom,
! [V_y_2,V_x_2,V_A_2,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,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))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Diff1__fold__graph) ).
fof(fact_psubset__imp__ex__mem,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ? [B_b] : 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))) ),
file('theBenchmark.p',fact_psubset__imp__ex__mem) ).
fof(fact_ivl__disj__int_I8_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I8_J) ).
fof(fact_compl__unique,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ),
file('theBenchmark.p',fact_compl__unique) ).
fof(fact_ivl__disj__un_I14_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I14_J) ).
fof(fact_ComplI,axiom,
! [V_A_2,V_ca_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
file('theBenchmark.p',fact_ComplI) ).
fof(fact_minus__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ),
file('theBenchmark.p',fact_minus__minus) ).
fof(fact_equation__minus__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
<=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ),
file('theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_minus__equation__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
<=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ),
file('theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_double__compl,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ),
file('theBenchmark.p',fact_double__compl) ).
fof(fact_uminus__apply,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Groups_Ouminus(T_b)
=> 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)) ),
file('theBenchmark.p',fact_uminus__apply) ).
fof(fact_compl__eq__compl__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Oboolean__algebra(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_compl__mono,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> 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))) ) ),
file('theBenchmark.p',fact_compl__mono) ).
fof(fact_compl__le__compl__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Oboolean__algebra(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_le__imp__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_neg__le__iff__le,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_minus__le__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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))
<=> 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)) ) ),
file('theBenchmark.p',fact_minus__le__iff) ).
fof(fact_le__minus__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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)))
<=> 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))) ) ),
file('theBenchmark.p',fact_le__minus__iff) ).
fof(fact_neg__less__iff__less,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_minus__less__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ),
file('theBenchmark.p',fact_minus__less__iff) ).
fof(fact_less__minus__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ),
file('theBenchmark.p',fact_less__minus__iff) ).
fof(fact_ComplE,axiom,
! [V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
file('theBenchmark.p',fact_ComplE) ).
fof(fact_ComplD,axiom,
! [V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
file('theBenchmark.p',fact_ComplD) ).
fof(fact_Compl__iff,axiom,
! [V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
<=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
file('theBenchmark.p',fact_Compl__iff) ).
fof(fact_minus__diff__eq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> 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) ),
file('theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_Compl__subset__Compl__iff,axiom,
! [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(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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
file('theBenchmark.p',fact_Compl__subset__Compl__iff) ).
fof(fact_Compl__anti__mono,axiom,
! [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),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_Compl__anti__mono) ).
fof(fact_atLeastLessThan__eq__iff,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
<=> ( V_b_2 = V_d_2
& V_a_2 = V_ca_2 ) ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
=> V_a_2 = V_ca_2 ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__inj_I2_J,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
=> V_b_2 = V_d_2 ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_empty__fold__graphE,axiom,
! [V_x_2,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_x_2))
=> V_x_2 = V_z_2 ),
file('theBenchmark.p',fact_empty__fold__graphE) ).
fof(fact_fold__graph_OemptyI,axiom,
! [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)),
file('theBenchmark.p',fact_fold__graph_OemptyI) ).
fof(fact_fold__graph_Oequations_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
fof(fact_compl__inf__bot,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> 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) ),
file('theBenchmark.p',fact_compl__inf__bot) ).
fof(fact_inf__compl__bot,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> 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) ),
file('theBenchmark.p',fact_inf__compl__bot) ).
fof(fact_diff__eq,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> 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)) ),
file('theBenchmark.p',fact_diff__eq) ).
fof(fact_compl__top__eq,axiom,
! [T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ),
file('theBenchmark.p',fact_compl__top__eq) ).
fof(fact_compl__bot__eq,axiom,
! [T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ),
file('theBenchmark.p',fact_compl__bot__eq) ).
fof(fact_compl__sup,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> 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)) ),
file('theBenchmark.p',fact_compl__sup) ).
fof(fact_compl__inf,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> 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)) ),
file('theBenchmark.p',fact_compl__inf) ).
fof(fact_compl__sup__top,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> 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) ),
file('theBenchmark.p',fact_compl__sup__top) ).
fof(fact_sup__compl__top,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> 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) ),
file('theBenchmark.p',fact_sup__compl__top) ).
fof(fact_subset__Compl__self__eq,axiom,
! [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(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)) ),
file('theBenchmark.p',fact_subset__Compl__self__eq) ).
fof(fact_Compl__empty__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_Compl__UNIV__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_Compl__disjoint,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__disjoint) ).
fof(fact_Compl__disjoint2,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__disjoint2) ).
fof(fact_Compl__partition,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__partition) ).
fof(fact_Compl__partition2,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__partition2) ).
fof(fact_Compl__Int,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__Int) ).
fof(fact_Compl__Un,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__Un) ).
fof(fact_Compl__eq__Diff__UNIV,axiom,
! [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),
file('theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
fof(fact_Compl__Diff__eq,axiom,
! [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),
file('theBenchmark.p',fact_Compl__Diff__eq) ).
fof(fact_Diff__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Diff__eq) ).
fof(fact_Diff__Compl,axiom,
! [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),
file('theBenchmark.p',fact_Diff__Compl) ).
fof(fact_Compl__atLeast,axiom,
! [V_k_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_Compl__atLeast) ).
fof(fact_Compl__lessThan,axiom,
! [V_k_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_Compl__lessThan) ).
fof(fact_atLeastLessThan__empty,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
=> 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)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty) ).
fof(fact_atLeastLessThan__empty__iff2,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
fof(fact_atLeastLessThan__empty__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( 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))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
fof(fact_Compl__atMost,axiom,
! [V_k_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_Compl__atMost) ).
fof(fact_Compl__greaterThan,axiom,
! [V_k_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_Compl__greaterThan) ).
fof(fact_atLeastLessThan__subset__iff,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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_ca_2),V_d_2)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_ivl__disj__un_I17_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I17_J) ).
fof(fact_fold__graph_OinsertI,axiom,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
=> 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))) ) ),
file('theBenchmark.p',fact_fold__graph_OinsertI) ).
fof(fact_ivl__diff,axiom,
! [V_m_2,V_n_2,V_i_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__diff) ).
fof(fact_ivl__disj__int_I11_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I11_J) ).
fof(fact_disjoint__eq__subset__Compl,axiom,
! [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_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> 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))) ),
file('theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
fof(fact_ivl__disj__un_I21_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I21_J) ).
fof(fact_ivl__disj__int_I15_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I15_J) ).
fof(fact_ivl__disj__un_I8_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> 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) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I8_J) ).
fof(fact_ivl__disj__int_I2_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I2_J) ).
fof(fact_ivl__disj__int_I9_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_ivl__disj__int_I9_J) ).
fof(fact_fold1Set_Ointros,axiom,
! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_fold1Set_Ointros) ).
fof(fact_fold__graph__permute__diff,axiom,
! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_fold__graph__permute__diff) ).
fof(fact_folding__one_Osingleton,axiom,
! [V_x_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> 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 ),
file('theBenchmark.p',fact_folding__one_Osingleton) ).
fof(fact_fold1Set__sing,axiom,
! [V_b_2,V_a_2,V_f_2,T_b] :
( 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))
<=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_fold1Set__sing) ).
fof(fact_nonempty__iff,axiom,
! [T_b,V_A_2] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ? [B_x,B_B] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B))
& V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B) ) ),
file('theBenchmark.p',fact_nonempty__iff) ).
fof(fact_Pow__insert,axiom,
! [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))),
file('theBenchmark.p',fact_Pow__insert) ).
fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ? [B_y_H] :
( 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))
& V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) ) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).
fof(fact_Inf__fin_Oidem,axiom,
! [V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_Inf__fin_Oidem) ).
fof(fact_Sup__fin_Oidem,axiom,
! [V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_Sup__fin_Oidem) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( V_x != V_y
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
file('theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_image__eqI,axiom,
! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
( V_b_2 = hAPP(V_f_2,V_x_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_image__eqI) ).
fof(fact_double__complement,axiom,
! [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,
file('theBenchmark.p',fact_double__complement) ).
fof(fact_Compl__eq__Compl__iff,axiom,
! [V_B_2,V_A_2,T_b] :
( 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)
<=> V_A_2 = V_B_2 ),
file('theBenchmark.p',fact_Compl__eq__Compl__iff) ).
fof(fact_image__Pow__surj,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
=> 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) ),
file('theBenchmark.p',fact_image__Pow__surj) ).
fof(fact_mult__left__idem,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> 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) ),
file('theBenchmark.p',fact_mult__left__idem) ).
fof(fact_mult__idem,axiom,
! [V_x,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_mult__idem) ).
fof(fact_times_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_times_Oidem) ).
fof(fact_fun__left__comm_Ofun__left__comm,axiom,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> 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)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__mult(T_a)
=> 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)) ),
file('theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_fun__left__comm,axiom,
! [T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
file('theBenchmark.p',fact_fun__left__comm) ).
fof(fact_minus__mult__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_minus__mult__right) ).
fof(fact_minus__mult__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> 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) ),
file('theBenchmark.p',fact_minus__mult__left) ).
fof(fact_minus__mult__commute,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_minus__mult__minus,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> 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) ),
file('theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_square__eq__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oidom(T_b)
=> ( 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)
<=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_square__eq__iff) ).
fof(fact_image__iff,axiom,
! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
<=> ? [B_x] :
( V_z_2 = hAPP(V_f_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_image__iff) ).
fof(fact_imageI,axiom,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_imageI) ).
fof(fact_rev__image__eqI,axiom,
! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_b_2 = hAPP(V_f_2,V_x_2)
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_image__is__empty,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( 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))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_image__is__empty) ).
fof(fact_image__empty,axiom,
! [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)),
file('theBenchmark.p',fact_image__empty) ).
fof(fact_empty__is__image,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_empty__is__image) ).
fof(fact_image__insert,axiom,
! [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)),
file('theBenchmark.p',fact_image__insert) ).
fof(fact_image__mono,axiom,
! [V_f_2,T_c,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),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_image__mono) ).
fof(fact_subset__image__iff,axiom,
! [V_A_2,V_f_2,T_c,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(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
<=> ? [B_AA] :
( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) ),
file('theBenchmark.p',fact_subset__image__iff) ).
fof(fact_image__Un,axiom,
! [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)),
file('theBenchmark.p',fact_image__Un) ).
fof(fact_image__Pow__mono,axiom,
! [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),V_A_2)),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_image__Pow__mono) ).
fof(fact_insert__image,axiom,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ),
file('theBenchmark.p',fact_insert__image) ).
fof(fact_range__eqI,axiom,
! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
( V_b_2 = hAPP(V_f_2,V_x_2)
=> 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))))) ),
file('theBenchmark.p',fact_range__eqI) ).
fof(fact_rangeI,axiom,
! [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))))),
file('theBenchmark.p',fact_rangeI) ).
fof(fact_image__Int__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_image__Int__subset) ).
fof(fact_image__diff__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_image__diff__subset) ).
fof(fact_image__uminus__atLeastAtMost,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_image__uminus__atLeastAtMost) ).
fof(fact_type__definition_OAbs__image,axiom,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> 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)) ),
file('theBenchmark.p',fact_type__definition_OAbs__image) ).
fof(fact_type__definition_ORep__range,axiom,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> 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 ),
file('theBenchmark.p',fact_type__definition_ORep__range) ).
fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
=> V_y_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).
fof(fact_image__uminus__greaterThanLessThan,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).
fof(fact_empty__fold1SetE,axiom,
! [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)),
file('theBenchmark.p',fact_empty__fold1SetE) ).
fof(fact_fold1Set__nonempty,axiom,
! [V_x_2,V_A_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_fold1Set__nonempty) ).
fof(fact_image__uminus__atLeastLessThan,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_image__uminus__atLeastLessThan) ).
fof(fact_image__uminus__greaterThanAtMost,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).
fof(fact_image__uminus__lessThan,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_image__uminus__lessThan) ).
fof(fact_image__uminus__greaterThan,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_image__uminus__greaterThan) ).
fof(fact_image__uminus__atLeast,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_image__uminus__atLeast) ).
fof(fact_image__uminus__atMost,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_image__uminus__atMost) ).
fof(fact_fold__graph__insert__swap,axiom,
! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( 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))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_fold__graph__insert__swap) ).
fof(fact_surj__Compl__image__subset,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( 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))
=> 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)))) ),
file('theBenchmark.p',fact_surj__Compl__image__subset) ).
fof(fact_Cantors__paradox,axiom,
! [V_A_2,T_b] :
~ ? [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),
file('theBenchmark.p',fact_Cantors__paradox) ).
fof(fact_folding__one_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),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_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))
=> 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)))))) )
& ( 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))
=> hAPP(V_F_2,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oremove) ).
fof(fact_insert__fold1SetE,axiom,
! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
( 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))
=> ~ ! [B_a,B_A] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ),
file('theBenchmark.p',fact_insert__fold1SetE) ).
fof(fact_fold1Set_Oequations,axiom,
! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
( 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))
<=> ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
& hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) ),
file('theBenchmark.p',fact_fold1Set_Oequations) ).
fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( 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))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ~ ! [B_y] :
( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
=> ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
fof(fact_folding__one_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Ounion__inter) ).
fof(fact_folding__one_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(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) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Ounion__disjoint) ).
fof(fact_folding__one_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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_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))
=> 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)))))) )
& ( 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))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oinsert__remove) ).
fof(fact_finite_OemptyI,axiom,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_finite_OemptyI) ).
fof(fact_finite_OinsertI,axiom,
! [V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ),
file('theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_finite__imageI,axiom,
! [V_h_2,T_c,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ),
file('theBenchmark.p',fact_finite__imageI) ).
fof(fact_finite__Int,axiom,
! [V_Ga_2,V_F_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
=> 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_Ga_2))) ),
file('theBenchmark.p',fact_finite__Int) ).
fof(fact_finite__Diff,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_finite__Diff) ).
fof(fact_finite__Inter,axiom,
! [V_M_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ),
file('theBenchmark.p',fact_finite__Inter) ).
fof(fact_finite__UN,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ),
file('theBenchmark.p',fact_finite__UN) ).
fof(fact_finite,axiom,
! [V_A_2,T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite) ).
fof(fact_finite__code,axiom,
! [V_A_2,T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__code) ).
fof(fact_finite__Prod__UNIV,axiom,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
=> 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)))) ) ),
file('theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_finite__option__UNIV,axiom,
! [T_b] :
( 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))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [T_c,T_b] :
( 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))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__UnionD,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
file('theBenchmark.p',fact_finite__UnionD) ).
fof(fact_finite__Pow__iff,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__Pow__iff) ).
fof(fact_finite_Oequations_I1_J,axiom,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(fact_finite__insert,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__insert) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [T_c,T_b] :
( 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))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_finite__subset,axiom,
! [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),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_finite__UNIV,axiom,
! [T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__UNIV) ).
fof(fact_finite__UnI,axiom,
! [V_Ga_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
=> 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_Ga_2))) ) ),
file('theBenchmark.p',fact_finite__UnI) ).
fof(fact_finite__Un,axiom,
! [V_Ga_2,V_F_2,T_b] :
( 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_Ga_2)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__Un) ).
fof(fact_finite__Diff2,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__Diff2) ).
fof(fact_fold__graph__imp__finite,axiom,
! [V_x_2,V_A_2,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,V_A_2),V_x_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_fold__graph__imp__finite) ).
fof(fact_finite__surj,axiom,
! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_finite__surj) ).
fof(fact_finite__Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] :
( 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))))
<=> 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))) ),
file('theBenchmark.p',fact_finite__Diff__insert) ).
fof(fact_finite__compl,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__compl) ).
fof(fact_folding__one_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oinsert) ).
fof(fact_folding__image__simple_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> 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)))))) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oremove) ).
fof(fact_folding__image__simple_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).
fof(fact_folding__image__simple_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> 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)))))) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
fof(fact_Inf__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),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_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))
=> 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)))))) )
& ( 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))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oremove) ).
fof(fact_Sup__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),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_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))
=> 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)))))) )
& ( 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))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oremove) ).
fof(fact_folding__one_Oclosed,axiom,
! [V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [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))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oclosed) ).
fof(fact_fun__upd__image,axiom,
! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,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)))))) ) ),
file('theBenchmark.p',fact_fun__upd__image) ).
fof(fact_finite__empty__induct,axiom,
! [V_Pa_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(V_Pa_2,V_A_2))
=> ( ! [B_a,B_A] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
=> ( hBOOL(hAPP(V_Pa_2,B_A))
=> 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)))))) ) ) )
=> hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
file('theBenchmark.p',fact_finite__empty__induct) ).
fof(fact_folding__one__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).
fof(fact_fun__upd__triv,axiom,
! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2,
file('theBenchmark.p',fact_fun__upd__triv) ).
fof(fact_fun__upd__idem,axiom,
! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
( hAPP(V_f_2,V_x_2) = V_y_2
=> c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ),
file('theBenchmark.p',fact_fun__upd__idem) ).
fof(fact_fun__upd__other,axiom,
! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
( V_z_2 != V_x_2
=> 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) ),
file('theBenchmark.p',fact_fun__upd__other) ).
fof(fact_fun__upd__twist,axiom,
! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
( V_a_2 != V_ca_2
=> c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2) ),
file('theBenchmark.p',fact_fun__upd__twist) ).
fof(fact_fun__upd__apply,axiom,
! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
( ( V_z_2 != V_x_2
=> 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) )
& ( V_z_2 = V_x_2
=> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) ),
file('theBenchmark.p',fact_fun__upd__apply) ).
fof(fact_fun__upd__same,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2,
file('theBenchmark.p',fact_fun__upd__same) ).
fof(fact_fun__upd__upd,axiom,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2),
file('theBenchmark.p',fact_fun__upd__upd) ).
fof(fact_fun__upd__idem__iff,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
<=> hAPP(V_f_2,V_x_2) = V_y_2 ),
file('theBenchmark.p',fact_fun__upd__idem__iff) ).
fof(fact_folding__one__idem_Oidem,axiom,
! [V_x_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ),
file('theBenchmark.p',fact_folding__one__idem_Oidem) ).
fof(fact_ball__UN,axiom,
! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
( ! [B_x] :
( 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)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
=> hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ),
file('theBenchmark.p',fact_ball__UN) ).
fof(fact_Inf__le__Sup,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))) ) ) ),
file('theBenchmark.p',fact_Inf__le__Sup) ).
fof(fact_folding__image__simple_Oempty,axiom,
! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ),
file('theBenchmark.p',fact_folding__image__simple_Oempty) ).
fof(fact_Inf__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> 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 ),
file('theBenchmark.p',fact_Inf__fin_Osingleton) ).
fof(fact_Sup__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> 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 ),
file('theBenchmark.p',fact_Sup__fin_Osingleton) ).
fof(fact_Sup__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oin__idem) ).
fof(fact_sup__Inf__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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 ) ) ),
file('theBenchmark.p',fact_sup__Inf__absorb) ).
fof(fact_Inf__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oin__idem) ).
fof(fact_inf__Sup__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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 ) ) ),
file('theBenchmark.p',fact_inf__Sup__absorb) ).
fof(fact_Sup__fin__Sup,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin__Sup) ).
fof(fact_Inf__fin__Inf,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin__Inf) ).
fof(fact_folding__one__idem_Oin__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
fof(fact_Sup__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).
fof(fact_Inf__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).
fof(fact_Sup__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Osubset__idem) ).
fof(fact_Inf__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Osubset__idem) ).
fof(fact_Sup__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ounion__idem) ).
fof(fact_Inf__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__idem) ).
fof(fact_folding__image__simple_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oinsert) ).
fof(fact_folding__image__simple_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).
fof(fact_Sup__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert) ).
fof(fact_Inf__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert) ).
fof(fact_Sup__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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_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))
=> 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)))))) )
& ( 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))
=> 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 ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).
fof(fact_Inf__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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_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))
=> 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)))))) )
& ( 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))
=> 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 ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).
fof(fact_Sup__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ounion__inter) ).
fof(fact_Sup__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(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) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).
fof(fact_Inf__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__inter) ).
fof(fact_Inf__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(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) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).
fof(fact_folding__one__idem_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
fof(fact_folding__one__idem_Osubset__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
fof(fact_Inf__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [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))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oclosed) ).
fof(fact_Sup__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [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))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oclosed) ).
fof(fact_finite__Union,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
=> ( ! [B_M] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ),
file('theBenchmark.p',fact_finite__Union) ).
fof(fact_Inf__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( ! [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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ohom__commute) ).
fof(fact_Sup__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( ! [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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ohom__commute) ).
fof(fact_finite__subset__induct,axiom,
! [V_Pa_2,V_A_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
=> ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ( ! [B_a,B_F] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
=> ( hBOOL(hAPP(V_Pa_2,B_F))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
=> hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ),
file('theBenchmark.p',fact_finite__subset__induct) ).
fof(fact_fun__left__comm_Ofold__rec,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)))))) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).
fof(fact_fold1__Un,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(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) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__Un) ).
fof(fact_folding__one__idem_Ohom__commute,axiom,
! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( ! [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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
fof(fact_fold__empty,axiom,
! [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,
file('theBenchmark.p',fact_fold__empty) ).
fof(fact_fold1__eq__fold__idem,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_fold1__eq__fold__idem) ).
fof(fact_fold1__eq__fold,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_fold1__eq__fold) ).
fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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)) = 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) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
fof(fact_fold1__singleton__def,axiom,
! [V_a_2,V_f_2,T_b,V_g_2] :
( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
=> 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 ),
file('theBenchmark.p',fact_fold1__singleton__def) ).
fof(fact_fold1__singleton,axiom,
! [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,
file('theBenchmark.p',fact_fold1__singleton) ).
fof(fact_fun__left__comm_Ofold__equality,axiom,
! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
fof(fact_folding__one_Oeq__fold,axiom,
! [V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__one_Oeq__fold) ).
fof(fact_union__fold__insert,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(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) = 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) ),
file('theBenchmark.p',fact_union__fold__insert) ).
fof(fact_fold__sup__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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),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)) ) ),
file('theBenchmark.p',fact_fold__sup__insert) ).
fof(fact_fold__inf__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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),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)) ) ),
file('theBenchmark.p',fact_fold__inf__insert) ).
fof(fact_sup__Sup__fold__sup,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_sup__Sup__fold__sup) ).
fof(fact_inf__Inf__fold__inf,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_inf__Inf__fold__inf) ).
fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).
fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
fof(fact_Sup__fin_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_Sup__fin_OF__eq) ).
fof(fact_Inf__fin_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_Inf__fin_OF__eq) ).
fof(fact_sup__le__fold__sup,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_sup__le__fold__sup) ).
fof(fact_fold__inf__le__inf,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_fold__inf__le__inf) ).
fof(fact_Sup__fold__sup,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_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)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fold__sup) ).
fof(fact_Inf__fold__inf,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_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)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fold__inf) ).
fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).
fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).
fof(fact_fun__left__comm_Ofold__insert2,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).
fof(fact_fun__left__comm_Ofold__insert,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
fof(fact_folding__one_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
fof(fact_fold1__belowI,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_fold1__belowI) ).
fof(fact_below__fold1__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( 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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_below__fold1__iff) ).
fof(fact_fold1__insert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_fold1__insert__idem) ).
fof(fact_fold1__Un2,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__Un2) ).
fof(fact_Sup__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).
fof(fact_Inf__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).
fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)))))) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).
fof(fact_fold1__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_fold1__insert) ).
fof(fact_semilattice__big_OF__eq,axiom,
! [V_A_2,V_F_2,V_f_2,T_b] :
( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ),
file('theBenchmark.p',fact_semilattice__big_OF__eq) ).
fof(fact_fold1__in,axiom,
! [V_A_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [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))))))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_fold1__in) ).
fof(fact_hom__fold1__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( ! [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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_hom__fold1__commute) ).
fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( ! [B_x] :
( 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)))
=> hAPP(V_g_2,B_x) = V_z_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(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).
fof(fact_setsum__diff1__ring,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Rings_Oring(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_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))))) = 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)) ) ) ),
file('theBenchmark.p',fact_setsum__diff1__ring) ).
fof(fact_setsum__diff1,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_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))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_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))))) = 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)) ) ) ) ),
file('theBenchmark.p',fact_setsum__diff1) ).
fof(fact_setprod_Oremove,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)))))) ) ) ),
file('theBenchmark.p',fact_setprod_Oremove) ).
fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> 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) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
fof(fact_setsum__diff__nat__ivl,axiom,
! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_setsum__diff__nat__ivl) ).
fof(fact_fun__left__comm__idem__insert,axiom,
! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),
file('theBenchmark.p',fact_fun__left__comm__idem__insert) ).
fof(fact_fun__left__comm__idem,axiom,
! [T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
file('theBenchmark.p',fact_fun__left__comm__idem) ).
fof(fact_fun__left__comm__idem__sup,axiom,
! [T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ),
file('theBenchmark.p',fact_fun__left__comm__idem__sup) ).
fof(fact_fun__left__comm__idem__inf,axiom,
! [T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ),
file('theBenchmark.p',fact_fun__left__comm__idem__inf) ).
fof(fact_setsum__diff__nat,axiom,
! [V_f_2,V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_setsum__diff__nat) ).
fof(fact_setprod_Oinsert,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_setprod_Oinsert) ).
fof(fact_setprod__insert,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_setprod__insert) ).
fof(fact_setprod__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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),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)) ) ) ),
file('theBenchmark.p',fact_setprod__Un__Int) ).
fof(fact_setprod_Ounion__inter,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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),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)) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__inter) ).
fof(fact_setsum__diff1__nat,axiom,
! [V_f_2,V_A_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_setsum__diff1__nat) ).
fof(fact_setsum__diff,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_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),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)) ) ) ),
file('theBenchmark.p',fact_setsum__diff) ).
fof(fact_setprod_Oinsert__remove,axiom,
! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)))))) ) ),
file('theBenchmark.p',fact_setprod_Oinsert__remove) ).
fof(fact_setprod__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_setprod__Un__disjoint) ).
fof(fact_setprod_Ounion__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__disjoint) ).
fof(fact_setsum__strict__mono,axiom,
! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_setsum__strict__mono) ).
fof(fact_setsum__diff1_H,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)))))) ) ) ),
file('theBenchmark.p',fact_setsum__diff1_H) ).
fof(fact_setsum_Oremove,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)))))) ) ) ),
file('theBenchmark.p',fact_setsum_Oremove) ).
fof(fact_inf__le__fold__inf,axiom,
! [V_ca_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
=> 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_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_inf__le__fold__inf) ).
fof(fact_fold__sup__le__sup,axiom,
! [V_ca_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
=> 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_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_2))) ) ) ),
file('theBenchmark.p',fact_fold__sup__le__sup) ).
fof(fact_setsum__ivl__cong,axiom,
! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
( ( class_Orderings_Oord(T_b)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( V_a_2 = V_ca_2
=> ( V_b_2 = V_d_2
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
=> 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_ca_2),V_d_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__ivl__cong) ).
fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_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(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).
fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_finite__atLeastLessThan,axiom,
! [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))),
file('theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(fact_setsum__add__nat__ivl,axiom,
! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),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)) ) ) ),
file('theBenchmark.p',fact_setsum__add__nat__ivl) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [V_N_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
<=> ? [B_m] :
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ),
file('theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_add__left__cancel,axiom,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( class_Groups_Ocancel__semigroup__add(T_b)
=> ( 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_ca_2)
<=> V_b_2 = V_ca_2 ) ),
file('theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__right__cancel,axiom,
! [V_ca_2,V_a_2,V_b_2,T_b] :
( class_Groups_Ocancel__semigroup__add(T_b)
=> ( 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_ca_2),V_a_2)
<=> V_b_2 = V_ca_2 ) ),
file('theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__semigroup__add(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_a),V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__ab__semigroup__add(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_a),V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__right__imp__eq,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( 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)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_atLeastLessThan__add__Un,axiom,
! [V_k_2,V_j_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
=> 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))) ),
file('theBenchmark.p',fact_atLeastLessThan__add__Un) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ),
file('theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_add__le__imp__le__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__imp__le__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__mono) ).
fof(fact_add__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__le__cancel__left,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__cancel__right,axiom,
! [V_b_2,V_ca_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__less__cancel__left,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__cancel__right,axiom,
! [V_b_2,V_ca_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_combine__common__factor,axiom,
! [V_c,V_b,V_e,V_a,T_a] :
( class_Rings_Osemiring(T_a)
=> 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) ),
file('theBenchmark.p',fact_combine__common__factor) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring(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_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)) ),
file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_add__diff__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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 ),
file('theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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 ),
file('theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_minus__add__distrib,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_minus__add) ).
fof(fact_add__minus__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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 ),
file('theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_minus__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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 ),
file('theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_add__le__less__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_eq__add__iff1,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oring(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_ca_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)
<=> 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_ca_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oring(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_ca_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)
<=> V_ca_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) ) ),
file('theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_diff__def,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_diff__def) ).
fof(fact_ab__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__minus__eq__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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) ),
file('theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_le__add__iff1,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( 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_ca_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)))
<=> 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_ca_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_le__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( 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_ca_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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_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))) ) ),
file('theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff1,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( 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_ca_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)))
<=> 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_ca_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_less__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( 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_ca_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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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))) ) ),
file('theBenchmark.p',fact_less__add__iff2) ).
fof(fact_setsum__Un__nat,axiom,
! [V_f_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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__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))) ) ),
file('theBenchmark.p',fact_setsum__Un__nat) ).
fof(fact_setsum__insert,axiom,
! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_setsum__insert) ).
fof(fact_setsum_Oinsert,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_setsum_Oinsert) ).
fof(fact_setsum__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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),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)) ) ) ),
file('theBenchmark.p',fact_setsum__Un__Int) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_setsum_Oinsert__remove,axiom,
! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)))))) ) ),
file('theBenchmark.p',fact_setsum_Oinsert__remove) ).
fof(fact_setsum__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_setsum__Un__disjoint) ).
fof(fact_setsum__Un,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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__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))) ) ) ),
file('theBenchmark.p',fact_setsum__Un) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_nat__less__add__iff2,axiom,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
=> ( 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)))
<=> 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))) ) ),
file('theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_nat__less__add__iff1,axiom,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
=> ( 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)))
<=> 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)) ) ),
file('theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
=> ( 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)
<=> 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) ) ),
file('theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_nat__diff__add__eq2,axiom,
! [V_n,V_m,V_u,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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)) ),
file('theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_nat__le__add__iff2,axiom,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
=> ( 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)))
<=> 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))) ) ),
file('theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__eq__add__iff1,axiom,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
=> ( 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)
<=> 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 ) ),
file('theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__diff__add__eq1,axiom,
! [V_n,V_m,V_u,V_i,V_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
=> 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) ),
file('theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_finite__lessThan,axiom,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))),
file('theBenchmark.p',fact_finite__lessThan) ).
fof(fact_finite__greaterThanAtMost,axiom,
! [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))),
file('theBenchmark.p',fact_finite__greaterThanAtMost) ).
fof(fact_finite__greaterThanLessThan,axiom,
! [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))),
file('theBenchmark.p',fact_finite__greaterThanLessThan) ).
fof(fact_finite__atMost,axiom,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))),
file('theBenchmark.p',fact_finite__atMost) ).
fof(fact_finite__atLeastAtMost,axiom,
! [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))),
file('theBenchmark.p',fact_finite__atLeastAtMost) ).
fof(fact_left__add__mult__distrib,axiom,
! [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),
file('theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [V_N_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
<=> ? [B_m] :
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ),
file('theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_infinite__UNIV__nat,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('theBenchmark.p',fact_infinite__UNIV__nat) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(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_c),V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(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_b),V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_crossproduct__eq,axiom,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( 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))
<=> ( V_y_2 = V_z_2
| V_w_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [V_b,V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(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_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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_crossproduct__noteq,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( ( V_ca_2 != V_d_2
& V_a_2 != V_b_2 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_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_ca_2)) ) ),
file('theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_nat__le__add__iff1,axiom,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
=> ( 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)))
<=> 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)) ) ),
file('theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_diff__diff__right,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> 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) ),
file('theBenchmark.p',fact_diff__diff__right) ).
fof(fact_le__diff__conv,axiom,
! [V_i_2,V_k_2,V_j_2] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_le__diff__conv) ).
fof(fact_le__add__diff,axiom,
! [V_m,V_n,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
=> 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))) ),
file('theBenchmark.p',fact_le__add__diff) ).
fof(fact_le__add__diff__inverse,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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 ),
file('theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_add__diff__assoc,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> 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) ),
file('theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_le__diff__conv2,axiom,
! [V_i_2,V_j_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
=> ( 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)))
<=> 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)) ) ),
file('theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_le__add__diff__inverse2,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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 ),
file('theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_le__imp__diff__is__add,axiom,
! [V_k_2,V_j_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
<=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ),
file('theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_nat__less__cases,axiom,
! [V_Pa_2,V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
=> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
=> ( ( V_m_2 = V_n_2
=> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
=> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
fof(fact_less__not__refl3,axiom,
! [V_t,V_s] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
=> V_s != V_t ),
file('theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
=> V_m != V_n ),
file('theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__irrefl__nat,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
file('theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_linorder__neqE__nat,axiom,
! [V_y,V_x] :
( V_x != V_y
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ),
file('theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_nat__neq__iff,axiom,
! [V_n_2,V_m_2] :
( V_m_2 != V_n_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_less__not__refl,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
file('theBenchmark.p',fact_less__not__refl) ).
fof(fact_nat__add__commute,axiom,
! [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),
file('theBenchmark.p',fact_nat__add__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [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)),
file('theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_nat__add__assoc,axiom,
! [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)),
file('theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__add__left__cancel,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_nat__add__right__cancel,axiom,
! [V_n_2,V_k_2,V_m_2] :
( 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)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_le__antisym,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_le__antisym) ).
fof(fact_le__trans,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ),
file('theBenchmark.p',fact_le__trans) ).
fof(fact_eq__imp__le,axiom,
! [V_n,V_m] :
( V_m = V_n
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_eq__imp__le) ).
fof(fact_nat__le__linear,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_nat__le__linear) ).
fof(fact_le__refl,axiom,
! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)),
file('theBenchmark.p',fact_le__refl) ).
fof(fact_diff__commute,axiom,
! [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),
file('theBenchmark.p',fact_diff__commute) ).
fof(fact_nat__mult__commute,axiom,
! [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),
file('theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_nat__mult__assoc,axiom,
! [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)),
file('theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_not__add__less1,axiom,
! [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)),
file('theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [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)),
file('theBenchmark.p',fact_not__add__less2) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_trans__less__add1,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_trans__less__add1) ).
fof(fact_trans__less__add2,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_trans__less__add2) ).
fof(fact_add__less__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),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_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
file('theBenchmark.p',fact_add__less__mono1) ).
fof(fact_add__less__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
=> 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))) ) ),
file('theBenchmark.p',fact_add__less__mono) ).
fof(fact_less__add__eq__less,axiom,
! [V_n,V_m,V_l,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
=> ( 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)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__lessD1,axiom,
! [V_k,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_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ),
file('theBenchmark.p',fact_add__lessD1) ).
fof(fact_less__or__eq__imp__le,axiom,
! [V_n,V_m] :
( ( V_m = V_n
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_le__neq__implies__less,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> ( V_m != V_n
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_less__imp__le__nat,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_le__eq__less__or__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
<=> ( V_m_2 = V_n_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
<=> ( V_m_2 != V_n_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__less__le) ).
fof(fact_add__leE,axiom,
! [V_n,V_k,V_m] :
( 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))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ),
file('theBenchmark.p',fact_add__leE) ).
fof(fact_add__leD1,axiom,
! [V_n,V_k,V_m] :
( 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))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [V_n,V_k,V_m] :
( 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))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ),
file('theBenchmark.p',fact_add__leD2) ).
fof(fact_add__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
=> 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))) ) ),
file('theBenchmark.p',fact_add__le__mono) ).
fof(fact_add__le__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_add__le__mono1) ).
fof(fact_trans__le__add2,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_trans__le__add2) ).
fof(fact_trans__le__add1,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_trans__le__add1) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_le__iff__add,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
<=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ),
file('theBenchmark.p',fact_le__iff__add) ).
fof(fact_le__add1,axiom,
! [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))),
file('theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [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))),
file('theBenchmark.p',fact_le__add2) ).
fof(fact_diff__less__mono2,axiom,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
=> 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))) ) ),
file('theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_less__imp__diff__less,axiom,
! [V_n,V_k,V_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
=> 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)) ),
file('theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_diff__cancel2,axiom,
! [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),
file('theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__cancel,axiom,
! [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),
file('theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__diff__left,axiom,
! [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)),
file('theBenchmark.p',fact_diff__diff__left) ).
fof(fact_diff__add__inverse,axiom,
! [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,
file('theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [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,
file('theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_add__mult__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_add__mult__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_le__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ),
file('theBenchmark.p',fact_le__diff__iff) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
=> 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) ) ),
file('theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_eq__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
=> ( 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)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_diff__diff__cancel,axiom,
! [V_n,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
=> 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 ),
file('theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_diff__le__mono,axiom,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> 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))) ),
file('theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> 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))) ),
file('theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_diff__le__self,axiom,
! [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)),
file('theBenchmark.p',fact_diff__le__self) ).
fof(fact_le__square,axiom,
! [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))),
file('theBenchmark.p',fact_le__square) ).
fof(fact_le__cube,axiom,
! [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)))),
file('theBenchmark.p',fact_le__cube) ).
fof(fact_mult__le__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_mult__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
=> 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))) ) ),
file('theBenchmark.p',fact_mult__le__mono) ).
fof(fact_diff__mult__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_diff__mult__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__diff__inverse,axiom,
! [V_n,V_m] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> 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 ),
file('theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__diff__conv,axiom,
! [V_k_2,V_j_2,V_i_2] :
( 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)))
<=> 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)) ),
file('theBenchmark.p',fact_less__diff__conv) ).
fof(fact_less__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ),
file('theBenchmark.p',fact_less__diff__iff) ).
fof(fact_diff__less__mono,axiom,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
=> 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))) ) ),
file('theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__add__assoc2,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> 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) ),
file('theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_add__diff__assoc2,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> 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) ),
file('theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> 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)) ),
file('theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [V_y,V_z,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
=> 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))) ),
file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
=> 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))) ),
file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ),
file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
=> 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))) ),
file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [V_y,V_z,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
=> 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))) ),
file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_card__Diff2__less,axiom,
! [V_y_2,V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_card__Diff2__less) ).
fof(fact_card__Diff1__less,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_card__Diff1__less) ).
fof(fact_setsum__ub__add__nat,axiom,
! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( 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))))
=> 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)))) ) ),
file('theBenchmark.p',fact_setsum__ub__add__nat) ).
fof(fact_card__UNIV__unit,axiom,
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),
file('theBenchmark.p',fact_card__UNIV__unit) ).
fof(fact_one__reorient,axiom,
! [V_x_2,T_b] :
( class_Groups_Oone(T_b)
=> ( c_Groups_Oone__class_Oone(T_b) = V_x_2
<=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ),
file('theBenchmark.p',fact_one__reorient) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult__1__right) ).
fof(fact_mult__1,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_mult__1__left) ).
fof(fact_setprod__eq__1__iff,axiom,
! [V_f_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( 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)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_setprod__eq__1__iff) ).
fof(fact_nat__mult__1,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_nat__mult__1) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [V_n_2,V_m_2] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_nat__mult__1__right,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_card__lessThan,axiom,
! [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,
file('theBenchmark.p',fact_card__lessThan) ).
fof(fact_card_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_card_Oinsert) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( 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)))
=> V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_less__add__one,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_less__add__one) ).
fof(fact_less__1__mult,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
=> 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))) ) ) ),
file('theBenchmark.p',fact_less__1__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [V_a,V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_square__eq__1__iff,axiom,
! [V_x_2,T_b] :
( class_Rings_Oring__1__no__zero__divisors(T_b)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
<=> ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
file('theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_subset__card__intvl__is__intvl,axiom,
! [V_k_2,V_A_2] :
( 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)))))
=> 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))) ),
file('theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
fof(fact_card__atLeastLessThan,axiom,
! [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),
file('theBenchmark.p',fact_card__atLeastLessThan) ).
fof(fact_setprod_Oempty,axiom,
! [V_g_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> 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) ),
file('theBenchmark.p',fact_setprod_Oempty) ).
fof(fact_setprod__empty,axiom,
! [V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> 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) ),
file('theBenchmark.p',fact_setprod__empty) ).
fof(fact_setprod_Oinfinite,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_setprod_Oinfinite) ).
fof(fact_setprod__infinite,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_setprod__infinite) ).
fof(fact_card__Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),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),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)) ) ) ),
file('theBenchmark.p',fact_card__Diff__insert) ).
fof(fact_card_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(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)) = 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)))))) ),
file('theBenchmark.p',fact_card_Oinsert__remove) ).
fof(fact_card__greaterThanAtMost,axiom,
! [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),
file('theBenchmark.p',fact_card__greaterThanAtMost) ).
fof(fact_card_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)))))) ) ),
file('theBenchmark.p',fact_card_Oremove) ).
fof(fact_card__Diff__singleton,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_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),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)) ) ),
file('theBenchmark.p',fact_card__Diff__singleton) ).
fof(fact_card__Diff__singleton__if,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_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),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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_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),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)) ) ) ),
file('theBenchmark.p',fact_card__Diff__singleton__if) ).
fof(fact_card__insert__le,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)))) ),
file('theBenchmark.p',fact_card__insert__le) ).
fof(fact_card__seteq,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( 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)))
=> V_A_2 = V_B_2 ) ) ),
file('theBenchmark.p',fact_card__seteq) ).
fof(fact_card__mono,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> 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))) ) ),
file('theBenchmark.p',fact_card__mono) ).
fof(fact_card__image__le,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_card__image__le) ).
fof(fact_psubset__card__mono,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> 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))) ) ),
file('theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_card__Un__Int,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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)) = 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))) ) ),
file('theBenchmark.p',fact_card__Un__Int) ).
fof(fact_card_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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))) = 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)) ) ),
file('theBenchmark.p',fact_card_Ounion__inter) ).
fof(fact_card__Diff__subset,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_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)) = 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)) ) ),
file('theBenchmark.p',fact_card__Diff__subset) ).
fof(fact_card__Diff__subset__Int,axiom,
! [V_B_2,V_A_2,T_b] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_card__Diff__subset__Int) ).
fof(fact_diff__card__le__card__Diff,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> 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)))) ),
file('theBenchmark.p',fact_diff__card__le__card__Diff) ).
fof(fact_card__psubset,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card__psubset) ).
fof(fact_card__Un__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ),
file('theBenchmark.p',fact_card__Un__disjoint) ).
fof(fact_card__Diff1__le,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_card__Diff1__le) ).
fof(fact_setprod_Ounion__inter__neutral,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ! [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)))
=> hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(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_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)) ) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).
fof(fact_setprod__Un__one,axiom,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( ! [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_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_setprod__Un__one) ).
fof(fact_fold__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_fold__Un__disjoint) ).
fof(fact_setprod__mono__one__right,axiom,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( 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)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
=> 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) ) ) ) ),
file('theBenchmark.p',fact_setprod__mono__one__right) ).
fof(fact_setprod__mono__one__left,axiom,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( 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)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(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) ) ) ) ),
file('theBenchmark.p',fact_setprod__mono__one__left) ).
fof(fact_card__Suc__Diff1,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
file('theBenchmark.p',fact_card__Suc__Diff1) ).
fof(fact_fold__image__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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)) = 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))) ) ) ),
file('theBenchmark.p',fact_fold__image__Un__Int) ).
fof(fact_convex__bound__lt,axiom,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( class_Rings_Olinordered__semiring__1__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_less__zeroE,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_less__zeroE) ).
fof(fact_le0,axiom,
! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
file('theBenchmark.p',fact_le0) ).
fof(fact_zero__less__Suc,axiom,
! [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))),
file('theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_Suc__mono,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ),
file('theBenchmark.p',fact_Suc__mono) ).
fof(fact_lessI,axiom,
! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))),
file('theBenchmark.p',fact_lessI) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_One__nat__def) ).
fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
! [V_k_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(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,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)) ) ),
file('theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
fof(fact_zero__reorient,axiom,
! [V_x_2,T_b] :
( class_Groups_Ozero(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__reorient) ).
fof(fact_atLeast__Suc__greaterThan,axiom,
! [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),
file('theBenchmark.p',fact_atLeast__Suc__greaterThan) ).
fof(fact_greaterThan__Suc,axiom,
! [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)))),
file('theBenchmark.p',fact_greaterThan__Suc) ).
fof(fact_atLeast__Suc,axiom,
! [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)))),
file('theBenchmark.p',fact_atLeast__Suc) ).
fof(fact_setsum__shift__lb__Suc0__0,axiom,
! [V_k_2,V_f_2] :
( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)) ),
file('theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).
fof(fact_lessThan__Suc__eq__insert__0,axiom,
! [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))),
file('theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).
fof(fact_Zero__not__Suc,axiom,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
file('theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H),
file('theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_n__not__Suc__n,axiom,
! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
file('theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_Suc__not__Zero,axiom,
! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__n__not__n,axiom,
! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
file('theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_nat_Oinject,axiom,
! [V_nat_H_2,V_nat_2] :
( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
<=> V_nat_2 = V_nat_H_2 ),
file('theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Zero__neq__Suc,axiom,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
file('theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_Suc__neq__Zero,axiom,
! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_Suc__inject,axiom,
! [V_y,V_x] :
( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
=> V_x = V_y ),
file('theBenchmark.p',fact_Suc__inject) ).
fof(fact_greaterThan__0,axiom,
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))),
file('theBenchmark.p',fact_greaterThan__0) ).
fof(fact_mult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( 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))
<=> ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
<=> ( ? [B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
& V_m_2 = hAPP(c_Nat_OSuc,B_j) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_less__Suc0,axiom,
! [V_n_2] :
( 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))))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_less__Suc0) ).
fof(fact_gr0__conv__Suc,axiom,
! [V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
<=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ),
file('theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_one__is__add,axiom,
! [V_n_2,V_m_2] :
( 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)
<=> ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [V_n_2,V_m_2] :
( 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))
<=> ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_add__is__1) ).
fof(fact_Suc__pred,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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 ),
file('theBenchmark.p',fact_Suc__pred) ).
fof(fact_diff__Suc__less,axiom,
! [V_i,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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)) ),
file('theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_n__less__m__mult__n,axiom,
! [V_m,V_n] :
( 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))
=> ( 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))
=> 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))) ) ),
file('theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_n__less__n__mult__m,axiom,
! [V_m,V_n] :
( 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))
=> ( 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))
=> 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))) ) ),
file('theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_one__less__mult,axiom,
! [V_m,V_n] :
( 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))
=> ( 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))
=> 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))) ) ),
file('theBenchmark.p',fact_one__less__mult) ).
fof(fact_one__le__mult__iff,axiom,
! [V_n_2,V_m_2] :
( 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)))
<=> ( 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))
& 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)) ) ),
file('theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_setsum__eq__Suc0__iff,axiom,
! [V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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))
<=> ? [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( B_x != B_xa
=> hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
fof(fact_not__less__eq,axiom,
! [V_n_2,V_m_2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ),
file('theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
<=> ( V_m_2 = V_n_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__less__eq,axiom,
! [V_n_2,V_m_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [V_m_2,V_n_2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
<=> V_n_2 = V_m_2 ) ),
file('theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [V_m,V_n] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
file('theBenchmark.p',fact_less__SucI) ).
fof(fact_Suc__lessI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> ( hAPP(c_Nat_OSuc,V_m) != V_n
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ),
file('theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__trans__Suc,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ),
file('theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_less__SucE,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__SucE) ).
fof(fact_Suc__lessD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__less__SucD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_add__Suc__shift,axiom,
! [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)),
file('theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_add__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [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)),
file('theBenchmark.p',fact_add__Suc__right) ).
fof(fact_Suc__n__not__le__n,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)),
file('theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_not__less__eq__eq,axiom,
! [V_n_2,V_m_2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ),
file('theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_le__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
<=> ( V_m_2 = hAPP(c_Nat_OSuc,V_n_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_Suc__le__mono,axiom,
! [V_m_2,V_n_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_le__SucI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
file('theBenchmark.p',fact_le__SucI) ).
fof(fact_le__SucE,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> V_m = hAPP(c_Nat_OSuc,V_n) ) ),
file('theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__leD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__leD) ).
fof(fact_diff__Suc__Suc,axiom,
! [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),
file('theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_Suc__diff__diff,axiom,
! [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),
file('theBenchmark.p',fact_Suc__diff__diff) ).
fof(fact_Suc__mult__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_add__0__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_add__0) ).
fof(fact_double__zero__sym,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__iff,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_add__0__iff) ).
fof(fact_divisors__zero,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_mult__eq__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__no__zero__divisors(T_b)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_mult__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> 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) ),
file('theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> 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) ),
file('theBenchmark.p',fact_mult__zero__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_right__minus__eq,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_right__minus__eq) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( V_a_2 = V_b_2
<=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_diff__self,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_diff__self) ).
fof(fact_diff__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_diff__0__right) ).
fof(fact_one__neq__zero,axiom,
! [T_a] :
( class_Rings_Ozero__neq__one(T_a)
=> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_one__neq__zero) ).
fof(fact_zero__neq__one,axiom,
! [T_a] :
( class_Rings_Ozero__neq__one(T_a)
=> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_zero__neq__one) ).
fof(fact_minus__zero,axiom,
! [T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_minus__zero) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
<=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ),
file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_equal__neg__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_neg__equal__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_fold__image__empty,axiom,
! [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,
file('theBenchmark.p',fact_fold__image__empty) ).
fof(fact_not__less0,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_not__less0) ).
fof(fact_neq0__conv,axiom,
! [V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
file('theBenchmark.p',fact_neq0__conv) ).
fof(fact_less__nat__zero__code,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_gr__implies__not0,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_gr0I,axiom,
! [V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
file('theBenchmark.p',fact_gr0I) ).
fof(fact_add__eq__self__zero,axiom,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
=> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_add__is__0,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_add__is__0) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_atLeastLessThan__singleton,axiom,
! [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))),
file('theBenchmark.p',fact_atLeastLessThan__singleton) ).
fof(fact_image__Suc__atLeastLessThan,axiom,
! [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)),
file('theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le__0__eq,axiom,
! [V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_le__0__eq) ).
fof(fact_diff__0__eq__0,axiom,
! [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),
file('theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_diff__self__eq__0,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_diffs0__imp__equal,axiom,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_mult__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( 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)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel2) ).
fof(fact_mult__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mult__is__0,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__is__0) ).
fof(fact_mult__0__right,axiom,
! [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),
file('theBenchmark.p',fact_mult__0__right) ).
fof(fact_mult__0,axiom,
! [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),
file('theBenchmark.p',fact_mult__0) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)
<=> ( V_m_2 = V_n_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_image__Suc__atLeastAtMost,axiom,
! [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)),
file('theBenchmark.p',fact_image__Suc__atLeastAtMost) ).
fof(fact_lessThan__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_lessThan__Suc) ).
fof(fact_atLeastLessThan0,axiom,
! [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)),
file('theBenchmark.p',fact_atLeastLessThan0) ).
fof(fact_atMost__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_atMost__Suc) ).
fof(fact_card__atMost,axiom,
! [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),
file('theBenchmark.p',fact_card__atMost) ).
fof(fact_atLeast__0,axiom,
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)),
file('theBenchmark.p',fact_atLeast__0) ).
fof(fact_lessThan__0,axiom,
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)),
file('theBenchmark.p',fact_lessThan__0) ).
fof(fact_setsum_Oeq__fold,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_setsum_Oeq__fold) ).
fof(fact_setsum_OF__eq,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_setsum_OF__eq) ).
fof(fact_Suc__diff__1,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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))) = V_n ),
file('theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_atMost__0,axiom,
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))),
file('theBenchmark.p',fact_atMost__0) ).
fof(fact_setsum__op__ivl__Suc,axiom,
! [V_f_2,V_m_2,V_n_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_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,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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_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,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_setsum__op__ivl__Suc) ).
fof(fact_less__add__Suc1,axiom,
! [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)))),
file('theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [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)))),
file('theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_less__iff__Suc__add,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
<=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ),
file('theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__eq__Suc__le,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ),
file('theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_less__Suc__eq__le,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_Suc__le__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_le__imp__less__Suc,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
file('theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_Suc__leI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
file('theBenchmark.p',fact_Suc__leI) ).
fof(fact_le__less__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
<=> V_n_2 = V_m_2 ) ),
file('theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_setsum__cl__ivl__Suc,axiom,
! [V_f_2,V_m_2,V_n_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_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,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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_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,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_setsum__cl__ivl__Suc) ).
fof(fact_diff__less__Suc,axiom,
! [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))),
file('theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_mult__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_mult__Suc) ).
fof(fact_mult__Suc__right,axiom,
! [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)),
file('theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_Suc__diff__le,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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)) ),
file('theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_add__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__comm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ),
file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_add__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_split__mult__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
=> 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))) ) ),
file('theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_split__mult__pos__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
=> 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))) ) ),
file('theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_comm__mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__comm__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__right__mono) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__le__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( 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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( 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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__le__square,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> 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))) ),
file('theBenchmark.p',fact_zero__le__square) ).
fof(fact_pos__add__strict,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__pos__pos) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__comm__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__neg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_zero__less__mult__pos2,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_mult__pos__neg2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_mult__pos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [V_b_2,V_ca_2,V_a_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_not__square__less__zero,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ 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))) ),
file('theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_le__iff__diff__le__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
<=> 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))) ) ),
file('theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
<=> 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))) ) ),
file('theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_add__scale__eq__noteq,axiom,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_r != c_Groups_Ozero__class_Ozero(T_a)
=> ( ( V_c != V_d
& V_a = V_b )
=> 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)) ) ) ),
file('theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_zero__le__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> 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))) ),
file('theBenchmark.p',fact_zero__le__one) ).
fof(fact_not__one__le__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ 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))) ),
file('theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_zero__less__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_zero__less__one) ).
fof(fact_not__one__less__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_diff__Suc__1,axiom,
! [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,
file('theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_neg__0__le__iff__le,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_le__minus__self__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_minus__le__self__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( 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))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__0__less__iff__less,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_neg__less__0__iff__less,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__less__nonneg,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_less__minus__self__iff,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_right__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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) ),
file('theBenchmark.p',fact_right__minus) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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) ),
file('theBenchmark.p',fact_left__minus) ).
fof(fact_ab__left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> 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) ),
file('theBenchmark.p',fact_ab__left__minus) ).
fof(fact_minus__unique,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ),
file('theBenchmark.p',fact_minus__unique) ).
fof(fact_diff__0,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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) ),
file('theBenchmark.p',fact_diff__0) ).
fof(fact_atLeastLessThanSuc,axiom,
! [V_n_2,V_m_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> 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)) ) ),
file('theBenchmark.p',fact_atLeastLessThanSuc) ).
fof(fact_setsum__empty,axiom,
! [V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum__empty) ).
fof(fact_setsum_Oempty,axiom,
! [V_g_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum_Oempty) ).
fof(fact_setsum__infinite,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_setsum__infinite) ).
fof(fact_setsum_Oinfinite,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_setsum_Oinfinite) ).
fof(fact_setprod__pos__nat__iff,axiom,
! [V_f_2,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( 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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_setprod__pos__nat__iff) ).
fof(fact_atLeastAtMostSuc__conv,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
=> 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)) ),
file('theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
fof(fact_setprod__zero__iff,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( ( class_Rings_Ono__zero__divisors(T_c)
& class_Rings_Ocomm__semiring__1(T_c) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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)
<=> ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod__zero__iff) ).
fof(fact_setprod__zero,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Rings_Ocomm__semiring__1(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
=> 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) ) ) ),
file('theBenchmark.p',fact_setprod__zero) ).
fof(fact_card__atLeastAtMost,axiom,
! [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),
file('theBenchmark.p',fact_card__atLeastAtMost) ).
fof(fact_add__gr__0,axiom,
! [V_n_2,V_m_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
file('theBenchmark.p',fact_add__gr__0) ).
fof(fact_card_Oempty,axiom,
! [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),
file('theBenchmark.p',fact_card_Oempty) ).
fof(fact_card__infinite,axiom,
! [V_A_2,T_b] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_card__infinite) ).
fof(fact_diff__less,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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)),V_m)) ) ),
file('theBenchmark.p',fact_diff__less) ).
fof(fact_zero__less__diff,axiom,
! [V_m_2,V_n_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_zero__less__diff) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [V_n_2,V_m_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
file('theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_mult__less__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
file('theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
file('theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_mult__less__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
=> 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))) ) ),
file('theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
=> 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))) ) ),
file('theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> ( 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)
<=> V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_diff__add__0,axiom,
! [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),
file('theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__is__0__eq_H,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_diff__is__0__eq,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
! [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),
file('theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [V_n,V_m] :
( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
=> ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_setsum__eq__0__iff,axiom,
! [V_f_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( 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)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_setsum__eq__0__iff) ).
fof(fact_lessThan__Suc__atMost,axiom,
! [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),
file('theBenchmark.p',fact_lessThan__Suc__atMost) ).
fof(fact_atLeast0LessThan,axiom,
! [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),
file('theBenchmark.p',fact_atLeast0LessThan) ).
fof(fact_folding__image__simple_Oeq__fold__g,axiom,
! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
fof(fact_card__greaterThanLessThan,axiom,
! [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)),
file('theBenchmark.p',fact_card__greaterThanLessThan) ).
fof(fact_atLeast0AtMost,axiom,
! [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),
file('theBenchmark.p',fact_atLeast0AtMost) ).
fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
! [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),
file('theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).
fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
! [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),
file('theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [V_m,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> 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)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [V_m,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> 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)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_add__nonpos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__strict__increasing2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_mult__left__le__imp__le,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__right__le__imp__le,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__left__less__imp__less,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_mult__right__less__imp__less,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__less__le__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__left__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_mult__right__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_zero__less__two,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_zero__less__two) ).
fof(fact_card__eq__0__iff,axiom,
! [V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__eq__0__iff) ).
fof(fact_card__ge__0__finite,axiom,
! [V_A_2,T_b] :
( 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)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_nat__diff__split,axiom,
! [V_b_2,V_a_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
<=> ( ! [B_d] :
( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
=> hBOOL(hAPP(V_Pa_2,B_d)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
=> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_nat__diff__split) ).
fof(fact_nat__diff__split__asm,axiom,
! [V_b_2,V_a_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
<=> ~ ( ? [B_d] :
( ~ hBOOL(hAPP(V_Pa_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_mult__le__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_mult__le__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_setsum__eq__1__iff,axiom,
! [V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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)
<=> ? [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( B_x != B_xa
=> hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setsum__eq__1__iff) ).
fof(fact_card__insert__if,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_card__insert__if) ).
fof(fact_card__insert__disjoint,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_convex__bound__le,axiom,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( class_Rings_Olinordered__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__le) ).
fof(fact_setsum__head__upt__Suc,axiom,
! [V_f_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_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))) ) ),
file('theBenchmark.p',fact_setsum__head__upt__Suc) ).
fof(fact_fold__image__insert,axiom,
! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_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),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)) ) ) ),
file('theBenchmark.p',fact_fold__image__insert) ).
fof(fact_setsum__head__Suc,axiom,
! [V_f_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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,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))) ) ),
file('theBenchmark.p',fact_setsum__head__Suc) ).
fof(fact_card__gt__0__iff,axiom,
! [V_A_2,T_b] :
( 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)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__gt__0__iff) ).
fof(fact_setprod_OF__eq,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_setprod_OF__eq) ).
fof(fact_setprod_Oeq__fold,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_setprod_Oeq__fold) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> 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))))) ),
file('theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_card__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(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)) = 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)))))) ),
file('theBenchmark.p',fact_card__insert) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [T_c,T_b] :
( 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))))
=> ( 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))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_mult__eq__if,axiom,
! [V_n,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)) )
& ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__eq__if) ).
fof(fact_add__eq__if,axiom,
! [V_n,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)) )
& ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) ),
file('theBenchmark.p',fact_add__eq__if) ).
fof(fact_Suc__pred_H,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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))) ),
file('theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( 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))))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ 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))) ),
file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( 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)))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_sum__squares__ge__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_bot__nat__def,axiom,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bot__nat__def) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__ring__strict(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)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [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),
file('theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_Suc__eq__plus1,axiom,
! [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)),
file('theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [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),
file('theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_ex__nat__less,axiom,
! [V_Pa_2,V_n_2] :
( ? [B_m] :
( hBOOL(hAPP(V_Pa_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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))) ) ),
file('theBenchmark.p',fact_ex__nat__less) ).
fof(fact_all__nat__less,axiom,
! [V_Pa_2,V_n_2] :
( ! [B_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
=> hBOOL(hAPP(V_Pa_2,B_m)) )
<=> ! [B_x] :
( 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)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_all__nat__less) ).
fof(fact_ex__nat__less__eq,axiom,
! [V_Pa_2,V_n_2] :
( ? [B_m] :
( hBOOL(hAPP(V_Pa_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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))) ) ),
file('theBenchmark.p',fact_ex__nat__less__eq) ).
fof(fact_all__nat__less__eq,axiom,
! [V_Pa_2,V_n_2] :
( ! [B_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
=> hBOOL(hAPP(V_Pa_2,B_m)) )
<=> ! [B_x] :
( 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)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_even__less__0__iff,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_comm__monoid__big_OF__eq,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
fof(fact_card_Ounion__inter__neutral,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ( ? [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)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(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(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)) ) ) ),
file('theBenchmark.p',fact_card_Ounion__inter__neutral) ).
fof(fact_comm__monoid__big_Oinfinite,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ),
file('theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
fof(fact_double__eq__0__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_setsum__mono2,axiom,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( class_Groups_Oordered__comm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ! [B_b] :
( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono2) ).
fof(fact_fold__image__Un__one,axiom,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( ! [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_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(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)),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)) ) ) ) ),
file('theBenchmark.p',fact_fold__image__Un__one) ).
fof(fact_setsum_Ounion__inter__neutral,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ! [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)))
=> hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(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_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)) ) ) ) ),
file('theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).
fof(fact_setsum__Un__zero,axiom,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( ! [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_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_setsum__Un__zero) ).
fof(fact_card__Suc__eq,axiom,
! [V_k_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
<=> ? [B_b,B_B] :
( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
& V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) ) ),
file('theBenchmark.p',fact_card__Suc__eq) ).
fof(fact_setsum__mono3,axiom,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( ( class_Groups_Oordered__ab__semigroup__add(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ! [B_x] :
( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono3) ).
fof(fact_Ints__odd__less__0,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ),
file('theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_Ints__0,axiom,
! [T_b] :
( class_Rings_Oring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__0) ).
fof(fact_Ints__add,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_Ints__add) ).
fof(fact_Ints__mult,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_Ints__mult) ).
fof(fact_Ints__diff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_Ints__diff) ).
fof(fact_Ints__1,axiom,
! [T_b] :
( class_Rings_Oring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__1) ).
fof(fact_Ints__minus,axiom,
! [V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> 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))) ) ),
file('theBenchmark.p',fact_Ints__minus) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [V_a_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_Ints__odd__nonzero,axiom,
! [V_a_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(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) ) ),
file('theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_card__Plus__conv__if,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
=> 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) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
=> 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)) ) ),
file('theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_setprod__diff1,axiom,
! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
( class_Fields_Ofield(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_setprod__diff1) ).
fof(fact_ex__least__nat__less,axiom,
! [V_n_2,V_Pa_2] :
( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(V_Pa_2,V_n_2))
=> ? [B_k] :
( 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))))
& ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
=> ~ hBOOL(hAPP(V_Pa_2,B_i)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) ) ) ),
file('theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_setsum__mono__zero__right,axiom,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( 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)))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
=> 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) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono__zero__right) ).
fof(fact_setsum__mono__zero__left,axiom,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( 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)))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(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) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono__zero__left) ).
fof(fact_sgn__1__neg,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_sgn__sgn,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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) ),
file('theBenchmark.p',fact_sgn__sgn) ).
fof(fact_divide__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_divide__zero__left) ).
fof(fact_divide__zero,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> 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) ),
file('theBenchmark.p',fact_divide__zero) ).
fof(fact_add__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_times__divide__eq__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_diff__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_diff__divide__distrib) ).
fof(fact_divide__1,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_divide__1) ).
fof(fact_minus__divide__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_minus__divide__left) ).
fof(fact_sgn__0__0,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_sgn__0__0) ).
fof(fact_sgn0,axiom,
! [T_a] :
( class_Groups_Osgn__if(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_sgn0) ).
fof(fact_sgn__times,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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)) ),
file('theBenchmark.p',fact_sgn__times) ).
fof(fact_eq__divide__imp,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
=> V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ),
file('theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_divide__eq__imp,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ),
file('theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( class_Rings_Odivision__ring(T_b)
=> ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ),
file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Rings_Odivision__ring(T_b)
=> ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ),
file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_right__inverse__eq,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Rings_Odivision__ring(T_b)
=> ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
<=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_divide__self,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_divide__self) ).
fof(fact_divide__self__if,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) )
& ( V_a = c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divide__self__if) ).
fof(fact_nonzero__minus__divide__divide,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(fact_nonzero__minus__divide__right,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ),
file('theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(fact_sgn__less,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_sgn__less) ).
fof(fact_sgn__greater,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_sgn__greater) ).
fof(fact_finite__Plus__iff,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( 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)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__Plus,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> 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))) ) ),
file('theBenchmark.p',fact_finite__Plus) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( 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)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( 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)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
file('theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_sgn__pos,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_card__Plus,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> 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)) ) ),
file('theBenchmark.p',fact_card__Plus) ).
fof(fact_sgn__if,axiom,
! [V_x,T_a] :
( class_Groups_Osgn__if(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(T_a)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sgn__if) ).
fof(fact_sgn__neg,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_sgn__neg) ).
fof(fact_divide__left__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> ( 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)))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_divide__left__mono,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> ( 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)))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono) ).
fof(fact_neg__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_neg__divide__le__eq) ).
fof(fact_neg__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( 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_ca_2)))
<=> 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_ca_2))) ) ) ),
file('theBenchmark.p',fact_neg__le__divide__eq) ).
fof(fact_mult__imp__le__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( 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))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__imp__le__div__pos) ).
fof(fact_mult__imp__div__pos__le,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( 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)))
=> 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)) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__le) ).
fof(fact_times__divide__times__eq,axiom,
! [V_w,V_z,V_y,V_x,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> 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)) ),
file('theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_minus__divide__divide,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> 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) ),
file('theBenchmark.p',fact_minus__divide__divide) ).
fof(fact_minus__divide__right,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> 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)) ),
file('theBenchmark.p',fact_minus__divide__right) ).
fof(fact_divide__right__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_divide__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__right__mono) ).
fof(fact_divide__le__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( 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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_zero__le__divide__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( 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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_divide__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_divide__neg__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_divide__neg__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_divide__pos__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_divide__less__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( 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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( 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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_eq__divide__eq,axiom,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( class_Fields_Ofield__inverse__zero(T_b)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
<=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq) ).
fof(fact_divide__eq__eq,axiom,
! [V_a_2,V_ca_2,V_b_2,T_b] :
( class_Fields_Ofield__inverse__zero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
<=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_frac__eq__eq,axiom,
! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
( class_Fields_Ofield(T_b)
=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( 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)
<=> 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) ) ) ) ),
file('theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_divide__nonneg__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__nonneg__pos) ).
fof(fact_divide__nonneg__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__nonneg__neg) ).
fof(fact_frac__less2,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_frac__less2) ).
fof(fact_frac__less,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_frac__less) ).
fof(fact_frac__le,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
=> 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))) ) ) ) ) ),
file('theBenchmark.p',fact_frac__le) ).
fof(fact_divide__nonpos__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__nonpos__pos) ).
fof(fact_divide__nonpos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_divide__nonpos__neg) ).
fof(fact_divide__strict__left__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> ( 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)))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_divide__strict__left__mono,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> ( 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)))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_neg__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_neg__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( 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_ca_2)))
<=> 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_ca_2))) ) ) ),
file('theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( 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))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( 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)))
=> 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)) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_pos__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
<=> 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_ca_2))) ) ) ),
file('theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_pos__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( 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_ca_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_divide__less__eq,axiom,
! [V_a_2,V_ca_2,V_b_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> 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_ca_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq) ).
fof(fact_less__divide__eq,axiom,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( 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_ca_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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_ca_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq) ).
fof(fact_add__num__frac,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_add__num__frac) ).
fof(fact_add__divide__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_add__frac__num) ).
fof(fact_divide__add__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__eq,axiom,
! [V_w,V_x,V_z,V_y,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ) ),
file('theBenchmark.p',fact_add__frac__eq) ).
fof(fact_diff__frac__eq,axiom,
! [V_w,V_x,V_z,V_y,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ) ),
file('theBenchmark.p',fact_diff__frac__eq) ).
fof(fact_divide__diff__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_divide__diff__eq__iff) ).
fof(fact_diff__divide__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_diff__divide__eq__iff) ).
fof(fact_less__half__sum,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> 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))))) ) ),
file('theBenchmark.p',fact_less__half__sum) ).
fof(fact_gt__half__sum,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> 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)) ) ),
file('theBenchmark.p',fact_gt__half__sum) ).
fof(fact_le__divide__eq,axiom,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( 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_ca_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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_ca_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq) ).
fof(fact_divide__le__eq,axiom,
! [V_a_2,V_ca_2,V_b_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> 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_ca_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq) ).
fof(fact_pos__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( 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_ca_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_pos__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
<=> 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_ca_2))) ) ) ),
file('theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [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)),
file('theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_setprod__Un,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Fields_Ofield(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ! [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)))
=> hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_setprod__Un) ).
fof(fact_Plus__eq__empty__conv,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( 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))
<=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Plus__eq__empty__conv) ).
fof(fact_field__le__mult__one__interval,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( ! [B_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
=> 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)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_field__le__mult__one__interval) ).
fof(fact_setprod__pos__nat,axiom,
! [V_f_2,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> 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))) )
=> 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))) ) ),
file('theBenchmark.p',fact_setprod__pos__nat) ).
fof(fact_setsum__SucD,axiom,
! [V_n_2,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_Nat_OSuc,V_n_2)
=> ? [B_x] :
( 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)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_setsum__SucD) ).
fof(fact_card__partition,axiom,
! [V_k_2,V_C_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
=> ( ! [B_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
=> hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
=> ( ! [B_c1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
=> ! [B_c2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
=> ( B_c1 != B_c2
=> 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)) ) ) )
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_card__partition) ).
fof(fact_fold__image__1,axiom,
! [V_f_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(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) = c_Groups_Oone__class_Oone(T_c) ) ) ),
file('theBenchmark.p',fact_fold__image__1) ).
fof(fact_card_Oneutral,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_card_Oneutral) ).
fof(fact_fold__image__cong,axiom,
! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
=> 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) ) ) ),
file('theBenchmark.p',fact_fold__image__cong) ).
fof(fact_expand__Suc,axiom,
! [V_v] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_expand__Suc) ).
fof(fact_card__Pow,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ),
file('theBenchmark.p',fact_card__Pow) ).
fof(fact_eq__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Int_Oring__char__0(T_b)
& class_Int_Onumber__ring(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)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_eq__number__of) ).
fof(fact_number__of__reorient,axiom,
! [V_x_2,V_w_2,T_b] :
( class_Int_Onumber(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
<=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ),
file('theBenchmark.p',fact_number__of__reorient) ).
fof(fact_le__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_le__number__of) ).
fof(fact_less__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_less__number__of) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [V_q,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_number__of__add,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(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)) = 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)) ),
file('theBenchmark.p',fact_number__of__add) ).
fof(fact_add__number__of__eq,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_add__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_add__number__of__left) ).
fof(fact_number__of__mult,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(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)) = 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)) ),
file('theBenchmark.p',fact_number__of__mult) ).
fof(fact_arith__simps_I32_J,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_mult__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_diff__number__of__eq,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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))) ),
file('theBenchmark.p',fact_diff__number__of__eq) ).
fof(fact_number__of__diff,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_number__of__diff) ).
fof(fact_number__of__minus,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_number__of__minus) ).
fof(fact_arith__simps_I30_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_arith__simps_I30_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [V_q,V_p,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [V_w_2,V_v_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Int_Onumber(T_b) )
=> ( 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)))
<=> ~ 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))) ) ),
file('theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_left__distrib__number__of,axiom,
! [V_v,V_b,V_a,T_b] :
( ( class_Rings_Osemiring(T_b)
& class_Int_Onumber(T_b) )
=> 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))) ),
file('theBenchmark.p',fact_left__distrib__number__of) ).
fof(fact_right__distrib__number__of,axiom,
! [V_c,V_b,V_v,T_b] :
( ( class_Rings_Osemiring(T_b)
& class_Int_Onumber(T_b) )
=> 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)) ),
file('theBenchmark.p',fact_right__distrib__number__of) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_add__number__of__diff1,axiom,
! [V_c,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_add__number__of__diff1) ).
fof(fact_add__number__of__diff2,axiom,
! [V_w,V_c,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_add__number__of__diff2) ).
fof(fact_right__diff__distrib__number__of,axiom,
! [V_c,V_b,V_v,T_b] :
( ( class_Rings_Oring(T_b)
& class_Int_Onumber(T_b) )
=> 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)) ),
file('theBenchmark.p',fact_right__diff__distrib__number__of) ).
fof(fact_left__diff__distrib__number__of,axiom,
! [V_v,V_b,V_a,T_b] :
( ( class_Rings_Oring(T_b)
& class_Int_Onumber(T_b) )
=> 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))) ),
file('theBenchmark.p',fact_left__diff__distrib__number__of) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [V_q,V_p,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_minus__number__of__mult,axiom,
! [V_z,V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_minus__number__of__mult) ).
fof(fact_Ints__power,axiom,
! [V_n_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> 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))) ) ),
file('theBenchmark.p',fact_Ints__power) ).
fof(fact_Ints__number__of,axiom,
! [V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> 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))) ),
file('theBenchmark.p',fact_Ints__number__of) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(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))
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(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 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of1) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [V_ca_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(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_ca_2)
<=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_divide__eq__eq__number__of,axiom,
! [V_w_2,V_ca_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(T_b) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
<=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_ca_2 != c_Groups_Ozero__class_Ozero(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_ca_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_divide__eq__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(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
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(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)) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of1) ).
fof(fact_less__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( 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))))
<=> ( ( ~ 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)))
=> ( ( ~ 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( 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)))
=> 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)))) ) ) )
& ( 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)))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of1) ).
fof(fact_less__divide__eq__number__of,axiom,
! [V_ca_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( 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_ca_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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_ca_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> 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_ca_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_divide__less__eq__number__of,axiom,
! [V_w_2,V_ca_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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_ca_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> 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_ca_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_divide__less__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( 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))
<=> ( ( ~ 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)))
=> ( ( ~ 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( 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)))
=> 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)) ) ) )
& ( 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)))
=> 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)))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of1) ).
fof(fact_power__eq__if,axiom,
! [V_p,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)))) )
& ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_power__eq__if) ).
fof(fact_divide__le__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( 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))
<=> ( ( ~ 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)))
=> ( ( ~ 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( 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)))
=> 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)) ) ) )
& ( 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)))
=> 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)))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of1) ).
fof(fact_divide__le__eq__number__of,axiom,
! [V_w_2,V_ca_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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_ca_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> 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_ca_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_le__divide__eq__number__of,axiom,
! [V_ca_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( 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_ca_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
=> 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_ca_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
=> 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_ca_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_le__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( 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))))
<=> ( ( ~ 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)))
=> ( ( ~ 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( 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)))
=> 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)))) ) ) )
& ( 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)))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of1) ).
fof(fact_power__strict__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_power__strict__mono) ).
fof(fact_power__diff,axiom,
! [V_m,V_n,V_a,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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)) ) ) ),
file('theBenchmark.p',fact_power__diff) ).
fof(fact_one__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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))) ) ) ),
file('theBenchmark.p',fact_one__less__power) ).
fof(fact_power__le__imp__le__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_power__decreasing) ).
fof(fact_minus__numeral__code_I6_J,axiom,
! [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))),
file('theBenchmark.p',fact_minus__numeral__code_I6_J) ).
fof(fact_plus__numeral__code_I9_J,axiom,
! [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)),
file('theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_less__number__of__int__code,axiom,
! [V_l_2,V_k_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_times__numeral__code_I5_J,axiom,
! [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)),
file('theBenchmark.p',fact_times__numeral__code_I5_J) ).
fof(fact_minus__numeral__code_I5_J,axiom,
! [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)),
file('theBenchmark.p',fact_minus__numeral__code_I5_J) ).
fof(fact_less__eq__number__of__int__code,axiom,
! [V_l_2,V_k_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_less__eq__number__of__int__code) ).
fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
! [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),
file('theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).
fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
! [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),
file('theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).
fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
! [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),
file('theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).
fof(fact_zmult__1,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
file('theBenchmark.p',fact_zmult__1) ).
fof(fact_zmult__1__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zmult__1__right) ).
fof(fact_zle__add1__eq__le,axiom,
! [V_z_2,V_w_2] :
( 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))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_add1__zle__eq,axiom,
! [V_z_2,V_w_2] :
( 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))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zless__imp__add1__zle,axiom,
! [V_z,V_w] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
=> 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)) ),
file('theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_zless__add1__eq,axiom,
! [V_z_2,V_w_2] :
( 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))))
<=> ( V_w_2 = V_z_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_zadd__left__mono,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_zadd__zless__mono,axiom,
! [V_z,V_z_H,V_w,V_w_H] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
=> 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))) ) ),
file('theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_zless__le,axiom,
! [V_w_2,V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
<=> ( V_z_2 != V_w_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) ) ),
file('theBenchmark.p',fact_zless__le) ).
fof(fact_zle__refl,axiom,
! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)),
file('theBenchmark.p',fact_zle__refl) ).
fof(fact_zle__linear,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
file('theBenchmark.p',fact_zle__linear) ).
fof(fact_zle__trans,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ),
file('theBenchmark.p',fact_zle__trans) ).
fof(fact_zle__antisym,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
=> V_z = V_w ) ),
file('theBenchmark.p',fact_zle__antisym) ).
fof(fact_zminus__zminus,axiom,
! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z,
file('theBenchmark.p',fact_zminus__zminus) ).
fof(fact_zmult__zminus,axiom,
! [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)),
file('theBenchmark.p',fact_zmult__zminus) ).
fof(fact_zmult__commute,axiom,
! [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),
file('theBenchmark.p',fact_zmult__commute) ).
fof(fact_zmult__assoc,axiom,
! [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)),
file('theBenchmark.p',fact_zmult__assoc) ).
fof(fact_zless__linear,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) ),
file('theBenchmark.p',fact_zless__linear) ).
fof(fact_zadd__strict__right__mono,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_zadd__commute,axiom,
! [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),
file('theBenchmark.p',fact_zadd__commute) ).
fof(fact_zadd__left__commute,axiom,
! [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)),
file('theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_zadd__assoc,axiom,
! [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)),
file('theBenchmark.p',fact_zadd__assoc) ).
fof(fact_zadd__zmult__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_zminus__zadd__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_diff__int__def__symmetric,axiom,
! [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),
file('theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [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)),
file('theBenchmark.p',fact_diff__int__def) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_equal__int__def,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
<=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_equal__int__def) ).
fof(fact_zminus__0,axiom,
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),
file('theBenchmark.p',fact_zminus__0) ).
fof(fact_zmult__zless__mono2,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
=> 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))) ) ),
file('theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_less__bin__lemma,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
<=> 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))) ),
file('theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_zadd__0,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
file('theBenchmark.p',fact_zadd__0) ).
fof(fact_zadd__0__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zadd__0__right) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [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),
file('theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_odd__nonzero,axiom,
! [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),
file('theBenchmark.p',fact_odd__nonzero) ).
fof(fact_odd__less__0,axiom,
! [V_z_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_odd__less__0) ).
fof(fact_le__imp__0__less,axiom,
! [V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> 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))) ),
file('theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zle__diff1__eq,axiom,
! [V_z_2,V_w_2] :
( 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))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_int__0__less__1,axiom,
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))),
file('theBenchmark.p',fact_int__0__less__1) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_zsgn__def,axiom,
! [V_i] :
( ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zsgn__def) ).
fof(fact_zpower__zadd__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zpower__zpower,axiom,
! [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)),
file('theBenchmark.p',fact_zpower__zpower) ).
fof(fact_field__power__not__zero,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_power__mult__distrib,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_power__commutes,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power__commutes) ).
fof(fact_power__one,axiom,
! [V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> 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) ),
file('theBenchmark.p',fact_power__one) ).
fof(fact_power__mult,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> 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) ),
file('theBenchmark.p',fact_power__mult) ).
fof(fact_power__divide,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power__divide) ).
fof(fact_power__one__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ),
file('theBenchmark.p',fact_power__one__right) ).
fof(fact_zero__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> 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))) ) ),
file('theBenchmark.p',fact_zero__le__power) ).
fof(fact_power__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> 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))) ) ) ),
file('theBenchmark.p',fact_power__mono) ).
fof(fact_zero__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> 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))) ) ),
file('theBenchmark.p',fact_zero__less__power) ).
fof(fact_power__eq__0__iff,axiom,
! [V_n_2,V_a_2,T_b] :
( ( class_Rings_Ozero__neq__one(T_b)
& class_Rings_Ono__zero__divisors(T_b)
& class_Rings_Omult__zero(T_b)
& class_Power_Opower(T_b) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_one__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> 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))) ) ),
file('theBenchmark.p',fact_one__le__power) ).
fof(fact_power__0__Suc,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> 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) ),
file('theBenchmark.p',fact_power__0__Suc) ).
fof(fact_power__inject__exp,axiom,
! [V_n_2,V_m_2,V_a_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
=> ( 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)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
fof(fact_power__Suc2,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> 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) ),
file('theBenchmark.p',fact_power__Suc2) ).
fof(fact_power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Power_Opower(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power__Suc) ).
fof(fact_power__0,axiom,
! [V_a,T_a] :
( class_Power_Opower(T_a)
=> 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) ),
file('theBenchmark.p',fact_power__0) ).
fof(fact_power__add,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power__add) ).
fof(fact_nonzero__power__divide,axiom,
! [V_n,V_a,V_b,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ),
file('theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_power__one__over,axiom,
! [V_n,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> 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) ),
file('theBenchmark.p',fact_power__one__over) ).
fof(fact_power__Suc__0,axiom,
! [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)),
file('theBenchmark.p',fact_power__Suc__0) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [V_m_2,V_x_2] :
( 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))
<=> ( V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [V_n_2,V_x_2] :
( 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)))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) ),
file('theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_power__less__imp__less__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_power__le__imp__le__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( 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))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_power__inject__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(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))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> V_a = V_b ) ) ) ),
file('theBenchmark.p',fact_power__inject__base) ).
fof(fact_power__less__power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> 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)))) ) ),
file('theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_power__gt1__lemma,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> 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)))) ) ),
file('theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_power__0__left,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) ) ) ),
file('theBenchmark.p',fact_power__0__left) ).
fof(fact_power__gt1,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> 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)))) ) ),
file('theBenchmark.p',fact_power__gt1) ).
fof(fact_power__strict__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> 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))) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> 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))) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
fof(fact_power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power__minus) ).
fof(fact_nat__one__le__power,axiom,
! [V_n,V_i] :
( 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))
=> 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))) ),
file('theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_power__Suc__less,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_power__Suc__less) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(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)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> V_a = V_b ) ) ) ) ),
file('theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_power__Suc__less__one,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_power__strict__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_self__quotient__aux1,axiom,
! [V_q,V_r,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_self__quotient__aux2,axiom,
! [V_q,V_r,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_q__pos__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ),
file('theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_q__neg__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_unique__quotient__lemma,axiom,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ),
file('theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( 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)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_finite__atLeastAtMost__int,axiom,
! [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))),
file('theBenchmark.p',fact_finite__atLeastAtMost__int) ).
fof(fact_finite__atLeastLessThan__int,axiom,
! [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))),
file('theBenchmark.p',fact_finite__atLeastLessThan__int) ).
fof(fact_finite__greaterThanAtMost__int,axiom,
! [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))),
file('theBenchmark.p',fact_finite__greaterThanAtMost__int) ).
fof(fact_finite__greaterThanLessThan__int,axiom,
! [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))),
file('theBenchmark.p',fact_finite__greaterThanLessThan__int) ).
fof(fact_number__of__is__id,axiom,
! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k,
file('theBenchmark.p',fact_number__of__is__id) ).
fof(fact_eq__number__of__int__code,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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)))
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_eq__number__of__int__code) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('theBenchmark.p',fact_int__0__neq__1) ).
fof(fact_eq__int__refl,axiom,
! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)),
file('theBenchmark.p',fact_eq__int__refl) ).
fof(fact_finite__atLeastZeroLessThan__int,axiom,
! [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))),
file('theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( 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)
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ),
file('theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_simp__from__to,axiom,
! [V_i_2,V_j_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
=> 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)) ) ),
file('theBenchmark.p',fact_simp__from__to) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [V_n,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),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),V_x),V_n))) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
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))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_power__power__power,axiom,
! [T_b] :
( class_Power_Opower(T_b)
=> 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)) ),
file('theBenchmark.p',fact_power__power__power) ).
fof(fact_infinite__UNIV__int,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
file('theBenchmark.p',fact_infinite__UNIV__int) ).
fof(fact_power_Opower_Opower__0,axiom,
! [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,
file('theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
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))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_aset_I6_J,axiom,
! [V_A_2,V_t_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ( 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))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
=> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_aset_I6_J) ).
fof(fact_bset_I8_J,axiom,
! [V_B_2,V_t_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ( 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))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
=> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_bset_I8_J) ).
fof(fact_bset_I6_J,axiom,
! [V_t_2,V_B_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
=> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_bset_I6_J) ).
fof(fact_aset_I8_J,axiom,
! [V_t_2,V_A_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
=> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
=> 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))) ) ) ),
file('theBenchmark.p',fact_aset_I8_J) ).
fof(fact_periodic__finite__ex,axiom,
! [V_Pa_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
=> ( ! [B_x,B_k] :
( hBOOL(hAPP(V_Pa_2,B_x))
<=> 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)))) )
=> ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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))) ) ) ) ),
file('theBenchmark.p',fact_periodic__finite__ex) ).
fof(fact_aset_I4_J,axiom,
! [V_A_2,V_t_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
=> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( B_x != V_t_2
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ),
file('theBenchmark.p',fact_aset_I4_J) ).
fof(fact_bset_I3_J,axiom,
! [V_B_2,V_t_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ( 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))
=> ( ! [B_x] :
( 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)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
=> V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ),
file('theBenchmark.p',fact_bset_I3_J) ).
fof(fact_aset_I3_J,axiom,
! [V_A_2,V_t_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ( 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))
=> ( ! [B_x] :
( 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)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
=> V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ),
file('theBenchmark.p',fact_aset_I3_J) ).
fof(fact_aset_I5_J,axiom,
! [V_A_2,V_t_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
=> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_aset_I5_J) ).
fof(fact_bset_I7_J,axiom,
! [V_B_2,V_t_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
=> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_bset_I7_J) ).
fof(fact_bset_I4_J,axiom,
! [V_B_2,V_t_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
=> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( B_x != V_t_2
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ),
file('theBenchmark.p',fact_bset_I4_J) ).
fof(fact_aset_I7_J,axiom,
! [V_t_2,V_A_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
=> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
=> 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))) ) ) ),
file('theBenchmark.p',fact_aset_I7_J) ).
fof(fact_bset_I5_J,axiom,
! [V_t_2,V_B_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ! [B_x] :
( ! [B_xa] :
( 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)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
=> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_bset_I5_J) ).
fof(fact_tsub__def,axiom,
! [V_x,V_y] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
=> c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ),
file('theBenchmark.p',fact_tsub__def) ).
fof(fact_int__power__div__base,axiom,
! [V_k,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
=> 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)))) ) ),
file('theBenchmark.p',fact_int__power__div__base) ).
fof(fact_decr__mult__lemma,axiom,
! [V_k_2,V_Pa_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
=> ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> 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)))) ) ) ) ),
file('theBenchmark.p',fact_decr__mult__lemma) ).
fof(fact_incr__mult__lemma,axiom,
! [V_k_2,V_Pa_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
=> ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> 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)))) ) ) ) ),
file('theBenchmark.p',fact_incr__mult__lemma) ).
fof(fact_of__nat__number__of__lemma,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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) ) ) ),
file('theBenchmark.p',fact_of__nat__number__of__lemma) ).
fof(fact_negative__zle,axiom,
! [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))),
file('theBenchmark.p',fact_negative__zle) ).
fof(fact_negative__zless,axiom,
! [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))),
file('theBenchmark.p',fact_negative__zless) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
! [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)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
fof(fact_of__nat__eq__iff,axiom,
! [V_n_2,V_m_2,T_b] :
( class_Nat_Osemiring__char__0(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)
<=> V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_of__nat__eq__iff) ).
fof(fact_zdiv__zero,axiom,
! [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),
file('theBenchmark.p',fact_zdiv__zero) ).
fof(fact_zdiv__zminus__zminus,axiom,
! [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),
file('theBenchmark.p',fact_zdiv__zminus__zminus) ).
fof(fact_zdiv__zminus2,axiom,
! [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),
file('theBenchmark.p',fact_zdiv__zminus2) ).
fof(fact_div__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_div__0) ).
fof(fact_div__by__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_div__by__0) ).
fof(fact_div__by__1,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_div__by__1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
! [V_A_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
<=> 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))) ),
file('theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).
fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
! [V_B_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
<=> 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))) ),
file('theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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))) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_pos__imp__zdiv__neg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
fof(fact_neg__imp__zdiv__neg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_div__neg__pos__less0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_div__neg__pos__less0) ).
fof(fact_zdiv__self,axiom,
! [V_a] :
( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_zdiv__self) ).
fof(fact_int__0,axiom,
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),
file('theBenchmark.p',fact_int__0) ).
fof(fact_int__eq__0__conv,axiom,
! [V_n_2] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_int__eq__0__conv) ).
fof(fact_transfer__int__nat__numerals_I1_J,axiom,
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)),
file('theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
fof(fact_zero__zle__int,axiom,
! [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))),
file('theBenchmark.p',fact_zero__zle__int) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
! [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))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
! [V_Pa_2] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
<=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).
fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
! [V_Pa_2] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
<=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).
fof(fact_int__less__0__conv,axiom,
! [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))),
file('theBenchmark.p',fact_int__less__0__conv) ).
fof(fact_zless__int,axiom,
! [V_n_2,V_m_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_zless__int) ).
fof(fact_transfer__int__nat__relations_I2_J,axiom,
! [V_y_2,V_x_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).
fof(fact_zle__int,axiom,
! [V_n_2,V_m_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_zle__int) ).
fof(fact_transfer__int__nat__relations_I3_J,axiom,
! [V_y_2,V_x_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).
fof(fact_zadd__int,axiom,
! [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)),
file('theBenchmark.p',fact_zadd__int) ).
fof(fact_zadd__int__left,axiom,
! [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),
file('theBenchmark.p',fact_zadd__int__left) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(fact_zle__iff__zadd,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
<=> ? [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)) ),
file('theBenchmark.p',fact_zle__iff__zadd) ).
fof(fact_zero__le__imp__of__nat,axiom,
! [V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> 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))) ),
file('theBenchmark.p',fact_zero__le__imp__of__nat) ).
fof(fact_of__nat__0__le__iff,axiom,
! [V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> 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))) ),
file('theBenchmark.p',fact_of__nat__0__le__iff) ).
fof(fact_negative__eq__positive,axiom,
! [V_m_2,V_n_2] :
( 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)
<=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_negative__eq__positive) ).
fof(fact_of__nat__less__0__iff,axiom,
! [V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ 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))) ),
file('theBenchmark.p',fact_of__nat__less__0__iff) ).
fof(fact_not__int__zless__negative,axiom,
! [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)))),
file('theBenchmark.p',fact_not__int__zless__negative) ).
fof(fact_int__mult,axiom,
! [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)),
file('theBenchmark.p',fact_int__mult) ).
fof(fact_zmult__int,axiom,
! [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)),
file('theBenchmark.p',fact_zmult__int) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
fof(fact_of__nat__0,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__nat__0) ).
fof(fact_of__nat__less__imp__less,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_of__nat__less__imp__less) ).
fof(fact_less__imp__of__nat__less,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> 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))) ) ),
file('theBenchmark.p',fact_less__imp__of__nat__less) ).
fof(fact_of__nat__less__iff,axiom,
! [V_n_2,V_m_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_of__nat__less__iff) ).
fof(fact_int__1,axiom,
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),
file('theBenchmark.p',fact_int__1) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
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)),
file('theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_of__nat__le__iff,axiom,
! [V_n_2,V_m_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_of__nat__le__iff) ).
fof(fact_of__nat__add,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Osemiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_of__nat__add) ).
fof(fact_of__nat__mult,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Osemiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_of__nat__mult) ).
fof(fact_div__mult__mult1__if,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> 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) )
& ( V_c = c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ) ),
file('theBenchmark.p',fact_div__mult__mult1__if) ).
fof(fact_div__mult__self2__is__id,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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 ) ),
file('theBenchmark.p',fact_div__mult__self2__is__id) ).
fof(fact_div__mult__self1__is__id,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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 ) ),
file('theBenchmark.p',fact_div__mult__self1__is__id) ).
fof(fact_div__mult__mult2,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_div__mult__mult2) ).
fof(fact_div__mult__mult1,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_div__mult__mult1) ).
fof(fact_div__self,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_div__self) ).
fof(fact_of__nat__1,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__nat__1) ).
fof(fact_Ints__of__nat,axiom,
! [V_n_2,T_b] :
( class_Rings_Oring__1(T_b)
=> 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))) ),
file('theBenchmark.p',fact_Ints__of__nat) ).
fof(fact_of__nat__power,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Osemiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__nat__power) ).
fof(fact_int__power,axiom,
! [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),
file('theBenchmark.p',fact_int__power) ).
fof(fact_zpower__int,axiom,
! [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)),
file('theBenchmark.p',fact_zpower__int) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
! [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)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
! [V_A_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
<=> 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))) ),
file('theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
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))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).
fof(fact_zdiv__eq__0__iff,axiom,
! [V_k_2,V_i_2] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [V_i_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
=> ( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_zdiv__mono2,axiom,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) ) ),
file('theBenchmark.p',fact_div__nonneg__neg__le0) ).
fof(fact_div__pos__pos__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_zdiv__mono2__neg,axiom,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_div__neg__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_zdiv__mono1,axiom,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_zdiv__mono1__neg,axiom,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) ) ),
file('theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_int__div__less__self,axiom,
! [V_k,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
=> 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)) ) ),
file('theBenchmark.p',fact_int__div__less__self) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [V_b,V_a,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> 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) ),
file('theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_int__le__0__conv,axiom,
! [V_n_2] :
( 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)))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_int__le__0__conv) ).
fof(fact_int__Suc0__eq__1,axiom,
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),
file('theBenchmark.p',fact_int__Suc0__eq__1) ).
fof(fact_zless__iff__Suc__zadd,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
<=> ? [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))) ),
file('theBenchmark.p',fact_zless__iff__Suc__zadd) ).
fof(fact_int__zle__neg,axiom,
! [V_m_2,V_n_2] :
( 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))))
<=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_int__zle__neg) ).
fof(fact_int__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_int__Suc) ).
fof(fact_negative__zle__0,axiom,
! [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))),
file('theBenchmark.p',fact_negative__zle__0) ).
fof(fact_zdiff__int,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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)) ),
file('theBenchmark.p',fact_zdiff__int) ).
fof(fact_of__nat__Suc,axiom,
! [V_m,T_a] :
( class_Rings_Osemiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_of__nat__Suc) ).
fof(fact_of__nat__diff,axiom,
! [V_m,V_n,T_a] :
( class_Rings_Oring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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)) ) ),
file('theBenchmark.p',fact_of__nat__diff) ).
fof(fact_div__mult__self2,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ),
file('theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ),
file('theBenchmark.p',fact_div__mult__self1) ).
fof(fact_div__add__self1,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ),
file('theBenchmark.p',fact_div__add__self1) ).
fof(fact_div__add__self2,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ),
file('theBenchmark.p',fact_div__add__self2) ).
fof(fact_zero__less__int__conv,axiom,
! [V_n_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
file('theBenchmark.p',fact_zero__less__int__conv) ).
fof(fact_zmult__zless__mono2__lemma,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
=> 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))) ) ),
file('theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
fof(fact_not__zle__0__negative,axiom,
! [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))))),
file('theBenchmark.p',fact_not__zle__0__negative) ).
fof(fact_negative__zless__0,axiom,
! [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))),
file('theBenchmark.p',fact_negative__zless__0) ).
fof(fact_of__nat__0__less__iff,axiom,
! [V_n_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ),
file('theBenchmark.p',fact_of__nat__0__less__iff) ).
fof(fact_divmod__int__rel__div__eq,axiom,
! [V_r_1,V_y,V_b_1,V_a_1] :
( 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)
=> ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) ) ) )
=> ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ),
file('theBenchmark.p',fact_divmod__int__rel__div__eq) ).
fof(fact_split__zdiv,axiom,
! [V_k_2,V_n_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [B_i] :
( ? [B_j] :
( 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
=> hBOOL(hAPP(V_Pa_2,B_i)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_i] :
( ? [B_j] :
( 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
=> hBOOL(hAPP(V_Pa_2,B_i)) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_split__zdiv) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_zdiff__int__split,axiom,
! [V_y_2,V_x_2,V_Pa_2] :
( 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))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
=> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
=> 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)))) ) ) ),
file('theBenchmark.p',fact_zdiff__int__split) ).
fof(fact_tsub__eq,axiom,
! [V_x,V_y] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
=> c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ),
file('theBenchmark.p',fact_tsub__eq) ).
fof(fact_z3div__def,axiom,
! [V_k,V_l] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
=> 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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
=> c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) ),
file('theBenchmark.p',fact_z3div__def) ).
fof(fact_setsum__bounded,axiom,
! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
( ( class_Rings_Osemiring__1(T_c)
& class_Groups_Oordered__ab__semigroup__add(T_c) )
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
=> 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))) ) ),
file('theBenchmark.p',fact_setsum__bounded) ).
fof(fact_div__pos__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( 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)))
=> 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) ) ),
file('theBenchmark.p',fact_div__pos__neg__trivial) ).
fof(fact_split__neg__lemma,axiom,
! [V_n_2,V_Pa_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( 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)))
<=> ! [B_i,B_j] :
( ( 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
=> hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ),
file('theBenchmark.p',fact_split__neg__lemma) ).
fof(fact_split__pos__lemma,axiom,
! [V_n_2,V_Pa_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ( 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)))
<=> ! [B_i,B_j] :
( ( 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
=> hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ),
file('theBenchmark.p',fact_split__pos__lemma) ).
fof(fact_of__nat__number__of__eq,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) ) ) ),
file('theBenchmark.p',fact_of__nat__number__of__eq) ).
fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
! [V_B_2,V_A_2] :
( 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)),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) ),
file('theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).
fof(fact_transfer__int__nat__relations_I1_J,axiom,
! [V_y_2,V_x_2] :
( 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)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).
fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
! [V_B_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
<=> 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))) ),
file('theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).
fof(fact_int__int__eq,axiom,
! [V_n_2,V_m_2] :
( 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)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_int__int__eq) ).
fof(fact_not__neg__int,axiom,
! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
file('theBenchmark.p',fact_not__neg__int) ).
fof(fact_mod__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__0) ).
fof(fact_mod__by__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_mod__by__0) ).
fof(fact_mod__self,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__self) ).
fof(fact_neg__number__of__Min,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('theBenchmark.p',fact_neg__number__of__Min) ).
fof(fact_zmod__minus1__right,axiom,
! [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),
file('theBenchmark.p',fact_zmod__minus1__right) ).
fof(fact_mod__mod__trivial,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mod__trivial) ).
fof(fact_mod__add__self2,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__add__self2) ).
fof(fact_mod__add__self1,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__add__self1) ).
fof(fact_mod__add__right__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__add__right__eq) ).
fof(fact_mod__add__left__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__add__left__eq) ).
fof(fact_mod__add__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__add__eq) ).
fof(fact_zmod__simps_I2_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_zmod__simps_I2_J) ).
fof(fact_zmod__simps_I1_J,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_zmod__simps_I1_J) ).
fof(fact_mod__add__cong,axiom,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
=> ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
=> 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) ) ) ),
file('theBenchmark.p',fact_mod__add__cong) ).
fof(fact_mod__mult__right__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mult__right__eq) ).
fof(fact_mod__mult__left__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mult__left__eq) ).
fof(fact_mod__mult__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mult__eq) ).
fof(fact_mod__mult__mult1,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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)) ),
file('theBenchmark.p',fact_mod__mult__mult1) ).
fof(fact_mod__mult__mult2,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mult__mult2) ).
fof(fact_zmod__simps_I4_J,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_zmod__simps_I4_J) ).
fof(fact_mod__mult__cong,axiom,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
=> ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
=> 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) ) ) ),
file('theBenchmark.p',fact_mod__mult__cong) ).
fof(fact_mod__diff__cong,axiom,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
=> ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
=> 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) ) ) ),
file('theBenchmark.p',fact_mod__diff__cong) ).
fof(fact_mod__diff__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__diff__eq) ).
fof(fact_mod__diff__left__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__diff__left__eq) ).
fof(fact_mod__diff__right__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__diff__right__eq) ).
fof(fact_mod__minus__cong,axiom,
! [V_a_H,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
=> 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) ) ),
file('theBenchmark.p',fact_mod__minus__cong) ).
fof(fact_mod__minus__eq,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__minus__eq) ).
fof(fact_div__le__dividend,axiom,
! [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)),
file('theBenchmark.p',fact_div__le__dividend) ).
fof(fact_div__le__mono,axiom,
! [V_k,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> 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))) ),
file('theBenchmark.p',fact_div__le__mono) ).
fof(fact_div__mult2__eq,axiom,
! [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),
file('theBenchmark.p',fact_div__mult2__eq) ).
fof(fact_zmod__self,axiom,
! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zmod__self) ).
fof(fact_zmod__zero,axiom,
! [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),
file('theBenchmark.p',fact_zmod__zero) ).
fof(fact_zdiv__int,axiom,
! [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)),
file('theBenchmark.p',fact_zdiv__int) ).
fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).
fof(fact_rel__simps_I24_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I24_J) ).
fof(fact_rel__simps_I7_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I7_J) ).
fof(fact_zmod__zmult1__eq,axiom,
! [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),
file('theBenchmark.p',fact_zmod__zmult1__eq) ).
fof(fact_zmod__simps_I3_J,axiom,
! [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),
file('theBenchmark.p',fact_zmod__simps_I3_J) ).
fof(fact_zdiff__zmod__right,axiom,
! [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),
file('theBenchmark.p',fact_zdiff__zmod__right) ).
fof(fact_zdiff__zmod__left,axiom,
! [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),
file('theBenchmark.p',fact_zdiff__zmod__left) ).
fof(fact_zmod__zminus2,axiom,
! [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)),
file('theBenchmark.p',fact_zmod__zminus2) ).
fof(fact_zmod__zminus__zminus,axiom,
! [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)),
file('theBenchmark.p',fact_zmod__zminus__zminus) ).
fof(fact_zminus__zmod,axiom,
! [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),
file('theBenchmark.p',fact_zminus__zmod) ).
fof(fact_zpower__zmod,axiom,
! [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),
file('theBenchmark.p',fact_zpower__zmod) ).
fof(fact_eq__int__code_I6_J,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('theBenchmark.p',fact_eq__int__code_I6_J) ).
fof(fact_not__neg__0,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('theBenchmark.p',fact_not__neg__0) ).
fof(fact_not__neg__1,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('theBenchmark.p',fact_not__neg__1) ).
fof(fact_mod__mult__self1__is__0,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mult__self1__is__0) ).
fof(fact_mod__mult__self2__is__0,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mult__self2__is__0) ).
fof(fact_mod__mult__self2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mult__self2) ).
fof(fact_mod__mult__self1,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__mult__self1) ).
fof(fact_mod__by__1,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__by__1) ).
fof(fact_mod__div__trivial,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_mod__div__trivial) ).
fof(fact_div__1,axiom,
! [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,
file('theBenchmark.p',fact_div__1) ).
fof(fact_div__less,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_div__less) ).
fof(fact_nat__mult__div__cancel__disj,axiom,
! [V_n,V_m,V_k] :
( ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) )
& ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) ) ),
file('theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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))) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_zmod__le__nonneg__dividend,axiom,
! [V_k,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
=> 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)) ),
file('theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
fof(fact_neg__mod__bound,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) ),
file('theBenchmark.p',fact_neg__mod__bound) ).
fof(fact_pos__mod__bound,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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)) ),
file('theBenchmark.p',fact_pos__mod__bound) ).
fof(fact_zmod__eq__0__iff,axiom,
! [V_d_2,V_m_2] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ),
file('theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_bin__less__0__simps_I2_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
fof(fact_zmod__zminus2__not__zero,axiom,
! [V_l,V_k] :
( 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)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zmod__zminus2__not__zero) ).
fof(fact_zmod__zminus1__not__zero,axiom,
! [V_l,V_k] :
( 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)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zmod__zminus1__not__zero) ).
fof(fact_DIVISION__BY__ZERO,axiom,
! [V_a] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
& 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) ),
file('theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(fact_zmod__zdiv__trivial,axiom,
! [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),
file('theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(fact_zdiv__zadd1__eq,axiom,
! [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)),
file('theBenchmark.p',fact_zdiv__zadd1__eq) ).
fof(fact_Int_OMin__def,axiom,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_Int_OMin__def) ).
fof(fact_mult__Min,axiom,
! [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),
file('theBenchmark.p',fact_mult__Min) ).
fof(fact_zmod__minus1,axiom,
! [V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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)) ),
file('theBenchmark.p',fact_zmod__minus1) ).
fof(fact_not__neg__eq__ge__0,axiom,
! [V_x_2] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
file('theBenchmark.p',fact_not__neg__eq__ge__0) ).
fof(fact_neg__def,axiom,
! [V_Z_2] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_neg__def) ).
fof(fact_neg__zminus__int,axiom,
! [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))))),
file('theBenchmark.p',fact_neg__zminus__int) ).
fof(fact_div__mod__equality,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_div__mod__equality) ).
fof(fact_div__mod__equality2,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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) ),
file('theBenchmark.p',fact_div__mod__equality2) ).
fof(fact_mod__div__equality,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(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_a ),
file('theBenchmark.p',fact_mod__div__equality) ).
fof(fact_mod__div__equality2,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(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_a ),
file('theBenchmark.p',fact_mod__div__equality2) ).
fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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 ),
file('theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
fof(fact_div__le__mono2,axiom,
! [V_k,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> 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))) ) ),
file('theBenchmark.p',fact_div__le__mono2) ).
fof(fact_nat__mult__div__cancel1,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
=> 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) ),
file('theBenchmark.p',fact_nat__mult__div__cancel1) ).
fof(fact_div__mult__self1__is__m,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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 ),
file('theBenchmark.p',fact_div__mult__self1__is__m) ).
fof(fact_div__mult__self__is__m,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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 ),
file('theBenchmark.p',fact_div__mult__self__is__m) ).
fof(fact_div__less__dividend,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> 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)) ) ),
file('theBenchmark.p',fact_div__less__dividend) ).
fof(fact_mult__minus1__right,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_mult__minus1__right) ).
fof(fact_mult__minus1,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_mult__minus1) ).
fof(fact_mod__neg__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
file('theBenchmark.p',fact_mod__neg__neg__trivial) ).
fof(fact_neg__mod__conj,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( 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)))
& 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))) ) ),
file('theBenchmark.p',fact_neg__mod__conj) ).
fof(fact_neg__mod__sign,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) ),
file('theBenchmark.p',fact_neg__mod__sign) ).
fof(fact_mod__pos__pos__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
file('theBenchmark.p',fact_mod__pos__pos__trivial) ).
fof(fact_pos__mod__conj,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( 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))
& 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))) ) ),
file('theBenchmark.p',fact_pos__mod__conj) ).
fof(fact_pos__mod__sign,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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))) ),
file('theBenchmark.p',fact_pos__mod__sign) ).
fof(fact_number__of__Min,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_number__of__Min) ).
fof(fact_arith__simps_I31_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(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),c_Int_OMin) ),
file('theBenchmark.p',fact_arith__simps_I31_J) ).
fof(fact_divide__minus1,axiom,
! [V_x,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> 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) ),
file('theBenchmark.p',fact_divide__minus1) ).
fof(fact_zmod__zminus2__eq__if,axiom,
! [V_b,V_a] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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) ) ),
file('theBenchmark.p',fact_zmod__zminus2__eq__if) ).
fof(fact_zmod__zminus1__eq__if,axiom,
! [V_b,V_a] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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) ) ),
file('theBenchmark.p',fact_zmod__zminus1__eq__if) ).
fof(fact_zmod__zdiv__equality,axiom,
! [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)),
file('theBenchmark.p',fact_zmod__zdiv__equality) ).
fof(fact_zdiv__zmult1__eq,axiom,
! [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)),
file('theBenchmark.p',fact_zdiv__zmult1__eq) ).
fof(fact_zdiv__zmod__equality,axiom,
! [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),
file('theBenchmark.p',fact_zdiv__zmod__equality) ).
fof(fact_zdiv__zmod__equality2,axiom,
! [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),
file('theBenchmark.p',fact_zdiv__zmod__equality2) ).
fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> ( V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).
fof(fact_zmult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( ( V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_zmult__eq__1__iff) ).
fof(fact_zmult__div__cancel,axiom,
! [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)),
file('theBenchmark.p',fact_zmult__div__cancel) ).
fof(fact_zmod__zdiv__equality_H,axiom,
! [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)),
file('theBenchmark.p',fact_zmod__zdiv__equality_H) ).
fof(fact_zdiv__minus1__right,axiom,
! [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),
file('theBenchmark.p',fact_zdiv__minus1__right) ).
fof(fact_neg__imp__number__of__eq__0,axiom,
! [V_v] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_neg__imp__number__of__eq__0) ).
fof(fact_int__nat__number__of,axiom,
! [V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) ) ),
file('theBenchmark.p',fact_int__nat__number__of) ).
fof(fact_div__geq,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> 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)) ) ),
file('theBenchmark.p',fact_div__geq) ).
fof(fact_div__if,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_div__if) ).
fof(fact_split__div,axiom,
! [V_k_2,V_n_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
<=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
=> ( 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)
=> hBOOL(hAPP(V_Pa_2,B_i)) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_split__div) ).
fof(fact_mod__pos__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( 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)))
=> 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) ) ),
file('theBenchmark.p',fact_mod__pos__neg__trivial) ).
fof(fact_minus1__divide,axiom,
! [V_x,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> 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)) ),
file('theBenchmark.p',fact_minus1__divide) ).
fof(fact_div__eq__minus1,axiom,
! [V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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) ),
file('theBenchmark.p',fact_div__eq__minus1) ).
fof(fact_le__div__geq,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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)) ) ),
file('theBenchmark.p',fact_le__div__geq) ).
fof(fact_split__div__lemma,axiom,
! [V_m_2,V_q_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
=> ( ( 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))))
& 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)) )
<=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ),
file('theBenchmark.p',fact_split__div__lemma) ).
fof(fact_split__div_H,axiom,
! [V_n_2,V_m_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
<=> ( ? [B_q] :
( hBOOL(hAPP(V_Pa_2,B_q))
& 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))))
& 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)) )
| ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_split__div_H) ).
fof(fact_eq__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( 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)
<=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
=> V_v_2 = V_v_H_2 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_eq__nat__number__of) ).
fof(fact_nat__number__of__add__left,axiom,
! [V_k,V_v_H,V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
=> 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) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
=> 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) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) ) ),
file('theBenchmark.p',fact_nat__number__of__add__left) ).
fof(fact_split__zmod,axiom,
! [V_k_2,V_n_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [B_i,B_j] :
( ( 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
=> hBOOL(hAPP(V_Pa_2,B_j)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_i,B_j] :
( ( 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
=> hBOOL(hAPP(V_Pa_2,B_j)) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(V_Pa_2,V_n_2)) ) ) ),
file('theBenchmark.p',fact_split__zmod) ).
fof(fact_zmult2__lemma__aux3,axiom,
! [V_q,V_b,V_r,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma__aux3) ).
fof(fact_zmult2__lemma__aux4,axiom,
! [V_q,V_b,V_r,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma__aux4) ).
fof(fact_zmult2__lemma__aux1,axiom,
! [V_q,V_r,V_b,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma__aux1) ).
fof(fact_zmult2__lemma__aux2,axiom,
! [V_q,V_r,V_b,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma__aux2) ).
fof(fact_divmod__int__rel__mod__eq,axiom,
! [V_y,V_q_1,V_b_1,V_a_1] :
( 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)
=> ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) ) ) )
=> ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ),
file('theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
fof(fact_zmod__zmult2__eq,axiom,
! [V_b,V_a,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> 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)) ),
file('theBenchmark.p',fact_zmod__zmult2__eq) ).
fof(fact_zdiv__zminus2__eq__if,axiom,
! [V_a,V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) ) ) ),
file('theBenchmark.p',fact_zdiv__zminus2__eq__if) ).
fof(fact_zdiv__zminus1__eq__if,axiom,
! [V_a,V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) ) ) ),
file('theBenchmark.p',fact_zdiv__zminus1__eq__if) ).
fof(fact_z3mod__def,axiom,
! [V_k,V_l] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
=> c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) ),
file('theBenchmark.p',fact_z3mod__def) ).
fof(fact_Suc__nat__number__of__add,axiom,
! [V_n,V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) ) ),
file('theBenchmark.p',fact_Suc__nat__number__of__add) ).
fof(fact_Suc__nat__number__of,axiom,
! [V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_Suc__nat__number__of) ).
fof(fact_image__atLeastZeroLessThan__int,axiom,
! [V_u_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
=> 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))) ),
file('theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).
fof(fact_negD,axiom,
! [V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ? [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))) ),
file('theBenchmark.p',fact_negD) ).
fof(fact_mod__Suc__eq__Suc__mod,axiom,
! [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),
file('theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
fof(fact_mod__less,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ),
file('theBenchmark.p',fact_mod__less) ).
fof(fact_div__add1__eq,axiom,
! [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)),
file('theBenchmark.p',fact_div__add1__eq) ).
fof(fact_mod__less__eq__dividend,axiom,
! [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)),
file('theBenchmark.p',fact_mod__less__eq__dividend) ).
fof(fact_mod__mult__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_mod__mult__distrib) ).
fof(fact_mod__mult__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_mod__mult__distrib2) ).
fof(fact_nat__int,axiom,
! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n,
file('theBenchmark.p',fact_nat__int) ).
fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).
fof(fact_nat__mod__distrib,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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)) ) ),
file('theBenchmark.p',fact_nat__mod__distrib) ).
fof(fact_nat__0,axiom,
hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__0) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_mod__Suc,axiom,
! [V_n,V_m] :
( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
=> 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)) )
& ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mod__Suc) ).
fof(fact_mod__1,axiom,
! [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),
file('theBenchmark.p',fact_mod__1) ).
fof(fact_mod__less__divisor,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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)) ),
file('theBenchmark.p',fact_mod__less__divisor) ).
fof(fact_eq__nat__nat__iff,axiom,
! [V_z_H_2,V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
=> ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
<=> V_z_2 = V_z_H_2 ) ) ),
file('theBenchmark.p',fact_eq__nat__nat__iff) ).
fof(fact_ex__nat,axiom,
! [V_Pa_2] :
( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
file('theBenchmark.p',fact_ex__nat) ).
fof(fact_all__nat,axiom,
! [V_Pa_2] :
( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ),
file('theBenchmark.p',fact_all__nat) ).
fof(fact_transfer__nat__int__relations_I1_J,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
=> ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).
fof(fact_mod__eq__0__iff,axiom,
! [V_d_2,V_m_2] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ),
file('theBenchmark.p',fact_mod__eq__0__iff) ).
fof(fact_mod__geq,axiom,
! [V_n,V_m] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> 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) ),
file('theBenchmark.p',fact_mod__geq) ).
fof(fact_mod__if,axiom,
! [V_n,V_m] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ),
file('theBenchmark.p',fact_mod__if) ).
fof(fact_mod__mult__self3,axiom,
! [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),
file('theBenchmark.p',fact_mod__mult__self3) ).
fof(fact_mod__mult2__eq,axiom,
! [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)),
file('theBenchmark.p',fact_mod__mult2__eq) ).
fof(fact_div__mult1__eq,axiom,
! [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)),
file('theBenchmark.p',fact_div__mult1__eq) ).
fof(fact_le__mod__geq,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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) ),
file('theBenchmark.p',fact_le__mod__geq) ).
fof(fact_nat__number__of__def,axiom,
! [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)),
file('theBenchmark.p',fact_nat__number__of__def) ).
fof(fact_nat__number__of,axiom,
! [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),
file('theBenchmark.p',fact_nat__number__of) ).
fof(fact_div__mod__equality_H,axiom,
! [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)),
file('theBenchmark.p',fact_div__mod__equality_H) ).
fof(fact_mult__div__cancel,axiom,
! [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)),
file('theBenchmark.p',fact_mult__div__cancel) ).
fof(fact_Divides_Omod__div__equality_H,axiom,
! [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)),
file('theBenchmark.p',fact_Divides_Omod__div__equality_H) ).
fof(fact_transfer__nat__int__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
fof(fact_zmod__int,axiom,
! [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)),
file('theBenchmark.p',fact_zmod__int) ).
fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).
fof(fact_neg__nat,axiom,
! [V_z] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
=> hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_neg__nat) ).
fof(fact_not__neg__nat,axiom,
! [V_z] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ),
file('theBenchmark.p',fact_not__neg__nat) ).
fof(fact_transfer__int__nat__set__return__embed,axiom,
! [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,
file('theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
! [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))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J) ).
fof(fact_mod__nat__number__of,axiom,
! [V_v_H,V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
=> 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))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
=> 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) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) ) ),
file('theBenchmark.p',fact_mod__nat__number__of) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
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))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J) ).
fof(fact_nat__le__0,axiom,
! [V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_nat__le__0) ).
fof(fact_nat__0__iff,axiom,
! [V_i_2] :
( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_nat__0__iff) ).
fof(fact_nat__mono__iff,axiom,
! [V_w_2,V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_nat__mono__iff) ).
fof(fact_zless__nat__conj,axiom,
! [V_z_2,V_w_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
file('theBenchmark.p',fact_zless__nat__conj) ).
fof(fact_mod__le__divisor,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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)) ),
file('theBenchmark.p',fact_mod__le__divisor) ).
fof(fact_transfer__nat__int__relations_I3_J,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).
fof(fact_nat__1,axiom,
hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_nat__1) ).
fof(fact_mod__mult__self4,axiom,
! [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),
file('theBenchmark.p',fact_mod__mult__self4) ).
fof(fact_int__nat__eq,axiom,
! [V_z] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ),
file('theBenchmark.p',fact_int__nat__eq) ).
fof(fact_int__eq__iff,axiom,
! [V_z_2,V_m_2] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
& V_m_2 = hAPP(c_Int_Onat,V_z_2) ) ),
file('theBenchmark.p',fact_int__eq__iff) ).
fof(fact_nat__0__le,axiom,
! [V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ),
file('theBenchmark.p',fact_nat__0__le) ).
fof(fact_zless__nat__eq__int__zless,axiom,
! [V_z_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
<=> 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)) ),
file('theBenchmark.p',fact_zless__nat__eq__int__zless) ).
fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).
fof(fact_nat__div__distrib,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> 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)) ),
file('theBenchmark.p',fact_nat__div__distrib) ).
fof(fact_nat__zminus__int,axiom,
! [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),
file('theBenchmark.p',fact_nat__zminus__int) ).
fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
! [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))),
file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).
fof(fact_one__mod__nat__number__of,axiom,
! [V_v_H] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
=> 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))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
=> 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)) ) ),
file('theBenchmark.p',fact_one__mod__nat__number__of) ).
fof(fact_succ__def,axiom,
! [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)),
file('theBenchmark.p',fact_succ__def) ).
fof(fact_diff__bin__simps_I2_J,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k),
file('theBenchmark.p',fact_diff__bin__simps_I2_J) ).
fof(fact_card__atLeastZeroLessThan__int,axiom,
! [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),
file('theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).
fof(fact_card__atLeastLessThan__int,axiom,
! [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)),
file('theBenchmark.p',fact_card__atLeastLessThan__int) ).
fof(fact_zero__less__nat__eq,axiom,
! [V_z_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
file('theBenchmark.p',fact_zero__less__nat__eq) ).
fof(fact_nat__less__eq__zless,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_nat__less__eq__zless) ).
fof(fact_transfer__nat__int__relations_I2_J,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).
fof(fact_nat__eq__iff,axiom,
! [V_m_2,V_w_2] :
( hAPP(c_Int_Onat,V_w_2) = V_m_2
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
=> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
=> V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) ) ),
file('theBenchmark.p',fact_nat__eq__iff) ).
fof(fact_nat__eq__iff2,axiom,
! [V_w_2,V_m_2] :
( V_m_2 = hAPP(c_Int_Onat,V_w_2)
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
=> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
=> V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) ) ),
file('theBenchmark.p',fact_nat__eq__iff2) ).
fof(fact_nat__le__eq__zle,axiom,
! [V_z_2,V_w_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_nat__le__eq__zle) ).
fof(fact_split__nat,axiom,
! [V_i_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [B_n] :
( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
=> hBOOL(hAPP(V_Pa_2,B_n)) ) ) ),
file('theBenchmark.p',fact_split__nat) ).
fof(fact_split__mod,axiom,
! [V_k_2,V_n_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
<=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
=> ( 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)
=> hBOOL(hAPP(V_Pa_2,B_j)) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(V_Pa_2,V_n_2)) ) ) ),
file('theBenchmark.p',fact_split__mod) ).
fof(fact_mod__lemma,axiom,
! [V_q,V_b,V_r,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_mod__lemma) ).
fof(fact_nat__add__distrib,axiom,
! [V_z_H,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
=> 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)) ) ),
file('theBenchmark.p',fact_nat__add__distrib) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
fof(fact_int__eq__iff__number__of,axiom,
! [V_v_2,V_m_2] :
( 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)
<=> ( 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)))
& V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) ) ),
file('theBenchmark.p',fact_int__eq__iff__number__of) ).
fof(fact_nat__mult__distrib,axiom,
! [V_z_H,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> 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)) ),
file('theBenchmark.p',fact_nat__mult__distrib) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
! [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))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).
fof(fact_nat__diff__distrib,axiom,
! [V_z,V_z_H] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
=> 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)) ) ),
file('theBenchmark.p',fact_nat__diff__distrib) ).
fof(fact_Suc__times__mod__eq,axiom,
! [V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
=> 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) ),
file('theBenchmark.p',fact_Suc__times__mod__eq) ).
fof(fact_card__greaterThanAtMost__int,axiom,
! [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)),
file('theBenchmark.p',fact_card__greaterThanAtMost__int) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
! [V_n,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> 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)) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).
fof(fact_nat__power__eq,axiom,
! [V_n,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> 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) ),
file('theBenchmark.p',fact_nat__power__eq) ).
fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
! [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))),
file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> 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)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).
fof(fact_one__less__nat__eq,axiom,
! [V_z_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ),
file('theBenchmark.p',fact_one__less__nat__eq) ).
fof(fact_nat__less__iff,axiom,
! [V_m_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
<=> 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))) ) ),
file('theBenchmark.p',fact_nat__less__iff) ).
fof(fact_Suc__nat__eq__nat__zadd1,axiom,
! [V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> 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)) ),
file('theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).
fof(fact_number__of__succ,axiom,
! [V_k,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_number__of__succ) ).
fof(fact_nat__mult__distrib__neg,axiom,
! [V_z_H,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) ),
file('theBenchmark.p',fact_nat__mult__distrib__neg) ).
fof(fact_div__nat__number__of,axiom,
! [V_v_H,V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) ) ),
file('theBenchmark.p',fact_div__nat__number__of) ).
fof(fact_card__atLeastAtMost__int,axiom,
! [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))),
file('theBenchmark.p',fact_card__atLeastAtMost__int) ).
fof(fact_one__div__nat__number__of,axiom,
! [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))),
file('theBenchmark.p',fact_one__div__nat__number__of) ).
fof(fact_card__greaterThanLessThan__int,axiom,
! [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)))),
file('theBenchmark.p',fact_card__greaterThanLessThan__int) ).
fof(fact_power__nat__number__of__number__of,axiom,
! [V_w,V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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)) ) ),
file('theBenchmark.p',fact_power__nat__number__of__number__of) ).
fof(fact_power__nat__number__of,axiom,
! [V_n,V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> 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) ) ),
file('theBenchmark.p',fact_power__nat__number__of) ).
fof(fact_nat__aux__def,axiom,
! [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),
file('theBenchmark.p',fact_nat__aux__def) ).
fof(fact_transfer__morphism__nat__int,axiom,
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))),
file('theBenchmark.p',fact_transfer__morphism__nat__int) ).
fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
! [V_n_2,V_m_2] :
( c_Nat__Transfer_Ois__nat(V_m_2)
=> ( c_Nat__Transfer_Ois__nat(V_n_2)
=> 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))) ) ),
file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).
fof(fact_of__int__of__nat,axiom,
! [V_k,T_a] :
( class_Rings_Oring__1(T_a)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)))) ) ) ),
file('theBenchmark.p',fact_of__int__of__nat) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> 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))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).
fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
! [V_y_2,V_x_2] :
( c_Nat__Transfer_Ois__nat(V_x_2)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).
fof(fact_of__int__eq__iff,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Int_Oring__char__0(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)
<=> V_w_2 = V_z_2 ) ),
file('theBenchmark.p',fact_of__int__eq__iff) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> 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)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> 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)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
! [V_x_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
=> c_Nat__Transfer_Ois__nat(V_x_2) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).
fof(fact_number__of__eq,axiom,
! [V_k,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ),
file('theBenchmark.p',fact_number__of__eq) ).
fof(fact_int__number__of__def,axiom,
! [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),
file('theBenchmark.p',fact_int__number__of__def) ).
fof(fact_of__int__int__eq,axiom,
! [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),
file('theBenchmark.p',fact_of__int__int__eq) ).
fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( V_A_2 = V_B_2
<=> 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) ) ) ),
file('theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
! [V_n,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).
fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
! [V_A_2,V_x_2] :
( c_Nat__Transfer_Ois__nat(V_x_2)
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
<=> 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))) ) ) ),
file('theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).
fof(fact_of__int__eq__0__iff,axiom,
! [V_z_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_of__int__eq__0__iff) ).
fof(fact_of__int__0__eq__iff,axiom,
! [V_z_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_of__int__0__eq__iff) ).
fof(fact_of__int__0,axiom,
! [T_a] :
( class_Rings_Oring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__int__0) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
fof(fact_of__int__le__iff,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__le__iff) ).
fof(fact_of__int__less__iff,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__less__iff) ).
fof(fact_of__int__add,axiom,
! [V_z,V_w,T_a] :
( class_Rings_Oring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_of__int__add) ).
fof(fact_of__int__number__of__eq,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__int__number__of__eq) ).
fof(fact_of__int__mult,axiom,
! [V_z,V_w,T_a] :
( class_Rings_Oring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_of__int__mult) ).
fof(fact_of__int__1,axiom,
! [T_a] :
( class_Rings_Oring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__int__1) ).
fof(fact_of__int__diff,axiom,
! [V_z,V_w,T_a] :
( class_Rings_Oring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_of__int__diff) ).
fof(fact_of__int__of__nat__eq,axiom,
! [V_n,T_a] :
( class_Rings_Oring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__int__of__nat__eq) ).
fof(fact_of__int__minus,axiom,
! [V_z,T_a] :
( class_Rings_Oring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_of__int__minus) ).
fof(fact_Ints__of__int,axiom,
! [V_z_2,T_b] :
( class_Rings_Oring__1(T_b)
=> 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))) ),
file('theBenchmark.p',fact_Ints__of__int) ).
fof(fact_of__int__power,axiom,
! [V_n,V_z,T_a] :
( class_Rings_Oring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__int__power) ).
fof(fact_nat__set__def,axiom,
! [V_S_2] :
( c_Nat__Transfer_Onat__set(V_S_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
file('theBenchmark.p',fact_nat__set__def) ).
fof(fact_is__nat__def,axiom,
! [V_x_2] :
( c_Nat__Transfer_Ois__nat(V_x_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
file('theBenchmark.p',fact_is__nat__def) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
! [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)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).
fof(fact_of__int__m1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_of__int__m1) ).
fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> 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))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J) ).
fof(fact_transfer__nat__int__set__return__embed,axiom,
! [V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> 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 ),
file('theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
! [V_x_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).
fof(fact_of__int__0__le__iff,axiom,
! [V_z_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__0__le__iff) ).
fof(fact_of__int__le__0__iff,axiom,
! [V_z_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_of__int__le__0__iff) ).
fof(fact_of__int__0__less__iff,axiom,
! [V_z_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__0__less__iff) ).
fof(fact_of__int__less__0__iff,axiom,
! [V_z_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_of__int__less__0__iff) ).
fof(fact_of__nat__nat,axiom,
! [V_z,T_a] :
( class_Rings_Oring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> 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) ) ),
file('theBenchmark.p',fact_of__nat__nat) ).
fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
! [V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
<=> 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))) ) ),
file('theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
! [V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> 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)) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) ).
fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
<=> 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))) ) ) ),
file('theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).
fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
<=> 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))) ) ) ),
file('theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).
fof(fact_zero__less__imp__eq__int,axiom,
! [V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
=> ? [B_n] :
( V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) ),
file('theBenchmark.p',fact_zero__less__imp__eq__int) ).
fof(fact_decr__lemma,axiom,
! [V_z,V_x,V_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
=> 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)) ),
file('theBenchmark.p',fact_decr__lemma) ).
fof(fact_incr__lemma,axiom,
! [V_x,V_z,V_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
=> 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)))) ),
file('theBenchmark.p',fact_incr__lemma) ).
fof(fact_nat__1__add__number__of,axiom,
! [V_v] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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) ) ),
file('theBenchmark.p',fact_nat__1__add__number__of) ).
fof(fact_nat__number__of__add__1,axiom,
! [V_v] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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) ) ),
file('theBenchmark.p',fact_nat__number__of__add__1) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_Pls__def) ).
fof(fact_rel__simps_I19_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I19_J) ).
fof(fact_abs__ge__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
file('theBenchmark.p',fact_abs__ge__self) ).
fof(fact_abs__le__D1,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_abs__le__D1) ).
fof(fact_abs__add__abs,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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)) ),
file('theBenchmark.p',fact_abs__add__abs) ).
fof(fact_abs__mult__self,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(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_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
file('theBenchmark.p',fact_abs__mult__self) ).
fof(fact_abs__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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)) ),
file('theBenchmark.p',fact_abs__mult) ).
fof(fact_abs__minus__commute,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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)) ),
file('theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_abs__one,axiom,
! [T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__one) ).
fof(fact_abs__minus__cancel,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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) ),
file('theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_abs__idempotent,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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) ),
file('theBenchmark.p',fact_abs__idempotent) ).
fof(fact_abs__zero,axiom,
! [T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_abs__zero) ).
fof(fact_abs__eq__0,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_abs__eq__0) ).
fof(fact_abs__int__eq,axiom,
! [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),
file('theBenchmark.p',fact_abs__int__eq) ).
fof(fact_abs__divide,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> 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)) ),
file('theBenchmark.p',fact_abs__divide) ).
fof(fact_power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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) ),
file('theBenchmark.p',fact_power__abs) ).
fof(fact_abs__of__nat,axiom,
! [V_n,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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) ),
file('theBenchmark.p',fact_abs__of__nat) ).
fof(fact_rel__simps_I2_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I2_J) ).
fof(fact_add__Pls__right,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
file('theBenchmark.p',fact_add__Pls__right) ).
fof(fact_add__Pls,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
file('theBenchmark.p',fact_add__Pls) ).
fof(fact_mult__Pls,axiom,
! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
file('theBenchmark.p',fact_mult__Pls) ).
fof(fact_diff__bin__simps_I1_J,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
file('theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(fact_minus__Pls,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_minus__Pls) ).
fof(fact_rel__simps_I37_J,axiom,
c_Int_OPls != c_Int_OMin,
file('theBenchmark.p',fact_rel__simps_I37_J) ).
fof(fact_rel__simps_I40_J,axiom,
c_Int_OMin != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I40_J) ).
fof(fact_eq__int__code_I1_J,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('theBenchmark.p',fact_eq__int__code_I1_J) ).
fof(fact_abs__ge__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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))) ),
file('theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_abs__le__zero__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( 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)))
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_abs__of__nonneg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
file('theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__of__pos,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
file('theBenchmark.p',fact_abs__of__pos) ).
fof(fact_zero__less__abs__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( 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)))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact_abs__not__less__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ~ 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))) ),
file('theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_abs__triangle__ineq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_abs__mult__less,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_abs__mult__less) ).
fof(fact_abs__triangle__ineq3,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_abs__triangle__ineq2,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_abs__triangle__ineq2) ).
fof(fact_abs__triangle__ineq2__sym,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
fof(fact_abs__le__D2,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ),
file('theBenchmark.p',fact_abs__le__D2) ).
fof(fact_abs__leI,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ),
file('theBenchmark.p',fact_abs__leI) ).
fof(fact_abs__le__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( 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))
<=> ( 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))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__ge__minus__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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))) ),
file('theBenchmark.p',fact_abs__ge__minus__self) ).
fof(fact_abs__less__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_abs__less__iff) ).
fof(fact_nonzero__abs__divide,axiom,
! [V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> 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)) ) ),
file('theBenchmark.p',fact_nonzero__abs__divide) ).
fof(fact_abs__power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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)) ),
file('theBenchmark.p',fact_abs__power__minus) ).
fof(fact_abs__zmult__eq__1,axiom,
! [V_n,V_m] :
( 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)
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_number__of__Pls,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_number__of__Pls) ).
fof(fact_semiring__norm_I112_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ),
file('theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_add__numeral__0,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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 ),
file('theBenchmark.p',fact_add__numeral__0) ).
fof(fact_add__numeral__0__right,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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 ),
file('theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_abs__sgn,axiom,
! [V_k,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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)) ),
file('theBenchmark.p',fact_abs__sgn) ).
fof(fact_mult__sgn__abs,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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 ),
file('theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_bin__less__0__simps_I1_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(fact_semiring__norm_I113_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
file('theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(fact_nat__number__of__Pls,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__number__of__Pls) ).
fof(fact_zero__is__num__zero,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('theBenchmark.p',fact_zero__is__num__zero) ).
fof(fact_rel__simps_I23_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I23_J) ).
fof(fact_rel__simps_I20_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I20_J) ).
fof(fact_rel__simps_I3_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I3_J) ).
fof(fact_rel__simps_I6_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I6_J) ).
fof(fact_eq__number__of__Pls__Min,axiom,
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),
file('theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(fact_not__neg__number__of__Pls,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('theBenchmark.p',fact_not__neg__number__of__Pls) ).
fof(fact_eq__int__code_I5_J,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('theBenchmark.p',fact_eq__int__code_I5_J) ).
fof(fact_eq__int__code_I2_J,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('theBenchmark.p',fact_eq__int__code_I2_J) ).
fof(fact_succ__Min,axiom,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
file('theBenchmark.p',fact_succ__Min) ).
fof(fact_abs__mult__pos,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_abs__eq__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring__abs(T_a)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
=> 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)) ) ),
file('theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_abs__triangle__ineq4,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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))))) ),
file('theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_abs__of__nonpos,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ),
file('theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__minus__le__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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))) ),
file('theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_abs__of__neg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ),
file('theBenchmark.p',fact_abs__of__neg) ).
fof(fact_abs__if,axiom,
! [V_a,T_a] :
( class_Groups_Oabs__if(T_a)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ),
file('theBenchmark.p',fact_abs__if) ).
fof(fact_zero__le__power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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))) ),
file('theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_abs__div__pos,axiom,
! [V_x,V_y,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> 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)) ) ),
file('theBenchmark.p',fact_abs__div__pos) ).
fof(fact_abs__minus__one,axiom,
! [T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> 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) ),
file('theBenchmark.p',fact_abs__minus__one) ).
fof(fact_zabs__less__one__iff,axiom,
! [V_z_2] :
( 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)))
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_zabs__def,axiom,
! [V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) ),
file('theBenchmark.p',fact_zabs__def) ).
fof(fact_nat__abs__mult__distrib,axiom,
! [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))),
file('theBenchmark.p',fact_nat__abs__mult__distrib) ).
fof(fact_zero__le__zpower__abs,axiom,
! [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))),
file('theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_divide__Numeral0,axiom,
! [V_x,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> 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) ),
file('theBenchmark.p',fact_divide__Numeral0) ).
fof(fact_eq__number__of__0,axiom,
! [V_v_2] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_eq__0__number__of,axiom,
! [V_v_2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_number__of2,axiom,
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))),
file('theBenchmark.p',fact_number__of2) ).
fof(fact_less__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) ) ),
file('theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_le__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( 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)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ),
file('theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_abs__number__of,axiom,
! [V_x,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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)) ) ) ),
file('theBenchmark.p',fact_abs__number__of) ).
fof(fact_abs__power__minus__one,axiom,
! [V_n,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> 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) ),
file('theBenchmark.p',fact_abs__power__minus__one) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [V_n_2,V_x_2] :
( 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)))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_le__special_I1_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
file('theBenchmark.p',fact_le__special_I1_J) ).
fof(fact_le__special_I3_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
file('theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_less__special_I1_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
file('theBenchmark.p',fact_less__special_I1_J) ).
fof(fact_less__special_I3_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
file('theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_less__0__number__of,axiom,
! [V_v_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ),
file('theBenchmark.p',fact_less__0__number__of) ).
fof(fact_add__nat__number__of,axiom,
! [V_v_H,V_v] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
=> 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) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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) ) ),
file('theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_nat__number__of__mult__left,axiom,
! [V_k,V_v_H,V_v] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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) ) ),
file('theBenchmark.p',fact_nat__number__of__mult__left) ).
fof(fact_mult__nat__number__of,axiom,
! [V_v_H,V_v] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> 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) ) ),
file('theBenchmark.p',fact_mult__nat__number__of) ).
fof(fact_eq__special_I3_J,axiom,
! [V_x_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> 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)))) ) ),
file('theBenchmark.p',fact_eq__special_I3_J) ).
fof(fact_eq__special_I1_J,axiom,
! [V_y_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
<=> 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)))) ) ),
file('theBenchmark.p',fact_eq__special_I1_J) ).
fof(fact_nat__number__of__diff__1,axiom,
! [V_v] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
=> 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) ) ),
file('theBenchmark.p',fact_nat__number__of__diff__1) ).
fof(fact_Nats__number__of,axiom,
! [V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Nats__number__of) ).
fof(fact_Nitpick_Oint__lcm__def,axiom,
! [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)))),
file('theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).
fof(fact_succ__pred,axiom,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
file('theBenchmark.p',fact_succ__pred) ).
fof(fact_iszero__def,axiom,
! [V_z_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> ( c_Int_Oiszero(T_b,V_z_2)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_iszero__def) ).
fof(fact_iszero__0,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_iszero__0) ).
fof(fact_not__iszero__1,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_not__iszero__1) ).
fof(fact_le__iff__pred__less,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ),
file('theBenchmark.p',fact_le__iff__pred__less) ).
fof(fact_pred__Pls,axiom,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
file('theBenchmark.p',fact_pred__Pls) ).
fof(fact_pred__def,axiom,
! [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)),
file('theBenchmark.p',fact_pred__def) ).
fof(fact_add__Min__right,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k),
file('theBenchmark.p',fact_add__Min__right) ).
fof(fact_add__Min,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k),
file('theBenchmark.p',fact_add__Min) ).
fof(fact_iszero__Numeral0,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ),
file('theBenchmark.p',fact_iszero__Numeral0) ).
fof(fact_Nats__0,axiom,
! [T_b] :
( class_Rings_Osemiring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
file('theBenchmark.p',fact_Nats__0) ).
fof(fact_Nats__add,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_Nats__add) ).
fof(fact_Nats__mult,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_Nats__mult) ).
fof(fact_nonzero__number__of__Min,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ),
file('theBenchmark.p',fact_nonzero__number__of__Min) ).
fof(fact_Nats__1,axiom,
! [T_b] :
( class_Rings_Osemiring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
file('theBenchmark.p',fact_Nats__1) ).
fof(fact_of__nat__in__Nats,axiom,
! [V_n_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> 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))) ),
file('theBenchmark.p',fact_of__nat__in__Nats) ).
fof(fact_number__of__pred,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_number__of__pred) ).
fof(fact_neg__number__of__pred__iff__0,axiom,
! [V_v_2] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_neg__number__of__pred__iff__0) ).
fof(fact_eq__number__of__eq,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Int_Onumber__ring(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)
<=> 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)))) ) ),
file('theBenchmark.p',fact_eq__number__of__eq) ).
fof(fact_Suc__diff__number__of,axiom,
! [V_m,V_v] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
=> 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))) ),
file('theBenchmark.p',fact_Suc__diff__number__of) ).
fof(fact_Nitpick_Onat__lcm__def,axiom,
! [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)),
file('theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).
fof(fact_eq__special_I4_J,axiom,
! [V_x_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
<=> 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))))) ) ),
file('theBenchmark.p',fact_eq__special_I4_J) ).
fof(fact_eq__special_I2_J,axiom,
! [V_y_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
<=> 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)))) ) ),
file('theBenchmark.p',fact_eq__special_I2_J) ).
fof(fact_diff__special_I2_J,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_diff__special_I2_J) ).
fof(fact_diff__special_I1_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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))) ),
file('theBenchmark.p',fact_diff__special_I1_J) ).
fof(fact_Bit1__Min,axiom,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
file('theBenchmark.p',fact_Bit1__Min) ).
fof(fact_rel__simps_I43_J,axiom,
! [V_l_2] :
( c_Int_OMin = c_Int_OBit1(V_l_2)
<=> c_Int_OMin = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I43_J) ).
fof(fact_rel__simps_I47_J,axiom,
! [V_k_2] :
( c_Int_OBit1(V_k_2) = c_Int_OMin
<=> V_k_2 = c_Int_OMin ),
file('theBenchmark.p',fact_rel__simps_I47_J) ).
fof(fact_rel__simps_I51_J,axiom,
! [V_l_2,V_k_2] :
( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
<=> V_k_2 = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I51_J) ).
fof(fact_less__int__code_I16_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I16_J) ).
fof(fact_rel__simps_I17_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I17_J) ).
fof(fact_rel__simps_I34_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I34_J) ).
fof(fact_less__eq__int__code_I16_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__eq__int__code_I16_J) ).
fof(fact_rel__simps_I39_J,axiom,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
file('theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_rel__simps_I46_J,axiom,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I46_J) ).
fof(fact_eq__int__code_I16_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_eq__int__code_I16_J) ).
fof(fact_bin__less__0__simps_I4_J,axiom,
! [V_w_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
fof(fact_rel__simps_I22_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I22_J) ).
fof(fact_rel__simps_I12_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I12_J) ).
fof(fact_Bit1__def,axiom,
! [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),
file('theBenchmark.p',fact_Bit1__def) ).
fof(fact_rel__simps_I26_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I26_J) ).
fof(fact_rel__simps_I30_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_rel__simps_I30_J) ).
fof(fact_rel__simps_I13_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_rel__simps_I13_J) ).
fof(fact_rel__simps_I9_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I9_J) ).
fof(fact_neg__number__of__Bit1,axiom,
! [V_w_2] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ),
file('theBenchmark.p',fact_neg__number__of__Bit1) ).
fof(fact_eq__int__code_I4_J,axiom,
! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))),
file('theBenchmark.p',fact_eq__int__code_I4_J) ).
fof(fact_eq__int__code_I10_J,axiom,
! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)),
file('theBenchmark.p',fact_eq__int__code_I10_J) ).
fof(fact_minus__Bit1,axiom,
! [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))),
file('theBenchmark.p',fact_minus__Bit1) ).
fof(fact_eq__int__code_I8_J,axiom,
! [V_k2_2] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ),
file('theBenchmark.p',fact_eq__int__code_I8_J) ).
fof(fact_eq__int__code_I12_J,axiom,
! [V_k1_2] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_eq__int__code_I12_J) ).
fof(fact_iszero__number__of__Bit1,axiom,
! [V_w,T_a] :
( ( class_Int_Oring__char__0(T_a)
& class_Int_Onumber__ring(T_a) )
=> ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ),
file('theBenchmark.p',fact_iszero__number__of__Bit1) ).
fof(fact_succ__Pls,axiom,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
file('theBenchmark.p',fact_succ__Pls) ).
fof(fact_number__of__Bit1,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_mult__numeral__1,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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 ),
file('theBenchmark.p',fact_mult__numeral__1) ).
fof(fact_mult__numeral__1__right,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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 ),
file('theBenchmark.p',fact_mult__numeral__1__right) ).
fof(fact_semiring__norm_I110_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ),
file('theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(fact_numeral__1__eq__1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_numeral__1__eq__1) ).
fof(fact_rel__simps_I29_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I29_J) ).
fof(fact_rel__simps_I5_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I5_J) ).
fof(fact_divide__Numeral1,axiom,
! [V_x,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield(T_a) )
=> 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 ),
file('theBenchmark.p',fact_divide__Numeral1) ).
fof(fact_divide__numeral__1,axiom,
! [V_a,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield(T_a) )
=> 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 ),
file('theBenchmark.p',fact_divide__numeral__1) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_one__is__num__one) ).
fof(fact_Numeral1__eq1__nat,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(fact_nat__numeral__1__eq__1,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__numeral__1__eq__1) ).
fof(fact_diff__bin__simps_I4_J,axiom,
! [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)),
file('theBenchmark.p',fact_diff__bin__simps_I4_J) ).
fof(fact_minus__Min,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
file('theBenchmark.p',fact_minus__Min) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).
fof(fact_not__iszero__Numeral1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_not__iszero__Numeral1) ).
fof(fact_numeral__1__eq__Suc__0,axiom,
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)),
file('theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
fof(fact_numeral__3__eq__3,axiom,
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)))),
file('theBenchmark.p',fact_numeral__3__eq__3) ).
fof(fact_power3__eq__cube,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(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_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) ),
file('theBenchmark.p',fact_power3__eq__cube) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
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))))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_Suc3__eq__add__3,axiom,
! [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),
file('theBenchmark.p',fact_Suc3__eq__add__3) ).
fof(fact_transfer__int__nat__numerals_I4_J,axiom,
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)))),
file('theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).
fof(fact_transfer__nat__int__numerals_I4_J,axiom,
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)))),
file('theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).
fof(fact_le__special_I2_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
file('theBenchmark.p',fact_le__special_I2_J) ).
fof(fact_le__special_I4_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
file('theBenchmark.p',fact_le__special_I4_J) ).
fof(fact_less__special_I2_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
file('theBenchmark.p',fact_less__special_I2_J) ).
fof(fact_less__special_I4_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
file('theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_add__special_I3_J,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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))) ),
file('theBenchmark.p',fact_add__special_I3_J) ).
fof(fact_add__special_I2_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ),
file('theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_Suc__diff__eq__diff__pred,axiom,
! [V_m,V_n] :
( 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))
=> 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)))) ),
file('theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).
fof(fact_nat__gcd_Osimps,axiom,
! [V_x,V_y] :
( ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)) )
& ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) ),
file('theBenchmark.p',fact_nat__gcd_Osimps) ).
fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
! [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)),
file('theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).
fof(fact_Suc__mod__eq__add3__mod,axiom,
! [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),
file('theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).
fof(fact_mod__Suc__eq__mod__add3,axiom,
! [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)),
file('theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).
fof(fact_Suc__div__eq__add3__div__number__of,axiom,
! [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)),
file('theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).
fof(fact_Suc__div__eq__add3__div,axiom,
! [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),
file('theBenchmark.p',fact_Suc__div__eq__add3__div) ).
fof(fact_div__Suc__eq__div__add3,axiom,
! [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)),
file('theBenchmark.p',fact_div__Suc__eq__div__add3) ).
fof(fact_Nitpick_Oint__gcd__def,axiom,
! [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)))),
file('theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).
fof(fact_zmod__number__of__Bit1,axiom,
! [V_v,V_w] :
( ( ~ 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)))
=> 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)) )
& ( 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)))
=> 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)) ) ),
file('theBenchmark.p',fact_zmod__number__of__Bit1) ).
fof(fact_neg__zmod__mult__2,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)) ),
file('theBenchmark.p',fact_neg__zmod__mult__2) ).
fof(fact_pos__zdiv__mult__2,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> 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) ),
file('theBenchmark.p',fact_pos__zdiv__mult__2) ).
fof(fact_rel__simps_I50_J,axiom,
! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
file('theBenchmark.p',fact_rel__simps_I50_J) ).
fof(fact_rel__simps_I49_J,axiom,
! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
file('theBenchmark.p',fact_rel__simps_I49_J) ).
fof(fact_rel__simps_I44_J,axiom,
! [V_k_2] :
( c_Int_OBit0(V_k_2) = c_Int_OPls
<=> V_k_2 = c_Int_OPls ),
file('theBenchmark.p',fact_rel__simps_I44_J) ).
fof(fact_rel__simps_I38_J,axiom,
! [V_l_2] :
( c_Int_OPls = c_Int_OBit0(V_l_2)
<=> c_Int_OPls = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I38_J) ).
fof(fact_Bit0__Pls,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_Bit0__Pls) ).
fof(fact_less__eq__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__eq__int__code_I13_J) ).
fof(fact_rel__simps_I31_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I31_J) ).
fof(fact_rel__simps_I14_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I14_J) ).
fof(fact_less__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I13_J) ).
fof(fact_add__Bit0__Bit0,axiom,
! [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)),
file('theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(fact_Bit0__def,axiom,
! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
file('theBenchmark.p',fact_Bit0__def) ).
fof(fact_rel__simps_I48_J,axiom,
! [V_l_2,V_k_2] :
( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
<=> V_k_2 = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I48_J) ).
fof(fact_rel__simps_I45_J,axiom,
! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
file('theBenchmark.p',fact_rel__simps_I45_J) ).
fof(fact_rel__simps_I42_J,axiom,
! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
file('theBenchmark.p',fact_rel__simps_I42_J) ).
fof(fact_minus__Bit0,axiom,
! [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)),
file('theBenchmark.p',fact_minus__Bit0) ).
fof(fact_diff__bin__simps_I7_J,axiom,
! [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)),
file('theBenchmark.p',fact_diff__bin__simps_I7_J) ).
fof(fact_mult__Bit0,axiom,
! [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)),
file('theBenchmark.p',fact_mult__Bit0) ).
fof(fact_eq__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_eq__int__code_I13_J) ).
fof(fact_bin__less__0__simps_I3_J,axiom,
! [V_w_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
fof(fact_rel__simps_I21_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I21_J) ).
fof(fact_rel__simps_I27_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I27_J) ).
fof(fact_rel__simps_I32_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I32_J) ).
fof(fact_less__eq__int__code_I14_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__eq__int__code_I14_J) ).
fof(fact_rel__simps_I10_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I10_J) ).
fof(fact_rel__simps_I4_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I4_J) ).
fof(fact_less__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I15_J) ).
fof(fact_rel__simps_I16_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I16_J) ).
fof(fact_add__Bit1__Bit0,axiom,
! [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)),
file('theBenchmark.p',fact_add__Bit1__Bit0) ).
fof(fact_add__Bit0__Bit1,axiom,
! [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)),
file('theBenchmark.p',fact_add__Bit0__Bit1) ).
fof(fact_diff__bin__simps_I3_J,axiom,
! [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)),
file('theBenchmark.p',fact_diff__bin__simps_I3_J) ).
fof(fact_diff__bin__simps_I10_J,axiom,
! [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)),
file('theBenchmark.p',fact_diff__bin__simps_I10_J) ).
fof(fact_diff__bin__simps_I9_J,axiom,
! [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)),
file('theBenchmark.p',fact_diff__bin__simps_I9_J) ).
fof(fact_rel__simps_I28_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_rel__simps_I28_J) ).
fof(fact_rel__simps_I8_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I8_J) ).
fof(fact_zdiv__number__of__Bit0,axiom,
! [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)),
file('theBenchmark.p',fact_zdiv__number__of__Bit0) ).
fof(fact_neg__number__of__Bit0,axiom,
! [V_w_2] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ),
file('theBenchmark.p',fact_neg__number__of__Bit0) ).
fof(fact_pred__Bit0,axiom,
! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
file('theBenchmark.p',fact_pred__Bit0) ).
fof(fact_pred__Bit1,axiom,
! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
file('theBenchmark.p',fact_pred__Bit1) ).
fof(fact_eq__int__code_I9_J,axiom,
! [V_k1_2] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_eq__int__code_I9_J) ).
fof(fact_eq__int__code_I3_J,axiom,
! [V_k2_2] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ),
file('theBenchmark.p',fact_eq__int__code_I3_J) ).
fof(fact_eq__int__code_I15_J,axiom,
! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))),
file('theBenchmark.p',fact_eq__int__code_I15_J) ).
fof(fact_eq__int__code_I14_J,axiom,
! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))),
file('theBenchmark.p',fact_eq__int__code_I14_J) ).
fof(fact_pred__Min,axiom,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
file('theBenchmark.p',fact_pred__Min) ).
fof(fact_eq__int__code_I11_J,axiom,
! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)),
file('theBenchmark.p',fact_eq__int__code_I11_J) ).
fof(fact_eq__int__code_I7_J,axiom,
! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))),
file('theBenchmark.p',fact_eq__int__code_I7_J) ).
fof(fact_iszero__number__of__Bit0,axiom,
! [V_w_2,T_b] :
( ( class_Int_Oring__char__0(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ),
file('theBenchmark.p',fact_iszero__number__of__Bit0) ).
fof(fact_succ__Bit1,axiom,
! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
file('theBenchmark.p',fact_succ__Bit1) ).
fof(fact_succ__Bit0,axiom,
! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
file('theBenchmark.p',fact_succ__Bit0) ).
fof(fact_number__of__Bit0,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_number__of__Bit0) ).
fof(fact_rel__simps_I15_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I15_J) ).
fof(fact_less__int__code_I14_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I14_J) ).
fof(fact_rel__simps_I33_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I33_J) ).
fof(fact_less__eq__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__eq__int__code_I15_J) ).
fof(fact_card__UNIV__bool,axiom,
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))),
file('theBenchmark.p',fact_card__UNIV__bool) ).
fof(fact_mult__Bit1,axiom,
! [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),
file('theBenchmark.p',fact_mult__Bit1) ).
fof(fact_rel__simps_I25_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I25_J) ).
fof(fact_rel__simps_I11_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_rel__simps_I11_J) ).
fof(fact_diff__bin__simps_I5_J,axiom,
! [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)),
file('theBenchmark.p',fact_diff__bin__simps_I5_J) ).
fof(fact_diff__bin__simps_I6_J,axiom,
! [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)),
file('theBenchmark.p',fact_diff__bin__simps_I6_J) ).
fof(fact_diff__bin__simps_I8_J,axiom,
! [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)),
file('theBenchmark.p',fact_diff__bin__simps_I8_J) ).
fof(fact_add__Bit1__Bit1,axiom,
! [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))),
file('theBenchmark.p',fact_add__Bit1__Bit1) ).
fof(fact_double__number__of__Bit0,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_double__number__of__Bit0) ).
fof(fact_number__of1,axiom,
! [V_n] :
( 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)))
=> ( 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))))
& 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)))) ) ),
file('theBenchmark.p',fact_number__of1) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).
fof(fact_mult__2__right,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_mult__2__right) ).
fof(fact_mult__2,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(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_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ),
file('theBenchmark.p',fact_mult__2) ).
fof(fact_one__add__one__is__two,axiom,
! [T_a] :
( class_Int_Onumber__ring(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),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_one__add__one__is__two) ).
fof(fact_zero__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_zero__power2) ).
fof(fact_zero__eq__power2,axiom,
! [V_a_2,T_b] :
( class_Rings_Oring__1__no__zero__divisors(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)))) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_semiring__norm_I115_J,axiom,
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))),
file('theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_numeral__2__eq__2,axiom,
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))),
file('theBenchmark.p',fact_numeral__2__eq__2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_power2__eq__square,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(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_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
file('theBenchmark.p',fact_power2__eq__square) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
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))))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(fact_add__2__eq__Suc_H,axiom,
! [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)),
file('theBenchmark.p',fact_add__2__eq__Suc_H) ).
fof(fact_add__2__eq__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_add__2__eq__Suc) ).
fof(fact_one__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> 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) ),
file('theBenchmark.p',fact_one__power2) ).
fof(fact_power2__minus,axiom,
! [V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_power2__minus) ).
fof(fact_nat__mult__2__right,axiom,
! [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),
file('theBenchmark.p',fact_nat__mult__2__right) ).
fof(fact_nat__mult__2,axiom,
! [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),
file('theBenchmark.p',fact_nat__mult__2) ).
fof(fact_power__even__eq,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(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)) = 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)))) ),
file('theBenchmark.p',fact_power__even__eq) ).
fof(fact_transfer__int__nat__numerals_I3_J,axiom,
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)))),
file('theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).
fof(fact_transfer__nat__int__numerals_I3_J,axiom,
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)))),
file('theBenchmark.p',fact_transfer__nat__int__numerals_I3_J) ).
fof(fact_power2__abs,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_power2__abs) ).
fof(fact_abs__power2,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_abs__power2) ).
fof(fact_nat__1__add__1,axiom,
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))),
file('theBenchmark.p',fact_nat__1__add__1) ).
fof(fact_mod2__Suc__Suc,axiom,
! [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)))),
file('theBenchmark.p',fact_mod2__Suc__Suc) ).
fof(fact_div2__Suc__Suc,axiom,
! [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))))),
file('theBenchmark.p',fact_div2__Suc__Suc) ).
fof(fact_zmod__number__of__Bit0,axiom,
! [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))),
file('theBenchmark.p',fact_zmod__number__of__Bit0) ).
fof(fact_add__self__div__2,axiom,
! [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,
file('theBenchmark.p',fact_add__self__div__2) ).
fof(fact_half__gt__zero,axiom,
! [V_r,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
=> 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)))))) ) ),
file('theBenchmark.p',fact_half__gt__zero) ).
fof(fact_half__gt__zero__iff,axiom,
! [V_r_2,T_b] :
( ( class_Int_Onumber__ring(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( 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))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ),
file('theBenchmark.p',fact_half__gt__zero__iff) ).
fof(fact_zero__le__power2,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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)))))) ),
file('theBenchmark.p',fact_zero__le__power2) ).
fof(fact_power2__le__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( 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))))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_power2__eq__imp__eq,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(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))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> V_x = V_y ) ) ) ),
file('theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_power2__less__0,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ 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))) ),
file('theBenchmark.p',fact_power2__less__0) ).
fof(fact_zero__less__power2,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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))))))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__less__power2) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__idom(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)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
fof(fact_power2__eq__square__number__of,axiom,
! [V_w,T_b] :
( ( class_Int_Onumber(T_b)
& class_Groups_Omonoid__mult(T_b) )
=> 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)) ),
file('theBenchmark.p',fact_power2__eq__square__number__of) ).
fof(fact_less__2__cases,axiom,
! [V_n] :
( 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)))))
=> ( V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_less__2__cases) ).
fof(fact_nat__2,axiom,
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))),
file('theBenchmark.p',fact_nat__2) ).
fof(fact_power2__eq__1__iff,axiom,
! [V_a_2,T_b] :
( class_Rings_Oring__1__no__zero__divisors(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)))) = c_Groups_Oone__class_Oone(T_b)
<=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| V_a_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
file('theBenchmark.p',fact_power2__eq__1__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [V_n,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_power__minus__even,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power__minus__even) ).
fof(fact_power2__less__imp__less,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( 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))))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_power2__less__imp__less) ).
fof(fact_sum__power2__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_sum__power2__ge__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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))))))) ),
file('theBenchmark.p',fact_sum__power2__ge__zero) ).
fof(fact_sum__power2__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( 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)))))))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
fof(fact_not__sum__power2__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ 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))) ),
file('theBenchmark.p',fact_not__sum__power2__lt__zero) ).
fof(fact_power2__sum,axiom,
! [V_y,V_x,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power2__sum) ).
fof(fact_zero__le__even__power_H,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_zero__le__even__power_H) ).
fof(fact_power__odd__eq,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(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))) = 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))))) ),
file('theBenchmark.p',fact_power__odd__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
! [V_n,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
fof(fact_power__minus1__even,axiom,
! [V_n,T_a] :
( class_Rings_Oring__1(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))),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) ),
file('theBenchmark.p',fact_power__minus1__even) ).
fof(fact_zdiv__number__of__Bit1,axiom,
! [V_v,V_w] :
( ( ~ 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)))
=> 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)) )
& ( 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)))
=> 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)) ) ),
file('theBenchmark.p',fact_zdiv__number__of__Bit1) ).
fof(fact_mod2__gr__0,axiom,
! [V_m_2] :
( 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))))))
<=> 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) ),
file('theBenchmark.p',fact_mod2__gr__0) ).
fof(fact_div__2__gt__zero,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
=> 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)))))) ),
file('theBenchmark.p',fact_div__2__gt__zero) ).
fof(fact_power2__diff,axiom,
! [V_y,V_x,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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)) ),
file('theBenchmark.p',fact_power2__diff) ).
fof(fact_odd__0__le__power__imp__0__le,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( 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)))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ),
file('theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
fof(fact_odd__power__less__zero,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> 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))) ) ),
file('theBenchmark.p',fact_odd__power__less__zero) ).
fof(fact_power__minus1__odd,axiom,
! [V_n,T_a] :
( class_Rings_Oring__1(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))),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)) ),
file('theBenchmark.p',fact_power__minus1__odd) ).
fof(fact_power__m1__even,axiom,
! [V_n,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_power__m1__even) ).
fof(fact_power__m1__odd,axiom,
! [V_n,T_a] :
( class_Int_Onumber__ring(T_a)
=> 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) ),
file('theBenchmark.p',fact_power__m1__odd) ).
fof(fact_Suc__n__div__2__gt__zero,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> 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)))))) ),
file('theBenchmark.p',fact_Suc__n__div__2__gt__zero) ).
fof(fact_of__nat__double,axiom,
! [V_x,T_a] :
( class_Rings_Osemiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> 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))) ) ),
file('theBenchmark.p',fact_of__nat__double) ).
fof(fact_pos__zmod__mult__2,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> 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))) ),
file('theBenchmark.p',fact_pos__zmod__mult__2) ).
fof(fact_neg__zdiv__mult__2,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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) ),
file('theBenchmark.p',fact_neg__zdiv__mult__2) ).
fof(fact_int__of__code,axiom,
! [V_k] :
( ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> ( ( 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)
=> 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)) )
& ( 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)
=> 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)))))) ) ) )
& ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_int__of__code) ).
fof(fact_one__code__numeral__code,axiom,
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)),
file('theBenchmark.p',fact_one__code__numeral__code) ).
fof(fact_int__val__lemma,axiom,
! [V_k_2,V_f_2,V_n_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
=> 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))) )
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
=> ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
file('theBenchmark.p',fact_int__val__lemma) ).
fof(fact_nat0__intermed__int__val,axiom,
! [V_k_2,V_f_2,V_n_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
=> 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))) )
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
=> ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
file('theBenchmark.p',fact_nat0__intermed__int__val) ).
fof(fact_code__numeral__zero__minus__one,axiom,
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),
file('theBenchmark.p',fact_code__numeral__zero__minus__one) ).
fof(fact_zero__code__numeral__code,axiom,
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),
file('theBenchmark.p',fact_zero__code__numeral__code) ).
fof(fact_nat__of__aux__code,axiom,
! [V_n,V_i] :
( ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> 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)) )
& ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) ),
file('theBenchmark.p',fact_nat__of__aux__code) ).
fof(fact_code__numeral_Osize_I1_J,axiom,
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),
file('theBenchmark.p',fact_code__numeral_Osize_I1_J) ).
fof(fact_code__numeral_Osize_I3_J,axiom,
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),
file('theBenchmark.p',fact_code__numeral_Osize_I3_J) ).
fof(fact_code__numeral_Osimps_I4_J,axiom,
! [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,
file('theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).
fof(fact_code__numeral_Osize_I4_J,axiom,
! [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))),
file('theBenchmark.p',fact_code__numeral_Osize_I4_J) ).
fof(fact_code__numeral_Osize_I2_J,axiom,
! [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))),
file('theBenchmark.p',fact_code__numeral_Osize_I2_J) ).
fof(fact_nat__mod__eq__lemma,axiom,
! [V_y,V_n,V_x] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
=> ? [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)) ) ),
file('theBenchmark.p',fact_nat__mod__eq__lemma) ).
fof(fact_mod__induct__0,axiom,
! [V_i_2,V_Pa_2,V_p_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
=> ( hBOOL(hAPP(V_Pa_2,B_i))
=> hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
=> ( hBOOL(hAPP(V_Pa_2,V_i_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
=> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_mod__induct__0) ).
fof(fact_code__numeral_Oinject,axiom,
! [V_code__numeral_H_2,V_code__numeral_2] :
( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
<=> V_code__numeral_2 = V_code__numeral_H_2 ),
file('theBenchmark.p',fact_code__numeral_Oinject) ).
fof(fact_code__numeral_Osimps_I3_J,axiom,
! [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),
file('theBenchmark.p',fact_code__numeral_Osimps_I3_J) ).
fof(fact_code__numeral_Osimps_I2_J,axiom,
! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
file('theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).
fof(fact_code__numeral_Osimps_I5_J,axiom,
! [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),
file('theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).
fof(fact_Suc__code__numeral__minus__one,axiom,
! [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,
file('theBenchmark.p',fact_Suc__code__numeral__minus__one) ).
fof(fact_nat__intermed__int__val,axiom,
! [V_k_2,V_f_2,V_n_2,V_m_2] :
( ! [B_i] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) )
=> 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))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
=> ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) ) ) ) ) ),
file('theBenchmark.p',fact_nat__intermed__int__val) ).
fof(fact_log_Osimps,axiom,
! [V_i,V_b] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
| 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))) )
=> 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))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
| 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))) )
=> c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) ),
file('theBenchmark.p',fact_log_Osimps) ).
fof(fact_mod__div__decomp,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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)) ),
file('theBenchmark.p',fact_mod__div__decomp) ).
fof(fact_setprod__pos,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_setprod__pos) ).
fof(fact_minus__shift__def,axiom,
! [V_r,V_l,V_k] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
=> 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) ) ),
file('theBenchmark.p',fact_minus__shift__def) ).
fof(fact_inc__shift__def,axiom,
! [V_k,V_v] :
( ( V_v != V_k
=> 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)) )
& ( V_v = V_k
=> c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) ),
file('theBenchmark.p',fact_inc__shift__def) ).
fof(fact_setprod__nonneg,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_setprod__nonneg) ).
fof(fact_finite__induct,axiom,
! [V_Pa_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ( ! [B_x,B_F] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
=> ( hBOOL(hAPP(V_Pa_2,B_F))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
=> hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ),
file('theBenchmark.p',fact_finite__induct) ).
fof(fact_fold1__antimono,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_fold1__antimono) ).
fof(fact_field__le__epsilon,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( ! [B_e] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
=> 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))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_field__le__epsilon) ).
fof(fact_subtract__code__numeral__def,axiom,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',fact_subtract__code__numeral__def) ).
fof(fact_minus__code__numeral__code,axiom,
! [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),
file('theBenchmark.p',fact_minus__code__numeral__code) ).
fof(fact_min__0R,axiom,
! [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),
file('theBenchmark.p',fact_min__0R) ).
fof(fact_min__0L,axiom,
! [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),
file('theBenchmark.p',fact_min__0L) ).
fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ),
file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).
fof(fact_min__Suc__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_min__Suc__Suc) ).
fof(fact_Min_Oidem,axiom,
! [V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_Min_Oidem) ).
fof(fact_min__max_Oinf_Oidem,axiom,
! [V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_min__max_Oinf_Oidem) ).
fof(fact_min__max_Oinf_Ocommute,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Olinorder(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_b),V_a) ),
file('theBenchmark.p',fact_min__max_Oinf_Ocommute) ).
fof(fact_min__max_Oinf__commute,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(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_y),V_x) ),
file('theBenchmark.p',fact_min__max_Oinf__commute) ).
fof(fact_min__max_Oinf_Oleft__idem,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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) ),
file('theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).
fof(fact_min__max_Oinf__left__idem,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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) ),
file('theBenchmark.p',fact_min__max_Oinf__left__idem) ).
fof(fact_min__max_Oinf_Oleft__commute,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).
fof(fact_min__max_Oinf__left__commute,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Oinf__left__commute) ).
fof(fact_min__max_Oinf_Oassoc,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Oinf_Oassoc) ).
fof(fact_min__max_Oinf__assoc,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Oinf__assoc) ).
fof(fact_inf__min,axiom,
! [T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Lattices_Osemilattice__inf(T_b) )
=> c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ),
file('theBenchmark.p',fact_inf__min) ).
fof(fact_min__diff,axiom,
! [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),
file('theBenchmark.p',fact_min__diff) ).
fof(fact_min__diff__distrib__left,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__diff__distrib__left) ).
fof(fact_min__max_Ole__infE,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( 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)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__infE) ).
fof(fact_min__max_Oinf__mono,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__mono) ).
fof(fact_min__max_Oinf__greatest,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
=> 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))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__greatest) ).
fof(fact_min__max_Ole__infI,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> 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))) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__infI) ).
fof(fact_min__max_Oinf__absorb2,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ),
file('theBenchmark.p',fact_min__max_Oinf__absorb2) ).
fof(fact_min__max_Oinf__absorb1,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ),
file('theBenchmark.p',fact_min__max_Oinf__absorb1) ).
fof(fact_min__max_Ole__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_min__max_Ole__infI2) ).
fof(fact_min__max_Ole__infI1,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_min__max_Ole__infI1) ).
fof(fact_min__max_Ole__inf__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__inf__iff) ).
fof(fact_min__max_Ole__iff__inf,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ),
file('theBenchmark.p',fact_min__max_Ole__iff__inf) ).
fof(fact_min__max_Oinf__le2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Oinf__le2) ).
fof(fact_min__max_Oinf__le1,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Oinf__le1) ).
fof(fact_min__le__iff__disj,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_min__le__iff__disj) ).
fof(fact_min__add__distrib__left,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__add__distrib__left) ).
fof(fact_min__max_Oless__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_min__max_Oless__infI2) ).
fof(fact_min__max_Oless__infI1,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_min__max_Oless__infI1) ).
fof(fact_min__less__iff__disj,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_min__less__iff__disj) ).
fof(fact_min__less__iff__conj,axiom,
! [V_y_2,V_x_2,V_z_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_min__less__iff__conj) ).
fof(fact_min__number__of,axiom,
! [V_v,V_u,T_b] :
( ( class_Orderings_Oord(T_b)
& class_Int_Onumber(T_b) )
=> ( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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) ) ) ),
file('theBenchmark.p',fact_min__number__of) ).
fof(fact_min__max_Ofold__inf__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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),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)) ) ),
file('theBenchmark.p',fact_min__max_Ofold__inf__insert) ).
fof(fact_Int__atLeastAtMostL1,axiom,
! [V_d_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_Int__atLeastAtMostL1) ).
fof(fact_Int__atLeastAtMostR1,axiom,
! [V_d_2,V_ca_2,V_b_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMostR1) ).
fof(fact_min__max_Ofold__inf__le__inf,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).
fof(fact_min__max_Ofold1__belowI,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold1__belowI) ).
fof(fact_min__max_Obelow__fold1__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( 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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).
fof(fact_fold1__below__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( 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))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__below__iff) ).
fof(fact_fold1__strict__below__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( 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))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__strict__below__iff) ).
fof(fact_strict__below__fold1__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( 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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_strict__below__fold1__iff) ).
fof(fact_min__ord__min,axiom,
! [T_b] :
( class_Orderings_Oord(T_b)
=> c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
file('theBenchmark.p',fact_min__ord__min) ).
fof(fact_Min_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),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_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))
=> 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)))))) )
& ( 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))
=> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Min_Oremove) ).
fof(fact_min__max_OInf__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),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_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))
=> 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)))))) )
& ( 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))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).
fof(fact_Min_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_Min_Oeq__fold_H) ).
fof(fact_inf__nat__def,axiom,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
file('theBenchmark.p',fact_inf__nat__def) ).
fof(fact_Min_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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 ),
file('theBenchmark.p',fact_Min_Osingleton) ).
fof(fact_min__max_OInf__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).
fof(fact_Min__le,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_Min__le) ).
fof(fact_min__max_OInf__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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 ),
file('theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).
fof(fact_Min__in,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ),
file('theBenchmark.p',fact_Min__in) ).
fof(fact_Min_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Min_Oin__idem) ).
fof(fact_min__max_OInf__fin_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).
fof(fact_Min_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_Min_OF__eq) ).
fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).
fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_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_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) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).
fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).
fof(fact_Min__antimono,axiom,
! [V_N_2,V_M_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
=> ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_Min__antimono) ).
fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).
fof(fact_Min__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_Min__insert) ).
fof(fact_Min_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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) ) ) ) ),
file('theBenchmark.p',fact_Min_Osubset__idem) ).
fof(fact_Min__Un,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_Min__Un) ).
fof(fact_Min_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).
fof(fact_min__max_OInf__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).
fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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_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))
=> 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)))))) )
& ( 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))
=> 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 ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).
fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).
fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(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) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).
fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).
fof(fact_Min_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Min_Oinsert) ).
fof(fact_Min_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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_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))
=> 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)))))) )
& ( 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))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Min_Oinsert__remove) ).
fof(fact_Min_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Min_Ounion__inter) ).
fof(fact_Min_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(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) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Min_Ounion__disjoint) ).
fof(fact_min__max_OInf__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [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))))))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).
fof(fact_Min_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [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))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Oclosed) ).
fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).
fof(fact_Min_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Min_Ohom__commute) ).
fof(fact_minus__Max__eq__Min,axiom,
! [V_S_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_minus__Max__eq__Min) ).
fof(fact_minus__Min__eq__Max,axiom,
! [V_S_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_minus__Min__eq__Max) ).
fof(fact_min__max_Oinf__le__fold__inf,axiom,
! [V_ca_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).
fof(fact_Min__eqI,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Min__eqI) ).
fof(fact_Max_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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 ),
file('theBenchmark.p',fact_Max_Osingleton) ).
fof(fact_Max__ge,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_Max__ge) ).
fof(fact_Max__in,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ),
file('theBenchmark.p',fact_Max__in) ).
fof(fact_Max__mono,axiom,
! [V_N_2,V_M_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
=> ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_Max__mono) ).
fof(fact_Max_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),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_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))
=> 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)))))) )
& ( 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))
=> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Max_Oremove) ).
fof(fact_Max__eqI,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Max__eqI) ).
fof(fact_Max_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_Max_Oeq__fold_H) ).
fof(fact_Max_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Max_Ounion__inter) ).
fof(fact_min__max_Osup__inf__absorb,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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 ),
file('theBenchmark.p',fact_min__max_Osup__inf__absorb) ).
fof(fact_min__max_Oinf__sup__absorb,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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 ),
file('theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).
fof(fact_min__max_Osup__inf__distrib1,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(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)) ),
file('theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).
fof(fact_min__max_Oinf__sup__distrib1,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Oinf__sup__distrib1) ).
fof(fact_min__max_Osup__inf__distrib2,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).
fof(fact_min__max_Oinf__sup__distrib2,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).
fof(fact_max__0R,axiom,
! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_max__0R) ).
fof(fact_max__0L,axiom,
! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_max__0L) ).
fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ),
file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).
fof(fact_max__Suc__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_max__Suc__Suc) ).
fof(fact_Max_Oidem,axiom,
! [V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_Max_Oidem) ).
fof(fact_min__max_Osup_Oidem,axiom,
! [V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_min__max_Osup_Oidem) ).
fof(fact_min__max_Osup_Ocommute,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Olinorder(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_b),V_a) ),
file('theBenchmark.p',fact_min__max_Osup_Ocommute) ).
fof(fact_min__max_Osup__commute,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(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_y),V_x) ),
file('theBenchmark.p',fact_min__max_Osup__commute) ).
fof(fact_min__max_Osup_Oleft__idem,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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) ),
file('theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).
fof(fact_min__max_Osup__left__idem,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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) ),
file('theBenchmark.p',fact_min__max_Osup__left__idem) ).
fof(fact_min__max_Osup_Oleft__commute,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).
fof(fact_min__max_Osup__left__commute,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Osup__left__commute) ).
fof(fact_min__max_Osup_Oassoc,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Osup_Oassoc) ).
fof(fact_min__max_Osup__assoc,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)) ),
file('theBenchmark.p',fact_min__max_Osup__assoc) ).
fof(fact_sup__max,axiom,
! [T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Lattices_Osemilattice__sup(T_b) )
=> c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ),
file('theBenchmark.p',fact_sup__max) ).
fof(fact_max__diff__distrib__left,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_max__diff__distrib__left) ).
fof(fact_min__max_Ole__supE,axiom,
! [V_x,V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( 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))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__supE) ).
fof(fact_min__max_Osup__mono,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__mono) ).
fof(fact_min__max_Osup__least,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
=> 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)) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__least) ).
fof(fact_min__max_Ole__supI,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
=> 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)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__supI) ).
fof(fact_min__max_Osup__absorb1,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ),
file('theBenchmark.p',fact_min__max_Osup__absorb1) ).
fof(fact_min__max_Osup__absorb2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ),
file('theBenchmark.p',fact_min__max_Osup__absorb2) ).
fof(fact_min__max_Ole__supI2,axiom,
! [V_a,V_b,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_min__max_Ole__supI2) ).
fof(fact_min__max_Ole__supI1,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> 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))) ) ),
file('theBenchmark.p',fact_min__max_Ole__supI1) ).
fof(fact_min__max_Ole__sup__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__sup__iff) ).
fof(fact_min__max_Ole__iff__sup,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ),
file('theBenchmark.p',fact_min__max_Ole__iff__sup) ).
fof(fact_le__maxI2,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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))) ),
file('theBenchmark.p',fact_le__maxI2) ).
fof(fact_le__maxI1,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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))) ),
file('theBenchmark.p',fact_le__maxI1) ).
fof(fact_le__max__iff__disj,axiom,
! [V_y_2,V_x_2,V_z_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_le__max__iff__disj) ).
fof(fact_max__add__distrib__left,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> 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)) ),
file('theBenchmark.p',fact_max__add__distrib__left) ).
fof(fact_min__max_Oless__supI2,axiom,
! [V_a,V_b,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_min__max_Oless__supI2) ).
fof(fact_min__max_Oless__supI1,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
=> 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))) ) ),
file('theBenchmark.p',fact_min__max_Oless__supI1) ).
fof(fact_max__less__iff__conj,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_max__less__iff__conj) ).
fof(fact_less__max__iff__disj,axiom,
! [V_y_2,V_x_2,V_z_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_less__max__iff__disj) ).
fof(fact_max__number__of,axiom,
! [V_v,V_u,T_b] :
( ( class_Orderings_Oord(T_b)
& class_Int_Onumber(T_b) )
=> ( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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) ) ) ),
file('theBenchmark.p',fact_max__number__of) ).
fof(fact_min__max_Odistrib__inf__le,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_min__max_Odistrib__inf__le) ).
fof(fact_min__max_Odistrib__sup__le,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> 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)))) ),
file('theBenchmark.p',fact_min__max_Odistrib__sup__le) ).
fof(fact_minus__min__eq__max,axiom,
! [V_y,V_x,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_minus__min__eq__max) ).
fof(fact_minus__max__eq__min,axiom,
! [V_y,V_x,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_minus__max__eq__min) ).
fof(fact_nat__minus__add__max,axiom,
! [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),
file('theBenchmark.p',fact_nat__minus__add__max) ).
fof(fact_min__max_Ofold__sup__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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),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)) ) ),
file('theBenchmark.p',fact_min__max_Ofold__sup__insert) ).
fof(fact_Max_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Max_Oin__idem) ).
fof(fact_Int__atLeastAtMost,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMost) ).
fof(fact_Int__atLeastLessThan,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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_ca_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_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastLessThan) ).
fof(fact_Int__greaterThanAtMost,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__greaterThanAtMost) ).
fof(fact_Int__greaterThanLessThan,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__greaterThanLessThan) ).
fof(fact_Int__atLeastAtMostL2,axiom,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2) ),
file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).
fof(fact_Int__atLeastAtMostR2,axiom,
! [V_d_2,V_ca_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ),
file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).
fof(fact_Max_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_Max_OF__eq) ).
fof(fact_min__max_Osup__le__fold__sup,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).
fof(fact_Max__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_Max__insert) ).
fof(fact_Max_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> 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) ) ) ) ),
file('theBenchmark.p',fact_Max_Osubset__idem) ).
fof(fact_min__max_Osup__Inf__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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 ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).
fof(fact_Max__Un,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_Max__Un) ).
fof(fact_Max_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).
fof(fact_Max_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Max_Oinsert) ).
fof(fact_Max_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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_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))
=> 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)))))) )
& ( 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))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Max_Oinsert__remove) ).
fof(fact_Max_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(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) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Max_Ounion__disjoint) ).
fof(fact_max__ord__max,axiom,
! [T_b] :
( class_Orderings_Oord(T_b)
=> c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
file('theBenchmark.p',fact_max__ord__max) ).
fof(fact_Max_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [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))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Oclosed) ).
fof(fact_min__max_OInf__le__Sup,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__le__Sup) ).
fof(fact_min__max_OSup__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),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_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))
=> 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)))))) )
& ( 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))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).
fof(fact_sup__nat__def,axiom,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
file('theBenchmark.p',fact_sup__nat__def) ).
fof(fact_min__max_OSup__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).
fof(fact_min__max_OSup__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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 ),
file('theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).
fof(fact_min__max_OSup__fin_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).
fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).
fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_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_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) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).
fof(fact_min__max_Oinf__Sup__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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 ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).
fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).
fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).
fof(fact_min__max_OSup__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).
fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(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_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))
=> 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)))))) )
& ( 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))
=> 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 ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).
fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).
fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(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) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).
fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).
fof(fact_min__max_OSup__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [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))))))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).
fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).
fof(fact_Max_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_Max_Ohom__commute) ).
fof(fact_min__max_Ofold__sup__le__sup,axiom,
! [V_ca_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
=> 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_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).
fof(fact_pair__box_Osize_I1_J,axiom,
! [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))),
file('theBenchmark.p',fact_pair__box_Osize_I1_J) ).
fof(fact_arith__series__int,axiom,
! [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)))),
file('theBenchmark.p',fact_arith__series__int) ).
fof(fact_negDivAlg__eqn__1__number__of,axiom,
! [V_w] :
( 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)))
=> ( ( ~ 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))))
=> 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)))) )
& ( 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))))
=> 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))) ) ) ),
file('theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).
fof(fact_nat_Osize_I2_J,axiom,
! [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))),
file('theBenchmark.p',fact_nat_Osize_I2_J) ).
fof(fact_INF2__E,axiom,
! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( 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_ca_2))
=> ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INF2__E) ).
fof(fact_INF2__D,axiom,
! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( 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_ca_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_INF2__D) ).
fof(fact_INF1__E,axiom,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
=> ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INF1__E) ).
fof(fact_INF1__D,axiom,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_INF1__D) ).
fof(fact_INT__D,axiom,
! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
file('theBenchmark.p',fact_INT__D) ).
fof(fact_INT__E,axiom,
! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
( 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)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INT__E) ).
fof(fact_SUP2__I,axiom,
! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
=> 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_ca_2)) ) ),
file('theBenchmark.p',fact_SUP2__I) ).
fof(fact_finite__INT,axiom,
! [V_A_2,T_c,V_I_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) )
=> 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))) ),
file('theBenchmark.p',fact_finite__INT) ).
fof(fact_CollectI,axiom,
! [T_b,V_a_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_a_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
file('theBenchmark.p',fact_CollectI) ).
fof(fact_finite__Collect__conjI,axiom,
! [V_Qa_2,V_Pa_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) )
=> 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)))) ),
file('theBenchmark.p',fact_finite__Collect__conjI) ).
fof(fact_UN__I,axiom,
! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
=> 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))) ) ),
file('theBenchmark.p',fact_UN__I) ).
fof(fact_SUP1__I,axiom,
! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
=> 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)) ) ),
file('theBenchmark.p',fact_SUP1__I) ).
fof(fact_finite__Collect__less__nat,axiom,
! [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)))),
file('theBenchmark.p',fact_finite__Collect__less__nat) ).
fof(fact_finite__Collect__le__nat,axiom,
! [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)))),
file('theBenchmark.p',fact_finite__Collect__le__nat) ).
fof(fact_setsum__abs,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> 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))) ),
file('theBenchmark.p',fact_setsum__abs) ).
fof(fact_setsum__abs__ge__zero,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> 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))) ),
file('theBenchmark.p',fact_setsum__abs__ge__zero) ).
fof(fact_finite__Collect__subsets,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)))) ),
file('theBenchmark.p',fact_finite__Collect__subsets) ).
fof(fact_insert__def,axiom,
! [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),
file('theBenchmark.p',fact_insert__def) ).
fof(fact_UN__extend__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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 ) ),
file('theBenchmark.p',fact_UN__extend__simps_I2_J) ).
fof(fact_UN__extend__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(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),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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(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),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 ) ),
file('theBenchmark.p',fact_UN__extend__simps_I3_J) ).
fof(fact_UN__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_UN__simps_I2_J) ).
fof(fact_UN__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_UN__simps_I3_J) ).
fof(fact_UN__insert,axiom,
! [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)),
file('theBenchmark.p',fact_UN__insert) ).
fof(fact_Collect__imp__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Collect__imp__eq) ).
fof(fact_sup__Un__eq,axiom,
! [V_x_2,V_S_2,V_R_2,T_b] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_sup__Un__eq) ).
fof(fact_sup__Un__eq2,axiom,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_sup__Un__eq2) ).
fof(fact_UN__Un__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_UN__Un__distrib) ).
fof(fact_UN__Un,axiom,
! [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)),
file('theBenchmark.p',fact_UN__Un) ).
fof(fact_INT__simps_I7_J,axiom,
! [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)),
file('theBenchmark.p',fact_INT__simps_I7_J) ).
fof(fact_INT__simps_I6_J,axiom,
! [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),
file('theBenchmark.p',fact_INT__simps_I6_J) ).
fof(fact_INT__extend__simps_I7_J,axiom,
! [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)),
file('theBenchmark.p',fact_INT__extend__simps_I7_J) ).
fof(fact_Un__INT__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_Un__INT__distrib) ).
fof(fact_INT__extend__simps_I6_J,axiom,
! [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)),
file('theBenchmark.p',fact_INT__extend__simps_I6_J) ).
fof(fact_Un__INT__distrib2,axiom,
! [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))),
file('theBenchmark.p',fact_Un__INT__distrib2) ).
fof(fact_Collect__disj__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Collect__disj__eq) ).
fof(fact_sup__fun__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( class_Lattices_Olattice(T_b)
=> 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)) ),
file('theBenchmark.p',fact_sup__fun__def) ).
fof(fact_Un__Inter,axiom,
! [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)),
file('theBenchmark.p',fact_Un__Inter) ).
fof(fact_UN__absorb,axiom,
! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
=> 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) ),
file('theBenchmark.p',fact_UN__absorb) ).
fof(fact_Un__def,axiom,
! [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))),
file('theBenchmark.p',fact_Un__def) ).
fof(fact_INT__Un,axiom,
! [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)),
file('theBenchmark.p',fact_INT__Un) ).
fof(fact_Union__image__eq,axiom,
! [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),
file('theBenchmark.p',fact_Union__image__eq) ).
fof(fact_UNION__eq__Union__image,axiom,
! [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)),
file('theBenchmark.p',fact_UNION__eq__Union__image) ).
fof(fact_INT__simps_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_INT__simps_I1_J) ).
fof(fact_INT__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_INT__simps_I2_J) ).
fof(fact_inf__Int__eq,axiom,
! [V_x_2,V_S_2,V_R_2,T_b] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_INT__absorb,axiom,
! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
=> 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) ),
file('theBenchmark.p',fact_INT__absorb) ).
fof(fact_inf__Int__eq2,axiom,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_INT__insert,axiom,
! [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)),
file('theBenchmark.p',fact_INT__insert) ).
fof(fact_INT__extend__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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 ) ),
file('theBenchmark.p',fact_INT__extend__simps_I2_J) ).
fof(fact_INT__extend__simps_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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 ) ),
file('theBenchmark.p',fact_INT__extend__simps_I1_J) ).
fof(fact_Int__Union,axiom,
! [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)),
file('theBenchmark.p',fact_Int__Union) ).
fof(fact_Int__Union2,axiom,
! [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)),
file('theBenchmark.p',fact_Int__Union2) ).
fof(fact_UN__simps_I5_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__simps_I5_J) ).
fof(fact_UN__simps_I4_J,axiom,
! [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),
file('theBenchmark.p',fact_UN__simps_I4_J) ).
fof(fact_UN__extend__simps_I5_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__extend__simps_I5_J) ).
fof(fact_Int__UN__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_Int__UN__distrib) ).
fof(fact_UN__extend__simps_I4_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__extend__simps_I4_J) ).
fof(fact_Int__UN__distrib2,axiom,
! [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))),
file('theBenchmark.p',fact_Int__UN__distrib2) ).
fof(fact_INT__Int__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_INT__Int__distrib) ).
fof(fact_Collect__conj__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Collect__conj__eq) ).
fof(fact_inf__fun__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( class_Lattices_Olattice(T_b)
=> 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)) ),
file('theBenchmark.p',fact_inf__fun__def) ).
fof(fact_Int__Collect,axiom,
! [V_Pa_2,V_A_2,V_x_2,T_b] :
( 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))))
<=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__Collect) ).
fof(fact_Int__def,axiom,
! [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))),
file('theBenchmark.p',fact_Int__def) ).
fof(fact_setsum__shift__bounds__nat__ivl,axiom,
! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(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,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)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
fof(fact_card__eq__setsum,axiom,
! [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),
file('theBenchmark.p',fact_card__eq__setsum) ).
fof(fact_UN__UN__finite__eq,axiom,
! [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),
file('theBenchmark.p',fact_UN__UN__finite__eq) ).
fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
! [V_n_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(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,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)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).
fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
! [V_A_2,V_f_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> 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)) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).
fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(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,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)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).
fof(fact_nat_Osize_I1_J,axiom,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat_Osize_I1_J) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [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)),
file('theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_nat__number__of__Bit0,axiom,
! [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))),
file('theBenchmark.p',fact_nat__number__of__Bit0) ).
fof(fact_nat__seg__image__imp__finite,axiom,
! [V_n_2,V_f_2,T_b,V_A_2] :
( 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)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_nat__seg__image__imp__finite) ).
fof(fact_finite__M__bounded__by__nat,axiom,
! [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))))),
file('theBenchmark.p',fact_finite__M__bounded__by__nat) ).
fof(fact_INF__less__iff,axiom,
! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( 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))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_INF__less__iff) ).
fof(fact_less__SUP__iff,axiom,
! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( 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)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_less__SUP__iff) ).
fof(fact_setsum__addf,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_setsum__addf) ).
fof(fact_le__INF__iff,axiom,
! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( 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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ),
file('theBenchmark.p',fact_le__INF__iff) ).
fof(fact_SUP__le__iff,axiom,
! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( 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))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ),
file('theBenchmark.p',fact_SUP__le__iff) ).
fof(fact_INT__subset__iff,axiom,
! [V_A_2,V_I_2,T_c,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_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
=> 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))) ) ),
file('theBenchmark.p',fact_INT__subset__iff) ).
fof(fact_UN__subset__iff,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
( 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))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
=> 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)) ) ),
file('theBenchmark.p',fact_UN__subset__iff) ).
fof(fact_pred__subset__eq2,axiom,
! [V_S_2,V_R_2,T_c,T_b] :
( 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)))
<=> 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)) ),
file('theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_INT__lower,axiom,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_INT__lower) ).
fof(fact_pred__subset__eq,axiom,
! [V_S_2,V_R_2,T_b] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ),
file('theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_UN__upper,axiom,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_UN__upper) ).
fof(fact_setsum_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_setsum_Odistrib) ).
fof(fact_INF__leI,axiom,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_INF__leI) ).
fof(fact_le__SUPI,axiom,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_le__SUPI) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
! [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))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).
fof(fact_Pow__def,axiom,
! [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)),
file('theBenchmark.p',fact_Pow__def) ).
fof(fact_INT__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_INT__simps_I3_J) ).
fof(fact_INT__extend__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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) ) ),
file('theBenchmark.p',fact_INT__extend__simps_I3_J) ).
fof(fact_INT__extend__simps_I4_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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 ) ),
file('theBenchmark.p',fact_INT__extend__simps_I4_J) ).
fof(fact_UN__simps_I7_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__simps_I7_J) ).
fof(fact_UN__simps_I6_J,axiom,
! [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),
file('theBenchmark.p',fact_UN__simps_I6_J) ).
fof(fact_UN__extend__simps_I7_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__extend__simps_I7_J) ).
fof(fact_UN__extend__simps_I6_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__extend__simps_I6_J) ).
fof(fact_fun__diff__def,axiom,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( class_Groups_Ominus(T_b)
=> 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)) ),
file('theBenchmark.p',fact_fun__diff__def) ).
fof(fact_setsum__subtractf,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_setsum__subtractf) ).
fof(fact_set__diff__eq,axiom,
! [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)))),
file('theBenchmark.p',fact_set__diff__eq) ).
fof(fact_insert__compr,axiom,
! [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))),
file('theBenchmark.p',fact_insert__compr) ).
fof(fact_insert__compr__raw,axiom,
! [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))),
file('theBenchmark.p',fact_insert__compr__raw) ).
fof(fact_Collect__conv__if,axiom,
! [T_b,V_a_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_a_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,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)) )
& ( hBOOL(hAPP(V_Pa_2,V_a_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,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))) ) ),
file('theBenchmark.p',fact_Collect__conv__if) ).
fof(fact_Collect__conv__if2,axiom,
! [T_b,V_a_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_a_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(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hBOOL(hAPP(V_Pa_2,V_a_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(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))) ) ),
file('theBenchmark.p',fact_Collect__conv__if2) ).
fof(fact_singleton__conv,axiom,
! [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))),
file('theBenchmark.p',fact_singleton__conv) ).
fof(fact_singleton__conv2,axiom,
! [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))),
file('theBenchmark.p',fact_singleton__conv2) ).
fof(fact_UN__insert__distrib,axiom,
! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_u_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),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)) ),
file('theBenchmark.p',fact_UN__insert__distrib) ).
fof(fact_image__constant__conv,axiom,
! [V_ca_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_image__constant__conv) ).
fof(fact_abs__setprod,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Fields_Olinordered__field(T_b)
=> 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) ),
file('theBenchmark.p',fact_abs__setprod) ).
fof(fact_abs__setsum__abs,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> 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) ),
file('theBenchmark.p',fact_abs__setsum__abs) ).
fof(fact_INTER__eq__Inter__image,axiom,
! [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)),
file('theBenchmark.p',fact_INTER__eq__Inter__image) ).
fof(fact_Inter__image__eq,axiom,
! [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),
file('theBenchmark.p',fact_Inter__image__eq) ).
fof(fact_image__Union,axiom,
! [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)),
file('theBenchmark.p',fact_image__Union) ).
fof(fact_UN__simps_I10_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__simps_I10_J) ).
fof(fact_image__UN,axiom,
! [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)),
file('theBenchmark.p',fact_image__UN) ).
fof(fact_UN__extend__simps_I10_J,axiom,
! [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),
file('theBenchmark.p',fact_UN__extend__simps_I10_J) ).
fof(fact_image__image,axiom,
! [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),
file('theBenchmark.p',fact_image__image) ).
fof(fact_image__ident,axiom,
! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_image__ident) ).
fof(fact_INT__simps_I10_J,axiom,
! [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)),
file('theBenchmark.p',fact_INT__simps_I10_J) ).
fof(fact_INT__extend__simps_I10_J,axiom,
! [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),
file('theBenchmark.p',fact_INT__extend__simps_I10_J) ).
fof(fact_int__setsum,axiom,
! [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),
file('theBenchmark.p',fact_int__setsum) ).
fof(fact_INT__insert__distrib,axiom,
! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
=> 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)) ),
file('theBenchmark.p',fact_INT__insert__distrib) ).
fof(fact_bot__empty__eq2,axiom,
! [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))
<=> 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)))) ),
file('theBenchmark.p',fact_bot__empty__eq2) ).
fof(fact_bot__empty__eq,axiom,
! [V_x_2,T_b] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bot__empty__eq) ).
fof(fact_UN__iff,axiom,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( 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)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_UN__iff) ).
fof(fact_INT__iff,axiom,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( 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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ),
file('theBenchmark.p',fact_INT__iff) ).
fof(fact_pred__equals__eq,axiom,
! [V_S_2,V_R_2,T_b] :
( 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_R_2 = V_S_2 ),
file('theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [V_S_2,V_R_2,T_c,T_b] :
( 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_R_2 = V_S_2 ),
file('theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_CollectE,axiom,
! [V_Pa_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
=> hBOOL(hAPP(V_Pa_2,V_a_2)) ),
file('theBenchmark.p',fact_CollectE) ).
fof(fact_CollectD,axiom,
! [V_Pa_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
=> hBOOL(hAPP(V_Pa_2,V_a_2)) ),
file('theBenchmark.p',fact_CollectD) ).
fof(fact_mem__Collect__eq,axiom,
! [V_Pa_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
<=> hBOOL(hAPP(V_Pa_2,V_a_2)) ),
file('theBenchmark.p',fact_mem__Collect__eq) ).
fof(fact_Collect__mem__eq,axiom,
! [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,
file('theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_finite__Collect__disjI,axiom,
! [V_Qa_2,V_Pa_2,T_b] :
( 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))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
file('theBenchmark.p',fact_finite__Collect__disjI) ).
fof(fact_INT__simps_I5_J,axiom,
! [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)),
file('theBenchmark.p',fact_INT__simps_I5_J) ).
fof(fact_INT__extend__simps_I5_J,axiom,
! [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)),
file('theBenchmark.p',fact_INT__extend__simps_I5_J) ).
fof(fact_insert__Collect,axiom,
! [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)),
file('theBenchmark.p',fact_insert__Collect) ).
fof(fact_bot__fun__def,axiom,
! [V_x_2,T_c,T_b] :
( class_Orderings_Obot(T_b)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
file('theBenchmark.p',fact_bot__fun__def) ).
fof(fact_empty__def,axiom,
! [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)),
file('theBenchmark.p',fact_empty__def) ).
fof(fact_INF__const,axiom,
! [V_M_2,T_b,V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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 ) ),
file('theBenchmark.p',fact_INF__const) ).
fof(fact_UNION__empty__conv_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( 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)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
fof(fact_UN__empty2,axiom,
! [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)),
file('theBenchmark.p',fact_UN__empty2) ).
fof(fact_UN__constant,axiom,
! [V_ca_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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_ca_2)) = V_ca_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__constant) ).
fof(fact_UNION__empty__conv_I2_J,axiom,
! [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_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
fof(fact_SUP__const,axiom,
! [V_M_2,T_b,V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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 ) ),
file('theBenchmark.p',fact_SUP__const) ).
fof(fact_setsum__negf,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(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_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)) ),
file('theBenchmark.p',fact_setsum__negf) ).
fof(fact_setprod__timesf,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> 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)) ),
file('theBenchmark.p',fact_setprod__timesf) ).
fof(fact_setsum__product,axiom,
! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum__product) ).
fof(fact_setsum__left__distrib,axiom,
! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum__left__distrib) ).
fof(fact_setsum__right__distrib,axiom,
! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
( class_Rings_Osemiring__0(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum__right__distrib) ).
fof(fact_Collect__neg__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_fun__Compl__def,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Groups_Ouminus(T_b)
=> 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)) ),
file('theBenchmark.p',fact_fun__Compl__def) ).
fof(fact_Compl__UN,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__UN) ).
fof(fact_Compl__INT,axiom,
! [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)),
file('theBenchmark.p',fact_Compl__INT) ).
fof(fact_SUPR__apply,axiom,
! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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)) ),
file('theBenchmark.p',fact_SUPR__apply) ).
fof(fact_setsum__divide__distrib,axiom,
! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
( class_Fields_Ofield(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum__divide__distrib) ).
fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> 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)) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).
fof(fact_Pow__INT__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Pow__INT__eq) ).
fof(fact_Inter__def,axiom,
! [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))),
file('theBenchmark.p',fact_Inter__def) ).
fof(fact_INF__commute,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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))) ),
file('theBenchmark.p',fact_INF__commute) ).
fof(fact_INFI__apply,axiom,
! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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)) ),
file('theBenchmark.p',fact_INFI__apply) ).
fof(fact_INT__simps_I8_J,axiom,
! [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)),
file('theBenchmark.p',fact_INT__simps_I8_J) ).
fof(fact_INT__extend__simps_I8_J,axiom,
! [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),
file('theBenchmark.p',fact_INT__extend__simps_I8_J) ).
fof(fact_pair__box_Oinject,axiom,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( 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)
<=> ( V_b_2 = V_b_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_pair__box_Oinject) ).
fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> 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)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).
fof(fact_Union__def,axiom,
! [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))),
file('theBenchmark.p',fact_Union__def) ).
fof(fact_SUP1__iff,axiom,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_SUP1__iff) ).
fof(fact_UN__UN__flatten,axiom,
! [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)),
file('theBenchmark.p',fact_UN__UN__flatten) ).
fof(fact_UN__simps_I9_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__simps_I9_J) ).
fof(fact_INT__simps_I9_J,axiom,
! [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)),
file('theBenchmark.p',fact_INT__simps_I9_J) ).
fof(fact_UN__extend__simps_I9_J,axiom,
! [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),
file('theBenchmark.p',fact_UN__extend__simps_I9_J) ).
fof(fact_INT__extend__simps_I9_J,axiom,
! [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),
file('theBenchmark.p',fact_INT__extend__simps_I9_J) ).
fof(fact_SUP__commute,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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))) ),
file('theBenchmark.p',fact_SUP__commute) ).
fof(fact_fun__upd__def,axiom,
! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
( ( V_x_2 != V_a_2
=> 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) )
& ( V_x_2 = V_a_2
=> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 ) ),
file('theBenchmark.p',fact_fun__upd__def) ).
fof(fact_setsum__commute,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum__commute) ).
fof(fact_fold__image__def,axiom,
! [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)),
file('theBenchmark.p',fact_fold__image__def) ).
fof(fact_UN__extend__simps_I8_J,axiom,
! [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),
file('theBenchmark.p',fact_UN__extend__simps_I8_J) ).
fof(fact_UN__simps_I8_J,axiom,
! [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)),
file('theBenchmark.p',fact_UN__simps_I8_J) ).
fof(fact_int__setprod,axiom,
! [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),
file('theBenchmark.p',fact_int__setprod) ).
fof(fact_of__int__setsum,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Rings_Oring__1(T_b)
=> 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) ),
file('theBenchmark.p',fact_of__int__setsum) ).
fof(fact_of__int__setprod,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( ( class_Rings_Oring__1(T_b)
& class_Groups_Ocomm__monoid__mult(T_b) )
=> 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) ),
file('theBenchmark.p',fact_of__int__setprod) ).
fof(fact_setprod__dividef,axiom,
! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
( class_Fields_Ofield__inverse__zero(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_setprod__dividef) ).
fof(fact_Compl__eq,axiom,
! [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))),
file('theBenchmark.p',fact_Compl__eq) ).
fof(fact_setprod_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_setprod_Odistrib) ).
fof(fact_UN__extend__simps_I1_J,axiom,
! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))) ) ),
file('theBenchmark.p',fact_UN__extend__simps_I1_J) ).
fof(fact_UN__singleton,axiom,
! [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,
file('theBenchmark.p',fact_UN__singleton) ).
fof(fact_UN__simps_I1_J,axiom,
! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_UN__simps_I1_J) ).
fof(fact_UN__atMost__UNIV,axiom,
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)),
file('theBenchmark.p',fact_UN__atMost__UNIV) ).
fof(fact_INT__constant,axiom,
! [V_ca_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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_ca_2)) = V_ca_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__constant) ).
fof(fact_INT__empty,axiom,
! [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)),
file('theBenchmark.p',fact_INT__empty) ).
fof(fact_INTER__UNIV__conv_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( 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)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
fof(fact_INTER__UNIV__conv_I2_J,axiom,
! [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_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
fof(fact_UNIV__def,axiom,
! [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)),
file('theBenchmark.p',fact_UNIV__def) ).
fof(fact_setprod__1,axiom,
! [V_A_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> 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) ),
file('theBenchmark.p',fact_setprod__1) ).
fof(fact_setsum__0,axiom,
! [V_A_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum__0) ).
fof(fact_UN__lessThan__UNIV,axiom,
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)),
file('theBenchmark.p',fact_UN__lessThan__UNIV) ).
fof(fact_INF__INT__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_INF__INT__eq) ).
fof(fact_INF__INT__eq2,axiom,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_INF__INT__eq2) ).
fof(fact_SUP__UN__eq2,axiom,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_SUP__UN__eq2) ).
fof(fact_range__composition,axiom,
! [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)))),
file('theBenchmark.p',fact_range__composition) ).
fof(fact_UN__atLeast__UNIV,axiom,
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)),
file('theBenchmark.p',fact_UN__atLeast__UNIV) ).
fof(fact_finite__range__imageI,axiom,
! [V_f_2,T_d,V_g_2,T_c,T_b] :
( 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)))))
=> 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))))) ),
file('theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_SUP__UN__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( 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))
<=> 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))) ),
file('theBenchmark.p',fact_SUP__UN__eq) ).
fof(fact_finite__Collect__not,axiom,
! [V_Pa_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
=> ( 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))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Collect__not) ).
fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).
fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
! [V_n_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(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,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)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
fof(fact_of__nat__setsum,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__1(T_b)
=> 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) ),
file('theBenchmark.p',fact_of__nat__setsum) ).
fof(fact_Int__Inter__image,axiom,
! [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))),
file('theBenchmark.p',fact_Int__Inter__image) ).
fof(fact_UN__le__add__shift,axiom,
! [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),
file('theBenchmark.p',fact_UN__le__add__shift) ).
fof(fact_UN__Pow__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_UN__Pow__subset) ).
fof(fact_of__nat__setprod,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( ( class_Rings_Osemiring__1(T_b)
& class_Groups_Ocomm__monoid__mult(T_b) )
=> 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) ),
file('theBenchmark.p',fact_of__nat__setprod) ).
fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).
fof(fact_image__add__atLeastLessThan,axiom,
! [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)),
file('theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_image__add__atLeastAtMost,axiom,
! [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)),
file('theBenchmark.p',fact_image__add__atLeastAtMost) ).
fof(fact_setsum__delta_H,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_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(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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_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(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) ) ) ) ),
file('theBenchmark.p',fact_setsum__delta_H) ).
fof(fact_setsum__delta,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_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,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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_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,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) ) ) ) ),
file('theBenchmark.p',fact_setsum__delta) ).
fof(fact_image__constant,axiom,
! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_image__constant) ).
fof(fact_setsum__setsum__restrict,axiom,
! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_setsum__setsum__restrict) ).
fof(fact_INT__greaterThan__UNIV,axiom,
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)),
file('theBenchmark.p',fact_INT__greaterThan__UNIV) ).
fof(fact_setprod__delta_H,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> 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) ) ) ) ),
file('theBenchmark.p',fact_setprod__delta_H) ).
fof(fact_setprod__delta,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> 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) ) ) ) ),
file('theBenchmark.p',fact_setprod__delta) ).
fof(fact_image__eq__UN,axiom,
! [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)))),
file('theBenchmark.p',fact_image__eq__UN) ).
fof(fact_if__image__distrib,axiom,
! [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))))),
file('theBenchmark.p',fact_if__image__distrib) ).
fof(fact_INT__simps_I4_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_INT__simps_I4_J) ).
fof(fact_setsum__constant,axiom,
! [V_A_2,V_y_2,T_c,T_b] :
( class_Rings_Osemiring__1(T_b)
=> 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) ),
file('theBenchmark.p',fact_setsum__constant) ).
fof(fact_power__number__of__even,axiom,
! [V_w_2,V_z_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> 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))) ),
file('theBenchmark.p',fact_power__number__of__even) ).
fof(fact_fold__image__distrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_fold__image__distrib) ).
fof(fact_dual__max,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_dual__max) ).
fof(fact_dual__min,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_dual__min) ).
fof(fact_setprod__constant,axiom,
! [V_y_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_setprod__constant) ).
fof(fact_sup__SUPR__fold__sup,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_sup__SUPR__fold__sup) ).
fof(fact_inf__INFI__fold__inf,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_inf__INFI__fold__inf) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
! [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)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
! [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)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).
fof(fact_zpower__number__of__even,axiom,
! [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))),
file('theBenchmark.p',fact_zpower__number__of__even) ).
fof(fact_setsum__lessThan__Suc,axiom,
! [V_n_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(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),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)) ),
file('theBenchmark.p',fact_setsum__lessThan__Suc) ).
fof(fact_setsum__atMost__Suc,axiom,
! [V_n_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(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),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))) ),
file('theBenchmark.p',fact_setsum__atMost__Suc) ).
fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
! [V_A_2,V_f_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> 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)) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).
fof(fact_Un__Union__image,axiom,
! [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))),
file('theBenchmark.p',fact_Un__Union__image) ).
fof(fact_image__add__int__atLeastLessThan,axiom,
! [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),
file('theBenchmark.p',fact_image__add__int__atLeastLessThan) ).
fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> 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)) ) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).
fof(fact_Powp__Pow__eq,axiom,
! [V_x_2,V_A_2,T_b] :
( 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))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ),
file('theBenchmark.p',fact_Powp__Pow__eq) ).
fof(fact_setsum__restrict__set_H,axiom,
! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_setsum__restrict__set_H) ).
fof(fact_setsum__restrict__set,axiom,
! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_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)) = 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) ) ),
file('theBenchmark.p',fact_setsum__restrict__set) ).
fof(fact_setsum__image__gen,axiom,
! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> 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)) ) ),
file('theBenchmark.p',fact_setsum__image__gen) ).
fof(fact_image__eq__fold__image,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ),
file('theBenchmark.p',fact_image__eq__fold__image) ).
fof(fact_power__number__of__even__number__of,axiom,
! [V_w_2,V_v_2,T_b] :
( class_Int_Onumber__ring(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),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))) ),
file('theBenchmark.p',fact_power__number__of__even__number__of) ).
fof(fact_SUPR__fold__sup,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_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)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_SUPR__fold__sup) ).
fof(fact_card_Oeq__fold__g,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ),
file('theBenchmark.p',fact_card_Oeq__fold__g) ).
fof(fact_card__def,axiom,
! [V_A_2,T_b] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_card__def) ).
fof(fact_fun__left__comm__idem__remove,axiom,
! [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))))),
file('theBenchmark.p',fact_fun__left__comm__idem__remove) ).
fof(fact_INFI__fold__inf,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_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)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_INFI__fold__inf) ).
fof(fact_diff__nat__eq__if,axiom,
! [V_z_2,V_z_H_2] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
=> 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)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
=> 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) ) ),
file('theBenchmark.p',fact_diff__nat__eq__if) ).
fof(fact_negDivAlg__div__mod,axiom,
! [V_l,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
=> 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)) ) ),
file('theBenchmark.p',fact_negDivAlg__div__mod) ).
fof(fact_negDivAlg__minus1,axiom,
! [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))),
file('theBenchmark.p',fact_negDivAlg__minus1) ).
fof(fact_card__less__Suc2,axiom,
! [V_i_2,V_M_2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_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),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))))) ),
file('theBenchmark.p',fact_card__less__Suc2) ).
fof(fact_card__less,axiom,
! [V_i_2,V_M_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_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))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_card__less) ).
fof(fact_card__less__Suc,axiom,
! [V_i_2,V_M_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
=> 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))))) ),
file('theBenchmark.p',fact_card__less__Suc) ).
fof(fact_UN__le__eq__Un0,axiom,
! [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))),
file('theBenchmark.p',fact_UN__le__eq__Un0) ).
fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> 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)) ) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).
fof(fact_adjust__eq,axiom,
! [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))),
file('theBenchmark.p',fact_adjust__eq) ).
fof(fact_setsum__head,axiom,
! [V_Pa_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_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))) ) ),
file('theBenchmark.p',fact_setsum__head) ).
fof(fact_setsum__cases,axiom,
! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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))))) ) ),
file('theBenchmark.p',fact_setsum__cases) ).
fof(fact_minus__fold__remove,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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_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) ),
file('theBenchmark.p',fact_minus__fold__remove) ).
fof(fact_Suc__eq__number__of,axiom,
! [V_v_2,V_n_2] :
( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
<=> 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))))) ),
file('theBenchmark.p',fact_Suc__eq__number__of) ).
fof(fact_eq__number__of__Suc,axiom,
! [V_n_2,V_v_2] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
<=> 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))))) ),
file('theBenchmark.p',fact_eq__number__of__Suc) ).
fof(fact_nat__number__of__Bit1,axiom,
! [V_w_2] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> 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)))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__number__of__Bit1) ).
fof(fact_geometric__sum,axiom,
! [V_n_2,V_x_2,T_b] :
( class_Fields_Ofield(T_b)
=> ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
=> 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))) ) ),
file('theBenchmark.p',fact_geometric__sum) ).
fof(fact_gauss__sum,axiom,
! [V_n_2,T_b] :
( class_Rings_Ocomm__semiring__1(T_b)
=> 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))) ),
file('theBenchmark.p',fact_gauss__sum) ).
fof(fact_setsum__natinterval__difff,axiom,
! [V_f_2,V_n_2,V_m_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> 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)))) ) ) ),
file('theBenchmark.p',fact_setsum__natinterval__difff) ).
fof(fact_less__Suc__number__of,axiom,
! [V_v_2,V_n_2] :
( 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)))
<=> 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))))) ),
file('theBenchmark.p',fact_less__Suc__number__of) ).
fof(fact_less__number__of__Suc,axiom,
! [V_n_2,V_v_2] :
( 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)))
<=> 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)))) ),
file('theBenchmark.p',fact_less__number__of__Suc) ).
fof(fact_le__Suc__number__of,axiom,
! [V_v_2,V_n_2] :
( 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)))
<=> 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))))) ),
file('theBenchmark.p',fact_le__Suc__number__of) ).
fof(fact_le__number__of__Suc,axiom,
! [V_n_2,V_v_2] :
( 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)))
<=> 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)))) ),
file('theBenchmark.p',fact_le__number__of__Suc) ).
fof(fact_max__Suc__number__of,axiom,
! [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)))),
file('theBenchmark.p',fact_max__Suc__number__of) ).
fof(fact_max__number__of__Suc,axiom,
! [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)))),
file('theBenchmark.p',fact_max__number__of__Suc) ).
fof(fact_power__number__of__odd,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_power__number__of__odd) ).
fof(fact_setprod__gen__delta,axiom,
! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> 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_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> 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_ca_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_ca_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)))) ) ) ) ),
file('theBenchmark.p',fact_setprod__gen__delta) ).
fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
! [V_x_2,V_y_2,V_ca_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_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_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_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_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_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))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_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_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_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_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).
fof(fact_zpower__number__of__odd,axiom,
! [V_z_2,V_w_2] :
( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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))) ) ),
file('theBenchmark.p',fact_zpower__number__of__odd) ).
fof(fact_arith__series__general,axiom,
! [V_n_2,V_d_2,V_a_2,T_b] :
( class_Rings_Ocomm__semiring__1(T_b)
=> 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)))) ),
file('theBenchmark.p',fact_arith__series__general) ).
fof(fact_negDivAlg_Osimps,axiom,
! [V_b,V_a] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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))) )
=> 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))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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))) )
=> 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)) ) ),
file('theBenchmark.p',fact_negDivAlg_Osimps) ).
fof(fact_min__number__of__Suc,axiom,
! [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)))),
file('theBenchmark.p',fact_min__number__of__Suc) ).
fof(fact_min__Suc__number__of,axiom,
! [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)))),
file('theBenchmark.p',fact_min__Suc__number__of) ).
fof(fact_arith__series__nat,axiom,
! [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)))),
file('theBenchmark.p',fact_arith__series__nat) ).
fof(fact_power__number__of__odd__number__of,axiom,
! [V_v_2,V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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))) ) ) ),
file('theBenchmark.p',fact_power__number__of__odd__number__of) ).
fof(fact_negDivAlg__eqn__number__of,axiom,
! [V_w,V_v] :
( 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)))
=> ( ( ~ 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))))
=> 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)))) )
& ( 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))))
=> 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))) ) ) ),
file('theBenchmark.p',fact_negDivAlg__eqn__number__of) ).
fof(fact_negDivAlg__eqn,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( ( ~ 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)))
=> 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))) )
& ( 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)))
=> 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)) ) ) ),
file('theBenchmark.p',fact_negDivAlg__eqn) ).
fof(fact_diff__nat__number__of,axiom,
! [V_v_2,V_v_H_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
=> 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) ) ),
file('theBenchmark.p',fact_diff__nat__number__of) ).
fof(fact_norm__frac_Osimps,axiom,
! [V_a_2,V_b_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> 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))) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> 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)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)) ) ),
file('theBenchmark.p',fact_norm__frac_Osimps) ).
fof(fact_nat__case__add__eq__if,axiom,
! [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)))),
file('theBenchmark.p',fact_nat__case__add__eq__if) ).
fof(fact_posDivAlg__eqn__1__number__of,axiom,
! [V_w] :
( 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)))
=> ( ( ~ 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)))
=> 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)))) )
& ( 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)))
=> 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)) ) ) ),
file('theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).
fof(fact_posDivAlg_Osimps,axiom,
! [V_b,V_a] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
=> 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))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
=> 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) ) ),
file('theBenchmark.p',fact_posDivAlg_Osimps) ).
fof(fact_sup2CI,axiom,
! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
=> 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)) ),
file('theBenchmark.p',fact_sup2CI) ).
fof(fact_sup2E,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
=> ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_sup2E) ).
fof(fact_inf2I,axiom,
! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
=> 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)) ) ),
file('theBenchmark.p',fact_inf2I) ).
fof(fact_inf2E,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
=> ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
=> ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_inf2E) ).
fof(fact_bot2E,axiom,
! [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)),
file('theBenchmark.p',fact_bot2E) ).
fof(fact_INF1__iff,axiom,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ),
file('theBenchmark.p',fact_INF1__iff) ).
fof(fact_INF2__iff,axiom,
! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( 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_ca_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_INF2__iff) ).
fof(fact_SUP2__iff,axiom,
! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( 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_ca_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_SUP2__iff) ).
fof(fact_rev__predicate2D,axiom,
! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
=> ( 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))
=> hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_predicate2D,axiom,
! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
( 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))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_predicate2D) ).
fof(fact_less__by__empty,axiom,
! [V_B_2,T_b,V_A_2] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> 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)) ),
file('theBenchmark.p',fact_less__by__empty) ).
fof(fact_inf2D1,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
=> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
=> hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_inf2D2) ).
fof(fact_sup2I2,axiom,
! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
=> 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)) ),
file('theBenchmark.p',fact_sup2I2) ).
fof(fact_sup2I1,axiom,
! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
=> 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)) ),
file('theBenchmark.p',fact_sup2I1) ).
fof(fact_nat__case__0,axiom,
! [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,
file('theBenchmark.p',fact_nat__case__0) ).
fof(fact_nat__case__Suc,axiom,
! [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),
file('theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_posDivAlg__0,axiom,
! [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)),
file('theBenchmark.p',fact_posDivAlg__0) ).
fof(fact_max__Suc1,axiom,
! [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),
file('theBenchmark.p',fact_max__Suc1) ).
fof(fact_max__Suc2,axiom,
! [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),
file('theBenchmark.p',fact_max__Suc2) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
<=> 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)) ),
file('theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_diff__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_diff__Suc) ).
fof(fact_min__Suc2,axiom,
! [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),
file('theBenchmark.p',fact_min__Suc2) ).
fof(fact_min__Suc1,axiom,
! [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),
file('theBenchmark.p',fact_min__Suc1) ).
fof(fact_posDivAlg__div__mod,axiom,
! [V_l,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
=> 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)) ) ),
file('theBenchmark.p',fact_posDivAlg__div__mod) ).
fof(fact_nat__case__number__of,axiom,
! [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))),
file('theBenchmark.p',fact_nat__case__number__of) ).
fof(fact_posDivAlg__eqn,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> 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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> 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) ) ) ),
file('theBenchmark.p',fact_posDivAlg__eqn) ).
fof(fact_posDivAlg__eqn__number__of,axiom,
! [V_w,V_v] :
( 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)))
=> ( ( ~ 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)))
=> 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)))) )
& ( 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)))
=> 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)) ) ) ),
file('theBenchmark.p',fact_posDivAlg__eqn__number__of) ).
fof(fact_in__rel__def,axiom,
! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
<=> 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)) ),
file('theBenchmark.p',fact_in__rel__def) ).
fof(fact_div__mod__code__numeral__def,axiom,
! [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)),
file('theBenchmark.p',fact_div__mod__code__numeral__def) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [V_r_2,T_b] :
( c_Nitpick_Orefl_H(T_b,V_r_2)
<=> ! [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)) ),
file('theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_adjust__def,axiom,
! [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))))))),
file('theBenchmark.p',fact_adjust__def) ).
fof(fact_divmod__nat__step,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),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(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)) ) ),
file('theBenchmark.p',fact_divmod__nat__step) ).
fof(fact_nat__rec__add__eq__if,axiom,
! [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))))),
file('theBenchmark.p',fact_nat__rec__add__eq__if) ).
fof(fact_nat__rec__0,axiom,
! [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,
file('theBenchmark.p',fact_nat__rec__0) ).
fof(fact_nat__rec__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_nat__rec__Suc) ).
fof(fact_divmod__nat__zero,axiom,
! [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),
file('theBenchmark.p',fact_divmod__nat__zero) ).
fof(fact_divmod__nat__base,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> 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) ),
file('theBenchmark.p',fact_divmod__nat__base) ).
fof(fact_divmod__nat__div__mod,axiom,
! [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)),
file('theBenchmark.p',fact_divmod__nat__div__mod) ).
fof(fact_nat__rec__number__of,axiom,
! [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)))),
file('theBenchmark.p',fact_nat__rec__number__of) ).
fof(fact_pair__imageI,axiom,
! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( 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))
=> 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))) ),
file('theBenchmark.p',fact_pair__imageI) ).
fof(fact_of__int__num,axiom,
! [V_k_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_of__int__num) ).
fof(fact_semiring__1__class_Oof__nat__code,axiom,
! [V_n_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> 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)) ),
file('theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).
fof(fact_splitI,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
=> 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))) ),
file('theBenchmark.p',fact_splitI) ).
fof(fact_prod__caseI,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
=> 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))) ),
file('theBenchmark.p',fact_prod__caseI) ).
fof(fact_mem__splitI,axiom,
! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
=> 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_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ),
file('theBenchmark.p',fact_mem__splitI) ).
fof(fact_splitD,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( 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)))
=> hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
file('theBenchmark.p',fact_splitD) ).
fof(fact_splitD_H,axiom,
! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
( 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_ca_2))
=> hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ),
file('theBenchmark.p',fact_splitD_H) ).
fof(fact_of__nat__aux_Osimps_I1_J,axiom,
! [V_i_2,V_inc_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> 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 ),
file('theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
fof(fact_of__nat__aux_Osimps_I2_J,axiom,
! [V_i_2,V_n_2,V_inc_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> 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)) ),
file('theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
fof(fact_split__paired__All,axiom,
! [T_c,T_b,V_Pa_2] :
( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ),
file('theBenchmark.p',fact_split__paired__All) ).
fof(fact_Pair__eq,axiom,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( 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)
<=> ( V_b_2 = V_b_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_Pair__eq) ).
fof(fact_Pair__inject,axiom,
! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
( 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)
=> ~ ( V_a = V_a_H
=> V_b != V_b_H ) ),
file('theBenchmark.p',fact_Pair__inject) ).
fof(fact_split__weak__cong,axiom,
! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
( V_p_2 = V_q_2
=> hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ),
file('theBenchmark.p',fact_split__weak__cong) ).
fof(fact_divmod__int__mod__div,axiom,
! [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)),
file('theBenchmark.p',fact_divmod__int__mod__div) ).
fof(fact_prod_Osimps_I2_J,axiom,
! [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),
file('theBenchmark.p',fact_prod_Osimps_I2_J) ).
fof(fact_split__conv,axiom,
! [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),
file('theBenchmark.p',fact_split__conv) ).
fof(fact_divmod__nat__if,axiom,
! [V_m_2,V_n_2] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> 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)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> 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) ) ),
file('theBenchmark.p',fact_divmod__nat__if) ).
fof(fact_split__eta,axiom,
! [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,
file('theBenchmark.p',fact_split__eta) ).
fof(fact_split__twice,axiom,
! [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),
file('theBenchmark.p',fact_split__twice) ).
fof(fact_Nitpick_OFrac__def,axiom,
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)))),
file('theBenchmark.p',fact_Nitpick_OFrac__def) ).
fof(fact_divmod__int__def,axiom,
! [V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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))) )
& ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) ) ) ),
file('theBenchmark.p',fact_divmod__int__def) ).
fof(fact_divmod__int__pdivmod,axiom,
! [V_l_2,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)))) )
& ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) ) ),
file('theBenchmark.p',fact_divmod__int__pdivmod) ).
fof(fact_apsnd__conv,axiom,
! [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)),
file('theBenchmark.p',fact_apsnd__conv) ).
fof(fact_negateSnd__def,axiom,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
file('theBenchmark.p',fact_negateSnd__def) ).
fof(fact_negateSnd__eq,axiom,
! [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)),
file('theBenchmark.p',fact_negateSnd__eq) ).
fof(fact_pdivmod__def,axiom,
! [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))),
file('theBenchmark.p',fact_pdivmod__def) ).
fof(fact_pdivmod__posDivAlg,axiom,
! [V_k,V_l] :
( ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) )
& ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) ) ),
file('theBenchmark.p',fact_pdivmod__posDivAlg) ).
fof(fact_divmod__int__code,axiom,
! [V_l_2,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)))) )
& ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)) ) ),
file('theBenchmark.p',fact_divmod__int__code) ).
fof(fact_Nitpick_Oprod__def,axiom,
! [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)))),
file('theBenchmark.p',fact_Nitpick_Oprod__def) ).
fof(fact_int__ge__less__than2__def,axiom,
! [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)))),
file('theBenchmark.p',fact_int__ge__less__than2__def) ).
fof(fact_int__ge__less__than__def,axiom,
! [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)))),
file('theBenchmark.p',fact_int__ge__less__than__def) ).
fof(fact_divmod__nat__rel__mult1__eq,axiom,
! [V_a,V_r,V_q,V_c,V_b] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
=> 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)))) ) ),
file('theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).
fof(fact_divmod__nat__rel__mult2__eq,axiom,
! [V_c,V_r,V_q,V_b,V_a] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
=> 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)))) ) ) ),
file('theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).
fof(fact_pair__box_Osize_I2_J,axiom,
! [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),
file('theBenchmark.p',fact_pair__box_Osize_I2_J) ).
fof(fact_divmod__nat__rel__unique,axiom,
! [V_qr_H,V_qr,V_n,V_m] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
=> ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
=> V_qr = V_qr_H ) ),
file('theBenchmark.p',fact_divmod__nat__rel__unique) ).
fof(fact_divmod__nat__rel__divmod__nat,axiom,
! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))),
file('theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
fof(fact_divmod__nat__eq,axiom,
! [V_qr,V_n,V_m] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
=> c_Divides_Odivmod__nat(V_m,V_n) = V_qr ),
file('theBenchmark.p',fact_divmod__nat__eq) ).
fof(fact_mod__eq,axiom,
! [V_r,V_q,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),V_q),V_r)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ),
file('theBenchmark.p',fact_mod__eq) ).
fof(fact_div__eq,axiom,
! [V_r,V_q,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),V_q),V_r)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ),
file('theBenchmark.p',fact_div__eq) ).
fof(fact_divmod__nat__rel,axiom,
! [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)))),
file('theBenchmark.p',fact_divmod__nat__rel) ).
fof(fact_divmod__nat__rel__add1__eq,axiom,
! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
( 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)))
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
=> 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)))) ) ) ),
file('theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
fof(fact_pair__box_Orecs,axiom,
! [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),
file('theBenchmark.p',fact_pair__box_Orecs) ).
fof(fact_pair__box_Osimps_I2_J,axiom,
! [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),
file('theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
fof(fact_negDivAlg_Opsimps,axiom,
! [V_b_2,V_a_2] :
( 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)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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))) )
=> 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))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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))) )
=> 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)) ) ) ),
file('theBenchmark.p',fact_negDivAlg_Opsimps) ).
fof(fact_accp__downward,axiom,
! [V_a_2,V_b_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
file('theBenchmark.p',fact_accp__downward) ).
fof(fact_accp_Oequations,axiom,
! [V_a_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
file('theBenchmark.p',fact_accp_Oequations) ).
fof(fact_accp_Osimps,axiom,
! [V_a_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
file('theBenchmark.p',fact_accp_Osimps) ).
fof(fact_accp__subset,axiom,
! [V_R2_2,V_R1_2,T_b] :
( 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))
=> 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))) ),
file('theBenchmark.p',fact_accp__subset) ).
fof(fact_posDivAlg_Opsimps,axiom,
! [V_b_2,V_a_2] :
( 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)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
=> 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))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
=> 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) ) ) ),
file('theBenchmark.p',fact_posDivAlg_Opsimps) ).
fof(fact_norm__frac_Opsimps,axiom,
! [V_b_2,V_a_2] :
( 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)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> 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))) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> 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)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)) ) ) ),
file('theBenchmark.p',fact_norm__frac_Opsimps) ).
fof(fact_negDivAlg_Opinduct,axiom,
! [V_Pa_2,V_a1_2,V_a0_2] :
( 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)))
=> ( ! [B_a,B_b] :
( 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)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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))) )
=> 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))) )
=> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_negDivAlg_Opinduct) ).
fof(fact_posDivAlg_Opinduct,axiom,
! [V_Pa_2,V_a1_2,V_a0_2] :
( 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)))
=> ( ! [B_a,B_b] :
( 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)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
=> 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))) )
=> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_posDivAlg_Opinduct) ).
fof(fact_nat__gcd_Opsimps,axiom,
! [V_y_2,V_x_2] :
( 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)))
=> ( ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)) )
& ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) ) ),
file('theBenchmark.p',fact_nat__gcd_Opsimps) ).
fof(fact_zmult2__lemma,axiom,
! [V_c,V_r,V_q,V_b,V_a] :
( 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)))
=> ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> 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)))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma) ).
fof(fact_divmod__int__rel__0,axiom,
! [V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)))) ),
file('theBenchmark.p',fact_divmod__int__rel__0) ).
fof(fact_self__remainder,axiom,
! [V_r,V_q,V_a] :
( 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)))
=> ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_self__remainder) ).
fof(fact_unique__quotient,axiom,
! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
( 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)))
=> ( 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)))
=> ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> V_q = V_q_H ) ) ),
file('theBenchmark.p',fact_unique__quotient) ).
fof(fact_unique__remainder,axiom,
! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
( 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)))
=> ( 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)))
=> ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> V_r = V_r_H ) ) ),
file('theBenchmark.p',fact_unique__remainder) ).
fof(fact_divmod__int__rel__neg,axiom,
! [V_qr,V_b,V_a] :
( 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))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ),
file('theBenchmark.p',fact_divmod__int__rel__neg) ).
fof(fact_divmod__int__correct,axiom,
! [V_a,V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ),
file('theBenchmark.p',fact_divmod__int__correct) ).
fof(fact_self__quotient,axiom,
! [V_r,V_q,V_a] :
( 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)))
=> ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_self__quotient) ).
fof(fact_divmod__int__rel__mod,axiom,
! [V_r,V_q,V_b,V_a] :
( 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)))
=> ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ),
file('theBenchmark.p',fact_divmod__int__rel__mod) ).
fof(fact_divmod__int__rel__div,axiom,
! [V_r,V_q,V_b,V_a] :
( 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)))
=> ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ),
file('theBenchmark.p',fact_divmod__int__rel__div) ).
fof(fact_negDivAlg__correct,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ),
file('theBenchmark.p',fact_negDivAlg__correct) ).
fof(fact_divmod__int__rel__div__mod,axiom,
! [V_a,V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)))) ),
file('theBenchmark.p',fact_divmod__int__rel__div__mod) ).
fof(fact_posDivAlg__correct,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ),
file('theBenchmark.p',fact_posDivAlg__correct) ).
fof(fact_zadd1__lemma,axiom,
! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
( 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)))
=> ( 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)))
=> ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)))) ) ) ),
file('theBenchmark.p',fact_zadd1__lemma) ).
fof(fact_zminus1__lemma,axiom,
! [V_r_2,V_q_2,V_b_2,V_a_2] :
( 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)))
=> 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))))) ),
file('theBenchmark.p',fact_zminus1__lemma) ).
fof(fact_divmod__int__relI,axiom,
! [V_r,V_q,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),V_q)),V_r)
=> ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) ) ) )
=> 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))) ) ),
file('theBenchmark.p',fact_divmod__int__relI) ).
fof(fact_zmult1__lemma,axiom,
! [V_a,V_r,V_q,V_c,V_b] :
( 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)))
=> ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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)))) ) ),
file('theBenchmark.p',fact_zmult1__lemma) ).
fof(fact_divmod__int__rel__def,axiom,
! [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))))))),
file('theBenchmark.p',fact_divmod__int__rel__def) ).
fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
=> 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)) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).
fof(fact_mod__pos__neg__1__number__of,axiom,
! [V_w] :
( 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)))
=> 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))))) ),
file('theBenchmark.p',fact_mod__pos__neg__1__number__of) ).
fof(fact_in__measure,axiom,
! [V_f_2,V_y_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_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
<=> 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))) ),
file('theBenchmark.p',fact_in__measure) ).
fof(fact_snd__apsnd,axiom,
! [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)),
file('theBenchmark.p',fact_snd__apsnd) ).
fof(fact_apsnd__eq__conv,axiom,
! [V_g_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),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
<=> 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)) ),
file('theBenchmark.p',fact_apsnd__eq__conv) ).
fof(fact_snd__conv,axiom,
! [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,
file('theBenchmark.p',fact_snd__conv) ).
fof(fact_snd__eqD,axiom,
! [V_a,V_y,V_x,T_a,T_b] :
( 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
=> V_y = V_a ),
file('theBenchmark.p',fact_snd__eqD) ).
fof(fact_snd__def,axiom,
! [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),
file('theBenchmark.p',fact_snd__def) ).
fof(fact_mod__int__def,axiom,
! [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)),
file('theBenchmark.p',fact_mod__int__def) ).
fof(fact_mod__neg__pos,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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)) ) ),
file('theBenchmark.p',fact_mod__neg__pos) ).
fof(fact_mod__pos__pos,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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)) ) ),
file('theBenchmark.p',fact_mod__pos__pos) ).
fof(fact_mod__pos__pos__1__number__of,axiom,
! [V_w] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_mod__pos__pos__1__number__of) ).
fof(fact_mod__pos__neg,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)))) ) ),
file('theBenchmark.p',fact_mod__pos__neg) ).
fof(fact_mod__neg__neg,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)))) ) ),
file('theBenchmark.p',fact_mod__neg__neg) ).
fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
=> 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)) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).
fof(fact_norm__frac_Opinduct,axiom,
! [V_Pa_2,V_a1_2,V_a0_2] :
( 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)))
=> ( ! [B_a,B_b] :
( 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)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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))) )
=> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_norm__frac_Opinduct) ).
fof(fact_div__pos__neg__1__number__of,axiom,
! [V_w] :
( 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)))
=> 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))))) ),
file('theBenchmark.p',fact_div__pos__neg__1__number__of) ).
fof(fact_Pair__fst__snd__eq,axiom,
! [T_c,T_b,V_t_2,V_s_2] :
( V_s_2 = V_t_2
<=> ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
& hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) ) ),
file('theBenchmark.p',fact_Pair__fst__snd__eq) ).
fof(fact_prod__eqI,axiom,
! [V_q,V_p,T_b,T_a] :
( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
=> ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
=> V_p = V_q ) ),
file('theBenchmark.p',fact_prod__eqI) ).
fof(fact_fst__def,axiom,
! [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),
file('theBenchmark.p',fact_fst__def) ).
fof(fact_fst__eqD,axiom,
! [V_a,V_y,V_x,T_b,T_a] :
( 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
=> V_x = V_a ),
file('theBenchmark.p',fact_fst__eqD) ).
fof(fact_fst__conv,axiom,
! [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,
file('theBenchmark.p',fact_fst__conv) ).
fof(fact_fst__apsnd,axiom,
! [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),
file('theBenchmark.p',fact_fst__apsnd) ).
fof(fact_pair__collapse,axiom,
! [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,
file('theBenchmark.p',fact_pair__collapse) ).
fof(fact_surjective__pairing,axiom,
! [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)),
file('theBenchmark.p',fact_surjective__pairing) ).
fof(fact_prod__case__beta,axiom,
! [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)),
file('theBenchmark.p',fact_prod__case__beta) ).
fof(fact_div__int__def,axiom,
! [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)),
file('theBenchmark.p',fact_div__int__def) ).
fof(fact_mod__nat__def,axiom,
! [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)),
file('theBenchmark.p',fact_mod__nat__def) ).
fof(fact_split__comp__eq,axiom,
! [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)),
file('theBenchmark.p',fact_split__comp__eq) ).
fof(fact_split__beta,axiom,
! [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)),
file('theBenchmark.p',fact_split__beta) ).
fof(fact_split__def,axiom,
! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_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)),
file('theBenchmark.p',fact_split__def) ).
fof(fact_div__neg__pos,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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)) ) ),
file('theBenchmark.p',fact_div__neg__pos) ).
fof(fact_div__pos__pos,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> 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)) ) ),
file('theBenchmark.p',fact_div__pos__pos) ).
fof(fact_div__pos__pos__1__number__of,axiom,
! [V_w] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_div__pos__pos__1__number__of) ).
fof(fact_div__pos__neg,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)))) ) ),
file('theBenchmark.p',fact_div__pos__neg) ).
fof(fact_div__neg__neg,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> 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)))) ) ),
file('theBenchmark.p',fact_div__neg__neg) ).
fof(fact_prod__size__simp,axiom,
! [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))),
file('theBenchmark.p',fact_prod__size__simp) ).
fof(fact_exI__realizer,axiom,
! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
=> 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)))) ),
file('theBenchmark.p',fact_exI__realizer) ).
fof(fact_conjI__realizer,axiom,
! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_p_2))
=> ( hBOOL(hAPP(V_Qa_2,V_q_2))
=> ( 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))))
& 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)))) ) ) ),
file('theBenchmark.p',fact_conjI__realizer) ).
fof(fact_div__nat__def,axiom,
! [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)),
file('theBenchmark.p',fact_div__nat__def) ).
fof(fact_divmod__nat__rel__def,axiom,
! [V_qr_2,V_n_2,V_m_2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
<=> ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
=> ( 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)))
& 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))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
=> ( 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))
& 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))) ) ) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(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(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)) ) ),
file('theBenchmark.p',fact_divmod__nat__rel__def) ).
fof(fact_nat__def,axiom,
! [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)))))),
file('theBenchmark.p',fact_nat__def) ).
fof(fact_UN__finite2__subset,axiom,
! [V_B_2,V_k_2,V_A_2,T_b] :
( ! [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)))
=> 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))) ),
file('theBenchmark.p',fact_UN__finite2__subset) ).
fof(fact_nat__gcd_Opinduct,axiom,
! [V_Pa_2,V_a1_2,V_a0_2] :
( 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)))
=> ( ! [B_x,B_y] :
( 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)))
=> ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
=> hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_nat__gcd_Opinduct) ).
fof(fact_Rep__Integ__inject,axiom,
! [V_y_2,V_x_2] :
( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_Rep__Integ__inject) ).
fof(fact_range,axiom,
! [V_s,V_k] :
( 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))
=> 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)) ),
file('theBenchmark.p',fact_range) ).
fof(fact_setsum__multicount,axiom,
! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
=> 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 )
=> 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)) ) ) ),
file('theBenchmark.p',fact_setsum__multicount) ).
fof(fact_mlex__leq,axiom,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( 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)))
=> ( 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))
=> 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))) ) ),
file('theBenchmark.p',fact_mlex__leq) ).
fof(fact_mlex__less,axiom,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_mlex__less) ).
fof(fact_finite__psubset__def,axiom,
! [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)))),
file('theBenchmark.p',fact_finite__psubset__def) ).
fof(fact_min__max_Osup__Inf2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))))))) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).
fof(fact_min__max_Osup__Inf1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).
fof(fact_finite__Collect__bounded__ex,axiom,
! [V_Qa_2,T_c,V_Pa_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
=> ( 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)))))
<=> ! [B_y] :
( hBOOL(hAPP(V_Pa_2,B_y))
=> 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)))) ) ) ),
file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).
fof(fact_finite__image__set,axiom,
! [V_f_2,T_c,V_Pa_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
=> 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))))) ),
file('theBenchmark.p',fact_finite__image__set) ).
fof(fact_Pow__Compl,axiom,
! [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))))),
file('theBenchmark.p',fact_Pow__Compl) ).
fof(fact_add__Max__commute,axiom,
! [V_k_2,V_N_2,T_b] :
( class_Groups_Olinordered__ab__semigroup__add(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))))) ) ) ),
file('theBenchmark.p',fact_add__Max__commute) ).
fof(fact_add__Min__commute,axiom,
! [V_k_2,V_N_2,T_b] :
( class_Groups_Olinordered__ab__semigroup__add(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))))) ) ) ),
file('theBenchmark.p',fact_add__Min__commute) ).
fof(fact_sup__Inf1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))))) ) ) ),
file('theBenchmark.p',fact_sup__Inf1__distrib) ).
fof(fact_sup__Inf2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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),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))))))) ) ) ) ) ),
file('theBenchmark.p',fact_sup__Inf2__distrib) ).
fof(fact_inf__Sup1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))))) ) ) ),
file('theBenchmark.p',fact_inf__Sup1__distrib) ).
fof(fact_inf__Sup2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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),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))))))) ) ) ) ) ),
file('theBenchmark.p',fact_inf__Sup2__distrib) ).
fof(fact_in__finite__psubset,axiom,
! [V_B_2,V_A_2,T_b] :
( 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)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_min__max_Oinf__Sup2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))))))) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).
fof(fact_min__max_Oinf__Sup1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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))))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).
fof(fact_nat_Osize_I4_J,axiom,
! [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))),
file('theBenchmark.p',fact_nat_Osize_I4_J) ).
fof(fact_prod_Orecs,axiom,
! [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),
file('theBenchmark.p',fact_prod_Orecs) ).
fof(fact_UN__finite2__eq,axiom,
! [V_B_2,V_k_2,V_A_2,T_b] :
( ! [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)
=> 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) ),
file('theBenchmark.p',fact_UN__finite2__eq) ).
fof(fact_nat__size,axiom,
! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
file('theBenchmark.p',fact_nat__size) ).
fof(fact_nat_Osize_I3_J,axiom,
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),
file('theBenchmark.p',fact_nat_Osize_I3_J) ).
fof(fact_UN__finite__subset,axiom,
! [V_C_2,V_A_2,T_b] :
( ! [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))
=> 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)) ),
file('theBenchmark.p',fact_UN__finite__subset) ).
fof(fact_setsum__multicount__gen,axiom,
! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
=> 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) )
=> 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) ) ) ),
file('theBenchmark.p',fact_setsum__multicount__gen) ).
fof(fact_in__lex__prod,axiom,
! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( 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)))
<=> ( ( 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))
& V_a_2 = V_a_H_2 )
| 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)) ) ),
file('theBenchmark.p',fact_in__lex__prod) ).
fof(fact_same__fstI,axiom,
! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
=> ( 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)))
=> 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))) ) ),
file('theBenchmark.p',fact_same__fstI) ).
fof(fact_setsum__nonneg__0,axiom,
! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
=> ( 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)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
=> hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ),
file('theBenchmark.p',fact_setsum__nonneg__0) ).
fof(fact_setsum__nonneg__leq__bound,axiom,
! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_setsum__nonneg__leq__bound) ).
fof(fact_sum__diff__distrib,axiom,
! [V_n_2,V_Pa_2,V_Qa_2] :
( ! [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)))
=> 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)) ),
file('theBenchmark.p',fact_sum__diff__distrib) ).
fof(fact_apfst__apsnd,axiom,
! [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))),
file('theBenchmark.p',fact_apfst__apsnd) ).
fof(fact_apsnd__apfst,axiom,
! [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))),
file('theBenchmark.p',fact_apsnd__apfst) ).
fof(fact_fst__apfst,axiom,
! [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)),
file('theBenchmark.p',fact_fst__apfst) ).
fof(fact_apfst__eq__conv,axiom,
! [V_g_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),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
<=> 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)) ),
file('theBenchmark.p',fact_apfst__eq__conv) ).
fof(fact_apfst__conv,axiom,
! [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),
file('theBenchmark.p',fact_apfst__conv) ).
fof(fact_snd__apfst,axiom,
! [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),
file('theBenchmark.p',fact_snd__apfst) ).
fof(fact_apsnd__apfst__commute,axiom,
! [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)),
file('theBenchmark.p',fact_apsnd__apfst__commute) ).
fof(fact_pair__lessI2,axiom,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
=> 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)) ) ),
file('theBenchmark.p',fact_pair__lessI2) ).
fof(fact_max__ext__additive,axiom,
! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
( 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)))
=> ( 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)))
=> 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))) ) ),
file('theBenchmark.p',fact_max__ext__additive) ).
fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( V_A_2 = V_B_2
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
=> 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) ) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).
fof(fact_pair__lessI1,axiom,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
=> 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)) ),
file('theBenchmark.p',fact_pair__lessI1) ).
fof(fact_max__extp__max__ext__eq,axiom,
! [V_xa_2,V_x_2,V_R_2,T_b] :
( 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)
<=> 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))) ),
file('theBenchmark.p',fact_max__extp__max__ext__eq) ).
fof(fact_pair__leqI2,axiom,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
=> 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)) ) ),
file('theBenchmark.p',fact_pair__leqI2) ).
fof(fact_smax__insertI,axiom,
! [V_X_2,V_x_2,V_Y_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
=> ( 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))
=> ( 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))
=> 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)) ) ) ),
file('theBenchmark.p',fact_smax__insertI) ).
fof(fact_smax__emptyI,axiom,
! [V_Y_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
=> ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_smax__emptyI) ).
fof(fact_max__strict__def,axiom,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('theBenchmark.p',fact_max__strict__def) ).
fof(fact_pair__leqI1,axiom,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
=> 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)) ),
file('theBenchmark.p',fact_pair__leqI1) ).
fof(fact_wmin__insertI,axiom,
! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
=> ( 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))
=> ( 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))
=> 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)) ) ) ),
file('theBenchmark.p',fact_wmin__insertI) ).
fof(fact_wmax__insertI,axiom,
! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
=> ( 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))
=> ( 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))
=> 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)) ) ) ),
file('theBenchmark.p',fact_wmax__insertI) ).
fof(fact_smin__insertI,axiom,
! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
=> ( 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))
=> ( 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))
=> 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)) ) ) ),
file('theBenchmark.p',fact_smin__insertI) ).
fof(fact_wmax__emptyI,axiom,
! [V_X_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),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)),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)) ),
file('theBenchmark.p',fact_wmax__emptyI) ).
fof(fact_smin__emptyI,axiom,
! [V_X_2] :
( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
=> 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)) ),
file('theBenchmark.p',fact_smin__emptyI) ).
fof(fact_wmin__emptyI,axiom,
! [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)),
file('theBenchmark.p',fact_wmin__emptyI) ).
fof(fact_max__weak__def,axiom,
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)))),
file('theBenchmark.p',fact_max__weak__def) ).
fof(fact_min__weak__def,axiom,
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)))),
file('theBenchmark.p',fact_min__weak__def) ).
fof(fact_min__rpair__set,axiom,
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)),
file('theBenchmark.p',fact_min__rpair__set) ).
fof(fact_max__rpair__set,axiom,
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)),
file('theBenchmark.p',fact_max__rpair__set) ).
fof(fact_min__strict__def,axiom,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('theBenchmark.p',fact_min__strict__def) ).
fof(fact_less__than__iff,axiom,
! [V_y_2,V_x_2] :
( 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))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_less__than__iff) ).
fof(fact_intrel__iff,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( 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))
<=> 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) ),
file('theBenchmark.p',fact_intrel__iff) ).
fof(fact_rp__inv__image__rp,axiom,
! [V_f_2,T_c,V_Pa_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
=> c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ),
file('theBenchmark.p',fact_rp__inv__image__rp) ).
fof(fact_pair__less__def,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_pair__less__def) ).
fof(fact_mlex__prod__def,axiom,
! [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))),
file('theBenchmark.p',fact_mlex__prod__def) ).
fof(fact_rp__inv__image__def,axiom,
! [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))),
file('theBenchmark.p',fact_rp__inv__image__def) ).
fof(fact_equiv__intrel__iff,axiom,
! [V_y_2,V_x_2] :
( 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))))
<=> 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)) ),
file('theBenchmark.p',fact_equiv__intrel__iff) ).
fof(fact_measure__def,axiom,
! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_measure__def) ).
fof(fact_Image__singleton,axiom,
! [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)),
file('theBenchmark.p',fact_Image__singleton) ).
fof(fact_Image__singleton__iff,axiom,
! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
( 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))))))
<=> 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)) ),
file('theBenchmark.p',fact_Image__singleton__iff) ).
fof(fact_inv__image__def,axiom,
! [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))),
file('theBenchmark.p',fact_inv__image__def) ).
fof(fact_Image__empty,axiom,
! [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)),
file('theBenchmark.p',fact_Image__empty) ).
fof(fact_Image__Un,axiom,
! [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)),
file('theBenchmark.p',fact_Image__Un) ).
fof(fact_Image__UN,axiom,
! [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)),
file('theBenchmark.p',fact_Image__UN) ).
fof(fact_Image__Int__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Image__Int__subset) ).
fof(fact_Image__mono,axiom,
! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
( 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))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Image__mono) ).
fof(fact_Un__Image,axiom,
! [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)),
file('theBenchmark.p',fact_Un__Image) ).
fof(fact_in__inv__image,axiom,
! [V_f_2,V_r_2,T_c,V_y_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_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
<=> 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)) ),
file('theBenchmark.p',fact_in__inv__image) ).
fof(fact_Image__INT__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Image__INT__subset) ).
fof(fact_rev__ImageI,axiom,
! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( 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))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ),
file('theBenchmark.p',fact_rev__ImageI) ).
fof(fact_Image__iff,axiom,
! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
<=> ? [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))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_Image__iff) ).
fof(fact_Image__eq__UN,axiom,
! [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))))),
file('theBenchmark.p',fact_Image__eq__UN) ).
fof(fact_of__int,axiom,
! [V_j_2,V_i_2,T_b] :
( class_Rings_Oring__1(T_b)
=> 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)) ),
file('theBenchmark.p',fact_of__int) ).
fof(fact_One__int__def,axiom,
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))))),
file('theBenchmark.p',fact_One__int__def) ).
fof(fact_mult,axiom,
! [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))))),
file('theBenchmark.p',fact_mult) ).
fof(fact_Rep__Integ__inverse,axiom,
! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_Rep__Integ__inverse) ).
fof(fact_minus,axiom,
! [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))))),
file('theBenchmark.p',fact_minus) ).
fof(fact_Zero__int__def,axiom,
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))))),
file('theBenchmark.p',fact_Zero__int__def) ).
fof(fact_int__def,axiom,
! [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))))),
file('theBenchmark.p',fact_int__def) ).
fof(fact_add,axiom,
! [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))))),
file('theBenchmark.p',fact_add) ).
fof(fact_nat,axiom,
! [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),
file('theBenchmark.p',fact_nat) ).
fof(fact_minus__int__def,axiom,
! [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))))))),
file('theBenchmark.p',fact_minus__int__def) ).
fof(fact_less,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( 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)))))))
<=> 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))) ),
file('theBenchmark.p',fact_less) ).
fof(fact_le,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( 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)))))))
<=> 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))) ),
file('theBenchmark.p',fact_le) ).
fof(fact_irrefl__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Oirrefl(T_b,V_r_2)
<=> ! [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)) ),
file('theBenchmark.p',fact_irrefl__def) ).
fof(fact_eq__Abs__Integ,axiom,
! [V_z_2] :
~ ! [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))))),
file('theBenchmark.p',fact_eq__Abs__Integ) ).
fof(fact_Field__insert,axiom,
! [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)),
file('theBenchmark.p',fact_Field__insert) ).
fof(fact_Field__Union,axiom,
! [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)),
file('theBenchmark.p',fact_Field__Union) ).
fof(fact_Field__empty,axiom,
! [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)),
file('theBenchmark.p',fact_Field__empty) ).
fof(fact_mono__Field,axiom,
! [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)),V_r_2),V_s_2))
=> 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))) ),
file('theBenchmark.p',fact_mono__Field) ).
fof(fact_Field__Un,axiom,
! [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)),
file('theBenchmark.p',fact_Field__Un) ).
fof(fact_finite__Field,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ),
file('theBenchmark.p',fact_finite__Field) ).
fof(fact_Id__on__def,axiom,
! [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)))),
file('theBenchmark.p',fact_Id__on__def) ).
fof(fact_quotient__def,axiom,
! [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)))),
file('theBenchmark.p',fact_quotient__def) ).
fof(fact_ImageE,axiom,
! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
=> ~ ! [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))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_ImageE) ).
fof(fact_quotient__is__empty,axiom,
! [V_r_2,V_A_2,T_b] :
( 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))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_quotient__is__empty) ).
fof(fact_quotient__is__empty2,axiom,
! [V_r_2,V_A_2,T_b] :
( 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)
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_quotient__is__empty2) ).
fof(fact_quotient__empty,axiom,
! [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)),
file('theBenchmark.p',fact_quotient__empty) ).
fof(fact_Id__on__def_H,axiom,
! [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)),
file('theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_Id__on__empty,axiom,
! [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)),
file('theBenchmark.p',fact_Id__on__empty) ).
fof(fact_Image__Id__on,axiom,
! [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),
file('theBenchmark.p',fact_Image__Id__on) ).
fof(fact_quotientI,axiom,
! [V_r_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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))) ),
file('theBenchmark.p',fact_quotientI) ).
fof(fact_Id__on__eqI,axiom,
! [V_A_2,T_b,V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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))) ) ),
file('theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Id__on__iff,axiom,
! [V_A_2,V_y_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_y_2)),c_Relation_OId__on(T_b,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
& V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Id__on__iff) ).
fof(fact_singleton__quotient,axiom,
! [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))),
file('theBenchmark.p',fact_singleton__quotient) ).
fof(fact_equiv__class__nondisjoint,axiom,
! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( 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)))))))
=> 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)) ) ),
file('theBenchmark.p',fact_equiv__class__nondisjoint) ).
fof(fact_subset__equiv__class,axiom,
! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( 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))))))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_subset__equiv__class) ).
fof(fact_quotientE,axiom,
! [V_r_2,V_A_2,V_X_2,T_b] :
( 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)))
=> ~ ! [B_x] :
( 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))))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_quotientE) ).
fof(fact_equiv__intrel,axiom,
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),
file('theBenchmark.p',fact_equiv__intrel) ).
fof(fact_Union__quotient,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> 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 ),
file('theBenchmark.p',fact_Union__quotient) ).
fof(fact_equiv__class__self,axiom,
! [V_a_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)))))) ) ),
file('theBenchmark.p',fact_equiv__class__self) ).
fof(fact_quotient__disj,axiom,
! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( 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)))
=> ( 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)))
=> ( 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))
| V_X_2 = V_Y_2 ) ) ) ),
file('theBenchmark.p',fact_quotient__disj) ).
fof(fact_equiv__class__eq,axiom,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( 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))
=> 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)))) ) ),
file('theBenchmark.p',fact_equiv__class__eq) ).
fof(fact_quotient__eq__iff,axiom,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( 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)))
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
=> ( V_X_2 = V_Y_2
<=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_quotient__eq__iff) ).
fof(fact_quotient__eqI,axiom,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( 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)))
=> ( 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)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
=> ( 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))
=> V_X_2 = V_Y_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_quotient__eqI) ).
fof(fact_equiv__class__eq__iff,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( 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))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
& 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)))) ) ) ),
file('theBenchmark.p',fact_equiv__class__eq__iff) ).
fof(fact_eq__equiv__class__iff,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> ( 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))))
<=> 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)) ) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class__iff) ).
fof(fact_eq__equiv__class,axiom,
! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
( 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))))
=> ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class) ).
fof(fact_equiv__class__subset,axiom,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( 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))
=> 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)))))) ) ),
file('theBenchmark.p',fact_equiv__class__subset) ).
fof(fact_eq__equiv__class__iff2,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> ( 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)
<=> 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)) ) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class__iff2) ).
fof(fact_UN__equiv__class,axiom,
! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class) ).
fof(fact_UN__equiv__class2,axiom,
! [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] :
( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
=> 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) ) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class2) ).
fof(fact_equivp__equiv,axiom,
! [V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
<=> 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)) ),
file('theBenchmark.p',fact_equivp__equiv) ).
fof(fact_equivp__transp,axiom,
! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_equivp__transp) ).
fof(fact_equivp__symp,axiom,
! [V_y_2,V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_equivp__symp) ).
fof(fact_equivp__reflp,axiom,
! [V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_equivp__reflp) ).
fof(fact_equivp__def,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
<=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ),
file('theBenchmark.p',fact_equivp__def) ).
fof(fact_identity__equivp,axiom,
! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
file('theBenchmark.p',fact_identity__equivp) ).
fof(fact_congruent2__implies__congruent,axiom,
! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
=> ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ),
file('theBenchmark.p',fact_congruent2__implies__congruent) ).
fof(fact_congruent2D,axiom,
! [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] :
( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
=> ( 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))
=> ( 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))
=> hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ),
file('theBenchmark.p',fact_congruent2D) ).
fof(fact_congruentD,axiom,
! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
=> ( 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))
=> hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ),
file('theBenchmark.p',fact_congruentD) ).
fof(fact_congruent2__implies__congruent__UN,axiom,
! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_congruent2__implies__congruent__UN) ).
fof(fact_UN__equiv__class__inject,axiom,
! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
=> ( 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)
=> ( 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)))
=> ( 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)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
=> 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)) ) ) )
=> V_X_2 = V_Y_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class__inject) ).
fof(fact_UN__equiv__class__type2,axiom,
! [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] :
( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( 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)))
=> ( 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)))
=> ( ! [B_x1] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
=> ! [B_x2] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
=> 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)) ) ) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class__type2) ).
fof(fact_UN__equiv__class__type,axiom,
! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
=> ( 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)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class__type) ).
fof(fact_Integ__def,axiom,
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),
file('theBenchmark.p',fact_Integ__def) ).
fof(fact_card__quotient__disjoint,axiom,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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)
=> 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) ) ),
file('theBenchmark.p',fact_card__quotient__disjoint) ).
fof(fact_Id__onE,axiom,
! [V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ),
file('theBenchmark.p',fact_Id__onE) ).
fof(fact_inj__on__empty,axiom,
! [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))),
file('theBenchmark.p',fact_inj__on__empty) ).
fof(fact_inj__uminus,axiom,
! [V_A_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ),
file('theBenchmark.p',fact_inj__uminus) ).
fof(fact_inj__on__Un__image__eq__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( 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))
=> ( 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)
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).
fof(fact_inj__on__id2,axiom,
! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2),
file('theBenchmark.p',fact_inj__on__id2) ).
fof(fact_subset__inj__on,axiom,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_subset__inj__on) ).
fof(fact_inj__on__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> 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)) ) ),
file('theBenchmark.p',fact_inj__on__Int) ).
fof(fact_inj__on__diff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> 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)) ),
file('theBenchmark.p',fact_inj__on__diff) ).
fof(fact_inj__on__def,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
=> B_x = B_xa ) ) ) ),
file('theBenchmark.p',fact_inj__on__def) ).
fof(fact_inj__onD,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_inj__onD) ).
fof(fact_inj__on__iff,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__on__contraD,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_x_2 != V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ),
file('theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_finite__imageD,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__imageD) ).
fof(fact_inj__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_injD) ).
fof(fact_inj__fun,axiom,
! [T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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))) ),
file('theBenchmark.p',fact_inj__fun) ).
fof(fact_inj__image__eq__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,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)
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_card__image,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> 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) ),
file('theBenchmark.p',fact_card__image) ).
fof(fact_inj__on__strict__subset,axiom,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> 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))) ) ),
file('theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_range__ex1__eq,axiom,
! [V_b_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( 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)))))
<=> ? [B_x] :
( ! [B_y] :
( V_b_2 = hAPP(V_f_2,B_y)
=> B_y = B_x )
& V_b_2 = hAPP(V_f_2,B_x) ) ) ),
file('theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_inj__image__mem__iff,axiom,
! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_inj__on__iff__surj,axiom,
! [V_A_H_2,T_c,T_b,V_A_2] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ? [B_f] :
( 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))
& c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
<=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ),
file('theBenchmark.p',fact_inj__on__iff__surj) ).
fof(fact_endo__inj__surj,axiom,
! [V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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))
=> ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
=> hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ),
file('theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_finite__surj__inj,axiom,
! [V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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)))
=> c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( 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))
=> c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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)) ) ),
file('theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_inj__image__subset__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_inj__on__image__Int,axiom,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_inj__on__image__Int) ).
fof(fact_image__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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)) ),
file('theBenchmark.p',fact_image__Int) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
<=> 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) ) ),
file('theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__image__set__diff,axiom,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_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),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)) ) ) ),
file('theBenchmark.p',fact_inj__on__image__set__diff) ).
fof(fact_image__set__diff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,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(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)) ),
file('theBenchmark.p',fact_image__set__diff) ).
fof(fact_pigeonhole,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)))
=> ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_pigeonhole) ).
fof(fact_inj__on__fun__updI,axiom,
! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__fun__updI) ).
fof(fact_inj__singleton,axiom,
! [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))),
file('theBenchmark.p',fact_inj__singleton) ).
fof(fact_Rep__Integ,axiom,
! [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)),
file('theBenchmark.p',fact_Rep__Integ) ).
fof(fact_card__bij__eq,axiom,
! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( 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))
=> ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
=> ( 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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_card__bij__eq) ).
fof(fact_inj__image__Compl__subset,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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)))) ),
file('theBenchmark.p',fact_inj__image__Compl__subset) ).
fof(fact_inj__on__insert,axiom,
! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
<=> ( ~ 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)))))))
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__insert) ).
fof(fact_inj__on__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( 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))
<=> ( 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))
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__Un) ).
fof(fact_card__inj__on__le,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( 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))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_inj__on__iff__card__le,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( ? [B_f] :
( 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))
& c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
<=> 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))) ) ) ),
file('theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_quotient__diff1,axiom,
! [V_a_2,V_A_2,V_r_2,T_b] :
( 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)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_quotient__diff1) ).
fof(fact_type__definition__Integ,axiom,
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),
file('theBenchmark.p',fact_type__definition__Integ) ).
fof(fact_image__INT,axiom,
! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> 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)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_image__INT) ).
fof(fact_the__inv__into__into,axiom,
! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_the__inv__into__into) ).
fof(fact_finite__conv__nat__seg__image,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
<=> ? [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))) ),
file('theBenchmark.p',fact_finite__conv__nat__seg__image) ).
fof(fact_inj__on__add__nat,axiom,
! [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),
file('theBenchmark.p',fact_inj__on__add__nat) ).
fof(fact_inj__Suc,axiom,
! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2),
file('theBenchmark.p',fact_inj__Suc) ).
fof(fact_inj__of__nat,axiom,
! [T_b] :
( class_Nat_Osemiring__char__0(T_b)
=> 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))) ),
file('theBenchmark.p',fact_inj__of__nat) ).
fof(fact_inj__int,axiom,
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))),
file('theBenchmark.p',fact_inj__int) ).
fof(fact_swap__inj__on,axiom,
! [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),
file('theBenchmark.p',fact_swap__inj__on) ).
fof(fact_the__inv__into__f__f,axiom,
! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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 ) ),
file('theBenchmark.p',fact_the__inv__into__f__f) ).
fof(fact_the__inv__into__f__eq,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
file('theBenchmark.p',fact_the__inv__into__f__eq) ).
fof(fact_the__inv__f__f,axiom,
! [V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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 ),
file('theBenchmark.p',fact_the__inv__f__f) ).
fof(fact_the__inv__into__onto,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> 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 ),
file('theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_inj__on__the__inv__into,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> 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)) ),
file('theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_inj__graph,axiom,
! [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))),
file('theBenchmark.p',fact_inj__graph) ).
fof(fact_f__the__inv__into__f,axiom,
! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> 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 ) ),
file('theBenchmark.p',fact_f__the__inv__into__f) ).
fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( V_A_2 = V_B_2
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
=> 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) ) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).
fof(fact_accp__acc__eq,axiom,
! [V_x_2,V_r_2,T_b] :
( 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))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_rel__comp__def,axiom,
! [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))))),
file('theBenchmark.p',fact_rel__comp__def) ).
fof(fact_rel__compI,axiom,
! [V_s_2,V_ca_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
( 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))
=> ( 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_ca_2)),V_s_2))
=> 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_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ),
file('theBenchmark.p',fact_rel__compI) ).
fof(fact_rel__comp__UNION__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_rel__comp__UNION__distrib) ).
fof(fact_rel__comp__UNION__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_rel__comp__UNION__distrib2) ).
fof(fact_rel__comp__empty1,axiom,
! [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)),
file('theBenchmark.p',fact_rel__comp__empty1) ).
fof(fact_rel__comp__empty2,axiom,
! [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)),
file('theBenchmark.p',fact_rel__comp__empty2) ).
fof(fact_rel__comp__distrib,axiom,
! [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)),
file('theBenchmark.p',fact_rel__comp__distrib) ).
fof(fact_rel__comp__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_rel__comp__distrib2) ).
fof(fact_O__assoc,axiom,
! [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)),
file('theBenchmark.p',fact_O__assoc) ).
fof(fact_rel__comp__mono,axiom,
! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
( 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))
=> ( 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))
=> 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))) ) ),
file('theBenchmark.p',fact_rel__comp__mono) ).
fof(fact_union__comp__emptyR,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( 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))
=> ( 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))
=> 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)) ) ),
file('theBenchmark.p',fact_union__comp__emptyR) ).
fof(fact_union__comp__emptyL,axiom,
! [V_B_2,V_C_2,V_A_2,T_b] :
( 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))
=> ( 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))
=> 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)) ) ),
file('theBenchmark.p',fact_union__comp__emptyL) ).
fof(fact_acc__subset,axiom,
! [V_R2_2,V_R1_2,T_b] :
( 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))
=> 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))) ),
file('theBenchmark.p',fact_acc__subset) ).
fof(fact_acc__downward,axiom,
! [V_a_2,V_r_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> ( 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))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downward) ).
fof(fact_acc_Osimps,axiom,
! [V_r_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
<=> ! [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),V_a_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc_Osimps) ).
fof(fact_max__ext__compat,axiom,
! [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_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> 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))) ),
file('theBenchmark.p',fact_max__ext__compat) ).
fof(fact_min__ext__compat,axiom,
! [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_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> 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))) ),
file('theBenchmark.p',fact_min__ext__compat) ).
fof(fact_pred__comp__rel__comp__eq,axiom,
! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(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))
<=> 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))) ),
file('theBenchmark.p',fact_pred__comp__rel__comp__eq) ).
fof(fact_reduction__pairI,axiom,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( 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))
=> 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)) ) ),
file('theBenchmark.p',fact_reduction__pairI) ).
fof(fact_max__extp_Oequations,axiom,
! [V_a2_2,V_a1_2,V_R_2,T_b] :
( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
file('theBenchmark.p',fact_max__extp_Oequations) ).
fof(fact_wf__less__than,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_wf__less__than) ).
fof(fact_pred__comp_Ointros,axiom,
! [T_d,T_c,T_b,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
=> hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_pred__comp_Ointros) ).
fof(fact_wf__empty,axiom,
! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_wf__empty) ).
fof(fact_wf__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_wf__inv__image) ).
fof(fact_wf__lex__prod,axiom,
! [V_rb_2,T_c,V_ra_2,T_b] :
( c_Wellfounded_Owf(T_b,V_ra_2)
=> ( c_Wellfounded_Owf(T_c,V_rb_2)
=> c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ),
file('theBenchmark.p',fact_wf__lex__prod) ).
fof(fact_wf__measure,axiom,
! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
file('theBenchmark.p',fact_wf__measure) ).
fof(fact_wf__comp__self,axiom,
! [V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
<=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ),
file('theBenchmark.p',fact_wf__comp__self) ).
fof(fact_min__ext__wf,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ),
file('theBenchmark.p',fact_min__ext__wf) ).
fof(fact_wf__finite__psubset,axiom,
! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
file('theBenchmark.p',fact_wf__finite__psubset) ).
fof(fact_pred__comp_Oequations,axiom,
! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
<=> ? [B_b] :
( hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
& hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) ) ),
file('theBenchmark.p',fact_pred__comp_Oequations) ).
fof(fact_wf__subset,axiom,
! [V_p_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( 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))
=> c_Wellfounded_Owf(T_b,V_p_2) ) ),
file('theBenchmark.p',fact_wf__subset) ).
fof(fact_wf__Int2,axiom,
! [V_r_H_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> 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)) ),
file('theBenchmark.p',fact_wf__Int2) ).
fof(fact_wf__Int1,axiom,
! [V_r_H_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> 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)) ),
file('theBenchmark.p',fact_wf__Int1) ).
fof(fact_wf__mlex,axiom,
! [V_f_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ),
file('theBenchmark.p',fact_wf__mlex) ).
fof(fact_wf__pair__less,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('theBenchmark.p',fact_wf__pair__less) ).
fof(fact_max__ext__wf,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ),
file('theBenchmark.p',fact_max__ext__wf) ).
fof(fact_wf__less,axiom,
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)))),
file('theBenchmark.p',fact_wf__less) ).
fof(fact_wf__irrefl,axiom,
! [V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ 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)) ),
file('theBenchmark.p',fact_wf__irrefl) ).
fof(fact_wf__asym,axiom,
! [V_x_2,V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( 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))
=> ~ 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)) ) ),
file('theBenchmark.p',fact_wf__asym) ).
fof(fact_wf__not__sym,axiom,
! [V_x_2,V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( 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))
=> ~ 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)) ) ),
file('theBenchmark.p',fact_wf__not__sym) ).
fof(fact_wf__not__refl,axiom,
! [V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ 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)) ),
file('theBenchmark.p',fact_wf__not__refl) ).
fof(fact_wf__int__ge__less__than,axiom,
! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)),
file('theBenchmark.p',fact_wf__int__ge__less__than) ).
fof(fact_wf__int__ge__less__than2,axiom,
! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)),
file('theBenchmark.p',fact_wf__int__ge__less__than2) ).
fof(fact_acc__wfD,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_acc__wfD) ).
fof(fact_wf__acc__iff,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_wf__acc__iff) ).
fof(fact_wf__no__loop,axiom,
! [V_R_2,T_b] :
( 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))
=> c_Wellfounded_Owf(T_b,V_R_2) ),
file('theBenchmark.p',fact_wf__no__loop) ).
fof(fact_wf__union__merge,axiom,
! [V_S_2,V_R_2,T_b] :
( 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))
<=> 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)) ),
file('theBenchmark.p',fact_wf__union__merge) ).
fof(fact_wf__iff__no__infinite__down__chain,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ~ ? [B_f] :
! [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)) ),
file('theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
fof(fact_wfE__pf,axiom,
! [V_A_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( 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)))
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_wfE__pf) ).
fof(fact_wf__union__compatible,axiom,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( c_Wellfounded_Owf(T_b,V_S_2)
=> ( 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))
=> 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)) ) ) ),
file('theBenchmark.p',fact_wf__union__compatible) ).
fof(fact_wf,axiom,
! [T_b] :
( class_Orderings_Owellorder(T_b)
=> 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)))) ),
file('theBenchmark.p',fact_wf) ).
fof(fact_reduction__pair__def,axiom,
! [V_Pa_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
<=> ( 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)))
& 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)) ) ),
file('theBenchmark.p',fact_reduction__pair__def) ).
fof(fact_reduction__pair__lemma,axiom,
! [V_S_2,V_R_2,V_Pa_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
=> ( 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)))
=> ( 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)))
=> ( c_Wellfounded_Owf(T_b,V_S_2)
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_reduction__pair__lemma) ).
fof(fact_wf__lenlex,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__lenlex) ).
fof(fact_wf__if__measure,axiom,
! [T_b,V_g_2,V_f_2,V_Pa_2] :
( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> 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))) )
=> 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))))) ),
file('theBenchmark.p',fact_wf__if__measure) ).
fof(fact_max__ext_Ointros,axiom,
! [V_R_2,V_Y_2,V_X_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
=> ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
=> ? [B_xa] :
( 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))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) ) )
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_max__ext_Ointros) ).
fof(fact_pred__nat__def,axiom,
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))),
file('theBenchmark.p',fact_pred__nat__def) ).
fof(fact_wf__lex,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__lex) ).
fof(fact_wf__lexn,axiom,
! [V_n_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ),
file('theBenchmark.p',fact_wf__lexn) ).
fof(fact_lex__def,axiom,
! [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)),
file('theBenchmark.p',fact_lex__def) ).
fof(fact_lexn_Osimps_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_lexn_Osimps_I1_J) ).
fof(fact_wf__pred__nat,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('theBenchmark.p',fact_wf__pred__nat) ).
fof(fact_wf__same__fst,axiom,
! [T_b,V_R_2,T_c,V_Pa_2] :
( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
=> c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ),
file('theBenchmark.p',fact_wf__same__fst) ).
fof(fact_Nitpick_Ozero__frac__def,axiom,
! [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))),
file('theBenchmark.p',fact_Nitpick_Ozero__frac__def) ).
fof(fact_inj__on__Inter,axiom,
! [V_f_2,T_c,T_b,V_S_2] :
( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
=> ( ! [B_A] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
=> 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)) ) ),
file('theBenchmark.p',fact_inj__on__Inter) ).
fof(fact_Nitpick_Oone__frac__def,axiom,
! [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))),
file('theBenchmark.p',fact_Nitpick_Oone__frac__def) ).
fof(fact_Nitpick_Onumber__of__frac__def,axiom,
! [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))),
file('theBenchmark.p',fact_Nitpick_Onumber__of__frac__def) ).
fof(fact_Nitpick_Ofrac__def,axiom,
! [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)),
file('theBenchmark.p',fact_Nitpick_Ofrac__def) ).
fof(fact_Range__Collect__split,axiom,
! [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))),
file('theBenchmark.p',fact_Range__Collect__split) ).
fof(fact_the__elem__def,axiom,
! [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))))),
file('theBenchmark.p',fact_the__elem__def) ).
fof(fact_wfP__def,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
<=> 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))) ),
file('theBenchmark.p',fact_wfP__def) ).
fof(fact_wfP__empty,axiom,
! [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))),
file('theBenchmark.p',fact_wfP__empty) ).
fof(fact_RangeI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( 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))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_RangeI) ).
fof(fact_wfP__accp__iff,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
<=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ),
file('theBenchmark.p',fact_wfP__accp__iff) ).
fof(fact_accp__wfPD,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ),
file('theBenchmark.p',fact_accp__wfPD) ).
fof(fact_the__eq__trivial,axiom,
! [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,
file('theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_the__sym__eq__trivial,axiom,
! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(fact_Range__Id__on,axiom,
! [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,
file('theBenchmark.p',fact_Range__Id__on) ).
fof(fact_wfP__subset,axiom,
! [V_p_2,V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> ( 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))
=> c_Wellfounded_OwfP(T_b,V_p_2) ) ),
file('theBenchmark.p',fact_wfP__subset) ).
fof(fact_Range__Diff__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Range__Diff__subset) ).
fof(fact_Range__Union,axiom,
! [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)),
file('theBenchmark.p',fact_Range__Union) ).
fof(fact_Range__empty,axiom,
! [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)),
file('theBenchmark.p',fact_Range__empty) ).
fof(fact_Range__empty__iff,axiom,
! [V_r_2,T_b,T_c] :
( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ),
file('theBenchmark.p',fact_Range__empty__iff) ).
fof(fact_Range__Un__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Range__Un__eq) ).
fof(fact_finite__Range,axiom,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_finite__Range) ).
fof(fact_snd__eq__Range,axiom,
! [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),
file('theBenchmark.p',fact_snd__eq__Range) ).
fof(fact_split__paired__The,axiom,
! [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)))),
file('theBenchmark.p',fact_split__paired__The) ).
fof(fact_The__split__eq,axiom,
! [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),
file('theBenchmark.p',fact_The__split__eq) ).
fof(fact_Range__iff,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
<=> ? [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)) ),
file('theBenchmark.p',fact_Range__iff) ).
fof(fact_the__inv__into__def,axiom,
! [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))),
file('theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_fold__def,axiom,
! [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)),
file('theBenchmark.p',fact_fold__def) ).
fof(fact_Range__insert,axiom,
! [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)),
file('theBenchmark.p',fact_Range__insert) ).
fof(fact_divmod__nat__def,axiom,
! [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)),
file('theBenchmark.p',fact_divmod__nat__def) ).
fof(fact_Range__Int__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_fold1__def,axiom,
! [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)),
file('theBenchmark.p',fact_fold1__def) ).
fof(fact_The__split,axiom,
! [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))),
file('theBenchmark.p',fact_The__split) ).
fof(fact_wf__in__rel,axiom,
! [V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ),
file('theBenchmark.p',fact_wf__in__rel) ).
fof(fact_wfP__wf__eq,axiom,
! [V_r_2,T_b] :
( 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))
<=> c_Wellfounded_Owf(T_b,V_r_2) ),
file('theBenchmark.p',fact_wfP__wf__eq) ).
fof(fact_RangeP__Range__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( 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))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_flat__lub__def,axiom,
! [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_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
=> 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)))))) )
& ( 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)))))
=> c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 ) ),
file('theBenchmark.p',fact_flat__lub__def) ).
fof(fact_RangeE,axiom,
! [V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
=> ~ ! [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)) ),
file('theBenchmark.p',fact_RangeE) ).
fof(fact_RangeP_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ),
file('theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_RangeP_Oequations,axiom,
! [V_a2_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
<=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ),
file('theBenchmark.p',fact_RangeP_Oequations) ).
fof(fact_inj__vimage__singleton,axiom,
! [V_a_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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))))) ),
file('theBenchmark.p',fact_inj__vimage__singleton) ).
fof(fact_wfP__acyclicP,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> 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))) ),
file('theBenchmark.p',fact_wfP__acyclicP) ).
fof(fact_wf__Un,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( c_Wellfounded_Owf(T_b,V_s_2)
=> ( 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))
=> 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)) ) ) ),
file('theBenchmark.p',fact_wf__Un) ).
fof(fact_vimageI,axiom,
! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
( hAPP(V_f_2,V_a_2) = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ),
file('theBenchmark.p',fact_vimageI) ).
fof(fact_DomainI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( 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))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_DomainI) ).
fof(fact_vimage__UN,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__UN) ).
fof(fact_vimage__Diff,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__Diff) ).
fof(fact_vimage__Un,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__Un) ).
fof(fact_vimage__mono,axiom,
! [V_f_2,T_c,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),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_vimage__mono) ).
fof(fact_vimageI2,axiom,
! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ),
file('theBenchmark.p',fact_vimageI2) ).
fof(fact_vimageD,axiom,
! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ),
file('theBenchmark.p',fact_vimageD) ).
fof(fact_vimage__eq,axiom,
! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ),
file('theBenchmark.p',fact_vimage__eq) ).
fof(fact_vimage__ident,axiom,
! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_vimage__ident) ).
fof(fact_vimage__INT,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__INT) ).
fof(fact_vimage__Int,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__Int) ).
fof(fact_vimage__Compl,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__Compl) ).
fof(fact_vimage__code,axiom,
! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
<=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ),
file('theBenchmark.p',fact_vimage__code) ).
fof(fact_Domain__Id__on,axiom,
! [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,
file('theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_vimage__UNIV,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__UNIV) ).
fof(fact_acyclic__subset,axiom,
! [V_r_2,V_s_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_s_2)
=> ( 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))
=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__subset) ).
fof(fact_wf__acyclic,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
file('theBenchmark.p',fact_wf__acyclic) ).
fof(fact_vimage__Collect__eq,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__Collect__eq) ).
fof(fact_vimage__empty,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__empty) ).
fof(fact_image__vimage__subset,axiom,
! [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)),
file('theBenchmark.p',fact_image__vimage__subset) ).
fof(fact_surj__image__vimage__eq,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( 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))
=> 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 ),
file('theBenchmark.p',fact_surj__image__vimage__eq) ).
fof(fact_vimage__def,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__def) ).
fof(fact_Domain__empty,axiom,
! [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)),
file('theBenchmark.p',fact_Domain__empty) ).
fof(fact_Domain__empty__iff,axiom,
! [V_r_2,T_c,T_b] :
( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ),
file('theBenchmark.p',fact_Domain__empty__iff) ).
fof(fact_Domain__mono,axiom,
! [V_s_2,V_r_2,T_c,T_b] :
( 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))
=> 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))) ),
file('theBenchmark.p',fact_Domain__mono) ).
fof(fact_Domain__Un__eq,axiom,
! [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)),
file('theBenchmark.p',fact_Domain__Un__eq) ).
fof(fact_finite__Domain,axiom,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_finite__Domain) ).
fof(fact_fst__eq__Domain,axiom,
! [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),
file('theBenchmark.p',fact_fst__eq__Domain) ).
fof(fact_vimage__Union,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__Union) ).
fof(fact_vimage__singleton__eq,axiom,
! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
( 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))))))
<=> hAPP(V_f_2,V_a_2) = V_b_2 ),
file('theBenchmark.p',fact_vimage__singleton__eq) ).
fof(fact_vimage__insert,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__insert) ).
fof(fact_finite__vimageD,axiom,
! [V_F_2,V_h_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
=> ( 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))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__vimageD) ).
fof(fact_vimage__subsetD,axiom,
! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
( 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))
=> ( 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))
=> 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))) ) ),
file('theBenchmark.p',fact_vimage__subsetD) ).
fof(fact_image__vimage__eq,axiom,
! [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)))),
file('theBenchmark.p',fact_image__vimage__eq) ).
fof(fact_finite__vimageI,axiom,
! [V_h_2,T_c,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ),
file('theBenchmark.p',fact_finite__vimageI) ).
fof(fact_inj__vimage__image__eq,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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 ),
file('theBenchmark.p',fact_inj__vimage__image__eq) ).
fof(fact_vimage__const,axiom,
! [T_c,V_A_2,V_ca_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_vimage__const) ).
fof(fact_vimage__eq__UN,axiom,
! [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))))),
file('theBenchmark.p',fact_vimage__eq__UN) ).
fof(fact_Domain__iff,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
<=> ? [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)) ),
file('theBenchmark.p',fact_Domain__iff) ).
fof(fact_Domain__insert,axiom,
! [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)),
file('theBenchmark.p',fact_Domain__insert) ).
fof(fact_wf__iff__acyclic__if__finite,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> ( c_Wellfounded_Owf(T_b,V_r_2)
<=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).
fof(fact_finite__acyclic__wf,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_finite__acyclic__wf) ).
fof(fact_Domain__Int__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_vimage__subsetI,axiom,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( 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)))
=> 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)) ) ),
file('theBenchmark.p',fact_vimage__subsetI) ).
fof(fact_Domain__Diff__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_Domain__Diff__subset) ).
fof(fact_Field__def,axiom,
! [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)),
file('theBenchmark.p',fact_Field__def) ).
fof(fact_vimage__if,axiom,
! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> 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_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> 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_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> 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_ca_2)),V_d_2)),V_A_2) = V_B_2 )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> 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_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ),
file('theBenchmark.p',fact_vimage__if) ).
fof(fact_Domain__Union,axiom,
! [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)),
file('theBenchmark.p',fact_Domain__Union) ).
fof(fact_Domain__Collect__split,axiom,
! [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)),
file('theBenchmark.p',fact_Domain__Collect__split) ).
fof(fact_DomainP__Domain__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( 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))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_Nitpick_Owf_H__def,axiom,
! [V_r_2,T_b] :
( c_Nitpick_Owf_H(T_b,V_r_2)
<=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
& c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_Nitpick_Owf_H__def) ).
fof(fact_DomainE,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
=> ~ ! [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)) ),
file('theBenchmark.p',fact_DomainE) ).
fof(fact_DomainP_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ),
file('theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_DomainP_Oequations,axiom,
! [V_a1_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
<=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ),
file('theBenchmark.p',fact_DomainP_Oequations) ).
fof(fact_image__split__eq__Sigma,axiom,
! [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))),
file('theBenchmark.p',fact_image__split__eq__Sigma) ).
fof(fact_Rep__Integ__cases,axiom,
! [V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
=> ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ),
file('theBenchmark.p',fact_Rep__Integ__cases) ).
fof(fact_Rep__Integ__induct,axiom,
! [V_Pa_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
=> ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
=> hBOOL(hAPP(V_Pa_2,V_y_2)) ) ),
file('theBenchmark.p',fact_Rep__Integ__induct) ).
fof(fact_SigmaI,axiom,
! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
=> 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))) ) ),
file('theBenchmark.p',fact_SigmaI) ).
fof(fact_Sigma__Union,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__Union) ).
fof(fact_Times__eq__cancel2,axiom,
! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
=> ( 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))
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_Times__eq__cancel2) ).
fof(fact_Sigma__empty1,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__empty1) ).
fof(fact_card__cartesian__product,axiom,
! [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)),
file('theBenchmark.p',fact_card__cartesian__product) ).
fof(fact_setsum__cartesian__product,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_setsum__cartesian__product) ).
fof(fact_Sigma__empty2,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__empty2) ).
fof(fact_Times__empty,axiom,
! [V_B_2,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),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
<=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Times__empty) ).
fof(fact_Compl__Times__UNIV2,axiom,
! [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)))),
file('theBenchmark.p',fact_Compl__Times__UNIV2) ).
fof(fact_Compl__Times__UNIV1,axiom,
! [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))),
file('theBenchmark.p',fact_Compl__Times__UNIV1) ).
fof(fact_setprod__cartesian__product,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> 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))) ),
file('theBenchmark.p',fact_setprod__cartesian__product) ).
fof(fact_Sigma__Un__distrib1,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__Un__distrib1) ).
fof(fact_Times__Un__distrib1,axiom,
! [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))),
file('theBenchmark.p',fact_Times__Un__distrib1) ).
fof(fact_Sigma__Un__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__Un__distrib2) ).
fof(fact_rel__comp__subset__Sigma,axiom,
! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
( 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))))
=> ( 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))))
=> 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)))) ) ),
file('theBenchmark.p',fact_rel__comp__subset__Sigma) ).
fof(fact_swap__product,axiom,
! [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)),
file('theBenchmark.p',fact_swap__product) ).
fof(fact_finite__cartesian__product,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> 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)))) ) ),
file('theBenchmark.p',fact_finite__cartesian__product) ).
fof(fact_equiv__type,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> 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)))) ),
file('theBenchmark.p',fact_equiv__type) ).
fof(fact_Sigma__Int__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(fact_Times__Int__distrib1,axiom,
! [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))),
file('theBenchmark.p',fact_Times__Int__distrib1) ).
fof(fact_Sigma__Int__distrib1,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__Int__distrib1) ).
fof(fact_Id__on__subset__Times,axiom,
! [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)))),
file('theBenchmark.p',fact_Id__on__subset__Times) ).
fof(fact_Sigma__Diff__distrib2,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__Diff__distrib2) ).
fof(fact_Times__Diff__distrib1,axiom,
! [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))),
file('theBenchmark.p',fact_Times__Diff__distrib1) ).
fof(fact_Sigma__Diff__distrib1,axiom,
! [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)),
file('theBenchmark.p',fact_Sigma__Diff__distrib1) ).
fof(fact_UNIV__Times__UNIV,axiom,
! [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)),
file('theBenchmark.p',fact_UNIV__Times__UNIV) ).
fof(fact_mem__Sigma__iff,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_mem__Sigma__iff) ).
fof(fact_SigmaD1,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( 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)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
file('theBenchmark.p',fact_SigmaD1) ).
fof(fact_SigmaD2,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( 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)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ),
file('theBenchmark.p',fact_SigmaD2) ).
fof(fact_SigmaE2,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( 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)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
file('theBenchmark.p',fact_SigmaE2) ).
fof(fact_card__cartesian__product__singleton,axiom,
! [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),
file('theBenchmark.p',fact_card__cartesian__product__singleton) ).
fof(fact_Times__subset__cancel2,axiom,
! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
=> ( 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))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_Times__subset__cancel2) ).
fof(fact_Image__subset,axiom,
! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
( 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))))
=> 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)) ),
file('theBenchmark.p',fact_Image__subset) ).
fof(fact_finite__cartesian__productD1,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( 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))))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__cartesian__productD1) ).
fof(fact_finite__cartesian__productD2,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( 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))))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_finite__cartesian__productD2) ).
fof(fact_Collect__split,axiom,
! [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))),
file('theBenchmark.p',fact_Collect__split) ).
fof(fact_SetCompr__Sigma__eq,axiom,
! [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)),
file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).
fof(fact_fst__image__times,axiom,
! [V_A_2,T_c,T_b,V_B_2] :
( ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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 )
& ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_fst__image__times) ).
fof(fact_snd__image__times,axiom,
! [V_B_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> 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)) ) ),
file('theBenchmark.p',fact_snd__image__times) ).
fof(fact_insert__times__insert,axiom,
! [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)))),
file('theBenchmark.p',fact_insert__times__insert) ).
fof(fact_finite__equiv__class,axiom,
! [V_X_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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))))
=> ( 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)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ),
file('theBenchmark.p',fact_finite__equiv__class) ).
fof(fact_UN__Times__distrib,axiom,
! [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))),
file('theBenchmark.p',fact_UN__Times__distrib) ).
fof(fact_Sigma__def,axiom,
! [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))))),
file('theBenchmark.p',fact_Sigma__def) ).
fof(fact_finite__quotient,axiom,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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))))
=> 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))) ) ),
file('theBenchmark.p',fact_finite__quotient) ).
fof(fact_setsum__mult__setsum__if__inj,axiom,
! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
( class_Rings_Osemiring__0(T_d)
=> ( 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)))
=> 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))))))) ) ),
file('theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).
fof(fact_Ex__inj__on__UNION__Sigma,axiom,
! [V_A_2,V_I_2,T_c,T_b] :
? [B_f] :
( 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)))
& 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)) ),
file('theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).
fof(fact_fold__image__Sigma,axiom,
! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
=> 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)) ) ) ),
file('theBenchmark.p',fact_fold__image__Sigma) ).
fof(fact_image__id,axiom,
! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_image__id) ).
fof(fact_vimage__id,axiom,
! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2,
file('theBenchmark.p',fact_vimage__id) ).
fof(fact_inj__on__id,axiom,
! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2),
file('theBenchmark.p',fact_inj__on__id) ).
fof(fact_apfst__id,axiom,
! [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)),
file('theBenchmark.p',fact_apfst__id) ).
fof(fact_apsnd__id,axiom,
! [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)),
file('theBenchmark.p',fact_apsnd__id) ).
fof(fact_id__apply,axiom,
! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x,
file('theBenchmark.p',fact_id__apply) ).
fof(fact_id__def,axiom,
! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1,
file('theBenchmark.p',fact_id__def) ).
fof(fact_of__int__eq__id,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('theBenchmark.p',fact_of__int__eq__id) ).
fof(fact_surj__id,axiom,
! [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)),
file('theBenchmark.p',fact_surj__id) ).
fof(fact_split__Pair,axiom,
! [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)),
file('theBenchmark.p',fact_split__Pair) ).
fof(fact_setsum__reindex__id,axiom,
! [V_B_2,V_f_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( c_Fun_Oinj__on(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),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)) ) ),
file('theBenchmark.p',fact_setsum__reindex__id) ).
fof(fact_setprod__reindex__id,axiom,
! [V_B_2,V_f_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( c_Fun_Oinj__on(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),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)) ) ),
file('theBenchmark.p',fact_setprod__reindex__id) ).
fof(fact_setprod__Sigma,axiom,
! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
=> 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)) ) ) ),
file('theBenchmark.p',fact_setprod__Sigma) ).
fof(fact_setsum__Sigma,axiom,
! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
=> 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)) ) ) ),
file('theBenchmark.p',fact_setsum__Sigma) ).
fof(fact_card__SigmaI,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
=> 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) ) ),
file('theBenchmark.p',fact_card__SigmaI) ).
fof(fact_finite__SigmaI,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
=> 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))) ) ),
file('theBenchmark.p',fact_finite__SigmaI) ).
fof(fact_SigmaE,axiom,
! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
=> V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ),
file('theBenchmark.p',fact_SigmaE) ).
fof(fact_map__pair__surj,axiom,
! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
( 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))
=> ( 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))
=> 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)) ) ),
file('theBenchmark.p',fact_map__pair__surj) ).
fof(fact_map__pair__imageI,axiom,
! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
( 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))
=> 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))) ),
file('theBenchmark.p',fact_map__pair__imageI) ).
fof(fact_fst__map__pair,axiom,
! [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)),
file('theBenchmark.p',fact_fst__map__pair) ).
fof(fact_snd__prod__fun,axiom,
! [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)),
file('theBenchmark.p',fact_snd__prod__fun) ).
fof(fact_map__pair__simp,axiom,
! [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)),
file('theBenchmark.p',fact_map__pair__simp) ).
fof(fact_map__pair__ident,axiom,
! [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,
file('theBenchmark.p',fact_map__pair__ident) ).
fof(fact_map__pair_Oidentity,axiom,
! [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)),
file('theBenchmark.p',fact_map__pair_Oidentity) ).
fof(fact_apfst__def,axiom,
! [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)),
file('theBenchmark.p',fact_apfst__def) ).
fof(fact_apsnd__def,axiom,
! [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),
file('theBenchmark.p',fact_apsnd__def) ).
fof(fact_map__pair_Oid,axiom,
! [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)),
file('theBenchmark.p',fact_map__pair_Oid) ).
fof(fact_map__pair__def,axiom,
! [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)),
file('theBenchmark.p',fact_map__pair__def) ).
fof(fact_map__pair__surj__on,axiom,
! [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] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
=> ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
=> 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)) ) ),
file('theBenchmark.p',fact_map__pair__surj__on) ).
fof(fact_wf__map__pair__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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)) ) ),
file('theBenchmark.p',fact_wf__map__pair__image) ).
fof(fact_map__pair__inj__on,axiom,
! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
=> 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))) ) ),
file('theBenchmark.p',fact_map__pair__inj__on) ).
fof(fact_prod__fun__imageE,axiom,
! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_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)))
=> ~ ! [B_x,B_y] :
( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
=> ~ 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)) ) ),
file('theBenchmark.p',fact_prod__fun__imageE) ).
fof(fact_refl__on__def,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> 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)) )
& 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)))) ) ),
file('theBenchmark.p',fact_refl__on__def) ).
fof(fact_inj__on__INTER,axiom,
! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
=> 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)) ) ),
file('theBenchmark.p',fact_inj__on__INTER) ).
fof(fact_refl__on__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_refl__on__Id__on) ).
fof(fact_refl__on__empty,axiom,
! [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))),
file('theBenchmark.p',fact_refl__on__empty) ).
fof(fact_refl__on__Un,axiom,
! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
=> 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)) ) ),
file('theBenchmark.p',fact_refl__on__Un) ).
fof(fact_refl__on__Int,axiom,
! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
=> 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)) ) ),
file('theBenchmark.p',fact_refl__on__Int) ).
fof(fact_refl__onD2,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( 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))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD2) ).
fof(fact_refl__onD1,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( 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))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD1) ).
fof(fact_refl__onD,axiom,
! [V_a_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_refl__onD) ).
fof(fact_reflp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Oreflp(T_b,V_r_2)
<=> 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))) ),
file('theBenchmark.p',fact_reflp__def) ).
fof(fact_refl__onI,axiom,
! [V_A_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)),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))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> 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)) )
=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_refl__onI) ).
fof(fact_pigeonhole__infinite,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> ? [B_x] :
( ~ 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))))))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_pigeonhole__infinite) ).
fof(fact_reflpE,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Predicate_Oreflp(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_reflpE) ).
fof(fact_refl__on__def_H,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> 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)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_refl__on__def_H) ).
fof(fact_Abs__Integ__induct,axiom,
! [V_x_2,V_Pa_2] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
=> hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
=> hBOOL(hAPP(V_Pa_2,V_x_2)) ),
file('theBenchmark.p',fact_Abs__Integ__induct) ).
fof(fact_Abs__Integ__cases,axiom,
! [V_x_2] :
~ ! [B_y] :
( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ),
file('theBenchmark.p',fact_Abs__Integ__cases) ).
fof(fact_INFI__bool__eq,axiom,
! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b),
file('theBenchmark.p',fact_INFI__bool__eq) ).
fof(fact_ball__empty,axiom,
! [V_Pa_2,T_b,B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> hBOOL(hAPP(V_Pa_2,B_x)) ),
file('theBenchmark.p',fact_ball__empty) ).
fof(fact_Powp__def,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
=> hBOOL(hAPP(V_A_2,B_x)) ) ),
file('theBenchmark.p',fact_Powp__def) ).
fof(fact_Collect__ball__eq,axiom,
! [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))),
file('theBenchmark.p',fact_Collect__ball__eq) ).
fof(fact_congruent__def,axiom,
! [V_f_2,V_r_2,T_c,T_b] :
( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
=> 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)) ) ),
file('theBenchmark.p',fact_congruent__def) ).
fof(fact_INTER__def,axiom,
! [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)))),
file('theBenchmark.p',fact_INTER__def) ).
fof(fact_Inf__Sup,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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))))) ),
file('theBenchmark.p',fact_Inf__Sup) ).
fof(fact_Sup__Inf,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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)))))) ),
file('theBenchmark.p',fact_Sup__Inf) ).
fof(fact_finite__UN__I,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
=> 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))) ) ),
file('theBenchmark.p',fact_finite__UN__I) ).
fof(fact_inj__on__diff__nat,axiom,
! [V_k_2,V_N_2] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
=> 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) ),
file('theBenchmark.p',fact_inj__on__diff__nat) ).
fof(fact_wfP__SUP,axiom,
! [T_b,V_r_2,T_c] :
( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
=> ( ! [B_i,B_j] :
( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
=> 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)) )
=> 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)) ) ),
file('theBenchmark.p',fact_wfP__SUP) ).
fof(fact_Inter__eq,axiom,
! [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)))),
file('theBenchmark.p',fact_Inter__eq) ).
fof(fact_mem__splitI2,axiom,
! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] :
( ! [B_a,B_b] :
( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
=> hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
=> 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_ca_2),V_p_2))) ),
file('theBenchmark.p',fact_mem__splitI2) ).
fof(fact_mem__splitE,axiom,
! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] :
( 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_ca_2),V_p_2)))
=> ~ ! [B_x,B_y] :
( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ),
file('theBenchmark.p',fact_mem__splitE) ).
fof(fact_vimage__Times,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__Times) ).
fof(fact_map__pair_Ocomp,axiom,
! [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)),
file('theBenchmark.p',fact_map__pair_Ocomp) ).
fof(fact_map__pair__compose,axiom,
! [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)),
file('theBenchmark.p',fact_map__pair__compose) ).
fof(fact_map__pair_Ocompositionality,axiom,
! [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),
file('theBenchmark.p',fact_map__pair_Ocompositionality) ).
fof(fact_comp__surj,axiom,
! [V_g_2,T_d,V_f_2,T_b,T_c] :
( 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))
=> ( 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))
=> 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)) ) ),
file('theBenchmark.p',fact_comp__surj) ).
fof(fact_image__compose,axiom,
! [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)),
file('theBenchmark.p',fact_image__compose) ).
fof(fact_comp__inj__on__iff,axiom,
! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( 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))
<=> 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) ) ),
file('theBenchmark.p',fact_comp__inj__on__iff) ).
fof(fact_comp__inj__on,axiom,
! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( 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))
=> 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) ) ),
file('theBenchmark.p',fact_comp__inj__on) ).
fof(fact_inj__on__imageI,axiom,
! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
( 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)
=> 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)) ),
file('theBenchmark.p',fact_inj__on__imageI) ).
fof(fact_inj__on__imageI2,axiom,
! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
( 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)
=> c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_inj__on__imageI2) ).
fof(fact_inj__comp,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
=> 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))) ) ),
file('theBenchmark.p',fact_inj__comp) ).
fof(fact_o__def,axiom,
! [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)),
file('theBenchmark.p',fact_o__def) ).
fof(fact_K__record__comp,axiom,
! [V_x_2,V_f_2,V_ca_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_ca_2)),V_f_2),V_x_2) = V_ca_2,
file('theBenchmark.p',fact_K__record__comp) ).
fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
! [V_x_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> 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) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).
fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_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)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).
fof(fact_o__eq__elim,axiom,
! [V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( 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_ca_2),V_d_2)
=> ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ),
file('theBenchmark.p',fact_o__eq__elim) ).
fof(fact_o__eq__dest,axiom,
! [V_v_2,V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( 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_ca_2),V_d_2)
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ),
file('theBenchmark.p',fact_o__eq__dest) ).
fof(fact_o__apply,axiom,
! [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)),
file('theBenchmark.p',fact_o__apply) ).
fof(fact_o__assoc,axiom,
! [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),
file('theBenchmark.p',fact_o__assoc) ).
fof(fact_o__eq__dest__lhs,axiom,
! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ),
file('theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(fact_comp__cong,axiom,
! [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] :
( 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))
=> 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) ),
file('theBenchmark.p',fact_comp__cong) ).
fof(fact_fun__upd__comp,axiom,
! [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),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = 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)),
file('theBenchmark.p',fact_fun__upd__comp) ).
fof(fact_apsnd__compose,axiom,
! [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),
file('theBenchmark.p',fact_apsnd__compose) ).
fof(fact_apfst__compose,axiom,
! [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),
file('theBenchmark.p',fact_apfst__compose) ).
fof(fact_vimage__compose,axiom,
! [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)),
file('theBenchmark.p',fact_vimage__compose) ).
fof(fact_o__id,axiom,
! [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,
file('theBenchmark.p',fact_o__id) ).
fof(fact_id__o,axiom,
! [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,
file('theBenchmark.p',fact_id__o) ).
fof(fact_o__eq__id__dest,axiom,
! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( 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_ca_2)
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ),
file('theBenchmark.p',fact_o__eq__id__dest) ).
fof(fact_setsum__reindex,axiom,
! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> 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) ) ),
file('theBenchmark.p',fact_setsum__reindex) ).
fof(fact_setprod__reindex,axiom,
! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> 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) ) ),
file('theBenchmark.p',fact_setprod__reindex) ).
fof(fact_setprod__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
=> ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
=> 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) ) ) ) ),
file('theBenchmark.p',fact_setprod__reindex__cong) ).
fof(fact_setsum_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
=> 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) ) ) ),
file('theBenchmark.p',fact_setsum_Oreindex) ).
fof(fact_setprod_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
=> 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) ) ) ),
file('theBenchmark.p',fact_setprod_Oreindex) ).
fof(fact_the__inv__into__comp,axiom,
! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
( 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))
=> ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
=> ( 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))))
=> 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) ) ) ),
file('theBenchmark.p',fact_the__inv__into__comp) ).
fof(fact_fold__image__reindex,axiom,
! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Oab__semigroup__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
=> 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) ) ) ),
file('theBenchmark.p',fact_fold__image__reindex) ).
fof(fact_folding_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_folding_Oremove) ).
fof(fact_folding__image_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
=> 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) ) ) ),
file('theBenchmark.p',fact_folding__image_Oreindex) ).
fof(fact_folding_Ounion,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( 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))
=> 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)) ) ) ) ),
file('theBenchmark.p',fact_folding_Ounion) ).
fof(fact_fst__comp__map__pair,axiom,
! [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)),
file('theBenchmark.p',fact_fst__comp__map__pair) ).
fof(fact_UN__o,axiom,
! [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),
file('theBenchmark.p',fact_UN__o) ).
fof(fact_folding_Ocommute__left__comp,axiom,
! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> 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)) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp) ).
fof(fact_folding_Ocommute__comp,axiom,
! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_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)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ),
file('theBenchmark.p',fact_folding_Ocommute__comp) ).
fof(fact_folding_Ocommute__comps_I1_J,axiom,
! [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] :
( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
=> 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) ),
file('theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
fof(fact_snd__comp__map__pair,axiom,
! [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)),
file('theBenchmark.p',fact_snd__comp__map__pair) ).
fof(fact_folding__image_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_folding__image_Odistrib) ).
fof(fact_split__comp,axiom,
! [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)),
file('theBenchmark.p',fact_split__comp) ).
fof(fact_folding_Ocommute__left__comp_H_H,axiom,
! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).
fof(fact_folding_Ocommute__comp_H_H,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).
fof(fact_folding_Ocommute__left__comp_H,axiom,
! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_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_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)) ) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).
fof(fact_folding_Ocommute__comp_H,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_folding_Ocommute__comp_H) ).
fof(fact_folding_Oempty,axiom,
! [V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ),
file('theBenchmark.p',fact_folding_Oempty) ).
fof(fact_folding_Oeq__fold,axiom,
! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_folding_Oeq__fold) ).
fof(fact_folding__image_Oeq__fold,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> 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) ) ),
file('theBenchmark.p',fact_folding__image_Oeq__fold) ).
fof(fact_folding_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_folding_Oinsert) ).
fof(fact_folding_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_folding_Ounion__inter) ).
fof(fact_folding_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_folding_Oinsert__remove) ).
fof(fact_setsum__reindex__nonzero,axiom,
! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
=> ( B_x != B_y
=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
=> hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
=> 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) ) ) ),
file('theBenchmark.p',fact_setsum__reindex__nonzero) ).
fof(fact_folding__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding__idem_Ounion__idem) ).
fof(fact_folding__idem_Osubset__comp__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_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)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).
fof(fact_folding__idem_Oidem__left__comp,axiom,
! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_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_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) ),
file('theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).
fof(fact_folding__idem_Oidem__comp,axiom,
! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> 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) ),
file('theBenchmark.p',fact_folding__idem_Oidem__comp) ).
fof(fact_folding__idem_Oin__comp__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(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)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).
fof(fact_folding__idem_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
fof(fact_strong__setprod__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> 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) )
=> 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) ) ) ) ),
file('theBenchmark.p',fact_strong__setprod__reindex__cong) ).
fof(fact_Eps__split,axiom,
! [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))),
file('theBenchmark.p',fact_Eps__split) ).
fof(fact_wfI__pf,axiom,
! [V_R_2,T_b] :
( ! [B_A] :
( 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)))
=> B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
=> c_Wellfounded_Owf(T_b,V_R_2) ),
file('theBenchmark.p',fact_wfI__pf) ).
fof(fact_tfl__some,axiom,
! [T_b,B_P] :
( ? [B_x] : hBOOL(hAPP(B_P,B_x))
=> hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ),
file('theBenchmark.p',fact_tfl__some) ).
fof(fact_someI,axiom,
! [T_b,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
=> hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ),
file('theBenchmark.p',fact_someI) ).
fof(fact_some__sym__eq__trivial,axiom,
! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(fact_some__eq__trivial,axiom,
! [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,
file('theBenchmark.p',fact_some__eq__trivial) ).
fof(fact_some__eq__ex,axiom,
! [T_b,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
<=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ),
file('theBenchmark.p',fact_some__eq__ex) ).
fof(fact_someI__ex,axiom,
! [T_b,V_Pa_2] :
( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
=> hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ),
file('theBenchmark.p',fact_someI__ex) ).
fof(fact_exE__some,axiom,
! [T_b,V_ca_2,V_Pa_2] :
( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
=> ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
=> hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ),
file('theBenchmark.p',fact_exE__some) ).
fof(fact_split__paired__Eps,axiom,
! [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)))),
file('theBenchmark.p',fact_split__paired__Eps) ).
fof(fact_Eps__split__eq,axiom,
! [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),
file('theBenchmark.p',fact_Eps__split__eq) ).
fof(fact_Sigma__mono,axiom,
! [V_D_2,V_B_2,T_c,V_C_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),V_C_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> 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))) )
=> 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))) ) ),
file('theBenchmark.p',fact_Sigma__mono) ).
fof(fact_not__acc__down,axiom,
! [V_R_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
=> ~ ! [B_z] :
( 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))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ),
file('theBenchmark.p',fact_not__acc__down) ).
fof(fact_acc_OaccI,axiom,
! [V_r_2,V_x_2,T_b] :
( ! [B_y] :
( 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))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_acc_OaccI) ).
fof(fact_max__ext_Osimps,axiom,
! [V_R_2,V_a2_2,V_a1_2,T_b] :
( 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)))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
=> ? [B_xa] :
( 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))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
file('theBenchmark.p',fact_max__ext_Osimps) ).
fof(fact_wf__no__infinite__down__chainE,axiom,
! [V_f_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ ! [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)) ),
file('theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
fof(fact_iterate_Osimps,axiom,
! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> 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)) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> 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) ) ),
file('theBenchmark.p',fact_iterate_Osimps) ).
fof(fact_setsum__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
=> 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) ) ) ) ),
file('theBenchmark.p',fact_setsum__reindex__cong) ).
fof(fact_scomp__apply,axiom,
! [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)),
file('theBenchmark.p',fact_scomp__apply) ).
fof(fact_Pair__scomp,axiom,
! [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),
file('theBenchmark.p',fact_Pair__scomp) ).
fof(fact_scomp__scomp,axiom,
! [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)),
file('theBenchmark.p',fact_scomp__scomp) ).
fof(fact_scomp__Pair,axiom,
! [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,
file('theBenchmark.p',fact_scomp__Pair) ).
fof(fact_scomp__def,axiom,
! [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)),
file('theBenchmark.p',fact_scomp__def) ).
fof(fact_scomp__unfold,axiom,
! [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))),
file('theBenchmark.p',fact_scomp__unfold) ).
fof(fact_less__eq,axiom,
! [V_n_2,V_m_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_less__eq) ).
fof(fact_wf__eq__minimal,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ! [B_Q] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
=> ? [B_x] :
( ! [B_y] :
( 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))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) ) ) ),
file('theBenchmark.p',fact_wf__eq__minimal) ).
fof(fact_wf__trancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__trancl) ).
fof(fact_less__than__def,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('theBenchmark.p',fact_less__than__def) ).
fof(fact_acyclic__def,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
<=> ! [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))) ),
file('theBenchmark.p',fact_acyclic__def) ).
fof(fact_trancl_Or__into__trancl,axiom,
! [V_r_2,V_b_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_b_2)),V_r_2))
=> 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))) ),
file('theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_trancl__subset__Field2,axiom,
! [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))))),
file('theBenchmark.p',fact_trancl__subset__Field2) ).
fof(fact_r__into__trancl_H,axiom,
! [V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_trancl__empty,axiom,
! [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)),
file('theBenchmark.p',fact_trancl__empty) ).
fof(fact_trancl__domain,axiom,
! [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),
file('theBenchmark.p',fact_trancl__domain) ).
fof(fact_trancl__range,axiom,
! [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),
file('theBenchmark.p',fact_trancl__range) ).
fof(fact_finite__trancl,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
file('theBenchmark.p',fact_finite__trancl) ).
fof(fact_r__r__into__trancl,axiom,
! [V_ca_2,V_R_2,V_b_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_b_2)),V_R_2))
=> ( 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_ca_2)),V_R_2))
=> 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
file('theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_trancl__into__trancl2,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),V_r_2))
=> ( 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( 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_ca_2)),V_r_2))
=> 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_trancl__trans,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__trans) ).
fof(fact_trancl__mono,axiom,
! [V_s_2,V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( 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))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ),
file('theBenchmark.p',fact_trancl__mono) ).
fof(fact_trancl__unfold,axiom,
! [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)),
file('theBenchmark.p',fact_trancl__unfold) ).
fof(fact_trancl__subset__Sigma,axiom,
! [V_A_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)),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))))
=> 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)))) ),
file('theBenchmark.p',fact_trancl__subset__Sigma) ).
fof(fact_trancl__Int__subset,axiom,
! [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)),V_r_2),V_s_2))
=> ( 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))
=> 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)) ) ),
file('theBenchmark.p',fact_trancl__Int__subset) ).
fof(fact_trancl__insert,axiom,
! [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)))))),
file('theBenchmark.p',fact_trancl__insert) ).
fof(fact_reflcl__set__eq,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( 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))
<=> 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)))) ),
file('theBenchmark.p',fact_reflcl__set__eq) ).
fof(fact_r__into__rtrancl,axiom,
! [V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [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))),
file('theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_IdI,axiom,
! [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))),
file('theBenchmark.p',fact_IdI) ).
fof(fact_trancl__into__rtrancl,axiom,
! [V_r_2,V_b_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_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> 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))) ),
file('theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [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),
file('theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [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),
file('theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_reflcl__trancl,axiom,
! [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),
file('theBenchmark.p',fact_reflcl__trancl) ).
fof(fact_trancl__reflcl,axiom,
! [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),
file('theBenchmark.p',fact_trancl__reflcl) ).
fof(fact_trancl__unfold__right,axiom,
! [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),
file('theBenchmark.p',fact_trancl__unfold__right) ).
fof(fact_trancl__unfold__left,axiom,
! [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)),
file('theBenchmark.p',fact_trancl__unfold__left) ).
fof(fact_rtrancl__r__diff__Id,axiom,
! [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),
file('theBenchmark.p',fact_rtrancl__r__diff__Id) ).
fof(fact_rtrancl__Int__subset,axiom,
! [V_r_2,V_s_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(T_b)),V_s_2))
=> ( 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))
=> 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)) ) ),
file('theBenchmark.p',fact_rtrancl__Int__subset) ).
fof(fact_r__comp__rtrancl__eq,axiom,
! [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),
file('theBenchmark.p',fact_r__comp__rtrancl__eq) ).
fof(fact_rtrancl__idemp__self__comp,axiom,
! [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),
file('theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
fof(fact_rtrancl__unfold,axiom,
! [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)),
file('theBenchmark.p',fact_rtrancl__unfold) ).
fof(fact_rtrancl__Un__subset,axiom,
! [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)))),
file('theBenchmark.p',fact_rtrancl__Un__subset) ).
fof(fact_rtrancl__reflcl,axiom,
! [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),
file('theBenchmark.p',fact_rtrancl__reflcl) ).
fof(fact_rtrancl__Un__rtrancl,axiom,
! [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)),
file('theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
fof(fact_rtrancl__reflcl__absorb,axiom,
! [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),
file('theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [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)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
=> 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))) ),
file('theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_rtrancl__subset,axiom,
! [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)),V_R_2),V_S_2))
=> ( 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)))
=> c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ),
file('theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_rtrancl__mono,axiom,
! [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)),V_r_2),V_s_2))
=> 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))) ),
file('theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_Image__closed__trancl,axiom,
! [V_X_2,V_r_2,T_b] :
( 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))
=> hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ),
file('theBenchmark.p',fact_Image__closed__trancl) ).
fof(fact_in__rtrancl__UnI,axiom,
! [V_S_2,V_R_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) )
=> 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)))) ),
file('theBenchmark.p',fact_in__rtrancl__UnI) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),V_r_2))
=> ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( 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_ca_2)),V_r_2))
=> 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_rtrancl__trans,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_rtrancl__idemp,axiom,
! [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),
file('theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_rtrancl__empty,axiom,
! [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),
file('theBenchmark.p',fact_rtrancl__empty) ).
fof(fact_Range__rtrancl,axiom,
! [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)),
file('theBenchmark.p',fact_Range__rtrancl) ).
fof(fact_Domain__rtrancl,axiom,
! [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)),
file('theBenchmark.p',fact_Domain__rtrancl) ).
fof(fact_refl__rtrancl,axiom,
! [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)),
file('theBenchmark.p',fact_refl__rtrancl) ).
fof(fact_Image__Id,axiom,
! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2,
file('theBenchmark.p',fact_Image__Id) ).
fof(fact_Id__O__R,axiom,
! [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,
file('theBenchmark.p',fact_Id__O__R) ).
fof(fact_R__O__Id,axiom,
! [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,
file('theBenchmark.p',fact_R__O__Id) ).
fof(fact_pair__in__Id__conv,axiom,
! [V_b_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_b_2)),c_Relation_OId(T_b)))
<=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_pair__in__Id__conv) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [V_R_2,V_y_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_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
<=> ( ( 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)))
& V_x_2 != V_y_2 )
| V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
fof(fact_rtrancl__into__trancl2,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),V_r_2))
=> ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_rtranclD,axiom,
! [V_R_2,V_b_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_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
=> ( ( 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)))
& V_a_2 != V_b_2 )
| V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_rtranclD) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( 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_ca_2)),V_r_2))
=> 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [V_ca_2,V_r_2,V_b_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_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [V_z_2,V_r_2,V_y_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_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( 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)))
=> 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))) ) ),
file('theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_Domain__Id,axiom,
! [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)),
file('theBenchmark.p',fact_Domain__Id) ).
fof(fact_Range__Id,axiom,
! [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)),
file('theBenchmark.p',fact_Range__Id) ).
fof(fact_refl__Id,axiom,
! [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)),
file('theBenchmark.p',fact_refl__Id) ).
fof(fact_pair__leq__def,axiom,
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))),
file('theBenchmark.p',fact_pair__leq__def) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [V_y_2,V_R_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
=> ( 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)))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_acc__downwards__aux,axiom,
! [V_r_2,V_a_2,V_b_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_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_acc__downwards,axiom,
! [V_b_2,V_r_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> ( 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)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards) ).
fof(fact_wf__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] :
( 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))
<=> ( ~ 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)))
& c_Wellfounded_Owf(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_wf__insert) ).
fof(fact_acyclic__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] :
( 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))
<=> ( ~ 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)))
& c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__insert) ).
fof(fact_refl__reflcl,axiom,
! [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))),
file('theBenchmark.p',fact_refl__reflcl) ).
fof(fact_Id__def,axiom,
! [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))))),
file('theBenchmark.p',fact_Id__def) ).
fof(fact_irrefl__diff__Id,axiom,
! [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))),
file('theBenchmark.p',fact_irrefl__diff__Id) ).
fof(fact_pred__nat__trancl__eq__le,axiom,
! [V_n_2,V_m_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
fof(fact_trancl__subset__Sigma__aux,axiom,
! [V_A_2,V_r_2,V_b_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_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( 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))))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
fof(fact_irrefl__tranclI,axiom,
! [V_x_2,V_r_2,T_b] :
( 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))
=> ~ 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))) ),
file('theBenchmark.p',fact_irrefl__tranclI) ).
fof(fact_sequence__trans,axiom,
! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
( ! [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)))
=> 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))) ),
file('theBenchmark.p',fact_sequence__trans) ).
fof(fact_rtrancl__converse,axiom,
! [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)),
file('theBenchmark.p',fact_rtrancl__converse) ).
fof(fact_converse__Id,axiom,
! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b),
file('theBenchmark.p',fact_converse__Id) ).
fof(fact_converse__INTER,axiom,
! [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)),
file('theBenchmark.p',fact_converse__INTER) ).
fof(fact_converse__UNION,axiom,
! [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)),
file('theBenchmark.p',fact_converse__UNION) ).
fof(fact_converse__iff,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( 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)))
<=> 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)) ),
file('theBenchmark.p',fact_converse__iff) ).
fof(fact_converseI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( 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))
=> 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))) ),
file('theBenchmark.p',fact_converseI) ).
fof(fact_converseD,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( 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)))
=> 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)) ),
file('theBenchmark.p',fact_converseD) ).
fof(fact_converse__rel__comp,axiom,
! [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)),
file('theBenchmark.p',fact_converse__rel__comp) ).
fof(fact_converse__Un,axiom,
! [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)),
file('theBenchmark.p',fact_converse__Un) ).
fof(fact_Field__converse,axiom,
! [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),
file('theBenchmark.p',fact_Field__converse) ).
fof(fact_converse__inv__image,axiom,
! [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),
file('theBenchmark.p',fact_converse__inv__image) ).
fof(fact_converse__converse,axiom,
! [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,
file('theBenchmark.p',fact_converse__converse) ).
fof(fact_converse__Int,axiom,
! [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)),
file('theBenchmark.p',fact_converse__Int) ).
fof(fact_finite__converse,axiom,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ),
file('theBenchmark.p',fact_finite__converse) ).
fof(fact_converse__Id__on,axiom,
! [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),
file('theBenchmark.p',fact_converse__Id__on) ).
fof(fact_acyclic__converse,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
file('theBenchmark.p',fact_acyclic__converse) ).
fof(fact_refl__on__converse,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_refl__on__converse) ).
fof(fact_trancl__converse,axiom,
! [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)),
file('theBenchmark.p',fact_trancl__converse) ).
fof(fact_wf__converse__trancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
=> c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_wf__converse__trancl) ).
fof(fact_equiv__comp__eq,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,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) = V_r_2 ),
file('theBenchmark.p',fact_equiv__comp__eq) ).
fof(fact_Range__converse,axiom,
! [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),
file('theBenchmark.p',fact_Range__converse) ).
fof(fact_Domain__converse,axiom,
! [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),
file('theBenchmark.p',fact_Domain__converse) ).
fof(fact_Range__def,axiom,
! [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)),
file('theBenchmark.p',fact_Range__def) ).
fof(fact_rtrancl__converseD,axiom,
! [V_r_2,V_y_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_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
=> 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))) ),
file('theBenchmark.p',fact_rtrancl__converseD) ).
fof(fact_rtrancl__converseI,axiom,
! [V_r_2,V_x_2,V_y_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_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> 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)))) ),
file('theBenchmark.p',fact_rtrancl__converseI) ).
fof(fact_trancl__converseD,axiom,
! [V_r_2,V_y_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_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
=> 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)))) ),
file('theBenchmark.p',fact_trancl__converseD) ).
fof(fact_trancl__converseI,axiom,
! [V_r_2,V_y_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_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
=> 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)))) ),
file('theBenchmark.p',fact_trancl__converseI) ).
fof(fact_Image__subset__eq,axiom,
! [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),V_A_2)),V_B_2))
<=> 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))))) ),
file('theBenchmark.p',fact_Image__subset__eq) ).
fof(fact_refl__on__comp__subset,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> 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))) ),
file('theBenchmark.p',fact_refl__on__comp__subset) ).
fof(fact_comp__equivI,axiom,
! [V_A_2,V_r_2,T_b] :
( 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
=> ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
=> c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_comp__equivI) ).
fof(fact_finite__acyclic__wf__converse,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
file('theBenchmark.p',fact_finite__acyclic__wf__converse) ).
fof(fact_converse__def,axiom,
! [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))),
file('theBenchmark.p',fact_converse__def) ).
fof(fact_Image__INT__eq,axiom,
! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,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)) ) ),
file('theBenchmark.p',fact_Image__INT__eq) ).
fof(fact_total__on__diff__Id,axiom,
! [V_r_2,V_A_2,T_b] :
( 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)))
<=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_total__on__diff__Id) ).
fof(fact_single__valued__Id,axiom,
! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_single__valued__Id) ).
fof(fact_single__valued__rel__comp,axiom,
! [V_s_2,T_d,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
=> ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
=> 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)) ) ),
file('theBenchmark.p',fact_single__valued__rel__comp) ).
fof(fact_single__valued__subset,axiom,
! [V_s_2,V_r_2,T_c,T_b] :
( 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))
=> ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
=> c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ),
file('theBenchmark.p',fact_single__valued__subset) ).
fof(fact_single__valued__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_single__valued__Id__on) ).
fof(fact_total__on__empty,axiom,
! [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),
file('theBenchmark.p',fact_total__on__empty) ).
fof(fact_total__on__converse,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_total__on__converse) ).
fof(fact_single__valuedD,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
=> ( 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))
=> ( 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))
=> V_y_2 = V_z_2 ) ) ),
file('theBenchmark.p',fact_single__valuedD) ).
fof(fact_single__valued__def,axiom,
! [V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
<=> ! [B_x,B_y] :
( 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))
=> ! [B_z] :
( 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))
=> B_y = B_z ) ) ),
file('theBenchmark.p',fact_single__valued__def) ).
fof(fact_total__on__def,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( B_x != B_xa
=> ( 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))
| 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)) ) ) ) ) ),
file('theBenchmark.p',fact_total__on__def) ).
fof(fact_single__valued__confluent,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
=> ( 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)))
=> ( 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)))
=> ( 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)))
| 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))) ) ) ) ),
file('theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_Image__Int__eq,axiom,
! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
=> 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)) ),
file('theBenchmark.p',fact_Image__Int__eq) ).
fof(fact_rtrancl__imp__UN__rel__pow,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
=> 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)))) ),
file('theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).
fof(fact_acyclicI,axiom,
! [V_r_2,T_b] :
( ! [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)))
=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
file('theBenchmark.p',fact_acyclicI) ).
fof(fact_single__valued__rel__pow,axiom,
! [V_n_2,V_R_2,T_b] :
( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
=> 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)) ),
file('theBenchmark.p',fact_single__valued__rel__pow) ).
fof(fact_funpow__swap1,axiom,
! [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)),
file('theBenchmark.p',fact_funpow__swap1) ).
fof(fact_funpow__mult,axiom,
! [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),
file('theBenchmark.p',fact_funpow__mult) ).
fof(fact_wf__exp,axiom,
! [V_R_2,V_n_2,T_b] :
( 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))
=> c_Wellfounded_Owf(T_b,V_R_2) ),
file('theBenchmark.p',fact_wf__exp) ).
fof(fact_comp__funpow,axiom,
! [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)),
file('theBenchmark.p',fact_comp__funpow) ).
fof(fact_rel__pow__1,axiom,
! [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,
file('theBenchmark.p',fact_rel__pow__1) ).
fof(fact_rel__pow__commute,axiom,
! [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),
file('theBenchmark.p',fact_rel__pow__commute) ).
fof(fact_rtrancl__power,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
<=> ? [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))) ),
file('theBenchmark.p',fact_rtrancl__power) ).
fof(fact_rel__pow__imp__rtrancl,axiom,
! [V_R_2,V_n_2,V_p_2,T_b] :
( 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)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
file('theBenchmark.p',fact_rel__pow__imp__rtrancl) ).
fof(fact_relpow_Osimps_I2_J,axiom,
! [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),
file('theBenchmark.p',fact_relpow_Osimps_I2_J) ).
fof(fact_rel__pow__add,axiom,
! [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)),
file('theBenchmark.p',fact_rel__pow__add) ).
fof(fact_relpow_Osimps_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_relpow_Osimps_I1_J) ).
fof(fact_rel__pow__0__E,axiom,
! [V_R_2,V_y_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_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)))
=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_rel__pow__0__E) ).
fof(fact_rel__pow__0__I,axiom,
! [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))),
file('theBenchmark.p',fact_rel__pow__0__I) ).
fof(fact_rel__pow__Suc__I2,axiom,
! [V_n_2,V_z_2,V_R_2,V_y_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_y_2)),V_R_2))
=> ( 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)))
=> 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))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__I2) ).
fof(fact_rel__pow__Suc__I,axiom,
! [V_z_2,V_R_2,V_n_2,V_y_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_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
=> ( 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))
=> 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))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__I) ).
fof(fact_funpow_Osimps_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_funpow_Osimps_I2_J) ).
fof(fact_funpow__add,axiom,
! [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)),
file('theBenchmark.p',fact_funpow__add) ).
fof(fact_funpow_Osimps_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_funpow_Osimps_I1_J) ).
fof(fact_trancl__power,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
<=> ? [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)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) ),
file('theBenchmark.p',fact_trancl__power) ).
fof(fact_rtrancl__is__UN__rel__pow,axiom,
! [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)),
file('theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).
fof(fact_funpow__code__def,axiom,
! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b),
file('theBenchmark.p',fact_funpow__code__def) ).
fof(fact_rel__pow__E2,axiom,
! [V_R_2,V_n_2,V_z_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_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_x_2 != V_z_2 )
=> ~ ! [B_y,B_m] :
( V_n_2 = hAPP(c_Nat_OSuc,B_m)
=> ( 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))
=> ~ 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))) ) ) ) ),
file('theBenchmark.p',fact_rel__pow__E2) ).
fof(fact_rel__pow__E,axiom,
! [V_R_2,V_n_2,V_z_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_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_x_2 != V_z_2 )
=> ~ ! [B_y,B_m] :
( V_n_2 = hAPP(c_Nat_OSuc,B_m)
=> ( 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)))
=> ~ 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)) ) ) ) ),
file('theBenchmark.p',fact_rel__pow__E) ).
fof(fact_rtrancl__Un__separatorE,axiom,
! [V_Qa_2,V_Pa_2,V_b_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_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))))
=> ( ! [B_x] :
( 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)))
=> ! [B_y] :
( 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))
=> B_x = B_y ) )
=> 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))) ) ),
file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).
fof(fact_rtrancl__Un__separator__converseE,axiom,
! [V_Qa_2,V_Pa_2,V_b_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_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))))
=> ( ! [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),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
=> ! [B_y] :
( 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))
=> B_y = B_x ) )
=> 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))) ) ),
file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
fof(fact_rel__pow__Suc__D2,axiom,
! [V_R_2,V_n_2,V_z_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_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)))
=> ? [B_y] :
( 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)))
& 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)) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__D2) ).
fof(fact_rel__pow__Suc__E,axiom,
! [V_R_2,V_n_2,V_z_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_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)))
=> ~ ! [B_y] :
( 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)))
=> ~ 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)) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__E) ).
fof(fact_rel__pow__Suc__E2,axiom,
! [V_R_2,V_n_2,V_z_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_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)))
=> ~ ! [B_y] :
( 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))
=> ~ 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))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__E2) ).
fof(fact_tranclD,axiom,
! [V_R_2,V_y_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_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
=> ? [B_z] :
( 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)))
& 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)) ) ),
file('theBenchmark.p',fact_tranclD) ).
fof(fact_tranclD2,axiom,
! [V_R_2,V_y_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_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
=> ? [B_z] :
( 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))
& 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))) ) ),
file('theBenchmark.p',fact_tranclD2) ).
fof(fact_IdE,axiom,
! [V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
=> ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ),
file('theBenchmark.p',fact_IdE) ).
fof(fact_transfer__nat__int__set__cong,axiom,
! [V_P_H_2,V_Pa_2] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> ( hBOOL(hAPP(V_Pa_2,B_x))
<=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
=> 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)) ),
file('theBenchmark.p',fact_transfer__nat__int__set__cong) ).
fof(fact_converseE,axiom,
! [V_r_2,V_yx_2,T_c,T_b] :
( 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)))
=> ~ ! [B_x,B_y] :
( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),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),B_y)),V_r_2)) ) ),
file('theBenchmark.p',fact_converseE) ).
fof(fact_rel__compE,axiom,
! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
( 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)))
=> ~ ! [B_x,B_y,B_z] :
( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
=> ( 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))
=> ~ 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)) ) ) ),
file('theBenchmark.p',fact_rel__compE) ).
fof(fact_Nitpick_Oplus__frac__def,axiom,
! [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))),
file('theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).
fof(fact_internal__split__def,axiom,
! [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),
file('theBenchmark.p',fact_internal__split__def) ).
fof(fact_internal__split__conv,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_internal__split__conv) ).
fof(fact_Nitpick_Otimes__frac__def,axiom,
! [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))),
file('theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).
fof(fact_Nitpick_Oof__frac__def,axiom,
! [V_q,T_a,T_b] :
( ( class_Rings_Oring__1(T_b)
& class_Rings_Oinverse(T_b) )
=> 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))) ),
file('theBenchmark.p',fact_Nitpick_Oof__frac__def) ).
fof(fact_Nitpick_Oinverse__frac__def,axiom,
! [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)),
file('theBenchmark.p',fact_Nitpick_Oinverse__frac__def) ).
fof(fact_Nitpick_Ouminus__frac__def,axiom,
! [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))),
file('theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).
fof(fact_Nitpick_Oless__frac__def,axiom,
! [V_r_2,V_q_2,T_b] :
( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
<=> 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))) ),
file('theBenchmark.p',fact_Nitpick_Oless__frac__def) ).
fof(fact_Nitpick_Oless__eq__frac__def,axiom,
! [V_r_2,V_q_2,T_b] :
( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
<=> 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))) ),
file('theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).
fof(fact_Nitpick_Odenom__def,axiom,
! [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)),
file('theBenchmark.p',fact_Nitpick_Odenom__def) ).
fof(fact_Nitpick_Onum__def,axiom,
! [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)),
file('theBenchmark.p',fact_Nitpick_Onum__def) ).
fof(fact_bool_Osize_I2_J,axiom,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(fact_bool_Osize_I1_J,axiom,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(fact_finite__less__ub,axiom,
! [V_u_2,V_f_2] :
( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
=> 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),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ),
file('theBenchmark.p',fact_finite__less__ub) ).
fof(fact_lenlex__def,axiom,
! [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)))),
file('theBenchmark.p',fact_lenlex__def) ).
fof(fact_lexn__length,axiom,
! [V_n_2,V_r_2,V_ys_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_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 ) ),
file('theBenchmark.p',fact_lexn__length) ).
fof(fact_neq__if__length__neq,axiom,
! [V_ys,V_xs,T_a] :
( 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)
=> V_xs != V_ys ),
file('theBenchmark.p',fact_neq__if__length__neq) ).
fof(fact_lenlex__conv,axiom,
! [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)))))),
file('theBenchmark.p',fact_lenlex__conv) ).
fof(fact_length__sublist,axiom,
! [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)))),
file('theBenchmark.p',fact_length__sublist) ).
fof(fact_lexn_Osimps_I2_J,axiom,
! [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)))))),
file('theBenchmark.p',fact_lexn_Osimps_I2_J) ).
fof(fact_impossible__Cons,axiom,
! [V_x,V_ys,V_xs,T_a] :
( 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)))
=> V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ),
file('theBenchmark.p',fact_impossible__Cons) ).
fof(fact_not__Cons__self,axiom,
! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
file('theBenchmark.p',fact_not__Cons__self) ).
fof(fact_not__Cons__self2,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
file('theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_list_Oinject,axiom,
! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
( 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)
<=> ( V_list_2 = V_list_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_list_Oinject) ).
fof(fact_list_Osize_I4_J,axiom,
! [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))),
file('theBenchmark.p',fact_list_Osize_I4_J) ).
fof(fact_Cons__in__lex,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_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)),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)))
<=> ( ( 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)))
& V_x_2 = V_y_2 )
| ( 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)
& 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)) ) ) ),
file('theBenchmark.p',fact_Cons__in__lex) ).
fof(fact_set__Cons__def,axiom,
! [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)))))),
file('theBenchmark.p',fact_set__Cons__def) ).
fof(fact_pick_Osimps,axiom,
! [V_xs,V_x,T_a,V_i] :
( ( ~ 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)))
=> 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))) )
& ( 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)))
=> 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) ) ),
file('theBenchmark.p',fact_pick_Osimps) ).
fof(fact_select__weight__cons__zero,axiom,
! [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),
file('theBenchmark.p',fact_select__weight__cons__zero) ).
fof(fact_lexord__cons__cons,axiom,
! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_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)),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)))
<=> ( ( 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)))
& V_a_2 = V_b_2 )
| 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)) ) ),
file('theBenchmark.p',fact_lexord__cons__cons) ).
fof(fact_lexord__lex,axiom,
! [V_r_2,V_y_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),V_y_2)),c_List_Olex(T_b,V_r_2)))
<=> ( 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)
& 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))) ) ),
file('theBenchmark.p',fact_lexord__lex) ).
fof(fact_rtrancl__listrel1__ConsI2,axiom,
! [V_ys_2,V_xs_2,V_r_2,V_y_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_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( 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))))
=> 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)))) ) ),
file('theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
fof(fact_list_Osize_I2_J,axiom,
! [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))),
file('theBenchmark.p',fact_list_Osize_I2_J) ).
fof(fact_Cons__acc__listrel1I,axiom,
! [V_xs_2,V_r_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> ( 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))))
=> 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)))) ) ),
file('theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_listrel1__mono,axiom,
! [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)),V_r_2),V_s_2))
=> 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))) ),
file('theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel1__converse,axiom,
! [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)),
file('theBenchmark.p',fact_listrel1__converse) ).
fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
! [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)))),
file('theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [V_x_2,V_r_2,V_ys_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_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> 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)))) ),
file('theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
fof(fact_listrel1I2,axiom,
! [V_x_2,V_r_2,V_ys_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_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> 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))) ),
file('theBenchmark.p',fact_listrel1I2) ).
fof(fact_rtrancl__listrel1__eq__len,axiom,
! [V_r_2,V_y_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),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> 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) ),
file('theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
fof(fact_listrel1__eq__len,axiom,
! [V_r_2,V_ys_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_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> 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) ),
file('theBenchmark.p',fact_listrel1__eq__len) ).
fof(fact_in__listrel1__converse,axiom,
! [V_r_2,V_y_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),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
<=> 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)))) ),
file('theBenchmark.p',fact_in__listrel1__converse) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_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)),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)))
<=> ( ( 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)))
& V_x_2 = V_y_2 )
| ( V_xs_2 = V_ys_2
& 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)) ) ) ),
file('theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_listrel1I1,axiom,
! [V_xs_2,V_r_2,V_y_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_y_2)),V_r_2))
=> 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))) ),
file('theBenchmark.p',fact_listrel1I1) ).
fof(fact_listrel__Cons,axiom,
! [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))))),
file('theBenchmark.p',fact_listrel__Cons) ).
fof(fact_lexord__linear,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( ! [B_a,B_b] :
( 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))
| B_a = B_b
| 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)) )
=> ( 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)))
| V_x_2 = V_y_2
| 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))) ) ),
file('theBenchmark.p',fact_lexord__linear) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [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)))),
file('theBenchmark.p',fact_listrel__rtrancl__refl) ).
fof(fact_listrel__mono,axiom,
! [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)),V_r_2),V_s_2))
=> 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))) ),
file('theBenchmark.p',fact_listrel__mono) ).
fof(fact_listrel__subset__rtrancl__listrel1,axiom,
! [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)))),
file('theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
fof(fact_listrel__eq__len,axiom,
! [V_r_2,V_ys_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_ys_2)),c_List_Olistrel(T_b,V_r_2)))
=> 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) ),
file('theBenchmark.p',fact_listrel__eq__len) ).
fof(fact_listrel__rtrancl__trans,axiom,
! [V_zs_2,V_r_2,V_ys_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_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
=> ( 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))))
=> 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)))) ) ),
file('theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [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)),
file('theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(fact_listrel__reflcl__if__listrel1,axiom,
! [V_r_2,V_ys_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_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> 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)))) ),
file('theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
fof(fact_listrel1__subset__listrel,axiom,
! [V_r_H_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)),V_r_2),V_r_H_2))
=> ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
=> 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))) ) ),
file('theBenchmark.p',fact_listrel1__subset__listrel) ).
fof(fact_rtrancl__listrel1__if__listrel,axiom,
! [V_r_2,V_ys_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_ys_2)),c_List_Olistrel(T_b,V_r_2)))
=> 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)))) ),
file('theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
fof(fact_listrel_OCons,axiom,
! [V_ys_2,V_xs_2,V_r_2,V_y_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_y_2)),V_r_2))
=> ( 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)))
=> 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))) ) ),
file('theBenchmark.p',fact_listrel_OCons) ).
fof(fact_listrelp__listrel__eq,axiom,
! [V_xa_2,V_x_2,V_r_2,T_b] :
( 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)
<=> 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))) ),
file('theBenchmark.p',fact_listrelp__listrel__eq) ).
fof(fact_listrel__Cons1,axiom,
! [V_r_2,V_xs_2,V_ys_2,V_y_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)),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)))
=> ~ ! [B_y,B_ys] :
( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
=> ( 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))
=> ~ 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))) ) ) ),
file('theBenchmark.p',fact_listrel__Cons1) ).
fof(fact_listrelp_OCons,axiom,
! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
=> 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)) ) ),
file('theBenchmark.p',fact_listrelp_OCons) ).
fof(fact_listrelp_Oequations_I2_J,axiom,
! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
( 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))
<=> ( c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
& hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ),
file('theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
fof(fact_listrel__Cons2,axiom,
! [V_r_2,V_ys_2,V_y_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),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
=> ~ ! [B_x,B_xs] :
( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
=> ( 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))
=> ~ 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))) ) ) ),
file('theBenchmark.p',fact_listrel__Cons2) ).
fof(fact_listrel__subset,axiom,
! [V_A_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)),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))))
=> 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))))) ),
file('theBenchmark.p',fact_listrel__subset) ).
fof(fact_lists__UNIV,axiom,
! [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)),
file('theBenchmark.p',fact_lists__UNIV) ).
fof(fact_lists__mono,axiom,
! [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),V_B_2))
=> 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))) ),
file('theBenchmark.p',fact_lists__mono) ).
fof(fact_equiv__listrel,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> 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)) ),
file('theBenchmark.p',fact_equiv__listrel) ).
fof(fact_listrel__refl__on,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> 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)) ),
file('theBenchmark.p',fact_listrel__refl__on) ).
fof(fact_Cons__in__lists__iff,axiom,
! [V_A_2,V_xs_2,V_x_2,T_b] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Cons__in__lists__iff) ).
fof(fact_lists__accD,axiom,
! [V_r_2,V_xs_2,T_b] :
( 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))))
=> 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)))) ),
file('theBenchmark.p',fact_lists__accD) ).
fof(fact_lists__accI,axiom,
! [V_r_2,V_xs_2,T_b] :
( 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))))
=> 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)))) ),
file('theBenchmark.p',fact_lists__accI) ).
fof(fact_listrel__iff__nth,axiom,
! [V_r_2,V_ys_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_ys_2)),c_List_Olistrel(T_b,V_r_2)))
<=> ( ! [B_n] :
( 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)))
=> 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)) )
& 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) ) ),
file('theBenchmark.p',fact_listrel__iff__nth) ).
fof(fact_lexord__irreflexive,axiom,
! [V_y_2,V_r_2,T_b] :
( ! [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))
=> ~ 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))) ),
file('theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_infinite__UNIV__listI,axiom,
! [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)))),
file('theBenchmark.p',fact_infinite__UNIV__listI) ).
fof(fact_list__eq__iff__nth__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> ( ! [B_i] :
( 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)))
=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) )
& 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) ) ),
file('theBenchmark.p',fact_list__eq__iff__nth__eq) ).
fof(fact_nth__Cons__Suc,axiom,
! [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),
file('theBenchmark.p',fact_nth__Cons__Suc) ).
fof(fact_nth__Cons__0,axiom,
! [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,
file('theBenchmark.p',fact_nth__Cons__0) ).
fof(fact_nth_Osimps,axiom,
! [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),
file('theBenchmark.p',fact_nth_Osimps) ).
fof(fact_nth__Cons_H,axiom,
! [V_xs,V_x,T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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))) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) ),
file('theBenchmark.p',fact_nth__Cons_H) ).
fof(fact_nth__Cons__number__of,axiom,
! [V_xs,V_x,T_a,V_v] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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 ) ),
file('theBenchmark.p',fact_nth__Cons__number__of) ).
fof(fact_lexord__take__index__conv,axiom,
! [V_r_2,V_y_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),V_y_2)),c_List_Olexord(T_b,V_r_2)))
<=> ( ? [B_i] :
( 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))
& hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
& 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)))) )
| ( 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
& 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))) ) ) ),
file('theBenchmark.p',fact_lexord__take__index__conv) ).
fof(fact_set__sublist,axiom,
! [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))))),
file('theBenchmark.p',fact_set__sublist) ).
fof(fact_finite__set,axiom,
! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_finite__set) ).
fof(fact_set__subset__Cons,axiom,
! [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)))),
file('theBenchmark.p',fact_set__subset__Cons) ).
fof(fact_take__all,axiom,
! [V_n,V_xs,T_a] :
( 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))
=> hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ),
file('theBenchmark.p',fact_take__all) ).
fof(fact_set__take__subset__set__take,axiom,
! [V_xs_2,T_b,V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> 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)))) ),
file('theBenchmark.p',fact_set__take__subset__set__take) ).
fof(fact_set__take__subset,axiom,
! [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))),
file('theBenchmark.p',fact_set__take__subset) ).
fof(fact_set__sublist__subset,axiom,
! [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))),
file('theBenchmark.p',fact_set__sublist__subset) ).
fof(fact_nth__take,axiom,
! [V_xs,T_a,V_n,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
=> 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) ),
file('theBenchmark.p',fact_nth__take) ).
fof(fact_take__Suc__Cons,axiom,
! [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)),
file('theBenchmark.p',fact_take__Suc__Cons) ).
fof(fact_set__ConsD,axiom,
! [V_xs_2,V_x_2,V_y_2,T_b] :
( 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))))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
| V_y_2 = V_x_2 ) ),
file('theBenchmark.p',fact_set__ConsD) ).
fof(fact_in__set__sublistD,axiom,
! [V_I_2,V_xs_2,V_x_2,T_b] :
( 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))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__sublistD) ).
fof(fact_in__set__takeD,axiom,
! [V_xs_2,V_n_2,V_x_2,T_b] :
( 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))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__takeD) ).
fof(fact_notin__set__sublistI,axiom,
! [V_I_2,V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ 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)))) ),
file('theBenchmark.p',fact_notin__set__sublistI) ).
fof(fact_length__take,axiom,
! [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),
file('theBenchmark.p',fact_length__take) ).
fof(fact_take__take,axiom,
! [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),
file('theBenchmark.p',fact_take__take) ).
fof(fact_List_Oset_Osimps_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
fof(fact_sublist__upt__eq__take,axiom,
! [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),
file('theBenchmark.p',fact_sublist__upt__eq__take) ).
fof(fact_card__length,axiom,
! [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))),
file('theBenchmark.p',fact_card__length) ).
fof(fact_all__set__conv__all__nth,axiom,
! [V_Pa_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
<=> ! [B_i] :
( 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)))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ),
file('theBenchmark.p',fact_all__set__conv__all__nth) ).
fof(fact_list__size__estimation,axiom,
! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
=> 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))) ) ),
file('theBenchmark.p',fact_list__size__estimation) ).
fof(fact_list__size__estimation_H,axiom,
! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
=> 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))) ) ),
file('theBenchmark.p',fact_list__size__estimation_H) ).
fof(fact_in__lists__conv__set,axiom,
! [V_A_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_in__lists__conv__set) ).
fof(fact_length__pos__if__in__set,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> 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))) ),
file('theBenchmark.p',fact_length__pos__if__in__set) ).
fof(fact_in__set__conv__nth,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_i] :
( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2
& 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))) ) ),
file('theBenchmark.p',fact_in__set__conv__nth) ).
fof(fact_nth__mem,axiom,
! [V_xs_2,T_b,V_n_2] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_nth__mem) ).
fof(fact_lists__eq__set,axiom,
! [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)),
file('theBenchmark.p',fact_lists__eq__set) ).
fof(fact_set__conv__nth,axiom,
! [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))))),
file('theBenchmark.p',fact_set__conv__nth) ).
fof(fact_finite__lists__length__eq,axiom,
! [V_n_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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))))) ),
file('theBenchmark.p',fact_finite__lists__length__eq) ).
fof(fact_finite__lists__length__le,axiom,
! [V_n_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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))))) ),
file('theBenchmark.p',fact_finite__lists__length__le) ).
fof(fact_listrel__iff__zip,axiom,
! [V_r_2,V_ys_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_ys_2)),c_List_Olistrel(T_b,V_r_2)))
<=> ( ! [B_x] :
( 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))))
=> 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)) )
& 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) ) ),
file('theBenchmark.p',fact_listrel__iff__zip) ).
fof(fact_set__zip,axiom,
! [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)))))),
file('theBenchmark.p',fact_set__zip) ).
fof(fact_take__zip,axiom,
! [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)),
file('theBenchmark.p',fact_take__zip) ).
fof(fact_length__zip,axiom,
! [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)),
file('theBenchmark.p',fact_length__zip) ).
fof(fact_zip__Cons__Cons,axiom,
! [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)),
file('theBenchmark.p',fact_zip__Cons__Cons) ).
fof(fact_list__eq__iff__zip__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> ( ! [B_x] :
( 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))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) )
& 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) ) ),
file('theBenchmark.p',fact_list__eq__iff__zip__eq) ).
fof(fact_in__set__zipE,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( 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))))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ),
file('theBenchmark.p',fact_in__set__zipE) ).
fof(fact_set__zip__rightD,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( 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))))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ),
file('theBenchmark.p',fact_set__zip__rightD) ).
fof(fact_set__zip__leftD,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( 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))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_set__zip__leftD) ).
fof(fact_zip__same,axiom,
! [V_xs_2,V_b_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_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))))
<=> ( V_a_2 = V_b_2
& hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_zip__same) ).
fof(fact_nth__zip,axiom,
! [V_ys,T_b,V_xs,T_a,V_i] :
( 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)))
=> ( 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)))
=> 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)) ) ),
file('theBenchmark.p',fact_nth__zip) ).
fof(fact_greaterThanLessThan__upto,axiom,
! [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)))),
file('theBenchmark.p',fact_greaterThanLessThan__upto) ).
fof(fact_listsum__setsum__nth,axiom,
! [V_xs_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_listsum__setsum__nth) ).
fof(fact_listsum__eq__0__nat__iff__nat,axiom,
! [V_ns_2] :
( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
=> B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).
fof(fact_atLeastAtMost__upto,axiom,
! [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)),
file('theBenchmark.p',fact_atLeastAtMost__upto) ).
fof(fact_set__upto,axiom,
! [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),
file('theBenchmark.p',fact_set__upto) ).
fof(fact_elem__le__listsum__nat,axiom,
! [V_ns,V_k] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_elem__le__listsum__nat) ).
fof(fact_listsum__simps_I2_J,axiom,
! [V_xs,V_x,T_a] :
( class_Groups_Omonoid__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_listsum__simps_I2_J) ).
fof(fact_atLeastLessThan__upto,axiom,
! [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)))),
file('theBenchmark.p',fact_atLeastLessThan__upto) ).
fof(fact_greaterThanAtMost__upto,axiom,
! [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)),
file('theBenchmark.p',fact_greaterThanAtMost__upto) ).
fof(fact_nat__list__def,axiom,
! [V_l_2] :
( c_List_Onat__list(V_l_2)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ),
file('theBenchmark.p',fact_nat__list__def) ).
fof(fact_list__size__pointwise,axiom,
! [V_g_2,V_f_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> 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))) ),
file('theBenchmark.p',fact_list__size__pointwise) ).
fof(fact_listsum__update__nat,axiom,
! [V_n,V_ns,V_k] :
( 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)))
=> 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)) ),
file('theBenchmark.p',fact_listsum__update__nat) ).
fof(fact_butlast__take,axiom,
! [V_xs,T_a,V_n] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_butlast__take) ).
fof(fact_list__update__beyond,axiom,
! [V_x,V_i,V_xs,T_a] :
( 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))
=> hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ),
file('theBenchmark.p',fact_list__update__beyond) ).
fof(fact_nth__list__update__neq,axiom,
! [V_x,V_xs,T_a,V_j,V_i] :
( V_i != V_j
=> 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) ),
file('theBenchmark.p',fact_nth__list__update__neq) ).
fof(fact_list__update__id,axiom,
! [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,
file('theBenchmark.p',fact_list__update__id) ).
fof(fact_butlast__list__update,axiom,
! [V_x,V_xs,T_a,V_k] :
( ( 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))
=> 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) )
& ( 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))
=> 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) ) ),
file('theBenchmark.p',fact_butlast__list__update) ).
fof(fact_length__list__update,axiom,
! [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),
file('theBenchmark.p',fact_length__list__update) ).
fof(fact_zip__update,axiom,
! [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)),
file('theBenchmark.p',fact_zip__update) ).
fof(fact_update__zip,axiom,
! [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))),
file('theBenchmark.p',fact_update__zip) ).
fof(fact_list__update__overwrite,axiom,
! [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),
file('theBenchmark.p',fact_list__update__overwrite) ).
fof(fact_list__update__swap,axiom,
! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
( V_i != V_i_H
=> 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) ),
file('theBenchmark.p',fact_list__update__swap) ).
fof(fact_list__update_Osimps_I2_J,axiom,
! [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),
file('theBenchmark.p',fact_list__update_Osimps_I2_J) ).
fof(fact_list__update__code_I3_J,axiom,
! [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)),
file('theBenchmark.p',fact_list__update__code_I3_J) ).
fof(fact_list__update__code_I2_J,axiom,
! [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),
file('theBenchmark.p',fact_list__update__code_I2_J) ).
fof(fact_in__set__butlastD,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__butlastD) ).
fof(fact_set__update__subsetI,axiom,
! [V_i_2,V_x_2,V_A_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)),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_set__update__subsetI) ).
fof(fact_set__update__subset__insert,axiom,
! [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)))),
file('theBenchmark.p',fact_set__update__subset__insert) ).
fof(fact_nth__list__update__eq,axiom,
! [V_x,V_xs,T_a,V_i] :
( 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)))
=> 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 ),
file('theBenchmark.p',fact_nth__list__update__eq) ).
fof(fact_list__update__same__conv,axiom,
! [V_x_2,V_xs_2,T_b,V_i_2] :
( 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)))
=> ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
<=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ),
file('theBenchmark.p',fact_list__update__same__conv) ).
fof(fact_nth__list__update,axiom,
! [V_x,V_j,V_xs,T_a,V_i] :
( 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)))
=> ( ( V_i != V_j
=> 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) )
& ( V_i = V_j
=> 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 ) ) ),
file('theBenchmark.p',fact_nth__list__update) ).
fof(fact_take__butlast,axiom,
! [V_xs,T_a,V_n] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_take__butlast) ).
fof(fact_length__butlast,axiom,
! [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)),
file('theBenchmark.p',fact_length__butlast) ).
fof(fact_set__update__memI,axiom,
! [V_x_2,V_xs_2,T_b,V_n_2] :
( 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)))
=> 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)))) ),
file('theBenchmark.p',fact_set__update__memI) ).
fof(fact_butlast__conv__take,axiom,
! [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),
file('theBenchmark.p',fact_butlast__conv__take) ).
fof(fact_listrel1__iff__update,axiom,
! [V_r_2,V_ys_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_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
<=> ? [B_y,B_n] :
( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
& 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)))
& 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)) ) ),
file('theBenchmark.p',fact_listrel1__iff__update) ).
fof(fact_distinct__list__update,axiom,
! [V_i_2,V_a_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( ~ 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))))))
=> hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ),
file('theBenchmark.p',fact_distinct__list__update) ).
fof(fact_distinct__upto,axiom,
! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))),
file('theBenchmark.p',fact_distinct__upto) ).
fof(fact_distinct__take,axiom,
! [V_i,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ),
file('theBenchmark.p',fact_distinct__take) ).
fof(fact_distinct__sublistI,axiom,
! [V_I_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ),
file('theBenchmark.p',fact_distinct__sublistI) ).
fof(fact_distinct__zipI1,axiom,
! [V_ys,T_b,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ),
file('theBenchmark.p',fact_distinct__zipI1) ).
fof(fact_distinct__zipI2,axiom,
! [V_xs,T_b,V_ys,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ),
file('theBenchmark.p',fact_distinct__zipI2) ).
fof(fact_distinct_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
<=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_distinct_Osimps_I2_J) ).
fof(fact_distinct__card,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> 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) ),
file('theBenchmark.p',fact_distinct__card) ).
fof(fact_card__distinct,axiom,
! [V_xs_2,T_b] :
( 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)
=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_card__distinct) ).
fof(fact_nth__eq__iff__index__eq,axiom,
! [V_j_2,V_i_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( 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)))
=> ( 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)))
=> ( 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)
<=> V_i_2 = V_j_2 ) ) ) ),
file('theBenchmark.p',fact_nth__eq__iff__index__eq) ).
fof(fact_distinct__conv__nth,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
<=> ! [B_i] :
( 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)))
=> ! [B_j] :
( 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)))
=> ( B_i != B_j
=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ),
file('theBenchmark.p',fact_distinct__conv__nth) ).
fof(fact_distinct__listsum__conv__Setsum,axiom,
! [V_xs_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> 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)) ) ),
file('theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).
fof(fact_Nitpick_Ocard_H__def,axiom,
! [V_A_2,T_b] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)))) ) ),
file('theBenchmark.p',fact_Nitpick_Ocard_H__def) ).
fof(fact_nth__take__lemma,axiom,
! [V_ys,V_xs,T_a,V_k] :
( 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)))
=> ( 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)))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
=> hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
=> hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ),
file('theBenchmark.p',fact_nth__take__lemma) ).
fof(fact_set__remove1__eq,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> 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)))) ),
file('theBenchmark.p',fact_set__remove1__eq) ).
fof(fact_take__Cons__number__of,axiom,
! [V_xs,V_x,T_a,V_v] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) ) ),
file('theBenchmark.p',fact_take__Cons__number__of) ).
fof(fact_lists_ONil,axiom,
! [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))),
file('theBenchmark.p',fact_lists_ONil) ).
fof(fact_listrel__Nil2,axiom,
! [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_Olistrel(T_b,V_r_2)))
=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_listrel__Nil2) ).
fof(fact_listrel__Nil1,axiom,
! [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_Olistrel(T_b,V_r_2)))
=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_distinct__butlast,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ),
file('theBenchmark.p',fact_distinct__butlast) ).
fof(fact_distinct__remove1,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ),
file('theBenchmark.p',fact_distinct__remove1) ).
fof(fact_distinct_Osimps_I1_J,axiom,
! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))),
file('theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact_butlast_Osimps_I1_J,axiom,
! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_butlast_Osimps_I1_J) ).
fof(fact_butlast_Osimps_I2_J,axiom,
! [V_x,T_a,V_xs] :
( ( V_xs != c_List_Olist_ONil(T_a)
=> 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)) )
& ( V_xs = c_List_Olist_ONil(T_a)
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
file('theBenchmark.p',fact_butlast_Osimps_I2_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [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),
file('theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_list_Osimps_I3_J,axiom,
! [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),
file('theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_remove1_Osimps_I2_J,axiom,
! [V_xs,T_a,V_y,V_x] :
( ( V_x != V_y
=> 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)) )
& ( V_x = V_y
=> c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) ),
file('theBenchmark.p',fact_remove1_Osimps_I2_J) ).
fof(fact_upto__empty,axiom,
! [V_i,V_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
=> c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ),
file('theBenchmark.p',fact_upto__empty) ).
fof(fact_take__Nil,axiom,
! [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),
file('theBenchmark.p',fact_take__Nil) ).
fof(fact_take__eq__Nil,axiom,
! [V_xs_2,V_n_2,T_b] :
( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> ( V_xs_2 = c_List_Olist_ONil(T_b)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_take__eq__Nil) ).
fof(fact_take__0,axiom,
! [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),
file('theBenchmark.p',fact_take__0) ).
fof(fact_sublist__nil,axiom,
! [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),
file('theBenchmark.p',fact_sublist__nil) ).
fof(fact_remove1__commute,axiom,
! [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)),
file('theBenchmark.p',fact_remove1__commute) ).
fof(fact_remove1_Osimps_I1_J,axiom,
! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_remove1_Osimps_I1_J) ).
fof(fact_listrelp_Oequations_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(fact_listrelp_ONil,axiom,
! [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)),
file('theBenchmark.p',fact_listrelp_ONil) ).
fof(fact_zip__Nil,axiom,
! [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)),
file('theBenchmark.p',fact_zip__Nil) ).
fof(fact_zip_Osimps_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_zip_Osimps_I1_J) ).
fof(fact_listsum__simps_I1_J,axiom,
! [T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_listsum__simps_I1_J) ).
fof(fact_length__0__conv,axiom,
! [V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_length__0__conv) ).
fof(fact_list_Osize_I3_J,axiom,
! [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),
file('theBenchmark.p',fact_list_Osize_I3_J) ).
fof(fact_List_Oset_Osimps_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(fact_set__empty2,axiom,
! [V_xs_2,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_set__empty2) ).
fof(fact_set__empty,axiom,
! [V_xs_2,T_b] :
( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_set__empty) ).
fof(fact_list_Osize_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_list_Osize_I1_J) ).
fof(fact_list__update__code_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_list__update__code_I1_J) ).
fof(fact_list__update_Osimps_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_list__update_Osimps_I1_J) ).
fof(fact_list__update__nonempty,axiom,
! [V_x_2,V_k_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_list__update__nonempty) ).
fof(fact_in__set__remove1,axiom,
! [V_xs_2,T_b,V_b_2,V_a_2] :
( V_a_2 != V_b_2
=> ( 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))))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_in__set__remove1) ).
fof(fact_notin__set__remove1,axiom,
! [V_y_2,V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ 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)))) ),
file('theBenchmark.p',fact_notin__set__remove1) ).
fof(fact_remove1__idem,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_remove1__idem) ).
fof(fact_sublist__empty,axiom,
! [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),
file('theBenchmark.p',fact_sublist__empty) ).
fof(fact_set__remove1__subset,axiom,
! [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))),
file('theBenchmark.p',fact_set__remove1__subset) ).
fof(fact_length__greater__0__conv,axiom,
! [V_xs_2,T_b] :
( 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)))
<=> V_xs_2 != c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_length__greater__0__conv) ).
fof(fact_take__1__Cons,axiom,
! [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)),
file('theBenchmark.p',fact_take__1__Cons) ).
fof(fact_not__listrel1__Nil,axiom,
! [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))),
file('theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_not__Nil__listrel1,axiom,
! [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))),
file('theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_listrel_ONil,axiom,
! [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))),
file('theBenchmark.p',fact_listrel_ONil) ).
fof(fact_lexord__Nil__right,axiom,
! [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))),
file('theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_Nil2__notin__lex,axiom,
! [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))),
file('theBenchmark.p',fact_Nil2__notin__lex) ).
fof(fact_Nil__notin__lex,axiom,
! [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))),
file('theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_take__Cons,axiom,
! [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),
file('theBenchmark.p',fact_take__Cons) ).
fof(fact_upto_Osimps,axiom,
! [V_j,V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
=> c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
=> 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)) ) ),
file('theBenchmark.p',fact_upto_Osimps) ).
fof(fact_sublist__singleton,axiom,
! [V_x_2,T_b,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
=> 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)) ) ),
file('theBenchmark.p',fact_sublist__singleton) ).
fof(fact_lists__empty,axiom,
! [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))),
file('theBenchmark.p',fact_lists__empty) ).
fof(fact_take__Cons_H,axiom,
! [V_xs,V_x,T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) ) ),
file('theBenchmark.p',fact_take__Cons_H) ).
fof(fact_upto__rec__number__of,axiom,
! [V_n,V_m] :
( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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))) ) ),
file('theBenchmark.p',fact_upto__rec__number__of) ).
fof(fact_listrel__Nil,axiom,
! [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))),
file('theBenchmark.p',fact_listrel__Nil) ).
fof(fact_set__Cons__sing__Nil,axiom,
! [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),
file('theBenchmark.p',fact_set__Cons__sing__Nil) ).
fof(fact_length__remove1,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> 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) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> 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)) ) ),
file('theBenchmark.p',fact_length__remove1) ).
fof(fact_upto_Opsimps,axiom,
! [V_j_2,V_i_2] :
( 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)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
=> c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_upto_Opsimps) ).
fof(fact_select,axiom,
! [V_s_2,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> 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))) ),
file('theBenchmark.p',fact_select) ).
fof(fact_listset_Osimps_I1_J,axiom,
! [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))),
file('theBenchmark.p',fact_listset_Osimps_I1_J) ).
fof(fact_zip__Cons1,axiom,
! [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),
file('theBenchmark.p',fact_zip__Cons1) ).
fof(fact_list_Osimps_I5_J,axiom,
! [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),
file('theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact_list_Osimps_I4_J,axiom,
! [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,
file('theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_listset_Osimps_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_listset_Osimps_I2_J) ).
fof(fact_zip__Cons,axiom,
! [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),
file('theBenchmark.p',fact_zip__Cons) ).
fof(fact_sorted__list__of__set__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_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))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ),
file('theBenchmark.p',fact_sorted__list__of__set__remove) ).
fof(fact_upto_Opinduct,axiom,
! [V_Pa_2,V_a1_2,V_a0_2] :
( 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)))
=> ( ! [B_i,B_j] :
( 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)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
=> 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)) )
=> hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_upto_Opinduct) ).
fof(fact_sorted__list__of__set__empty,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_sorted__list__of__set__empty) ).
fof(fact_anamorph_Osimps,axiom,
! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = 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))))),hAPP(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)) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(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) ) ),
file('theBenchmark.p',fact_anamorph_Osimps) ).
fof(fact_sublist__Cons,axiom,
! [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)))),
file('theBenchmark.p',fact_sublist__Cons) ).
fof(fact_append__eq__Cons__conv,axiom,
! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
( 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)
<=> ( ? [B_ys_H] :
( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2
& V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
| ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
& V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_append__eq__Cons__conv) ).
fof(fact_Cons__eq__append__conv,axiom,
! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
( 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)
<=> ( ? [B_ys_H] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
& hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 )
| ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2
& V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_Cons__eq__append__conv) ).
fof(fact_append1__eq__conv,axiom,
! [V_y_2,V_ys_2,V_x_2,V_xs_2,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)))
<=> ( V_x_2 = V_y_2
& V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_append1__eq__conv) ).
fof(fact_append__Cons,axiom,
! [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)),
file('theBenchmark.p',fact_append__Cons) ).
fof(fact_Cons__eq__appendI,axiom,
! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
=> ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
=> hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ),
file('theBenchmark.p',fact_Cons__eq__appendI) ).
fof(fact_append__in__lists__conv,axiom,
! [V_A_2,V_ys_2,V_xs_2,T_b] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ),
file('theBenchmark.p',fact_append__in__lists__conv) ).
fof(fact_append__eq__appendI,axiom,
! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
=> ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
=> hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ),
file('theBenchmark.p',fact_append__eq__appendI) ).
fof(fact_append__same__eq,axiom,
! [V_zs_2,V_xs_2,V_ys_2,T_b] :
( 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)
<=> V_ys_2 = V_zs_2 ),
file('theBenchmark.p',fact_append__same__eq) ).
fof(fact_same__append__eq,axiom,
! [V_zs_2,V_ys_2,V_xs_2,T_b] :
( 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)
<=> V_ys_2 = V_zs_2 ),
file('theBenchmark.p',fact_same__append__eq) ).
fof(fact_append__eq__append__conv2,axiom,
! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
( 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)
<=> ? [B_us] :
( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2)
& hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 )
| ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) ) ),
file('theBenchmark.p',fact_append__eq__append__conv2) ).
fof(fact_append__assoc,axiom,
! [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)),
file('theBenchmark.p',fact_append__assoc) ).
fof(fact_listsum__append,axiom,
! [V_ys,V_xs,T_a] :
( class_Groups_Omonoid__add(T_a)
=> 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)) ),
file('theBenchmark.p',fact_listsum__append) ).
fof(fact_length__append,axiom,
! [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)),
file('theBenchmark.p',fact_length__append) ).
fof(fact_zip__append,axiom,
! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
( 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)
=> ( 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)
=> 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)) ) ),
file('theBenchmark.p',fact_zip__append) ).
fof(fact_set__append,axiom,
! [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)),
file('theBenchmark.p',fact_set__append) ).
fof(fact_append__Nil,axiom,
! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys,
file('theBenchmark.p',fact_append__Nil) ).
fof(fact_Nil__is__append__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> ( V_ys_2 = c_List_Olist_ONil(T_b)
& V_xs_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_Nil__is__append__conv) ).
fof(fact_append__Nil2,axiom,
! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs,
file('theBenchmark.p',fact_append__Nil2) ).
fof(fact_self__append__conv,axiom,
! [V_ys_2,T_b,V_xs_2] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> V_ys_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_self__append__conv) ).
fof(fact_self__append__conv2,axiom,
! [V_xs_2,T_b,V_ys_2] :
( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_self__append__conv2) ).
fof(fact_append__is__Nil__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
<=> ( V_ys_2 = c_List_Olist_ONil(T_b)
& V_xs_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_append__self__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
<=> V_ys_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_append__self__conv) ).
fof(fact_append__self__conv2,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_append__self__conv2) ).
fof(fact_eq__Nil__appendI,axiom,
! [T_a,V_ys,V_xs] :
( V_xs = V_ys
=> V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ),
file('theBenchmark.p',fact_eq__Nil__appendI) ).
fof(fact_butlast__append,axiom,
! [V_xs,T_a,V_ys] :
( ( V_ys != c_List_Olist_ONil(T_a)
=> 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)) )
& ( V_ys = c_List_Olist_ONil(T_a)
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) ),
file('theBenchmark.p',fact_butlast__append) ).
fof(fact_nth__append__length,axiom,
! [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,
file('theBenchmark.p',fact_nth__append__length) ).
fof(fact_nth__append__length__plus,axiom,
! [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),
file('theBenchmark.p',fact_nth__append__length__plus) ).
fof(fact_take__append,axiom,
! [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)),
file('theBenchmark.p',fact_take__append) ).
fof(fact_list__update__append1,axiom,
! [V_x,V_ys,V_xs,T_a,V_i] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_list__update__append1) ).
fof(fact_list__update__length,axiom,
! [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)),
file('theBenchmark.p',fact_list__update__length) ).
fof(fact_remove1__append,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> 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)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> 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) ) ),
file('theBenchmark.p',fact_remove1__append) ).
fof(fact_in__set__butlast__appendI,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2))))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) )
=> 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))))) ),
file('theBenchmark.p',fact_in__set__butlast__appendI) ).
fof(fact_butlast__snoc,axiom,
! [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,
file('theBenchmark.p',fact_butlast__snoc) ).
fof(fact_append__listrel1I,axiom,
! [V_vs_2,V_us_2,V_r_2,V_ys_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_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2)))
& V_xs_2 = V_ys_2 )
| ( V_us_2 = V_vs_2
& 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))) ) )
=> 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))) ),
file('theBenchmark.p',fact_append__listrel1I) ).
fof(fact_lexord__append__leftI,axiom,
! [V_x_2,V_r_2,V_v_2,V_u_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_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
=> 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))) ),
file('theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_distinct__append,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
<=> ( 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))
& hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
& hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__append) ).
fof(fact_nth__append,axiom,
! [V_ys,V_xs,T_a,V_n] :
( ( ~ 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)))
=> 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))) )
& ( 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)))
=> 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) ) ),
file('theBenchmark.p',fact_nth__append) ).
fof(fact_list__update__append,axiom,
! [V_x,V_ys,V_xs,T_a,V_n] :
( ( ~ 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)))
=> 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)) )
& ( 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)))
=> 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) ) ),
file('theBenchmark.p',fact_list__update__append) ).
fof(fact_sublist__append,axiom,
! [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)))),
file('theBenchmark.p',fact_sublist__append) ).
fof(fact_listrel1I,axiom,
! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_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_y_2)),V_r_2))
=> ( 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))
=> ( 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))
=> 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))) ) ) ),
file('theBenchmark.p',fact_listrel1I) ).
fof(fact_lexord__append__left__rightI,axiom,
! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_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_b_2)),V_r_2))
=> 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))) ),
file('theBenchmark.p',fact_lexord__append__left__rightI) ).
fof(fact_take__Suc__conv__app__nth,axiom,
! [V_xs,T_a,V_i] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_take__Suc__conv__app__nth) ).
fof(fact_snoc__listrel1__snoc__iff,axiom,
! [V_r_2,V_y_2,V_ys_2,V_x_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)),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)))
<=> ( ( 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))
& V_xs_2 = V_ys_2 )
| ( V_x_2 = V_y_2
& 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))) ) ) ),
file('theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
fof(fact_listrel1E,axiom,
! [V_r_2,V_ys_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_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> ~ ! [B_x,B_y] :
( 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))
=> ! [B_us,B_vs] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
=> V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ),
file('theBenchmark.p',fact_listrel1E) ).
fof(fact_lexord__append__leftD,axiom,
! [V_r_2,V_v_2,V_u_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)),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)))
=> ( ! [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))
=> 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))) ) ),
file('theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_rotate1__def,axiom,
! [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),
file('theBenchmark.p',fact_rotate1__def) ).
fof(fact_upd__conv__take__nth__drop,axiom,
! [V_a,V_xs,T_a,V_i] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_upd__conv__take__nth__drop) ).
fof(fact_append__take__drop__id,axiom,
! [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,
file('theBenchmark.p',fact_append__take__drop__id) ).
fof(fact_drop__1__Cons,axiom,
! [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,
file('theBenchmark.p',fact_drop__1__Cons) ).
fof(fact_drop__Suc__Cons,axiom,
! [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),
file('theBenchmark.p',fact_drop__Suc__Cons) ).
fof(fact_nth__via__drop,axiom,
! [V_ys,V_y,V_xs,V_n,T_a] :
( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
=> hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ),
file('theBenchmark.p',fact_nth__via__drop) ).
fof(fact_distinct__drop,axiom,
! [V_i,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
file('theBenchmark.p',fact_distinct__drop) ).
fof(fact_distinct1__rotate,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct1__rotate) ).
fof(fact_butlast__drop,axiom,
! [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)),
file('theBenchmark.p',fact_butlast__drop) ).
fof(fact_drop__butlast,axiom,
! [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)),
file('theBenchmark.p',fact_drop__butlast) ).
fof(fact_drop__take,axiom,
! [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)),
file('theBenchmark.p',fact_drop__take) ).
fof(fact_take__drop,axiom,
! [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)),
file('theBenchmark.p',fact_take__drop) ).
fof(fact_drop__drop,axiom,
! [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),
file('theBenchmark.p',fact_drop__drop) ).
fof(fact_drop__0,axiom,
! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs,
file('theBenchmark.p',fact_drop__0) ).
fof(fact_drop__zip,axiom,
! [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)),
file('theBenchmark.p',fact_drop__zip) ).
fof(fact_length__rotate1,axiom,
! [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),
file('theBenchmark.p',fact_length__rotate1) ).
fof(fact_length__drop,axiom,
! [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),
file('theBenchmark.p',fact_length__drop) ).
fof(fact_set__rotate1,axiom,
! [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),
file('theBenchmark.p',fact_set__rotate1) ).
fof(fact_in__set__dropD,axiom,
! [V_xs_2,V_n_2,V_x_2,T_b] :
( 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))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__dropD) ).
fof(fact_set__drop__subset,axiom,
! [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))),
file('theBenchmark.p',fact_set__drop__subset) ).
fof(fact_drop__Nil,axiom,
! [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),
file('theBenchmark.p',fact_drop__Nil) ).
fof(fact_rotate1__is__Nil__conv,axiom,
! [V_xs_2,T_b] :
( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(fact_set__drop__subset__set__drop,axiom,
! [V_xs_2,T_b,V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
=> 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)))) ),
file('theBenchmark.p',fact_set__drop__subset__set__drop) ).
fof(fact_drop__eq__Nil,axiom,
! [V_xs_2,V_n_2,T_b] :
( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(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)),V_xs_2)),V_n_2)) ),
file('theBenchmark.p',fact_drop__eq__Nil) ).
fof(fact_drop__all,axiom,
! [V_n,V_xs,T_a] :
( 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))
=> hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',fact_drop__all) ).
fof(fact_drop__append,axiom,
! [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)),
file('theBenchmark.p',fact_drop__append) ).
fof(fact_append__eq__conv__conj,axiom,
! [V_zs_2,V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
<=> ( 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)
& 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) ) ),
file('theBenchmark.p',fact_append__eq__conv__conj) ).
fof(fact_drop__Cons,axiom,
! [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),
file('theBenchmark.p',fact_drop__Cons) ).
fof(fact_drop__Cons_H,axiom,
! [V_xs,V_x,T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) ) ),
file('theBenchmark.p',fact_drop__Cons_H) ).
fof(fact_nth__drop,axiom,
! [V_xs,T_a,V_i,V_n] :
( 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)))
=> 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)) ),
file('theBenchmark.p',fact_nth__drop) ).
fof(fact_append__eq__append__conv__if,axiom,
! [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] :
( 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)
<=> ( ( ~ 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)))
=> ( 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
& 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 ) )
& ( 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)))
=> ( 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)
& 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) ) ) ) ),
file('theBenchmark.p',fact_append__eq__append__conv__if) ).
fof(fact_nth__drop_H,axiom,
! [V_xs,T_a,V_i] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_nth__drop_H) ).
fof(fact_rotate__simps,axiom,
! [V_xs,V_x,T_b,T_a] :
( 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)))
& hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',fact_rotate__simps) ).
fof(fact_drop__Cons__number__of,axiom,
! [V_xs,V_x,T_a,V_v] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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) ) ),
file('theBenchmark.p',fact_drop__Cons__number__of) ).
fof(fact_take__add,axiom,
! [V_xs,T_a,V_j,V_i] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_take__add) ).
fof(fact_rotate1__length01,axiom,
! [V_xs,T_a] :
( 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)))
=> hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ),
file('theBenchmark.p',fact_rotate1__length01) ).
fof(fact_zip__append1,axiom,
! [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))),
file('theBenchmark.p',fact_zip__append1) ).
fof(fact_zip__append2,axiom,
! [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)),
file('theBenchmark.p',fact_zip__append2) ).
fof(fact_id__take__nth__drop,axiom,
! [V_xs,T_a,V_i] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_id__take__nth__drop) ).
fof(fact_take__hd__drop,axiom,
! [V_xs,T_a,V_n] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_take__hd__drop) ).
fof(fact_hd__drop__conv__nth,axiom,
! [V_n,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> ( 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)))
=> 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) ) ),
file('theBenchmark.p',fact_hd__drop__conv__nth) ).
fof(fact_hd_Osimps,axiom,
! [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,
file('theBenchmark.p',fact_hd_Osimps) ).
fof(fact_hd__append2,axiom,
! [V_ys,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> 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) ),
file('theBenchmark.p',fact_hd__append2) ).
fof(fact_hd__append,axiom,
! [V_ys,T_a,V_xs] :
( ( V_xs != c_List_Olist_ONil(T_a)
=> 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) )
& ( V_xs = c_List_Olist_ONil(T_a)
=> 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) ) ),
file('theBenchmark.p',fact_hd__append) ).
fof(fact_hd__in__set,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> 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))) ),
file('theBenchmark.p',fact_hd__in__set) ).
fof(fact_hd__conv__nth,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> 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)) ),
file('theBenchmark.p',fact_hd__conv__nth) ).
fof(fact_rotate1__hd__tl,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> 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))) ),
file('theBenchmark.p',fact_rotate1__hd__tl) ).
fof(fact_hd__rotate__conv__nth,axiom,
! [V_n,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> 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))) ),
file('theBenchmark.p',fact_hd__rotate__conv__nth) ).
fof(fact_drop__tl,axiom,
! [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)),
file('theBenchmark.p',fact_drop__tl) ).
fof(fact_tl__drop,axiom,
! [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)),
file('theBenchmark.p',fact_tl__drop) ).
fof(fact_tl_Osimps_I2_J,axiom,
! [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,
file('theBenchmark.p',fact_tl_Osimps_I2_J) ).
fof(fact_distinct__tl,axiom,
! [V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ),
file('theBenchmark.p',fact_distinct__tl) ).
fof(fact_distinct__rotate,axiom,
! [V_xs_2,V_n_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct__rotate) ).
fof(fact_rotate__rotate,axiom,
! [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),
file('theBenchmark.p',fact_rotate__rotate) ).
fof(fact_rotate0,axiom,
! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_rotate0) ).
fof(fact_rotate__add,axiom,
! [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)),
file('theBenchmark.p',fact_rotate__add) ).
fof(fact_length__rotate,axiom,
! [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),
file('theBenchmark.p',fact_length__rotate) ).
fof(fact_set__rotate,axiom,
! [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),
file('theBenchmark.p',fact_set__rotate) ).
fof(fact_tl_Osimps_I1_J,axiom,
! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_tl_Osimps_I1_J) ).
fof(fact_rotate__is__Nil__conv,axiom,
! [V_xs_2,V_n_2,T_b] :
( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rotate__is__Nil__conv) ).
fof(fact_rotate1__rotate__swap,axiom,
! [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)),
file('theBenchmark.p',fact_rotate1__rotate__swap) ).
fof(fact_rotate__def,axiom,
! [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)),
file('theBenchmark.p',fact_rotate__def) ).
fof(fact_tl__append2,axiom,
! [V_ys,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> 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) ),
file('theBenchmark.p',fact_tl__append2) ).
fof(fact_take__tl,axiom,
! [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)),
file('theBenchmark.p',fact_take__tl) ).
fof(fact_rotate__conv__mod,axiom,
! [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),
file('theBenchmark.p',fact_rotate__conv__mod) ).
fof(fact_drop__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_drop__Suc) ).
fof(fact_rotate__Suc,axiom,
! [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)),
file('theBenchmark.p',fact_rotate__Suc) ).
fof(fact_tl__append,axiom,
! [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),
file('theBenchmark.p',fact_tl__append) ).
fof(fact_rotate__id,axiom,
! [V_xs,T_a,V_n] :
( 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)
=> hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
file('theBenchmark.p',fact_rotate__id) ).
fof(fact_rotate__length01,axiom,
! [V_n,V_xs,T_a] :
( 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)))
=> hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
file('theBenchmark.p',fact_rotate__length01) ).
fof(fact_length__tl,axiom,
! [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)),
file('theBenchmark.p',fact_length__tl) ).
fof(fact_tl__take,axiom,
! [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)),
file('theBenchmark.p',fact_tl__take) ).
fof(fact_take__Suc,axiom,
! [V_n,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> 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))) ),
file('theBenchmark.p',fact_take__Suc) ).
fof(fact_rotate__drop__take,axiom,
! [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)),
file('theBenchmark.p',fact_rotate__drop__take) ).
fof(fact_fold1__set,axiom,
! [V_xs_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( V_xs_2 != c_List_Olist_ONil(T_b)
=> 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)) ) ),
file('theBenchmark.p',fact_fold1__set) ).
fof(fact_sorted__list__of__set__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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)))))) ) ),
file('theBenchmark.p',fact_sorted__list__of__set__insert) ).
fof(fact_foldl__Nil,axiom,
! [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,
file('theBenchmark.p',fact_foldl__Nil) ).
fof(fact_insort__not__Nil,axiom,
! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> 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) ),
file('theBenchmark.p',fact_insort__not__Nil) ).
fof(fact_remove1__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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 ),
file('theBenchmark.p',fact_remove1__insort) ).
fof(fact_start__le__sum,axiom,
! [V_ns_2,V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> 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))) ),
file('theBenchmark.p',fact_start__le__sum) ).
fof(fact_foldl__absorb0,axiom,
! [V_zs_2,V_x_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> 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) ),
file('theBenchmark.p',fact_foldl__absorb0) ).
fof(fact_insort__key__left__comm,axiom,
! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
=> 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)) ) ),
file('theBenchmark.p',fact_insort__key__left__comm) ).
fof(fact_foldl__assoc,axiom,
! [V_zs_2,V_y_2,V_x_2,T_b] :
( class_Groups_Osemigroup__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_foldl__assoc) ).
fof(fact_insort__left__comm,axiom,
! [V_xs_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_insort__left__comm) ).
fof(fact_fun__left__comm__insort,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> 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))) ),
file('theBenchmark.p',fact_fun__left__comm__insort) ).
fof(fact_length__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> 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)) ),
file('theBenchmark.p',fact_length__insort) ).
fof(fact_set__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> 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)) ),
file('theBenchmark.p',fact_set__insort) ).
fof(fact_foldl__Cons,axiom,
! [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),
file('theBenchmark.p',fact_foldl__Cons) ).
fof(fact_insort__key_Osimps_I2_J,axiom,
! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ( ~ 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)))
=> 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)) )
& ( 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)))
=> 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)) ) ) ),
file('theBenchmark.p',fact_insort__key_Osimps_I2_J) ).
fof(fact_insort__key_Osimps_I1_J,axiom,
! [V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> 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)) ),
file('theBenchmark.p',fact_insort__key_Osimps_I1_J) ).
fof(fact_foldl__append,axiom,
! [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),
file('theBenchmark.p',fact_foldl__append) ).
fof(fact_listsum__foldl,axiom,
! [T_b] :
( class_Groups_Omonoid__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_listsum__foldl) ).
fof(fact_sum__eq__0__conv,axiom,
! [V_ns_2,V_m_2] :
( 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)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
=> B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_sum__eq__0__conv) ).
fof(fact_distinct__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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)))
<=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
file('theBenchmark.p',fact_distinct__insort) ).
fof(fact_fun__left__comm__idem_Ofold__set,axiom,
! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> 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) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).
fof(fact_Sup__set__fold,axiom,
! [V_xs_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Sup__set__fold) ).
fof(fact_Inf__set__fold,axiom,
! [V_xs_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Inf__set__fold) ).
fof(fact_Sup__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Sup__fin__set__fold) ).
fof(fact_Inf__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_Inf__fin__set__fold) ).
fof(fact_Min__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_Min__fin__set__fold) ).
fof(fact_Max__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_Max__fin__set__fold) ).
fof(fact_min__max_OInf__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).
fof(fact_min__max_OSup__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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) ),
file('theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).
fof(fact_SUPR__set__fold,axiom,
! [V_f_2,V_xs_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_SUPR__set__fold) ).
fof(fact_INFI__set__fold,axiom,
! [V_f_2,V_xs_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> 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) ),
file('theBenchmark.p',fact_INFI__set__fold) ).
fof(fact_elem__le__sum,axiom,
! [V_ns_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
=> 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))) ),
file('theBenchmark.p',fact_elem__le__sum) ).
fof(fact_insort__insert__insort__key,axiom,
! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(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),hAPP(c_List_Oset(T_c),V_xs_2))))
=> 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) ) ),
file('theBenchmark.p',fact_insort__insert__insort__key) ).
fof(fact_lexord__append__rightI,axiom,
! [V_r_2,V_x_2,T_b,V_y_2] :
( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
=> 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))) ),
file('theBenchmark.p',fact_lexord__append__rightI) ).
fof(fact_distinct__insort__insert,axiom,
! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> 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))) ) ),
file('theBenchmark.p',fact_distinct__insort__insert) ).
fof(fact_insort__insert__triv,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_insort__insert__triv) ).
fof(fact_set__insort__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_set__insort__insert) ).
fof(fact_insort__insert__key__triv,axiom,
! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(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),hAPP(c_List_Oset(T_c),V_xs_2))))
=> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_insort__insert__key__triv) ).
fof(fact_insort__insert__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> 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) ) ),
file('theBenchmark.p',fact_insort__insert__insort) ).
fof(fact_lexord__Nil__left,axiom,
! [V_r_2,V_y_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_y_2)),c_List_Olexord(T_b,V_r_2)))
<=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ),
file('theBenchmark.p',fact_lexord__Nil__left) ).
fof(fact_last__list__update,axiom,
! [V_x,V_k,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> ( ( 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))
=> 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) )
& ( 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))
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) ) ),
file('theBenchmark.p',fact_last__list__update) ).
fof(fact_last__ConsL,axiom,
! [V_x,T_a,V_xs] :
( V_xs = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ),
file('theBenchmark.p',fact_last__ConsL) ).
fof(fact_last__ConsR,axiom,
! [V_x,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_last__ConsR) ).
fof(fact_last_Osimps,axiom,
! [V_x,T_a,V_xs] :
( ( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) )
& ( V_xs = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ),
file('theBenchmark.p',fact_last_Osimps) ).
fof(fact_last__appendL,axiom,
! [V_xs,T_a,V_ys] :
( V_ys = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_last__appendL) ).
fof(fact_last__appendR,axiom,
! [V_xs,T_a,V_ys] :
( V_ys != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ),
file('theBenchmark.p',fact_last__appendR) ).
fof(fact_last__append,axiom,
! [V_xs,T_a,V_ys] :
( ( V_ys != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) )
& ( V_ys = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ),
file('theBenchmark.p',fact_last__append) ).
fof(fact_last__in__set,axiom,
! [T_b,V_as_2] :
( V_as_2 != c_List_Olist_ONil(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ),
file('theBenchmark.p',fact_last__in__set) ).
fof(fact_last__snoc,axiom,
! [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,
file('theBenchmark.p',fact_last__snoc) ).
fof(fact_last__drop,axiom,
! [V_xs,T_a,V_n] :
( 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)))
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_last__drop) ).
fof(fact_snoc__eq__iff__butlast,axiom,
! [V_ys_2,V_x_2,V_xs_2,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))) = V_ys_2
<=> ( c_List_Olast(T_b,V_ys_2) = V_x_2
& c_List_Obutlast(T_b,V_ys_2) = V_xs_2
& V_ys_2 != c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_append__butlast__last__id,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> 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 ),
file('theBenchmark.p',fact_append__butlast__last__id) ).
fof(fact_last__conv__nth,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> 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))) ),
file('theBenchmark.p',fact_last__conv__nth) ).
fof(fact_lists_Osimps,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
<=> ( ? [B_a,B_l] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
& V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
| V_a_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_lists_Osimps) ).
fof(fact_select__weigth__select,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> 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) ),
file('theBenchmark.p',fact_select__weigth__select) ).
fof(fact_inj__mapI,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> 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))) ),
file('theBenchmark.p',fact_inj__mapI) ).
fof(fact_last__map,axiom,
! [V_f_2,T_c,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> 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)) ),
file('theBenchmark.p',fact_last__map) ).
fof(fact_list__size__map,axiom,
! [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),
file('theBenchmark.p',fact_list__size__map) ).
fof(fact_map__map,axiom,
! [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),
file('theBenchmark.p',fact_map__map) ).
fof(fact_List_Omap_Ocompositionality,axiom,
! [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),
file('theBenchmark.p',fact_List_Omap_Ocompositionality) ).
fof(fact_map__comp__map,axiom,
! [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)),
file('theBenchmark.p',fact_map__comp__map) ).
fof(fact_List_Omap_Ocomp,axiom,
! [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)),
file('theBenchmark.p',fact_List_Omap_Ocomp) ).
fof(fact_List_Omap_Oid,axiom,
! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_List_Omap_Oid) ).
fof(fact_List_Omap_Oidentity,axiom,
! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_List_Omap_Oidentity) ).
fof(fact_drop__map,axiom,
! [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)),
file('theBenchmark.p',fact_drop__map) ).
fof(fact_hd__map,axiom,
! [V_f_2,T_c,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> 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)) ),
file('theBenchmark.p',fact_hd__map) ).
fof(fact_map__append,axiom,
! [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)),
file('theBenchmark.p',fact_map__append) ).
fof(fact_map_Osimps_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_map_Osimps_I2_J) ).
fof(fact_set__map,axiom,
! [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)),
file('theBenchmark.p',fact_set__map) ).
fof(fact_map__butlast,axiom,
! [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)),
file('theBenchmark.p',fact_map__butlast) ).
fof(fact_take__map,axiom,
! [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)),
file('theBenchmark.p',fact_take__map) ).
fof(fact_map__ident,axiom,
! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2,
file('theBenchmark.p',fact_map__ident) ).
fof(fact_inj__map__eq__map,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( 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)
<=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_inj__map__eq__map) ).
fof(fact_map__injective,axiom,
! [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),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_map__injective) ).
fof(fact_listsum__subtractf,axiom,
! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_listsum__subtractf) ).
fof(fact_listsum__addf,axiom,
! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_listsum__addf) ).
fof(fact_listsum__const__mult,axiom,
! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> 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_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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))) ),
file('theBenchmark.p',fact_listsum__const__mult) ).
fof(fact_listsum__mult__const,axiom,
! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> 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_ca_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_ca_2) ),
file('theBenchmark.p',fact_listsum__mult__const) ).
fof(fact_listsum__0,axiom,
! [V_xs_2,T_c,T_b] :
( class_Groups_Omonoid__add(T_b)
=> 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) ),
file('theBenchmark.p',fact_listsum__0) ).
fof(fact_map__eq__imp__length__eq,axiom,
! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
( 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)
=> 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) ),
file('theBenchmark.p',fact_map__eq__imp__length__eq) ).
fof(fact_length__map,axiom,
! [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),
file('theBenchmark.p',fact_length__map) ).
fof(fact_map__eq__conv,axiom,
! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
( 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)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ),
file('theBenchmark.p',fact_map__eq__conv) ).
fof(fact_map__update,axiom,
! [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)),
file('theBenchmark.p',fact_map__update) ).
fof(fact_Nil__is__map__conv,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_Nil__is__map__conv) ).
fof(fact_map_Osimps_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(fact_map__is__Nil__conv,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_map__is__Nil__conv) ).
fof(fact_zip__same__conv__map,axiom,
! [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),
file('theBenchmark.p',fact_zip__same__conv__map) ).
fof(fact_zip__map2,axiom,
! [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)),
file('theBenchmark.p',fact_zip__map2) ).
fof(fact_map__zip__map2,axiom,
! [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)),
file('theBenchmark.p',fact_map__zip__map2) ).
fof(fact_map__zip__map,axiom,
! [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)),
file('theBenchmark.p',fact_map__zip__map) ).
fof(fact_zip__map1,axiom,
! [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)),
file('theBenchmark.p',fact_zip__map1) ).
fof(fact_zip__map__map,axiom,
! [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)),
file('theBenchmark.p',fact_zip__map__map) ).
fof(fact_map__tl,axiom,
! [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)),
file('theBenchmark.p',fact_map__tl) ).
fof(fact_rotate__map,axiom,
! [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)),
file('theBenchmark.p',fact_rotate__map) ).
fof(fact_foldl__map,axiom,
! [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),
file('theBenchmark.p',fact_foldl__map) ).
fof(fact_inj__on__map__eq__map,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
( 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)))
=> ( 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)
<=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_inj__on__map__eq__map) ).
fof(fact_map__inj__on,axiom,
! [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),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
=> ( 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)))
=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_map__inj__on) ).
fof(fact_nth__map,axiom,
! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
( 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)))
=> 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)) ),
file('theBenchmark.p',fact_nth__map) ).
fof(fact_map__fun__upd,axiom,
! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),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) ),
file('theBenchmark.p',fact_map__fun__upd) ).
fof(fact_distinct__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
<=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
& hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__map) ).
fof(fact_listsum__abs,axiom,
! [V_xs_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> 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)))) ),
file('theBenchmark.p',fact_listsum__abs) ).
fof(fact_uminus__listsum__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_uminus__listsum__map) ).
fof(fact_inj__on__mapI,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_inj__on__mapI) ).
fof(fact_inj__mapD,axiom,
! [V_f_2,T_c,T_b] :
( 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)))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__mapD) ).
fof(fact_inj__map,axiom,
! [V_f_2,T_c,T_b] :
( 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)))
<=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__map) ).
fof(fact_listsum__distinct__conv__setsum__set,axiom,
! [V_f_2,V_xs_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> 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)) ) ),
file('theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).
fof(fact_listsum__triv,axiom,
! [V_xs_2,V_r_2,T_c,T_b] :
( class_Rings_Osemiring__1(T_b)
=> 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) ),
file('theBenchmark.p',fact_listsum__triv) ).
fof(fact_listsum__map__remove1,axiom,
! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> 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)))) ) ),
file('theBenchmark.p',fact_listsum__map__remove1) ).
fof(fact_Nitpick_Osetsum_H__def,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> 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))))) ) ) ),
file('theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).
fof(fact_pick__same,axiom,
! [V_xs_2,T_b,V_l_2] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_pick__same) ).
fof(fact_Code__Numeral_Oof__nat__code,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).
fof(fact_times__code__numeral__code,axiom,
! [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)),
file('theBenchmark.p',fact_times__code__numeral__code) ).
fof(fact_Code__Numeral_Oof__nat__inject,axiom,
! [V_m_2,V_n_2] :
( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
<=> V_n_2 = V_m_2 ),
file('theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
fof(fact_zero__code__numeral__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_zero__code__numeral__def) ).
fof(fact_one__code__numeral__def,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_one__code__numeral__def) ).
fof(fact_less__code__numeral__code,axiom,
! [V_m_2,V_n_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_less__code__numeral__code) ).
fof(fact_code__numeral_Oof__nat__inject,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).
fof(fact_map__fst__zip,axiom,
! [V_ys_2,T_c,V_xs_2,T_b] :
( 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)
=> 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 ),
file('theBenchmark.p',fact_map__fst__zip) ).
fof(fact_map__snd__zip,axiom,
! [V_ys_2,T_c,V_xs_2,T_b] :
( 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)
=> 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 ),
file('theBenchmark.p',fact_map__snd__zip) ).
fof(fact_number__of__code__numeral__def,axiom,
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),
file('theBenchmark.p',fact_number__of__code__numeral__def) ).
fof(fact_zip__map__fst__snd,axiom,
! [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,
file('theBenchmark.p',fact_zip__map__fst__snd) ).
fof(fact_plus__code__numeral__code,axiom,
! [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)),
file('theBenchmark.p',fact_plus__code__numeral__code) ).
fof(fact_less__eq__code__numeral__code,axiom,
! [V_m_2,V_n_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_less__eq__code__numeral__code) ).
fof(fact_subtract__code__numeral__code,axiom,
! [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)),
file('theBenchmark.p',fact_subtract__code__numeral__code) ).
fof(fact_pick__member,axiom,
! [V_xs_2,T_b,V_i_2] :
( 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))))
=> 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)))) ),
file('theBenchmark.p',fact_pick__member) ).
fof(fact_zip__eq__conv,axiom,
! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
( 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)
=> ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = 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_ys_2
& 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 ) ) ),
file('theBenchmark.p',fact_zip__eq__conv) ).
fof(fact_list__size__conv__listsum,axiom,
! [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)),
file('theBenchmark.p',fact_list__size__conv__listsum) ).
fof(fact_code__numeral__not__eq__zero,axiom,
! [V_i_2] :
( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> 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)) ),
file('theBenchmark.p',fact_code__numeral__not__eq__zero) ).
fof(fact_interv__listsum__conv__setsum__set__int,axiom,
! [V_l_2,V_k_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).
fof(fact_setsum__set__upto__conv__listsum__int,axiom,
! [V_j_2,V_i_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).
fof(fact_select__weight__member,axiom,
! [V_s_2,V_xs_2,T_b] :
( 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))))
=> 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)))) ),
file('theBenchmark.p',fact_select__weight__member) ).
fof(fact_select__weight__def,axiom,
! [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))),
file('theBenchmark.p',fact_select__weight__def) ).
fof(fact_select__def,axiom,
! [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))),
file('theBenchmark.p',fact_select__def) ).
fof(fact_listsum__mono,axiom,
! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
( ( class_Groups_Oordered__ab__semigroup__add(T_c)
& class_Groups_Omonoid__add(T_c) )
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> 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)))) ) ),
file('theBenchmark.p',fact_listsum__mono) ).
fof(fact_times__code__numeral__def,axiom,
! [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))),
file('theBenchmark.p',fact_times__code__numeral__def) ).
fof(fact_nat__of__of__nat,axiom,
! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
file('theBenchmark.p',fact_nat__of__of__nat) ).
fof(fact_of__nat__nat__of,axiom,
! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
file('theBenchmark.p',fact_of__nat__nat__of) ).
fof(fact_nat__of__inverse,axiom,
! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
file('theBenchmark.p',fact_nat__of__inverse) ).
fof(fact_code__numeral_Onat__of__inject,axiom,
! [V_y_2,V_x_2] :
( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
fof(fact_Code__Numeral_Onat__of__inject,axiom,
! [V_l_2,V_k_2] :
( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
<=> V_k_2 = V_l_2 ),
file('theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
fof(fact_type__definition__code__numeral,axiom,
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))),
file('theBenchmark.p',fact_type__definition__code__numeral) ).
fof(fact_less__code__numeral__def,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
<=> 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))) ),
file('theBenchmark.p',fact_less__code__numeral__def) ).
fof(fact_nat__of,axiom,
! [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)))),
file('theBenchmark.p',fact_nat__of) ).
fof(fact_nat__of__number,axiom,
! [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),
file('theBenchmark.p',fact_nat__of__number) ).
fof(fact_int__of__def,axiom,
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),
file('theBenchmark.p',fact_int__of__def) ).
fof(fact_less__eq__code__numeral__def,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
<=> 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))) ),
file('theBenchmark.p',fact_less__eq__code__numeral__def) ).
fof(fact_nat__of__code,axiom,
! [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)),
file('theBenchmark.p',fact_nat__of__code) ).
fof(fact_nat__of__aux__def,axiom,
! [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),
file('theBenchmark.p',fact_nat__of__aux__def) ).
fof(fact_Suc__code__numeral__def,axiom,
! [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))),
file('theBenchmark.p',fact_Suc__code__numeral__def) ).
fof(fact_minus__code__numeral__def,axiom,
! [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))),
file('theBenchmark.p',fact_minus__code__numeral__def) ).
fof(fact_of__nat__inverse,axiom,
! [V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_of__nat__inverse) ).
fof(fact_plus__code__numeral__def,axiom,
! [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))),
file('theBenchmark.p',fact_plus__code__numeral__def) ).
fof(fact_div__code__numeral__def,axiom,
! [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))),
file('theBenchmark.p',fact_div__code__numeral__def) ).
fof(fact_mod__code__numeral__def,axiom,
! [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))),
file('theBenchmark.p',fact_mod__code__numeral__def) ).
fof(fact_code__numeral__decr,axiom,
! [V_k] :
( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> 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))) ),
file('theBenchmark.p',fact_code__numeral__decr) ).
fof(fact_New__DSequence_Opos__not__seq__def,axiom,
! [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))),
file('theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).
fof(fact_partition__set,axiom,
! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
( 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)
=> 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) ),
file('theBenchmark.p',fact_partition__set) ).
fof(fact_partition__P,axiom,
! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
( 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)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ) ),
file('theBenchmark.p',fact_partition__P) ).
fof(fact_partition_Osimps_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_partition_Osimps_I2_J) ).
fof(fact_lists__Int__eq,axiom,
! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,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_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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(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_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(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))),c_List_Olists(T_b,V_B_2))),
file('theBenchmark.p',fact_lists__Int__eq) ).
fof(fact_lists__IntI,axiom,
! [V_B_2,V_A_2,V_l_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
=> hBOOL(hAPP(c_List_Olistsp(T_b,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_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))),V_l_2)) ) ),
file('theBenchmark.p',fact_lists__IntI) ).
fof(fact_listsp_ONil,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
file('theBenchmark.p',fact_listsp_ONil) ).
fof(fact_append__in__listsp__conv,axiom,
! [V_ys_2,V_xs_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2))
& hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_append__in__listsp__conv) ).
fof(fact_listsp_Oequations_I2_J,axiom,
! [V_a2_2,V_a1_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2))
& hBOOL(hAPP(V_A_2,V_a1_2)) ) ),
file('theBenchmark.p',fact_listsp_Oequations_I2_J) ).
fof(fact_listsp__infI,axiom,
! [V_B_2,V_l_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
=> hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ),
file('theBenchmark.p',fact_listsp__infI) ).
fof(fact_listsp__inf__eq,axiom,
! [V_B_2,V_A_2,T_b] : c_List_Olistsp(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_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)),
file('theBenchmark.p',fact_listsp__inf__eq) ).
fof(fact_listsp__conj__eq,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(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_A_2)),V_B_2)),V_x_2))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2))
& hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) ) ),
file('theBenchmark.p',fact_listsp__conj__eq) ).
fof(fact_in__listsp__conv__set,axiom,
! [V_xs_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_A_2,B_x)) ) ),
file('theBenchmark.p',fact_in__listsp__conv__set) ).
fof(fact_listsp_Oequations_I1_J,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
file('theBenchmark.p',fact_listsp_Oequations_I1_J) ).
fof(fact_listsp__mono,axiom,
! [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),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ),
file('theBenchmark.p',fact_listsp__mono) ).
fof(fact_listsp__lists__eq,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(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))
<=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ),
file('theBenchmark.p',fact_listsp__lists__eq) ).
fof(fact_product_Osimps_I2_J,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)),
file('theBenchmark.p',fact_product_Osimps_I2_J) ).
fof(fact_list__all2__def,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),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))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) )
& 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) ) ),
file('theBenchmark.p',fact_list__all2__def) ).
fof(fact_list__all2__map1,axiom,
! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
<=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2) ),
file('theBenchmark.p',fact_list__all2__map1) ).
fof(fact_list__all2__map2,axiom,
! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
<=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ),
file('theBenchmark.p',fact_list__all2__map2) ).
fof(fact_list__all2__Nil2,axiom,
! [V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c))
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_list__all2__Nil2) ).
fof(fact_list__all2__Nil,axiom,
! [V_ys_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2)
<=> V_ys_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_list__all2__Nil) ).
fof(fact_list__all2__lengthD,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
=> 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) ),
file('theBenchmark.p',fact_list__all2__lengthD) ).
fof(fact_list__all2__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ),
file('theBenchmark.p',fact_list__all2__eq) ).
fof(fact_list__all2__takeI,axiom,
! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
=> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ),
file('theBenchmark.p',fact_list__all2__takeI) ).
fof(fact_list__all2__Cons,axiom,
! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
<=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
& hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_list__all2__Cons) ).
fof(fact_list__all2__append,axiom,
! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
( 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)
=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
<=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2)
& c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ),
file('theBenchmark.p',fact_list__all2__append) ).
fof(fact_list__all2__appendI,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2)
=> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ),
file('theBenchmark.p',fact_list__all2__appendI) ).
fof(fact_list__all2__dropI,axiom,
! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2)
=> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ),
file('theBenchmark.p',fact_list__all2__dropI) ).
fof(fact_product_Osimps_I1_J,axiom,
! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
file('theBenchmark.p',fact_product_Osimps_I1_J) ).
fof(fact_list__all2__conv__all__nth,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
<=> ( ! [B_i] :
( 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)))
=> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) )
& 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) ) ),
file('theBenchmark.p',fact_list__all2__conv__all__nth) ).
fof(fact_list__all2__nthD,axiom,
! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ),
file('theBenchmark.p',fact_list__all2__nthD) ).
fof(fact_list__all2__nthD2,axiom,
! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
=> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ),
file('theBenchmark.p',fact_list__all2__nthD2) ).
fof(fact_list__all2__update__cong,axiom,
! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] :
( 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)))
=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
=> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_list__all2__update__cong) ).
fof(fact_list__all2__update__cong2,axiom,
! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
=> ( 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)))
=> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_list__all2__update__cong2) ).
fof(fact_distinct__product,axiom,
! [V_ys,T_b,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ),
file('theBenchmark.p',fact_distinct__product) ).
fof(fact_product__list__set,axiom,
! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))),
file('theBenchmark.p',fact_product__list__set) ).
fof(fact_sublists__powset,axiom,
! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_sublists__powset) ).
fof(fact_length__sublists,axiom,
! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = 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_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),
file('theBenchmark.p',fact_length__sublists) ).
fof(fact_sublists_Osimps_I1_J,axiom,
! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
file('theBenchmark.p',fact_sublists_Osimps_I1_J) ).
fof(fact_sublists_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))),
file('theBenchmark.p',fact_sublists_Osimps_I2_J) ).
fof(fact_distinct__set__sublists,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ),
file('theBenchmark.p',fact_distinct__set__sublists) ).
fof(fact_set__n__lists,axiom,
! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = 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_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))),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))),hAPP(c_List_Oset(T_b),V_xs_2)))),
file('theBenchmark.p',fact_set__n__lists) ).
fof(fact_enum__the__def,axiom,
! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2),
file('theBenchmark.p',fact_enum__the__def) ).
fof(fact_distinct__n__lists,axiom,
! [V_n,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ),
file('theBenchmark.p',fact_distinct__n__lists) ).
fof(fact_n__lists_Osimps_I1_J,axiom,
! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
file('theBenchmark.p',fact_n__lists_Osimps_I1_J) ).
fof(fact_n__lists__Nil,axiom,
! [T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ) ),
file('theBenchmark.p',fact_n__lists__Nil) ).
fof(fact_length__n__lists,axiom,
! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
file('theBenchmark.p',fact_length__n__lists) ).
fof(fact_length__n__lists__elem,axiom,
! [V_xs_2,V_n_2,V_ys_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ),
file('theBenchmark.p',fact_length__n__lists__elem) ).
fof(fact_list__all2I,axiom,
! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_list__all2I) ).
fof(fact_all__nth__imp__all__set,axiom,
! [V_x_2,V_Pa_2,V_xs_2,T_b] :
( ! [B_i] :
( 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)))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
file('theBenchmark.p',fact_all__nth__imp__all__set) ).
fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> 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),c_List_Oremdups(T_b,V_xs_2)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).
fof(fact_map__removeAll__inj__on,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ),
file('theBenchmark.p',fact_map__removeAll__inj__on) ).
fof(fact_distinct__remdups,axiom,
! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
file('theBenchmark.p',fact_distinct__remdups) ).
fof(fact_length__remdups__leq,axiom,
! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
file('theBenchmark.p',fact_length__remdups__leq) ).
fof(fact_remdups__id__iff__distinct,axiom,
! [V_xs_2,T_b] :
( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_remdups__id__iff__distinct) ).
fof(fact_distinct__removeAll,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ),
file('theBenchmark.p',fact_distinct__removeAll) ).
fof(fact_distinct__remdups__id,axiom,
! [V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> c_List_Oremdups(T_a,V_xs) = V_xs ),
file('theBenchmark.p',fact_distinct__remdups__id) ).
fof(fact_length__remdups__eq,axiom,
! [V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
<=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_length__remdups__eq) ).
fof(fact_set__remdups,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__remdups) ).
fof(fact_remdups__remdups,axiom,
! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs),
file('theBenchmark.p',fact_remdups__remdups) ).
fof(fact_removeAll__append,axiom,
! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)),
file('theBenchmark.p',fact_removeAll__append) ).
fof(fact_removeAll_Osimps_I2_J,axiom,
! [V_xs,T_a,V_y,V_x] :
( ( V_x != V_y
=> hAPP(c_List_OremoveAll(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),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) )
& ( V_x = V_y
=> hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ),
file('theBenchmark.p',fact_removeAll_Osimps_I2_J) ).
fof(fact_remdups_Osimps_I1_J,axiom,
! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_remdups_Osimps_I1_J) ).
fof(fact_remdups__eq__nil__right__iff,axiom,
! [V_x_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
<=> V_x_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_remdups__eq__nil__right__iff) ).
fof(fact_removeAll_Osimps_I1_J,axiom,
! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_removeAll_Osimps_I1_J) ).
fof(fact_remdups__eq__nil__iff,axiom,
! [V_x_2,T_b] :
( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
<=> V_x_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_remdups__eq__nil__iff) ).
fof(fact_remdups__map__remdups,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_remdups__map__remdups) ).
fof(fact_remove1__remdups,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ),
file('theBenchmark.p',fact_remove1__remdups) ).
fof(fact_removeAll__id,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_removeAll__id) ).
fof(fact_distinct__remove1__removeAll,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ),
file('theBenchmark.p',fact_distinct__remove1__removeAll) ).
fof(fact_remdups_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremdups(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),c_List_Oremdups(T_b,V_xs_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_remdups_Osimps_I2_J) ).
fof(fact_length__remdups__card__conv,axiom,
! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_length__remdups__card__conv) ).
fof(fact_map__removeAll__inj,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ),
file('theBenchmark.p',fact_map__removeAll__inj) ).
fof(fact_set__removeAll,axiom,
! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(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)))),
file('theBenchmark.p',fact_set__removeAll) ).
fof(fact_length__remdups__concat,axiom,
! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),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_xss_2)),c_List_Oset(T_b))),
file('theBenchmark.p',fact_length__remdups__concat) ).
fof(fact_sorted__list__of__set__sort__remdups,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ),
file('theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).
fof(fact_concat__conv__foldl,axiom,
! [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),
file('theBenchmark.p',fact_concat__conv__foldl) ).
fof(fact_foldl__conv__concat,axiom,
! [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)),
file('theBenchmark.p',fact_foldl__conv__concat) ).
fof(fact_sort__key__simps_I1_J,axiom,
! [V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_sort__key__simps_I1_J) ).
fof(fact_set__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ),
file('theBenchmark.p',fact_set__sort) ).
fof(fact_length__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_length__sort) ).
fof(fact_distinct__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__sort) ).
fof(fact_concat_Osimps_I1_J,axiom,
! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_concat_Osimps_I1_J) ).
fof(fact_concat_Osimps_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_concat_Osimps_I2_J) ).
fof(fact_Nil__eq__concat__conv,axiom,
! [V_xss_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_Nil__eq__concat__conv) ).
fof(fact_concat__eq__Nil__conv,axiom,
! [V_xss_2,T_b] :
( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_concat__eq__Nil__conv) ).
fof(fact_map__concat,axiom,
! [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)),
file('theBenchmark.p',fact_map__concat) ).
fof(fact_length__concat,axiom,
! [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)),
file('theBenchmark.p',fact_length__concat) ).
fof(fact_set__concat,axiom,
! [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)),
file('theBenchmark.p',fact_set__concat) ).
fof(fact_sort__key__simps_I2_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ),
file('theBenchmark.p',fact_sort__key__simps_I2_J) ).
fof(fact_concat__append,axiom,
! [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)),
file('theBenchmark.p',fact_concat__append) ).
fof(fact_sort__foldl__insort,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(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_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_sort__foldl__insort) ).
fof(fact_concat__eq__concat__iff,axiom,
! [V_ys_2,V_xs_2,T_b] :
( ! [B_x] :
( 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))))
=> 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)) )
=> ( 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)
=> ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
<=> V_xs_2 = V_ys_2 ) ) ),
file('theBenchmark.p',fact_concat__eq__concat__iff) ).
fof(fact_concat__injective,axiom,
! [V_ys_2,V_xs_2,T_b] :
( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
=> ( 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)
=> ( ! [B_x] :
( 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))))
=> 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)) )
=> V_xs_2 = V_ys_2 ) ) ),
file('theBenchmark.p',fact_concat__injective) ).
fof(fact_concat__map__singleton,axiom,
! [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),
file('theBenchmark.p',fact_concat__map__singleton) ).
fof(fact_n__lists_Osimps_I2_J,axiom,
! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),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))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))),
file('theBenchmark.p',fact_n__lists_Osimps_I2_J) ).
fof(fact_transpose_Osimps_I3_J,axiom,
! [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))))),
file('theBenchmark.p',fact_transpose_Osimps_I3_J) ).
fof(fact_transpose__aux__filter__head,axiom,
! [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)),
file('theBenchmark.p',fact_transpose__aux__filter__head) ).
fof(fact_filter__concat,axiom,
! [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)),
file('theBenchmark.p',fact_filter__concat) ).
fof(fact_filter__sort,axiom,
! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ),
file('theBenchmark.p',fact_filter__sort) ).
fof(fact_distinct__filter,axiom,
! [V_Pa_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ),
file('theBenchmark.p',fact_distinct__filter) ).
fof(fact_length__filter__le,axiom,
! [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))),
file('theBenchmark.p',fact_length__filter__le) ).
fof(fact_sum__length__filter__compl,axiom,
! [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),
file('theBenchmark.p',fact_sum__length__filter__compl) ).
fof(fact_filter__id__conv,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_filter__id__conv) ).
fof(fact_filter__is__subset,axiom,
! [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))),
file('theBenchmark.p',fact_filter__is__subset) ).
fof(fact_remove1__filter__not,axiom,
! [V_xs_2,T_b,V_x_2,V_Pa_2] :
( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> 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) ),
file('theBenchmark.p',fact_remove1__filter__not) ).
fof(fact_filter__remove1,axiom,
! [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)),
file('theBenchmark.p',fact_filter__remove1) ).
fof(fact_filter__filter,axiom,
! [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),
file('theBenchmark.p',fact_filter__filter) ).
fof(fact_filter__insort__triv,axiom,
! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> 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) ) ),
file('theBenchmark.p',fact_filter__insort__triv) ).
fof(fact_partition__filter1,axiom,
! [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),
file('theBenchmark.p',fact_partition__filter1) ).
fof(fact_partition__filter__conv,axiom,
! [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)),
file('theBenchmark.p',fact_partition__filter__conv) ).
fof(fact_partition__filter2,axiom,
! [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),
file('theBenchmark.p',fact_partition__filter2) ).
fof(fact_filter__map,axiom,
! [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)),
file('theBenchmark.p',fact_filter__map) ).
fof(fact_filter__append,axiom,
! [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)),
file('theBenchmark.p',fact_filter__append) ).
fof(fact_filter_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> 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) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> 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)) ) ),
file('theBenchmark.p',fact_filter_Osimps_I2_J) ).
fof(fact_transpose_Osimps_I1_J,axiom,
! [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)),
file('theBenchmark.p',fact_transpose_Osimps_I1_J) ).
fof(fact_filter_Osimps_I1_J,axiom,
! [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),
file('theBenchmark.p',fact_filter_Osimps_I1_J) ).
fof(fact_filter__empty__conv,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_filter__empty__conv) ).
fof(fact_length__filter__map,axiom,
! [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)),
file('theBenchmark.p',fact_length__filter__map) ).
fof(fact_removeAll__filter__not__eq,axiom,
! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))),
file('theBenchmark.p',fact_removeAll__filter__not__eq) ).
fof(fact_removeAll__filter__not,axiom,
! [V_xs_2,T_b,V_x_2,V_Pa_2] :
( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> hAPP(c_List_OremoveAll(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) ),
file('theBenchmark.p',fact_removeAll__filter__not) ).
fof(fact_remdups__filter,axiom,
! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)),
file('theBenchmark.p',fact_remdups__filter) ).
fof(fact_transpose_Osimps_I2_J,axiom,
! [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),
file('theBenchmark.p',fact_transpose_Osimps_I2_J) ).
fof(fact_nth__transpose,axiom,
! [V_xs_2,T_b,V_i_2] :
( 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))))
=> 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)) ),
file('theBenchmark.p',fact_nth__transpose) ).
fof(fact_transpose__map__map,axiom,
! [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)),
file('theBenchmark.p',fact_transpose__map__map) ).
fof(fact_set__filter,axiom,
! [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)),
file('theBenchmark.p',fact_set__filter) ).
fof(fact_length__filter__less,axiom,
! [V_Pa_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> 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))) ) ),
file('theBenchmark.p',fact_length__filter__less) ).
fof(fact_set__minus__filter__out,axiom,
! [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)),
file('theBenchmark.p',fact_set__minus__filter__out) ).
fof(fact_filter__in__sublist,axiom,
! [V_s_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> 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) ),
file('theBenchmark.p',fact_filter__in__sublist) ).
fof(fact_transpose__empty,axiom,
! [V_xs_2,T_b] :
( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_transpose__empty) ).
fof(fact_length__filter__conv__card,axiom,
! [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))))),
file('theBenchmark.p',fact_length__filter__conv__card) ).
fof(fact_transpose__aux__filter__tail,axiom,
! [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)),
file('theBenchmark.p',fact_transpose__aux__filter__tail) ).
fof(fact_transpose_Opsimps_I3_J,axiom,
! [V_xss_2,V_xs_2,V_x_2,T_b] :
( 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)))
=> 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))))) ),
file('theBenchmark.p',fact_transpose_Opsimps_I3_J) ).
fof(fact_transpose_Opsimps_I2_J,axiom,
! [V_xss_2,T_b] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_transpose_Opsimps_I2_J) ).
fof(fact_sublist__shift__lemma__Suc,axiom,
! [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)))),
file('theBenchmark.p',fact_sublist__shift__lemma__Suc) ).
fof(fact_pick__drop__zero,axiom,
! [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),
file('theBenchmark.p',fact_pick__drop__zero) ).
fof(fact_select__weigth__drop__zero,axiom,
! [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),
file('theBenchmark.p',fact_select__weigth__drop__zero) ).
fof(fact_transpose_Opsimps_I1_J,axiom,
! [T_b] :
( 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))))
=> c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ),
file('theBenchmark.p',fact_transpose_Opsimps_I1_J) ).
fof(fact_transpose__max__length,axiom,
! [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)),
file('theBenchmark.p',fact_transpose__max__length) ).
fof(fact_transpose__aux__max,axiom,
! [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)))),
file('theBenchmark.p',fact_transpose__aux__max) ).
fof(fact_foldr__append,axiom,
! [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)),
file('theBenchmark.p',fact_foldr__append) ).
fof(fact_foldr_Osimps_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_foldr_Osimps_I2_J) ).
fof(fact_foldr_Osimps_I1_J,axiom,
! [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,
file('theBenchmark.p',fact_foldr_Osimps_I1_J) ).
fof(fact_foldr__conv__foldl,axiom,
! [V_a_2,V_xs_2,T_b] :
( class_Groups_Oab__semigroup__add(T_b)
=> 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) ),
file('theBenchmark.p',fact_foldr__conv__foldl) ).
fof(fact_foldr__map,axiom,
! [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),
file('theBenchmark.p',fact_foldr__map) ).
fof(fact_foldl__foldr1__lemma,axiom,
! [V_xs_2,V_a_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_foldl__foldr1__lemma) ).
fof(fact_foldl__foldr1,axiom,
! [V_xs_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> 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)) ),
file('theBenchmark.p',fact_foldl__foldr1) ).
fof(fact_length__transpose,axiom,
! [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)),
file('theBenchmark.p',fact_length__transpose) ).
fof(fact_sublist__def,axiom,
! [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))))),
file('theBenchmark.p',fact_sublist__def) ).
fof(fact_sublist__shift__lemma,axiom,
! [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))))),
file('theBenchmark.p',fact_sublist__shift__lemma) ).
fof(fact_set__upt,axiom,
! [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),
file('theBenchmark.p',fact_set__upt) ).
fof(fact_atLeastLessThan__upt,axiom,
! [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)),
file('theBenchmark.p',fact_atLeastLessThan__upt) ).
fof(fact_upt__0,axiom,
! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
file('theBenchmark.p',fact_upt__0) ).
fof(fact_upt__eq__Nil__conv,axiom,
! [V_j_2,V_i_2] :
( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
| V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_upt__eq__Nil__conv) ).
fof(fact_upt__conv__Nil,axiom,
! [V_i,V_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
=> c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ),
file('theBenchmark.p',fact_upt__conv__Nil) ).
fof(fact_upt__conv__Cons,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> 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)) ),
file('theBenchmark.p',fact_upt__conv__Cons) ).
fof(fact_upt__rec,axiom,
! [V_j,V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> 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)) ) ),
file('theBenchmark.p',fact_upt__rec) ).
fof(fact_upt__add__eq__append,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_upt__add__eq__append) ).
fof(fact_upt__Suc,axiom,
! [V_j,V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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))) ) ),
file('theBenchmark.p',fact_upt__Suc) ).
fof(fact_upt__Suc__append,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> 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))) ),
file('theBenchmark.p',fact_upt__Suc__append) ).
fof(fact_drop__upt,axiom,
! [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),
file('theBenchmark.p',fact_drop__upt) ).
fof(fact_hd__upt,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ),
file('theBenchmark.p',fact_hd__upt) ).
fof(fact_sorted__list__of__set__range,axiom,
! [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),
file('theBenchmark.p',fact_sorted__list__of__set__range) ).
fof(fact_take__upt,axiom,
! [V_n,V_m,V_i] :
( 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))
=> 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)) ),
file('theBenchmark.p',fact_take__upt) ).
fof(fact_distinct__upt,axiom,
! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))),
file('theBenchmark.p',fact_distinct__upt) ).
fof(fact_length__upt,axiom,
! [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),
file('theBenchmark.p',fact_length__upt) ).
fof(fact_upt__rec__number__of,axiom,
! [V_n,V_m] :
( ( ~ 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)))
=> 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) )
& ( 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)))
=> 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))) ) ),
file('theBenchmark.p',fact_upt__rec__number__of) ).
fof(fact_upt__eq__Cons__conv,axiom,
! [V_xs_2,V_x_2,V_j_2,V_i_2] :
( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
<=> ( 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
& V_i_2 = V_x_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) ) ),
file('theBenchmark.p',fact_upt__eq__Cons__conv) ).
fof(fact_last__upt,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> 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)) ),
file('theBenchmark.p',fact_last__upt) ).
fof(fact_map__Suc__upt,axiom,
! [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)),
file('theBenchmark.p',fact_map__Suc__upt) ).
fof(fact_atLeastAtMost__upt,axiom,
! [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))),
file('theBenchmark.p',fact_atLeastAtMost__upt) ).
fof(fact_atLeast__upt,axiom,
! [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)),
file('theBenchmark.p',fact_atLeast__upt) ).
fof(fact_nth__upt,axiom,
! [V_j,V_k,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_k)),V_j))
=> 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) ),
file('theBenchmark.p',fact_nth__upt) ).
fof(fact_greaterThanAtMost__upt,axiom,
! [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))),
file('theBenchmark.p',fact_greaterThanAtMost__upt) ).
fof(fact_greaterThanLessThan__upt,axiom,
! [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)),
file('theBenchmark.p',fact_greaterThanLessThan__upt) ).
fof(fact_atMost__upto,axiom,
! [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))),
file('theBenchmark.p',fact_atMost__upto) ).
fof(fact_map__nth,axiom,
! [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,
file('theBenchmark.p',fact_map__nth) ).
fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
! [V_n_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).
fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
! [V_n_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> 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))) ),
file('theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).
fof(fact_nth__map__upt,axiom,
! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
( 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)))
=> 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)) ),
file('theBenchmark.p',fact_nth__map__upt) ).
fof(fact_transpose__rectangle,axiom,
! [V_n_2,T_b,V_xs_2] :
( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> ( ! [B_i] :
( 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)))
=> 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 )
=> 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)) ) ),
file('theBenchmark.p',fact_transpose__rectangle) ).
fof(fact_insort__key__remove1,axiom,
! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
=> ( 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
=> 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 ) ) ) ),
file('theBenchmark.p',fact_insort__key__remove1) ).
fof(fact_sorted_ONil,axiom,
! [T_a] :
( class_Orderings_Olinorder(T_a)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ),
file('theBenchmark.p',fact_sorted_ONil) ).
fof(fact_sorted__single,axiom,
! [V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ),
file('theBenchmark.p',fact_sorted__single) ).
fof(fact_sorted__upt,axiom,
! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)),
file('theBenchmark.p',fact_sorted__upt) ).
fof(fact_sorted__sort,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_sorted__sort) ).
fof(fact_sorted__insort__insert,axiom,
! [V_x_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> 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)) ) ),
file('theBenchmark.p',fact_sorted__insort__insert) ).
fof(fact_sorted__tl,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ),
file('theBenchmark.p',fact_sorted__tl) ).
fof(fact_sorted__remove1,axiom,
! [V_a,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ),
file('theBenchmark.p',fact_sorted__remove1) ).
fof(fact_sorted__take,axiom,
! [V_n,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ),
file('theBenchmark.p',fact_sorted__take) ).
fof(fact_sorted__upto,axiom,
! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)),
file('theBenchmark.p',fact_sorted__upto) ).
fof(fact_sorted__drop,axiom,
! [V_n,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ),
file('theBenchmark.p',fact_sorted__drop) ).
fof(fact_sorted__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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))
<=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_sorted__insort) ).
fof(fact_sorted__many,axiom,
! [V_zs,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
=> 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))) ) ) ),
file('theBenchmark.p',fact_sorted__many) ).
fof(fact_sorted__many__eq,axiom,
! [V_zs_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_sorted__many__eq) ).
fof(fact_sorted_Oequations_I1_J,axiom,
! [T_a] :
( class_Orderings_Olinorder(T_a)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ),
file('theBenchmark.p',fact_sorted_Oequations_I1_J) ).
fof(fact_sorted__butlast,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_xs != c_List_Olist_ONil(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ),
file('theBenchmark.p',fact_sorted__butlast) ).
fof(fact_sorted__remdups,axiom,
! [V_l,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_l)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ),
file('theBenchmark.p',fact_sorted__remdups) ).
fof(fact_sorted__distinct__set__unique,axiom,
! [V_ys_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
=> ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
=> V_xs_2 = V_ys_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_sorted__distinct__set__unique) ).
fof(fact_sorted__sort__key,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ),
file('theBenchmark.p',fact_sorted__sort__key) ).
fof(fact_sorted__insort__insert__key,axiom,
! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> 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))) ) ),
file('theBenchmark.p',fact_sorted__insort__insert__key) ).
fof(fact_sorted__map__remove1,axiom,
! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> 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))) ) ),
file('theBenchmark.p',fact_sorted__map__remove1) ).
fof(fact_sorted__insort__key,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( 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)))
<=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__insort__key) ).
fof(fact_sorted__map__same,axiom,
! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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))) ),
file('theBenchmark.p',fact_sorted__map__same) ).
fof(fact_sorted__filter,axiom,
! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> 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))) ) ),
file('theBenchmark.p',fact_sorted__filter) ).
fof(fact_sorted__same,axiom,
! [V_xs_2,V_g_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> 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)) ),
file('theBenchmark.p',fact_sorted__same) ).
fof(fact_sorted__Cons,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
& c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
file('theBenchmark.p',fact_sorted__Cons) ).
fof(fact_sorted__append,axiom,
! [V_ys_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
& c_List_Olinorder__class_Osorted(T_b,V_ys_2)
& c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
file('theBenchmark.p',fact_sorted__append) ).
fof(fact_filter__insort,axiom,
! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> 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)) ) ) ),
file('theBenchmark.p',fact_filter__insort) ).
fof(fact_sorted_Oequations_I2_J,axiom,
! [V_a1_2,V_a2_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
<=> ( c_List_Olinorder__class_Osorted(T_b,V_a1_2)
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) ) ) ),
file('theBenchmark.p',fact_sorted_Oequations_I2_J) ).
fof(fact_sorted__list__of__set,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))
& c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
& hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 ) ) ),
file('theBenchmark.p',fact_sorted__list__of__set) ).
fof(fact_insort__remove1,axiom,
! [V_xs_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> 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 ) ) ),
file('theBenchmark.p',fact_insort__remove1) ).
fof(fact_sorted__equals__nth__mono,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
<=> ! [B_j] :
( 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)))
=> ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_sorted__equals__nth__mono) ).
fof(fact_sorted__nth__mono,axiom,
! [V_j,V_i,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> ( 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)))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_sorted__nth__mono) ).
fof(fact_map__sorted__distinct__set__unique,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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)))
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
=> ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
=> V_xs_2 = V_ys_2 ) ) ) ) ) ) ),
file('theBenchmark.p',fact_map__sorted__distinct__set__unique) ).
fof(fact_transpose__column,axiom,
! [V_i_2,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))),V_xs_2)))
=> ( 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)))
=> 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) ) ),
file('theBenchmark.p',fact_transpose__column) ).
fof(fact_nth__nth__transpose__sorted,axiom,
! [V_j_2,V_i_2,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))),V_xs_2)))
=> ( 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))))
=> ( 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))))
=> 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) ) ) ),
file('theBenchmark.p',fact_nth__nth__transpose__sorted) ).
fof(fact_inj__on__rev,axiom,
! [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),
file('theBenchmark.p',fact_inj__on__rev) ).
fof(fact_distinct__rev,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct__rev) ).
fof(fact_rev__append,axiom,
! [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)),
file('theBenchmark.p',fact_rev__append) ).
fof(fact_rev__singleton__conv,axiom,
! [V_x_2,V_xs_2,T_b] :
( 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))
<=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
file('theBenchmark.p',fact_rev__singleton__conv) ).
fof(fact_singleton__rev__conv,axiom,
! [V_xs_2,V_x_2,T_b] :
( 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)
<=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
file('theBenchmark.p',fact_singleton__rev__conv) ).
fof(fact_rev_Osimps_I1_J,axiom,
! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_rev_Osimps_I1_J) ).
fof(fact_Nil__is__rev__conv,axiom,
! [V_xs_2,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_Nil__is__rev__conv) ).
fof(fact_rev__is__Nil__conv,axiom,
! [V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rev__is__Nil__conv) ).
fof(fact_rev__concat,axiom,
! [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))),
file('theBenchmark.p',fact_rev__concat) ).
fof(fact_rev__map,axiom,
! [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)),
file('theBenchmark.p',fact_rev__map) ).
fof(fact_rev__filter,axiom,
! [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)),
file('theBenchmark.p',fact_rev__filter) ).
fof(fact_zip__rev,axiom,
! [V_ys,T_b,V_xs,T_a] :
( 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)
=> 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)) ),
file('theBenchmark.p',fact_zip__rev) ).
fof(fact_set__rev,axiom,
! [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),
file('theBenchmark.p',fact_set__rev) ).
fof(fact_list__all2__rev1,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
<=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ),
file('theBenchmark.p',fact_list__all2__rev1) ).
fof(fact_list__all2__rev,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
<=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ),
file('theBenchmark.p',fact_list__all2__rev) ).
fof(fact_rev__is__rev__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
<=> V_xs_2 = V_ys_2 ),
file('theBenchmark.p',fact_rev__is__rev__conv) ).
fof(fact_rev__swap,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
<=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ),
file('theBenchmark.p',fact_rev__swap) ).
fof(fact_rev__rev__ident,axiom,
! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
file('theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_listsum__rev,axiom,
! [V_xs,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> 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) ),
file('theBenchmark.p',fact_listsum__rev) ).
fof(fact_length__rev,axiom,
! [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),
file('theBenchmark.p',fact_length__rev) ).
fof(fact_foldr__foldl,axiom,
! [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)),
file('theBenchmark.p',fact_foldr__foldl) ).
fof(fact_foldl__foldr,axiom,
! [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),
file('theBenchmark.p',fact_foldl__foldr) ).
fof(fact_rev_Osimps_I2_J,axiom,
! [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))),
file('theBenchmark.p',fact_rev_Osimps_I2_J) ).
fof(fact_rev__eq__Cons__iff,axiom,
! [V_ys_2,V_y_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
<=> 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))) ),
file('theBenchmark.p',fact_rev__eq__Cons__iff) ).
fof(fact_last__rev,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ),
file('theBenchmark.p',fact_last__rev) ).
fof(fact_hd__rev,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_hd__rev) ).
fof(fact_sorted__transpose,axiom,
! [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)))),
file('theBenchmark.p',fact_sorted__transpose) ).
fof(fact_rev__foldl__cons,axiom,
! [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),
file('theBenchmark.p',fact_rev__foldl__cons) ).
fof(fact_rev__take,axiom,
! [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)),
file('theBenchmark.p',fact_rev__take) ).
fof(fact_rev__drop,axiom,
! [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)),
file('theBenchmark.p',fact_rev__drop) ).
fof(fact_rotate__rev,axiom,
! [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)),
file('theBenchmark.p',fact_rotate__rev) ).
fof(fact_rev__nth,axiom,
! [V_xs,T_a,V_n] :
( 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)))
=> 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))) ),
file('theBenchmark.p',fact_rev__nth) ).
fof(fact_rev__update,axiom,
! [V_y,V_xs,T_a,V_k] :
( 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)))
=> 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) ),
file('theBenchmark.p',fact_rev__update) ).
fof(fact_sorted__rev__nth__mono,axiom,
! [V_j,V_i,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> ( 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)))
=> 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))) ) ) ) ),
file('theBenchmark.p',fact_sorted__rev__nth__mono) ).
fof(fact_foldr__max__sorted,axiom,
! [V_y_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
=> ( ( V_xs_2 != c_List_Olist_ONil(T_b)
=> 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) )
& ( V_xs_2 = c_List_Olist_ONil(T_b)
=> c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_foldr__max__sorted) ).
fof(fact_length__transpose__sorted,axiom,
! [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))),V_xs_2)))
=> ( ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
=> 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))) )
& ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_length__transpose__sorted) ).
fof(fact_transpose__column__length,axiom,
! [V_i_2,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))),V_xs_2)))
=> ( 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)))
=> 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)) ) ),
file('theBenchmark.p',fact_transpose__column__length) ).
fof(fact_transpose__transpose,axiom,
! [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))),V_xs_2)))
=> 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) ),
file('theBenchmark.p',fact_transpose__transpose) ).
fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
file('theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).
fof(fact_sorted__takeWhile,axiom,
! [V_Pa_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__takeWhile) ).
fof(fact_length__takeWhile__le,axiom,
! [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)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_length__takeWhile__le) ).
fof(fact_takeWhile__eq__all__conv,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).
fof(fact_set__takeWhileD,axiom,
! [V_xs_2,V_Pa_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_set__takeWhileD) ).
fof(fact_zip__takeWhile__fst,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__takeWhile__fst) ).
fof(fact_zip__takeWhile__snd,axiom,
! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__takeWhile__snd) ).
fof(fact_takeWhile__map,axiom,
! [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)),
file('theBenchmark.p',fact_takeWhile__map) ).
fof(fact_takeWhile_Osimps_I1_J,axiom,
! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(fact_takeWhile_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OtakeWhile(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),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
fof(fact_takeWhile__tail,axiom,
! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ),
file('theBenchmark.p',fact_takeWhile__tail) ).
fof(fact_takeWhile__eq__take,axiom,
! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2),
file('theBenchmark.p',fact_takeWhile__eq__take) ).
fof(fact_distinct__takeWhile,axiom,
! [V_Pa_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ),
file('theBenchmark.p',fact_distinct__takeWhile) ).
fof(fact_return__list__def,axiom,
! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2),
file('theBenchmark.p',fact_return__list__def) ).
fof(fact_takeWhile__append1,axiom,
! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__append1) ).
fof(fact_takeWhile__nth,axiom,
! [V_xs_2,V_Pa_2,T_b,V_j_2] :
( 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)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ),
file('theBenchmark.p',fact_takeWhile__nth) ).
fof(fact_nth__length__takeWhile,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ),
file('theBenchmark.p',fact_nth__length__takeWhile) ).
fof(fact_takeWhile__not__last,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> c_List_OtakeWhile(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),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__not__last) ).
fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
=> hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ),
file('theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).
fof(fact_transfer__nat__int__list__return__embed,axiom,
! [V_l] :
( c_List_Onat__list(V_l)
=> c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ),
file('theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).
fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
file('theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).
fof(fact_embed__list__def,axiom,
! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
file('theBenchmark.p',fact_embed__list__def) ).
fof(fact_takeWhile__neq__rev,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_OtakeWhile(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_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(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_x_2)),V_xs_2))) ) ),
file('theBenchmark.p',fact_takeWhile__neq__rev) ).
fof(fact_dropWhile__neq__rev,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_OdropWhile(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_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(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_x_2)),V_xs_2))) ) ),
file('theBenchmark.p',fact_dropWhile__neq__rev) ).
fof(fact_takeWhile__dropWhile__id,axiom,
! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2,
file('theBenchmark.p',fact_takeWhile__dropWhile__id) ).
fof(fact_hd__dropWhile,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
=> ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ),
file('theBenchmark.p',fact_hd__dropWhile) ).
fof(fact_sorted__dropWhile,axiom,
! [V_Pa_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__dropWhile) ).
fof(fact_length__dropWhile__le,axiom,
! [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)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_length__dropWhile__le) ).
fof(fact_dropWhile__eq__Nil__conv,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).
fof(fact_dropWhile_Osimps_I1_J,axiom,
! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
fof(fact_dropWhile_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OdropWhile(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),V_xs_2) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) ) ),
file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
fof(fact_distinct__dropWhile,axiom,
! [V_Pa_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ),
file('theBenchmark.p',fact_distinct__dropWhile) ).
fof(fact_dropWhile__map,axiom,
! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(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_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_dropWhile__map) ).
fof(fact_dropWhile__append1,axiom,
! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OdropWhile(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),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ),
file('theBenchmark.p',fact_dropWhile__append1) ).
fof(fact_dropWhile__eq__Cons__conv,axiom,
! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
<=> ( ~ hBOOL(hAPP(V_Pa_2,V_y_2))
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
file('theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
fof(fact_dropWhile__eq__drop,axiom,
! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2),
file('theBenchmark.p',fact_dropWhile__eq__drop) ).
fof(fact_dropWhile__nth,axiom,
! [V_xs_2,V_Pa_2,T_b,V_j_2] :
( 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)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ),
file('theBenchmark.p',fact_dropWhile__nth) ).
fof(fact_listsum__map__filter,axiom,
! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] :
( class_Groups_Omonoid__add(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_Pa_2,B_x))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_listsum__map__filter) ).
fof(fact_sorted__nth__monoI,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
=> c_List_Olinorder__class_Osorted(T_a,V_xs) ) ),
file('theBenchmark.p',fact_sorted__nth__monoI) ).
fof(fact_takeWhile__eq__filter,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) )
=> c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ),
file('theBenchmark.p',fact_takeWhile__eq__filter) ).
fof(fact_takeWhile__eq__take__P__nth,axiom,
! [V_Pa_2,V_xs_2,T_b,V_n_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
=> ( 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)))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
=> ( ( 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)))
=> ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
=> c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).
fof(fact_length__takeWhile__less__P__nth,axiom,
! [V_xs_2,T_b,V_Pa_2,V_j_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ),
file('theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
fof(fact_sorted_Osimps,axiom,
! [V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
<=> ( ? [B_xs,B_x] :
( c_List_Olinorder__class_Osorted(T_b,B_xs)
& ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
& V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) )
| V_a_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_sorted_Osimps) ).
fof(fact_List_Oinsert__def,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_List_Oinsert__def) ).
fof(fact_not__in__set__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_not__in__set__insert) ).
fof(fact_insert__remdups,axiom,
! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)),
file('theBenchmark.p',fact_insert__remdups) ).
fof(fact_distinct__insert,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ),
file('theBenchmark.p',fact_distinct__insert) ).
fof(fact_in__set__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_in__set__insert) ).
fof(fact_List_Oset__insert,axiom,
! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(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)),
file('theBenchmark.p',fact_List_Oset__insert) ).
fof(fact_insert__Nil,axiom,
! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
file('theBenchmark.p',fact_insert__Nil) ).
fof(fact_concat__map__maps,axiom,
! [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)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2),
file('theBenchmark.p',fact_concat__map__maps) ).
fof(fact_maps__def,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_maps__def) ).
fof(fact_maps__simps_I2_J,axiom,
! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_maps__simps_I2_J) ).
fof(fact_maps__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(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_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)),
file('theBenchmark.p',fact_maps__simps_I1_J) ).
fof(fact_distinct__concat,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
=> ( ! [B_ys] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
=> ( ! [B_ys] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> ! [B_zs] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> ( B_ys != B_zs
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ),
file('theBenchmark.p',fact_distinct__concat) ).
fof(fact_measures__lesseq,axiom,
! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
( 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)))
=> ( 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_List_Omeasures(T_b,V_fs_2)))
=> 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_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ),
file('theBenchmark.p',fact_measures__lesseq) ).
fof(fact_wf__measures,axiom,
! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)),
file('theBenchmark.p',fact_wf__measures) ).
fof(fact_in__measures_I1_J,axiom,
! [V_y_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_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))),
file('theBenchmark.p',fact_in__measures_I1_J) ).
fof(fact_measures__def,axiom,
! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)),
file('theBenchmark.p',fact_measures__def) ).
fof(fact_measures__less,axiom,
! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
( 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)))
=> 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_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ),
file('theBenchmark.p',fact_measures__less) ).
fof(fact_in__measures_I2_J,axiom,
! [V_fs_2,V_f_2,V_y_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_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
<=> ( ( 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_List_Omeasures(T_b,V_fs_2)))
& hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) )
| 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))) ) ),
file('theBenchmark.p',fact_in__measures_I2_J) ).
fof(fact_foldl__apply,axiom,
! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) )
=> hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ),
file('theBenchmark.p',fact_foldl__apply) ).
fof(fact_order__fun_I2_J,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Orderings_Oorder(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(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_g_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ),
file('theBenchmark.p',fact_order__fun_I2_J) ).
fof(fact_enum__ex__prod__def,axiom,
! [V_Pa_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Enum_Oenum(T_c) )
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),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))))) ) ),
file('theBenchmark.p',fact_enum__ex__prod__def) ).
fof(fact_exists__code,axiom,
! [V_Pa_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ),
file('theBenchmark.p',fact_exists__code) ).
fof(fact_enum__ex,axiom,
! [V_Pa_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
<=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
file('theBenchmark.p',fact_enum__ex) ).
fof(fact_zip__obtain__same__length,axiom,
! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),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))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),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))),V_ys_2))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),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))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),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))),V_ys_2)))) )
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ),
file('theBenchmark.p',fact_zip__obtain__same__length) ).
fof(fact_pos__not__random__dseq__def,axiom,
! [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)),
file('theBenchmark.p',fact_pos__not__random__dseq__def) ).
fof(fact_dropWhile__append2,axiom,
! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
=> c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ),
file('theBenchmark.p',fact_dropWhile__append2) ).
fof(fact_list__all2__all__nthI,axiom,
! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
=> ( ! [B_n] :
( 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_a_2)))
=> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_list__all2__all__nthI) ).
fof(fact_finite__sorted__distinct__unique,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(c_List_Odistinct(T_b),B_y))
& c_List_Olinorder__class_Osorted(T_b,B_y)
& hAPP(c_List_Oset(T_b),B_y) = V_A_2 )
=> B_y = B_x )
& hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
& c_List_Olinorder__class_Osorted(T_b,B_x)
& hAPP(c_List_Oset(T_b),B_x) = V_A_2 ) ) ),
file('theBenchmark.p',fact_finite__sorted__distinct__unique) ).
fof(fact_takeWhile__append2,axiom,
! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
=> c_List_OtakeWhile(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),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)) ),
file('theBenchmark.p',fact_takeWhile__append2) ).
fof(fact_insort__is__Cons,axiom,
! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__is__Cons) ).
fof(fact_filter__eq__Cons__iff,axiom,
! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
<=> ? [B_us,B_vs] :
( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs)
& hBOOL(hAPP(V_Pa_2,V_x_2))
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) )
& V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) ),
file('theBenchmark.p',fact_filter__eq__Cons__iff) ).
fof(fact_Cons__eq__filter__iff,axiom,
! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)
<=> ? [B_us,B_vs] :
( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs)
& hBOOL(hAPP(V_Pa_2,V_x_2))
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) )
& V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) ),
file('theBenchmark.p',fact_Cons__eq__filter__iff) ).
fof(fact_order__fun_I1_J,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Orderings_Oorder(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ),
file('theBenchmark.p',fact_order__fun_I1_J) ).
fof(fact_enum__all,axiom,
! [V_Pa_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
<=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
file('theBenchmark.p',fact_enum__all) ).
fof(fact_all__code,axiom,
! [V_Pa_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ),
file('theBenchmark.p',fact_all__code) ).
fof(fact_enum__all__prod__def,axiom,
! [V_Pa_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Enum_Oenum(T_c) )
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),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))))) ) ),
file('theBenchmark.p',fact_enum__all__prod__def) ).
fof(fact_list__ball__nth,axiom,
! [V_Pa_2,V_xs_2,T_b,V_n_2] :
( 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)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ),
file('theBenchmark.p',fact_list__ball__nth) ).
fof(fact_sorted_OCons,axiom,
! [V_x_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ),
file('theBenchmark.p',fact_sorted_OCons) ).
fof(fact_list__ex__length,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
<=> ? [B_n] :
( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)))
& 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))) ) ),
file('theBenchmark.p',fact_list__ex__length) ).
fof(fact_in__set__conv__decomp,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ),
file('theBenchmark.p',fact_in__set__conv__decomp) ).
fof(fact_list__ex__simps_I2_J,axiom,
! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__ex__simps_I2_J) ).
fof(fact_list__ex__append,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( c_List_Olist__ex(T_b,V_Pa_2,V_ys_2)
| c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ),
file('theBenchmark.p',fact_list__ex__append) ).
fof(fact_list__ex__iff,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__iff) ).
fof(fact_list__ex__rev,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
<=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ),
file('theBenchmark.p',fact_list__ex__rev) ).
fof(fact_list__ex__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_Pa_2,T_b] :
( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
| hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
file('theBenchmark.p',fact_list__ex__simps_I1_J) ).
fof(fact_in__set__conv__decomp__first,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys)))
& ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ),
file('theBenchmark.p',fact_in__set__conv__decomp__first) ).
fof(fact_in__set__conv__decomp__last,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys,B_zs] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs)))
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ),
file('theBenchmark.p',fact_in__set__conv__decomp__last) ).
fof(fact_list__all__length,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
<=> ! [B_n] :
( 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)))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ),
file('theBenchmark.p',fact_list__all__length) ).
fof(fact_measure__function__int,axiom,
c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
file('theBenchmark.p',fact_measure__function__int) ).
fof(fact_list__all__simps_I2_J,axiom,
! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__all__simps_I2_J) ).
fof(fact_list__all__append,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( c_List_Olist__all(T_b,V_Pa_2,V_ys_2)
& c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ),
file('theBenchmark.p',fact_list__all__append) ).
fof(fact_measure__size,axiom,
! [T_b] :
( class_Nat_Osize(T_b)
=> c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ),
file('theBenchmark.p',fact_measure__size) ).
fof(fact_is__measure_Ointros,axiom,
! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2),
file('theBenchmark.p',fact_is__measure_Ointros) ).
fof(fact_is__measure_Oequations,axiom,
! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
file('theBenchmark.p',fact_is__measure_Oequations) ).
fof(fact_is__measure_Osimps,axiom,
! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
file('theBenchmark.p',fact_is__measure_Osimps) ).
fof(fact_list__all__iff,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_list__all__iff) ).
fof(fact_measure__snd,axiom,
! [T_c,V_f_2,T_b] :
( c_FunDef_Ois__measure(T_b,V_f_2)
=> c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ),
file('theBenchmark.p',fact_measure__snd) ).
fof(fact_measure__fst,axiom,
! [T_c,V_f_2,T_b] :
( c_FunDef_Ois__measure(T_b,V_f_2)
=> c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ),
file('theBenchmark.p',fact_measure__fst) ).
fof(fact_list__all__rev,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
<=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ),
file('theBenchmark.p',fact_list__all__rev) ).
fof(fact_list__all__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_Pa_2,T_b] :
( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
& hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
file('theBenchmark.p',fact_list__all__simps_I1_J) ).
fof(fact_Ball__set__list__all,axiom,
! [V_Pa_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
<=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ),
file('theBenchmark.p',fact_Ball__set__list__all) ).
fof(fact_list__all__iff__raw,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_list__all__iff__raw) ).
fof(fact_list__ex1__simps_I2_J,axiom,
! [V_xs_2,V_x_2,V_Pa_2,T_b] :
( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_Olist__all(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) ) ),
file('theBenchmark.p',fact_list__ex1__simps_I2_J) ).
fof(fact_transfer__morphism__int__nat,axiom,
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)),
file('theBenchmark.p',fact_transfer__morphism__int__nat) ).
fof(fact_list__ex1__simps_I1_J,axiom,
! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__ex1__simps_I1_J) ).
fof(fact_bool_Osize_I3_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bool_Osize_I3_J) ).
fof(fact_bool_Osize_I4_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bool_Osize_I4_J) ).
fof(fact_list__ex1__iff,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
<=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(V_Pa_2,B_y))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
=> B_y = B_x )
& hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex1__iff) ).
fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> 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)) )
& ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> 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) ) ),
file('theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).
fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(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)) )
& ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> 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) ) ),
file('theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).
fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
! [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)),
file('theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).
fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
! [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)),
file('theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).
fof(fact_New__DSequence_Oneg__bind__def,axiom,
! [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)),
file('theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).
fof(fact_New__DSequence_Opos__empty__def,axiom,
! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a),
file('theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
fof(fact_pos__empty__def,axiom,
! [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),
file('theBenchmark.p',fact_pos__empty__def) ).
fof(fact_neg__bind__def,axiom,
! [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)),
file('theBenchmark.p',fact_neg__bind__def) ).
fof(fact_New__DSequence_Opos__bind__def,axiom,
! [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) = hAPP(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)),
file('theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).
fof(fact_neg__map__def,axiom,
! [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)),
file('theBenchmark.p',fact_neg__map__def) ).
fof(fact_neg__single__def,axiom,
! [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),
file('theBenchmark.p',fact_neg__single__def) ).
fof(fact_pos__bind__def,axiom,
! [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)),
file('theBenchmark.p',fact_pos__bind__def) ).
fof(fact_New__DSequence_Oneg__single__def,axiom,
! [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),
file('theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
fof(fact_pos__map__def,axiom,
! [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)),
file('theBenchmark.p',fact_pos__map__def) ).
fof(fact_pos__single__def,axiom,
! [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),
file('theBenchmark.p',fact_pos__single__def) ).
fof(fact_length__splice,axiom,
! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(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)),
file('theBenchmark.p',fact_length__splice) ).
fof(fact_splice_Osimps_I3_J,axiom,
! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))),
file('theBenchmark.p',fact_splice_Osimps_I3_J) ).
fof(fact_splice__Nil2,axiom,
! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs,
file('theBenchmark.p',fact_splice__Nil2) ).
fof(fact_splice_Osimps_I1_J,axiom,
! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys,
file('theBenchmark.p',fact_splice_Osimps_I1_J) ).
fof(fact_splice_Osimps_I2_J,axiom,
! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),
file('theBenchmark.p',fact_splice_Osimps_I2_J) ).
fof(fact_New__DSequence_Opos__single__def,axiom,
! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x),
file('theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
fof(fact_acyclicP__converse,axiom,
! [V_r_2,T_b] :
( 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),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
<=> 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))) ),
file('theBenchmark.p',fact_acyclicP__converse) ).
fof(fact_converse__meet,axiom,
! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
file('theBenchmark.p',fact_converse__meet) ).
fof(fact_converse__join,axiom,
! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
file('theBenchmark.p',fact_converse__join) ).
fof(fact_conversep__eq,axiom,
! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal,
file('theBenchmark.p',fact_conversep__eq) ).
fof(fact_conversep__conversep,axiom,
! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2,
file('theBenchmark.p',fact_conversep__conversep) ).
fof(fact_conversep__iff,axiom,
! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversep__iff) ).
fof(fact_conversep_Oequations,axiom,
! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
<=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ),
file('theBenchmark.p',fact_conversep_Oequations) ).
fof(fact_conversep_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversep_Ointros) ).
fof(fact_conversepD,axiom,
! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversepD) ).
fof(fact_conversep__noteq,axiom,
! [V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
<=> V_x_2 != V_y_2 ),
file('theBenchmark.p',fact_conversep__noteq) ).
fof(fact_converse__pred__comp,axiom,
! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)),
file('theBenchmark.p',fact_converse__pred__comp) ).
fof(fact_conversep__converse__eq,axiom,
! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(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),V_y_2))
<=> 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_Relation_Oconverse(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_conversep__converse__eq) ).
fof(fact_,axiom,
! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),
file('theBenchmark.p',fact_) ).
fof(fact_tl__replicate,axiom,
! [V_x,T_a,V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ),
file('theBenchmark.p',fact_tl__replicate) ).
fof(fact_replicate__length__filter,axiom,
! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2),
file('theBenchmark.p',fact_replicate__length__filter) ).
fof(fact_length__replicate,axiom,
! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n,
file('theBenchmark.p',fact_length__replicate) ).
fof(fact_map__replicate__const,axiom,
! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2),
file('theBenchmark.p',fact_map__replicate__const) ).
fof(fact_replicate__app__Cons__same,axiom,
! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),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_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)),
file('theBenchmark.p',fact_replicate__app__Cons__same) ).
fof(fact_replicate__Suc,axiom,
! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)),
file('theBenchmark.p',fact_replicate__Suc) ).
fof(fact_rev__replicate,axiom,
! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x),
file('theBenchmark.p',fact_rev__replicate) ).
fof(fact_take__replicate,axiom,
! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x),
file('theBenchmark.p',fact_take__replicate) ).
fof(fact_hd__replicate,axiom,
! [V_x,T_a,V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
file('theBenchmark.p',fact_hd__replicate) ).
fof(fact_drop__replicate,axiom,
! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x),
file('theBenchmark.p',fact_drop__replicate) ).
fof(fact_last__replicate,axiom,
! [V_x,T_a,V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
file('theBenchmark.p',fact_last__replicate) ).
fof(fact_zip__replicate,axiom,
! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
file('theBenchmark.p',fact_zip__replicate) ).
fof(fact_Ball__set__replicate,axiom,
! [V_Pa_2,V_a_2,V_n_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(V_Pa_2,V_a_2)) ) ),
file('theBenchmark.p',fact_Ball__set__replicate) ).
fof(fact_Bex__set__replicate,axiom,
! [V_Pa_2,V_a_2,V_n_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) )
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(V_Pa_2,V_a_2)) ) ),
file('theBenchmark.p',fact_Bex__set__replicate) ).
fof(fact_replicate__eq__replicate,axiom,
! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
<=> ( ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_x_2 = V_y_2 )
& V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_replicate__eq__replicate) ).
fof(fact_nth__replicate,axiom,
! [V_x,T_a,V_n,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
=> hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ),
file('theBenchmark.p',fact_nth__replicate) ).
fof(fact_append__replicate__commute,axiom,
! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)),
file('theBenchmark.p',fact_append__replicate__commute) ).
fof(fact_replicate__add,axiom,
! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)),
file('theBenchmark.p',fact_replicate__add) ).
fof(fact_filter__replicate,axiom,
! [V_n_2,T_b,V_x_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) ) ),
file('theBenchmark.p',fact_filter__replicate) ).
fof(fact_concat__replicate__trivial,axiom,
! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_concat__replicate__trivial) ).
fof(fact_replicate__empty,axiom,
! [V_x_2,V_n_2,T_b] :
( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_replicate__empty) ).
fof(fact_empty__replicate,axiom,
! [V_x_2,V_n_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_empty__replicate) ).
fof(fact_replicate__0,axiom,
! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_replicate__0) ).
fof(fact_map__replicate,axiom,
! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_map__replicate) ).
fof(fact_in__set__replicate,axiom,
! [V_y_2,V_n_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2))))
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_in__set__replicate) ).
fof(fact_replicate__append__same,axiom,
! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)),
file('theBenchmark.p',fact_replicate__append__same) ).
fof(fact_map__replicate__trivial,axiom,
! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2),
file('theBenchmark.p',fact_map__replicate__trivial) ).
fof(fact_set__replicate,axiom,
! [V_x_2,T_b,V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,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))) ),
file('theBenchmark.p',fact_set__replicate) ).
fof(fact_set__replicate__conv__if,axiom,
! [V_x_2,T_b,V_n_2] :
( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,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))) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_set__replicate__conv__if) ).
fof(fact_set__replicate__Suc,axiom,
! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),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))),
file('theBenchmark.p',fact_set__replicate__Suc) ).
fof(fact_small__lazy__list_Osimps,axiom,
! [V_d_2,T_b] :
( class_Lazy__Sequence_Osmall__lazy(T_b)
=> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ),
file('theBenchmark.p',fact_small__lazy__list_Osimps) ).
fof(fact_eq__comp__r,axiom,
! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2,
file('theBenchmark.p',fact_eq__comp__r) ).
fof(fact_small__lazy__prod__def,axiom,
! [V_d,T_b,T_a] :
( ( class_Lazy__Sequence_Osmall__lazy(T_b)
& class_Lazy__Sequence_Osmall__lazy(T_a) )
=> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ),
file('theBenchmark.p',fact_small__lazy__prod__def) ).
fof(fact_New__DSequence_Opos__union__def,axiom,
! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)),
file('theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
fof(fact_lazy__sequence_Osize_I4_J,axiom,
! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_lazy__sequence_Osize_I4_J) ).
fof(fact__01,axiom,
! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)),
file('theBenchmark.p',fact__01) ).
fof(fact_lazy__sequence_Oinject,axiom,
! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
<=> ( V_lazy__sequence_2 = V_lazy__sequence_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_lazy__sequence_Oinject) ).
fof(fact_pos__union__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)),
file('theBenchmark.p',fact_pos__union__def) ).
fof(fact_lazy__sequence_Osize_I2_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_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(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_lazy__sequence_Osize_I2_J) ).
fof(fact_small__lazy_H_Osimps,axiom,
! [V_i,V_d] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
=> c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
=> c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_small__lazy_H_Osimps) ).
fof(fact_small__lazy_H_Opsimps,axiom,
! [V_i_2,V_d_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
=> c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
=> c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_small__lazy_H_Opsimps) ).
fof(fact_small__lazy__int__def,axiom,
! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)),
file('theBenchmark.p',fact_small__lazy__int__def) ).
fof(fact_small__lazy_H_Opinduct,axiom,
! [V_Pa_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
=> ( ! [B_d,B_i] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
=> hBOOL(hAPP(hAPP(V_Pa_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
=> hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_small__lazy_H_Opinduct) ).
fof(fact_size__code,axiom,
! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
file('theBenchmark.p',fact_size__code) ).
fof(fact_lazy__sequence__size__code,axiom,
! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
file('theBenchmark.p',fact_lazy__sequence__size__code) ).
fof(fact_seq__case,axiom,
! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)),
file('theBenchmark.p',fact_seq__case) ).
fof(fact_yieldn__def,axiom,
! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)),
file('theBenchmark.p',fact_yieldn__def) ).
fof(fact_lazy__sequence_Osimps_I5_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),
file('theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).
fof(fact_refl__on__INTER,axiom,
! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
=> c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ),
file('theBenchmark.p',fact_refl__on__INTER) ).
fof(fact_List_Omember__def,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_List_Omember__def) ).
fof(fact_member__rec_I2_J,axiom,
! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)),
file('theBenchmark.p',fact_member__rec_I2_J) ).
fof(fact_member__set,axiom,
! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b),
file('theBenchmark.p',fact_member__set) ).
fof(fact_member__rec_I1_J,axiom,
! [V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2))
<=> ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2))
| V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_member__rec_I1_J) ).
fof(fact_in__set__member,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ),
file('theBenchmark.p',fact_in__set__member) ).
fof(fact_list__ex1__iff__raw,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
<=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(V_Pa_2,B_y))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
=> B_y = B_x )
& hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex1__iff__raw) ).
fof(fact_setsum__UNION__zero,axiom,
! [V_f_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
=> ( ! [B_T1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
=> ! [B_T2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
=> ( B_T1 != B_T2
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__UNION__zero) ).
fof(fact_THE__default__def,axiom,
! [V_d_2,T_b,V_Pa_2] :
( ( ~ ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(V_Pa_2,B_y))
=> B_y = B_x )
& hBOOL(hAPP(V_Pa_2,B_x)) )
=> c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 )
& ( ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(V_Pa_2,B_y))
=> B_y = B_x )
& hBOOL(hAPP(V_Pa_2,B_x)) )
=> c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ) ),
file('theBenchmark.p',fact_THE__default__def) ).
fof(fact_INF2__I,axiom,
! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) )
=> 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_ca_2)) ),
file('theBenchmark.p',fact_INF2__I) ).
fof(fact_SUP2__E,axiom,
! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( 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_ca_2))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_SUP2__E) ).
fof(fact_finite__maxlen,axiom,
! [V_M_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
=> ? [B_n] :
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ),
file('theBenchmark.p',fact_finite__maxlen) ).
fof(fact_lazy__sequence_Osize_I3_J,axiom,
! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_lazy__sequence_Osize_I3_J) ).
fof(fact_lazy__sequence_Osize_I1_J,axiom,
! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_lazy__sequence_Osize_I1_J) ).
fof(fact__02,axiom,
! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq,
file('theBenchmark.p',fact__02) ).
fof(fact_lazy__sequence_Osimps_I3_J,axiom,
! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),
file('theBenchmark.p',fact_lazy__sequence_Osimps_I3_J) ).
fof(fact_lazy__sequence_Osimps_I2_J,axiom,
! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H),
file('theBenchmark.p',fact_lazy__sequence_Osimps_I2_J) ).
fof(fact_lazy__sequence_Osimps_I4_J,axiom,
! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
file('theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).
fof(fact_list__all__iff__all__interval__int,axiom,
! [V_j_2,V_i_2,V_Pa_2] :
( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
<=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ),
file('theBenchmark.p',fact_list__all__iff__all__interval__int) ).
fof(fact_list__ex__iff__not__all__inverval__int,axiom,
! [V_j_2,V_i_2,V_Pa_2] :
( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
<=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_Pa_2),V_i_2,V_j_2) ),
file('theBenchmark.p',fact_list__ex__iff__not__all__inverval__int) ).
fof(fact_all__interval__int__def,axiom,
! [V_j_2,V_i_2,V_Pa_2] :
( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_all__interval__int__def) ).
fof(fact_code__numeral_Orecs_I2_J,axiom,
! [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)),
file('theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).
fof(fact_Random_Osimps,axiom,
! [V_size_2,V_g_2,T_b,V_nrandom_2] :
( ( ~ 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)))
=> 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))))))) )
& ( 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)))
=> 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)) ) ),
file('theBenchmark.p',fact_Random_Osimps) ).
fof(fact_code__numeral_Orecs_I1_J,axiom,
! [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,
file('theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).
fof(fact_Random__Sequence_Oempty__def,axiom,
! [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)),
file('theBenchmark.p',fact_Random__Sequence_Oempty__def) ).
fof(fact_Random__Sequence_Osingle__def,axiom,
! [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)),
file('theBenchmark.p',fact_Random__Sequence_Osingle__def) ).
fof(fact_Random__Sequence_Omap__def,axiom,
! [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)),
file('theBenchmark.p',fact_Random__Sequence_Omap__def) ).
fof(fact_exE__realizer,axiom,
! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
( 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)))
=> ( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
=> hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
=> 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))) ) ),
file('theBenchmark.p',fact_exE__realizer) ).
fof(fact_Image__Collect__split,axiom,
! [V_A_2,V_Pa_2,T_b,T_c] : hAPP(c_Relation_OImage(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))),V_A_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_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_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2)))),
file('theBenchmark.p',fact_Image__Collect__split) ).
fof(fact_lexord__trans,axiom,
! [V_z_2,V_r_2,V_y_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),V_y_2)),c_List_Olexord(T_b,V_r_2)))
=> ( 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_z_2)),c_List_Olexord(T_b,V_r_2)))
=> ( c_Relation_Otrans(T_b,V_r_2)
=> 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_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_lexord__trans) ).
fof(fact_trans__less__than,axiom,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_trans__less__than) ).
fof(fact_trans__lex__prod,axiom,
! [V_R2_2,T_c,V_R1_2,T_b] :
( c_Relation_Otrans(T_b,V_R1_2)
=> ( c_Relation_Otrans(T_c,V_R2_2)
=> c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ),
file('theBenchmark.p',fact_trans__lex__prod) ).
fof(fact_trans__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
<=> ! [B_x,B_y] :
( 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))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_trans__def) ).
fof(fact_transD,axiom,
! [V_ca_2,V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( 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))
=> ( 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_ca_2)),V_r_2))
=> 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_ca_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_transD) ).
fof(fact_Union__eq,axiom,
! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(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_OEx(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_fconj),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)))),
file('theBenchmark.p',fact_Union__eq) ).
fof(fact_trans__O__subset,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> 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_r_2)),V_r_2)) ),
file('theBenchmark.p',fact_trans__O__subset) ).
fof(fact_bex__UNIV,axiom,
! [V_Pa_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
<=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ),
file('theBenchmark.p',fact_bex__UNIV) ).
fof(fact_finite__Collect__bex,axiom,
! [V_Qa_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( 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),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Qa_2)))))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> 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_x)))) ) ) ),
file('theBenchmark.p',fact_finite__Collect__bex) ).
fof(fact_trans__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Otrans(T_b,V_r_2) ),
file('theBenchmark.p',fact_trans__converse) ).
fof(fact_bex__empty,axiom,
! [V_Pa_2,T_b] :
~ ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bex__empty) ).
fof(fact_listrel__trans,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_listrel__trans) ).
fof(fact_lexord__transI,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ),
file('theBenchmark.p',fact_lexord__transI) ).
fof(fact_trans__finite__psubset,axiom,
! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
file('theBenchmark.p',fact_trans__finite__psubset) ).
fof(fact_trans__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_trans__Id__on) ).
fof(fact_trans__trancl,axiom,
! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trans__trancl) ).
fof(fact_trancl__id,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_trancl__id) ).
fof(fact_trans__Id,axiom,
! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_trans__Id) ).
fof(fact_trans__rtrancl,axiom,
! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trans__rtrancl) ).
fof(fact_trans__Int,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_s_2)
=> c_Relation_Otrans(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_s_2)) ) ),
file('theBenchmark.p',fact_trans__Int) ).
fof(fact_SUPR__bool__eq,axiom,
! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b),
file('theBenchmark.p',fact_SUPR__bool__eq) ).
fof(fact_trans__reflclI,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(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))) ),
file('theBenchmark.p',fact_trans__reflclI) ).
fof(fact_trans__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_trans__inv__image) ).
fof(fact_list__ex__iff__raw,axiom,
! [V_xs_2,V_Pa_2,T_b] :
( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__iff__raw) ).
fof(fact_Bex__set__list__ex,axiom,
! [V_Pa_2,V_xs_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
<=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ),
file('theBenchmark.p',fact_Bex__set__list__ex) ).
fof(fact_UN__eq,axiom,
! [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_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
file('theBenchmark.p',fact_UN__eq) ).
fof(fact_INT__eq,axiom,
! [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_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
file('theBenchmark.p',fact_INT__eq) ).
fof(fact_Sup__apply,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Sup__apply) ).
fof(fact_Sup__fun__def,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Sup__fun__def) ).
fof(fact_Inf__apply,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Inf__apply) ).
fof(fact_Inf__fun__def,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Inf__fun__def) ).
fof(fact_max__extp_Ointros,axiom,
! [V_R_2,V_Y_2,V_X_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
=> ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) ) )
=> c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ),
file('theBenchmark.p',fact_max__extp_Ointros) ).
fof(fact_transp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Otransp(T_b,V_r_2)
<=> c_Relation_Otrans(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))) ),
file('theBenchmark.p',fact_transp__def) ).
fof(fact_transpE,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
( c_Predicate_Otransp(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_transpE) ).
fof(fact_equivp__reflp__symp__transp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
<=> ( c_Predicate_Otransp(T_b,V_R_2)
& c_Predicate_Osymp(T_b,V_R_2)
& c_Predicate_Oreflp(T_b,V_R_2) ) ),
file('theBenchmark.p',fact_equivp__reflp__symp__transp) ).
fof(fact_equivpI,axiom,
! [V_R_2,T_b] :
( c_Predicate_Oreflp(T_b,V_R_2)
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ( c_Predicate_Otransp(T_b,V_R_2)
=> c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_equivpI) ).
fof(fact_sympE,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( c_Predicate_Osymp(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_sympE) ).
fof(fact_equivpE,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ~ ( c_Predicate_Oreflp(T_b,V_R_2)
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_equivpE) ).
fof(fact_max__extp_Osimps,axiom,
! [V_a2_2,V_a1_2,V_R_2,T_b] :
( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
file('theBenchmark.p',fact_max__extp_Osimps) ).
fof(fact_trans__diff__Id,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( c_Relation_Oantisym(T_b,V_r_2)
=> c_Relation_Otrans(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))) ) ),
file('theBenchmark.p',fact_trans__diff__Id) ).
fof(fact_antisym__subset,axiom,
! [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)),V_r_2),V_s_2))
=> ( c_Relation_Oantisym(T_b,V_s_2)
=> c_Relation_Oantisym(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_antisym__subset) ).
fof(fact_antisym__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_antisym__Id__on) ).
fof(fact_antisym__Id,axiom,
! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_antisym__Id) ).
fof(fact_antisym__empty,axiom,
! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_antisym__empty) ).
fof(fact_antisym__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Oantisym(T_b,V_r_2) ),
file('theBenchmark.p',fact_antisym__converse) ).
fof(fact_antisymD,axiom,
! [V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Oantisym(T_b,V_r_2)
=> ( 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))
=> ( 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)),V_r_2))
=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_antisymD) ).
fof(fact_antisym__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(T_b,V_r_2)
<=> ! [B_x,B_y] :
( 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))
=> ( 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))
=> B_x = B_y ) ) ),
file('theBenchmark.p',fact_antisym__def) ).
fof(fact_antisym__reflcl,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(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_Relation_Oantisym(T_b,V_r_2) ),
file('theBenchmark.p',fact_antisym__reflcl) ).
fof(fact_acyclic__impl__antisym__rtrancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
=> c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
fof(fact_fun__lub__def,axiom,
! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))),
file('theBenchmark.p',fact_fun__lub__def) ).
fof(fact_sym__trans__comp__subset,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_r_2)
=> 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_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_sym__trans__comp__subset) ).
fof(fact_sym__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
<=> ! [B_x,B_y] :
( 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))
=> 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)) ) ),
file('theBenchmark.p',fact_sym__def) ).
fof(fact_symD,axiom,
! [V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( 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))
=> 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)),V_r_2)) ) ),
file('theBenchmark.p',fact_symD) ).
fof(fact_sym__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Osym(T_b,V_r_2) ),
file('theBenchmark.p',fact_sym__converse) ).
fof(fact_sym__conv__converse__eq,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
<=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_sym__conv__converse__eq) ).
fof(fact_listrel__sym,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_listrel__sym) ).
fof(fact_sym__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_sym__Id__on) ).
fof(fact_sym__trancl,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_sym__trancl) ).
fof(fact_sym__Un,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Osym(T_b,V_s_2)
=> c_Relation_Osym(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)) ) ),
file('theBenchmark.p',fact_sym__Un) ).
fof(fact_sym__Id,axiom,
! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_sym__Id) ).
fof(fact_sym__rtrancl,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_sym__rtrancl) ).
fof(fact_sym__Int,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Osym(T_b,V_s_2)
=> c_Relation_Osym(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_s_2)) ) ),
file('theBenchmark.p',fact_sym__Int) ).
fof(fact_sym__Un__converse,axiom,
! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
file('theBenchmark.p',fact_sym__Un__converse) ).
fof(fact_sym__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_sym__inv__image) ).
fof(fact_sym__Int__converse,axiom,
! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
file('theBenchmark.p',fact_sym__Int__converse) ).
fof(fact_equivE,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Osym(T_b,V_r_2)
=> ~ c_Relation_Otrans(T_b,V_r_2) ) ) ),
file('theBenchmark.p',fact_equivE) ).
fof(fact_equivI,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_r_2)
=> c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ),
file('theBenchmark.p',fact_equivI) ).
fof(fact_equiv__def,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
<=> ( c_Relation_Otrans(T_b,V_r_2)
& c_Relation_Osym(T_b,V_r_2)
& c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_equiv__def) ).
fof(fact_symp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Osymp(T_b,V_r_2)
<=> c_Relation_Osym(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))) ),
file('theBenchmark.p',fact_symp__def) ).
fof(fact_part__equivp__refl__symp__transp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
<=> ( c_Predicate_Otransp(T_b,V_R_2)
& c_Predicate_Osymp(T_b,V_R_2)
& ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) ),
file('theBenchmark.p',fact_part__equivp__refl__symp__transp) ).
fof(fact_part__equivpI,axiom,
! [T_b,V_R_2] :
( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ( c_Predicate_Otransp(T_b,V_R_2)
=> c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_part__equivpI) ).
fof(fact_equivp__implies__part__equivp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ),
file('theBenchmark.p',fact_equivp__implies__part__equivp) ).
fof(fact_part__equivp__def,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
<=> ( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
<=> ( hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y)
& hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
& hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) )
& ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) ),
file('theBenchmark.p',fact_part__equivp__def) ).
fof(fact_part__equivp__symp,axiom,
! [V_y_2,V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_part__equivp__symp) ).
fof(fact_part__equivp__transp,axiom,
! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_part__equivp__transp) ).
fof(fact_part__equivpE,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_part__equivpE) ).
fof(fact_part__equivp__typedef,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),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_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ),
file('theBenchmark.p',fact_part__equivp__typedef) ).
fof(fact_inj__iff,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
<=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ),
file('theBenchmark.p',fact_inj__iff) ).
fof(fact_inv__o__cancel,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ),
file('theBenchmark.p',fact_inv__o__cancel) ).
fof(fact_o__inv__o__cancel,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ),
file('theBenchmark.p',fact_o__inv__o__cancel) ).
fof(fact_inv__id,axiom,
! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b),
file('theBenchmark.p',fact_inv__id) ).
fof(fact_image__inv__into__cancel,axiom,
! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
=> hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ),
file('theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_surj__iff__all,axiom,
! [V_f_2,T_b,T_c] :
( 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))
<=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ),
file('theBenchmark.p',fact_surj__iff__all) ).
fof(fact_surj__f__inv__f,axiom,
! [V_y_2,V_f_2,T_b,T_c] :
( 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))
=> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_surj__f__inv__f) ).
fof(fact_image__surj__f__inv__f,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( 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))
=> hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_image__surj__f__inv__f) ).
fof(fact_inv__into__injective,axiom,
! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_inv__into__injective) ).
fof(fact_inv__into__into,axiom,
! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ),
file('theBenchmark.p',fact_inv__into__into) ).
fof(fact_f__inv__into__f,axiom,
! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_inv__into__f__f,axiom,
! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ),
file('theBenchmark.p',fact_inv__into__f__f) ).
fof(fact_inv__into__f__eq,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
file('theBenchmark.p',fact_inv__into__f__eq) ).
fof(fact_inv__f__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ),
file('theBenchmark.p',fact_inv__f__eq) ).
fof(fact_inv__f__f,axiom,
! [V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Hilbert__Choice_Oinv__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 ),
file('theBenchmark.p',fact_inv__f__f) ).
fof(fact_inv__into__def,axiom,
! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(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))),
file('theBenchmark.p',fact_inv__into__def) ).
fof(fact_inv__def,axiom,
! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(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_y_2)),
file('theBenchmark.p',fact_inv__def) ).
fof(fact_inj__imp__surj__inv,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),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)) ),
file('theBenchmark.p',fact_inj__imp__surj__inv) ).
fof(fact_image__inv__f__f,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_image__inv__f__f) ).
fof(fact_inv__image__comp,axiom,
! [V_X_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ),
file('theBenchmark.p',fact_inv__image__comp) ).
fof(fact_surj__imp__inj__inv,axiom,
! [V_f_2,T_b,T_c] :
( 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))
=> c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_surj__imp__inj__inv) ).
fof(fact_inj__on__inv__into,axiom,
! [V_A_2,V_f_2,T_c,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(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ),
file('theBenchmark.p',fact_inj__on__inv__into) ).
fof(fact_inv__into__image__cancel,axiom,
! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
=> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ),
file('theBenchmark.p',fact_inv__into__image__cancel) ).
fof(fact_inv__into__comp,axiom,
! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
( 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))
=> ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
=> ( 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))))
=> hAPP(c_Hilbert__Choice_Oinv__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_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__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) ) ) ),
file('theBenchmark.p',fact_inv__into__comp) ).
fof(fact_surj__iff,axiom,
! [V_f_2,T_b,T_c] :
( 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))
<=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ),
file('theBenchmark.p',fact_surj__iff) ).
fof(fact_inj__transfer,axiom,
! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
=> hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
=> hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
file('theBenchmark.p',fact_inj__transfer) ).
fof(fact_fold__image__UN__disjoint,axiom,
! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
=> ( B_x != B_xa
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(hAPP(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)),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(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(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_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ),
file('theBenchmark.p',fact_fold__image__UN__disjoint) ).
fof(fact_nat__of__induct,axiom,
! [V_Pa_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
=> hBOOL(hAPP(V_Pa_2,V_y_2)) ) ),
file('theBenchmark.p',fact_nat__of__induct) ).
fof(fact_nat__of__cases,axiom,
! [V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ),
file('theBenchmark.p',fact_nat__of__cases) ).
fof(fact_of__nat__induct,axiom,
! [V_x_2,V_Pa_2] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
=> hBOOL(hAPP(V_Pa_2,V_x_2)) ),
file('theBenchmark.p',fact_of__nat__induct) ).
fof(fact_of__nat__cases,axiom,
! [V_x_2] :
~ ! [B_y] :
( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_of__nat__cases) ).
fof(fact_lazy__sequence_Orecs_I1_J,axiom,
! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
file('theBenchmark.p',fact_lazy__sequence_Orecs_I1_J) ).
fof(fact_beyond__def,axiom,
! [V_l,V_k] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
=> c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
=> c_Quickcheck_Obeyond(V_k,V_l) = V_l ) ),
file('theBenchmark.p',fact_beyond__def) ).
fof(fact_beyond__zero,axiom,
! [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),
file('theBenchmark.p',fact_beyond__zero) ).
fof(fact_lazy__sequence_Orecs_I2_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)),
file('theBenchmark.p',fact_lazy__sequence_Orecs_I2_J) ).
fof(fact_bij__image__Collect__eq,axiom,
! [V_Pa_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ),
file('theBenchmark.p',fact_bij__image__Collect__eq) ).
fof(fact_curry__def,axiom,
! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),
file('theBenchmark.p',fact_curry__def) ).
fof(fact_curryI,axiom,
! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
file('theBenchmark.p',fact_curryI) ).
fof(fact_bij__betw__id,axiom,
! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2),
file('theBenchmark.p',fact_bij__betw__id) ).
fof(fact_bij__imp__bij__inv,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),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))) ),
file('theBenchmark.p',fact_bij__imp__bij__inv) ).
fof(fact_inv__inv__eq,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ),
file('theBenchmark.p',fact_inv__inv__eq) ).
fof(fact_inv__into__inv__into__eq,axiom,
! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ),
file('theBenchmark.p',fact_inv__into__inv__into__eq) ).
fof(fact_bij__betw__inv__into,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ),
file('theBenchmark.p',fact_bij__betw__inv__into) ).
fof(fact_o__inv__distrib,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ),
file('theBenchmark.p',fact_o__inv__distrib) ).
fof(fact_bij__image__INT,axiom,
! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> 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)) ),
file('theBenchmark.p',fact_bij__image__INT) ).
fof(fact_bij__betw__comp__iff2,axiom,
! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2))
=> ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
<=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ),
file('theBenchmark.p',fact_bij__betw__comp__iff2) ).
fof(fact_bij__comp,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> ( c_Fun_Obij__betw(T_c,T_d,V_g_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)))
=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_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))) ) ),
file('theBenchmark.p',fact_bij__comp) ).
fof(fact_bij__betw__comp__iff,axiom,
! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
=> ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
<=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ),
file('theBenchmark.p',fact_bij__betw__comp__iff) ).
fof(fact_bij__betw__trans,axiom,
! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ),
file('theBenchmark.p',fact_bij__betw__trans) ).
fof(fact_curryE,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_curryE) ).
fof(fact_curryD,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_curryD) ).
fof(fact_curry__conv,axiom,
! [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)),
file('theBenchmark.p',fact_curry__conv) ).
fof(fact_finite__vimage__iff,axiom,
! [V_F_2,V_h_2,T_c,T_b] :
( c_Fun_Obij__betw(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)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__vimage__iff) ).
fof(fact_bij__image__Compl__eq,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> 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)) ),
file('theBenchmark.p',fact_bij__image__Compl__eq) ).
fof(fact_bij__is__inj,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_bij__is__inj) ).
fof(fact_bij__betw__imp__inj__on,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_bij__betw__imp__inj__on) ).
fof(fact_bij__betw__def,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
<=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_bij__betw__def) ).
fof(fact_inj__on__imp__bij__betw,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_inj__on__imp__bij__betw) ).
fof(fact_bij__betw__imp__surj,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_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)) ),
file('theBenchmark.p',fact_bij__betw__imp__surj) ).
fof(fact_bij__is__surj,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_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)) ),
file('theBenchmark.p',fact_bij__is__surj) ).
fof(fact_bij__betw__subset,axiom,
! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
=> c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ),
file('theBenchmark.p',fact_bij__betw__subset) ).
fof(fact_bij__id,axiom,
! [T_b] : c_Fun_Obij__betw(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))),
file('theBenchmark.p',fact_bij__id) ).
fof(fact_bij__betw__id__iff,axiom,
! [V_B_2,V_A_2,T_b] :
( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
<=> V_A_2 = V_B_2 ),
file('theBenchmark.p',fact_bij__betw__id__iff) ).
fof(fact_bij__betw__finite,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_bij__betw__finite) ).
fof(fact_BIJ,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
<=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ),
file('theBenchmark.p',fact_BIJ) ).
fof(fact_bij__betw__empty1,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_bij__betw__empty1) ).
fof(fact_bij__betw__empty2,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_bij__betw__empty2) ).
fof(fact_bij__betw__same__card,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ),
file('theBenchmark.p',fact_bij__betw__same__card) ).
fof(fact_bij__betw__the__inv__into,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ),
file('theBenchmark.p',fact_bij__betw__the__inv__into) ).
fof(fact_bij__betw__combine,axiom,
! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Fun_Obij__betw(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_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ),
file('theBenchmark.p',fact_bij__betw__combine) ).
fof(fact_bij__betw__Disj__Un,axiom,
! [V_f_2,V_B_H_2,V_A_H_2,T_c,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_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
=> ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
=> c_Fun_Obij__betw(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ),
file('theBenchmark.p',fact_bij__betw__Disj__Un) ).
fof(fact_bij__def,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
<=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_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))
& c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_bij__def) ).
fof(fact_bijI,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_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))
=> c_Fun_Obij__betw(T_b,T_c,V_f_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))) ) ),
file('theBenchmark.p',fact_bijI) ).
fof(fact_curry__split,axiom,
! [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,
file('theBenchmark.p',fact_curry__split) ).
fof(fact_split__curry,axiom,
! [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,
file('theBenchmark.p',fact_split__curry) ).
fof(fact_vimage__subset__eq,axiom,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> ( 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))
<=> 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))) ) ),
file('theBenchmark.p',fact_vimage__subset__eq) ).
fof(fact_bij__vimage__eq__inv__image,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_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)))
=> hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_bij__vimage__eq__inv__image) ).
fof(fact_ex__bij__betw__nat__finite__1,axiom,
! [V_M_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
=> ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ),
file('theBenchmark.p',fact_ex__bij__betw__nat__finite__1) ).
fof(fact_Cantor__Bernstein,axiom,
! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( 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))
=> ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
=> ( 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))
=> ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ),
file('theBenchmark.p',fact_Cantor__Bernstein) ).
fof(fact_ex__bij__betw__nat__finite,axiom,
! [V_M_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
=> ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ),
file('theBenchmark.p',fact_ex__bij__betw__nat__finite) ).
fof(fact_ex__bij__betw__finite__nat,axiom,
! [V_M_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
=> ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2))) ),
file('theBenchmark.p',fact_ex__bij__betw__finite__nat) ).
fof(fact_refl__on__UNION,axiom,
! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
=> c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ),
file('theBenchmark.p',fact_refl__on__UNION) ).
fof(fact_bex__reg__eqv,axiom,
! [V_Pa_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) )
<=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
file('theBenchmark.p',fact_bex__reg__eqv) ).
fof(fact_Respects__def,axiom,
! [V_x_2,V_R_2,T_b] :
( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
<=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_Respects__def) ).
fof(fact_in__respects,axiom,
! [V_R_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
<=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_in__respects) ).
fof(fact_bex__reg__right,axiom,
! [V_Pa_2,V_Qa_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ( ! [B_x] :
( hBOOL(hAPP(V_Qa_2,B_x))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
=> ( ? [B_x1] : hBOOL(hAPP(V_Qa_2,B_x1))
=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) ) ) ) ),
file('theBenchmark.p',fact_bex__reg__right) ).
fof(fact_babs__reg__eqv,axiom,
! [V_Pa_2,T_c,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ),
file('theBenchmark.p',fact_babs__reg__eqv) ).
fof(fact_Babs__def,axiom,
! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
=> hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ),
file('theBenchmark.p',fact_Babs__def) ).
fof(fact_wf__weak__decr__stable,axiom,
! [V_r_2,V_f_2,T_b] :
( ! [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)))
=> ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
=> ? [B_i] :
! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ),
file('theBenchmark.p',fact_wf__weak__decr__stable) ).
fof(fact_INT__anti__mono,axiom,
! [V_g_2,V_f_2,T_c,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),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> 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_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ),
file('theBenchmark.p',fact_INT__anti__mono) ).
fof(fact_INT__greatest,axiom,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_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))) ),
file('theBenchmark.p',fact_INT__greatest) ).
fof(fact_rtrancl__induct2,axiom,
! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
=> ( ! [B_a,B_b] :
( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ! [B_aa,B_ba] :
( 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
=> hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ),
file('theBenchmark.p',fact_rtrancl__induct2) ).
fof(fact_converse__rtranclE2,axiom,
! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
( 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_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2)
=> ~ ! [B_a,B_b] :
( 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_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2))
=> ~ 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ),
file('theBenchmark.p',fact_converse__rtranclE2) ).
fof(fact_converse__rtrancl__induct2,axiom,
! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
=> ( ! [B_a,B_b,B_aa,B_ba] :
( 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
=> ( 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),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
=> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) )
=> hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ),
file('theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(fact_congruentI,axiom,
! [T_c,V_f_2,V_r_2,T_b] :
( ! [B_y,B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
=> hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
=> c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ),
file('theBenchmark.p',fact_congruentI) ).
fof(fact_congruent2I_H,axiom,
! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
( ! [B_y1,B_z1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2))
=> ! [B_y2,B_z2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2))
=> hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
=> c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ),
file('theBenchmark.p',fact_congruent2I_H) ).
fof(fact__03,axiom,
! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)),
file('theBenchmark.p',fact__03) ).
fof(fact_all__interval__nat__def,axiom,
! [V_j_2,V_i_2,V_Pa_2] :
( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_all__interval__nat__def) ).
fof(fact__04,axiom,
! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),
file('theBenchmark.p',fact__04) ).
fof(fact_list__all__iff__all__interval__nat,axiom,
! [V_j_2,V_i_2,V_Pa_2] :
( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
<=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ),
file('theBenchmark.p',fact_list__all__iff__all__interval__nat) ).
fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
! [V_j_2,V_i_2,V_Pa_2] :
( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
<=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_Pa_2),V_i_2,V_j_2) ),
file('theBenchmark.p',fact_list__ex__iff__not__all__inverval__nat) ).
fof(fact__05,axiom,
! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)),
file('theBenchmark.p',fact__05) ).
fof(fact_folding__image_Ocong,axiom,
! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__image_Ocong) ).
fof(fact__06,axiom,
! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)),
file('theBenchmark.p',fact__06) ).
fof(fact__07,axiom,
! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b),
file('theBenchmark.p',fact__07) ).
fof(fact_New__DSequence_Opos__map__def,axiom,
! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)),
file('theBenchmark.p',fact_New__DSequence_Opos__map__def) ).
fof(fact_power__dvd__imp__le,axiom,
! [V_n,V_m,V_i] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_power__dvd__imp__le) ).
fof(fact_dvd_Oorder__refl,axiom,
! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
file('theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(fact_dvd__0__right,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_dvd__0__right) ).
fof(fact_dvd__1__left,axiom,
! [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)),
file('theBenchmark.p',fact_dvd__1__left) ).
fof(fact_dvd__imp__le,axiom,
! [V_n,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ),
file('theBenchmark.p',fact_dvd__imp__le) ).
fof(fact_nat__mult__dvd__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_dvd__mult__cancel,axiom,
! [V_n,V_m,V_k] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_setprod__dvd__setprod__subset,axiom,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( ( class_Rings_Odvd(T_c)
& class_Groups_Ocomm__monoid__mult(T_c) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> 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))) ) ) ),
file('theBenchmark.p',fact_setprod__dvd__setprod__subset) ).
fof(fact_inf__period_I4_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_b] :
( ( class_Rings_Odvd(T_b)
& class_Rings_Ocomm__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( 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)))
<=> 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))) ) ) ),
file('theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_inf__period_I3_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_b] :
( ( class_Rings_Odvd(T_b)
& class_Rings_Ocomm__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( 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)))
<=> 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))) ) ) ),
file('theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_dvd__div__eq__mult,axiom,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_ca_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_dvd__div__eq__mult) ).
fof(fact_dvd__div__div__eq__mult,axiom,
! [V_d_2,V_b_2,V_ca_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2))
=> ( 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_ca_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_dvd__div__div__eq__mult) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [V_n_2,V_m_2,V_k_2] :
( 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)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_div__mult__div__if__dvd,axiom,
! [V_w,V_z,V_x,V_y,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
=> 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)) ) ) ),
file('theBenchmark.p',fact_div__mult__div__if__dvd) ).
fof(fact_dvd__div__mult,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_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) ) ),
file('theBenchmark.p',fact_dvd__div__mult) ).
fof(fact_dvd__div__mult__self,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_b),V_a)),V_a) = V_b ) ),
file('theBenchmark.p',fact_dvd__div__mult__self) ).
fof(fact_div__mult__swap,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
=> 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) ) ),
file('theBenchmark.p',fact_div__mult__swap) ).
fof(fact_dvd__mult__div__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> 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 ) ),
file('theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(fact_dvd__mult__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( 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))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ),
file('theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_dvd__mult__left,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( 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))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvdI,axiom,
! [V_k,V_b,V_a,T_a] :
( class_Rings_Odvd(T_a)
=> ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ),
file('theBenchmark.p',fact_dvdI) ).
fof(fact_mult__dvd__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
=> 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))) ) ) ),
file('theBenchmark.p',fact_mult__dvd__mono) ).
fof(fact_dvd__mult,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
=> 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))) ) ),
file('theBenchmark.p',fact_dvd__mult) ).
fof(fact_dvd__mult2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> 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))) ) ),
file('theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__triv__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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))) ),
file('theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_dvd__triv__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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))) ),
file('theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( class_Rings_Oidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [V_b_2,V_ca_2,V_a_2,T_b] :
( class_Rings_Oidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_unity__coeff__ex,axiom,
! [V_l_2,V_Pa_2,T_b] :
( ( class_Rings_Osemiring__0(T_b)
& class_Rings_Odvd(T_b) )
=> ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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)))) ) ) ),
file('theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_le__imp__power__dvd,axiom,
! [V_a,V_n,V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> 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))) ) ),
file('theBenchmark.p',fact_le__imp__power__dvd) ).
fof(fact_dvd__power__le,axiom,
! [V_m,V_n,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> 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))) ) ) ),
file('theBenchmark.p',fact_dvd__power__le) ).
fof(fact_power__le__dvd,axiom,
! [V_m,V_b,V_n,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> 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)) ) ) ),
file('theBenchmark.p',fact_power__le__dvd) ).
fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2] :
( 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_ca_2,V_d_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_dvd_OatLeastatMost__subset__iff) ).
fof(fact_dvd__diffD1,axiom,
! [V_n,V_m,V_k] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ),
file('theBenchmark.p',fact_dvd__diffD1) ).
fof(fact_dvd__diffD,axiom,
! [V_n,V_m,V_k] :
( 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)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ),
file('theBenchmark.p',fact_dvd__diffD) ).
fof(fact_dvd_OlessThan__iff,axiom,
! [V_k_2,V_i_2] :
( 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)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_dvd_OlessThan__iff) ).
fof(fact_dvd_OgreaterThan__iff,axiom,
! [V_k_2,V_i_2] :
( 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)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_dvd_OgreaterThan__iff) ).
fof(fact_dvd_OatLeast__iff,axiom,
! [V_k_2,V_i_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ),
file('theBenchmark.p',fact_dvd_OatLeast__iff) ).
fof(fact_dvd_OatMost__iff,axiom,
! [V_k_2,V_i_2] :
( 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)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ),
file('theBenchmark.p',fact_dvd_OatMost__iff) ).
fof(fact_div__power,axiom,
! [V_n,V_x,V_y,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> 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)) ) ),
file('theBenchmark.p',fact_div__power) ).
fof(fact_dvd__imp__mod__0,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_dvd__imp__mod__0) ).
fof(fact_dvd__eq__mod__eq__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
<=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(fact_dvd__mod__iff,axiom,
! [V_m_2,V_n_2,V_k_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
=> ( 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)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_dvd__mod__iff) ).
fof(fact_mod__mod__cancel,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
=> 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) ) ),
file('theBenchmark.p',fact_mod__mod__cancel) ).
fof(fact_dvd__mod,axiom,
! [V_n,V_m,V_k,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ),
file('theBenchmark.p',fact_dvd__mod) ).
fof(fact_dvd__mod__imp__dvd,axiom,
! [V_n,V_m,V_k,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ),
file('theBenchmark.p',fact_dvd__mod__imp__dvd) ).
fof(fact_one__dvd,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ),
file('theBenchmark.p',fact_one__dvd) ).
fof(fact_dvd__0__left,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_dvd__0__left) ).
fof(fact_div__dvd__div,axiom,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))
=> ( 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_ca_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)) ) ) ) ),
file('theBenchmark.p',fact_div__dvd__div) ).
fof(fact_nat__dvd__1__iff__1,axiom,
! [V_m_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(fact_dvd__power__same,axiom,
! [V_n,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
=> 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))) ) ),
file('theBenchmark.p',fact_dvd__power__same) ).
fof(fact_dvd__refl,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ),
file('theBenchmark.p',fact_dvd__refl) ).
fof(fact_dvd__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_dvd__trans) ).
fof(fact_dvd_Oeq__iff,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd_Oeq__iff) ).
fof(fact_dvd_Ole__less,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd_Oless__le,axiom,
! [V_y_2,V_x_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [V_b,V_a] :
( V_a != V_b
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Oeq__refl,axiom,
! [V_y,V_x] :
( V_x = V_y
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
file('theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [V_x_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( V_x = V_y
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( V_a != V_b
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_dvd_Oord__eq__le__trans,axiom,
! [V_c,V_b,V_a] :
( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
fof(fact_dvd_Oord__le__eq__trans,axiom,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
fof(fact_dvd__antisym,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oantisym,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
=> V_x = V_y ) ),
file('theBenchmark.p',fact_dvd_Oantisym) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(arity_fun__Lattices_Obounded__lattice,axiom,
! [T_2,T_1] :
( class_Lattices_Obounded__lattice(T_1)
=> class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
! [T_2,T_1] :
( class_Complete__Lattice_Ocomplete__lattice(T_1)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
! [T_2,T_1] :
( class_Lattices_Obounded__lattice(T_1)
=> class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
! [T_2,T_1] :
( class_Lattices_Obounded__lattice(T_1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(arity_fun__Lattices_Osemilattice__sup,axiom,
! [T_2,T_1] :
( class_Lattices_Olattice(T_1)
=> class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(arity_fun__Lattices_Osemilattice__inf,axiom,
! [T_2,T_1] :
( class_Lattices_Olattice(T_1)
=> class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(arity_fun__Lattices_Odistrib__lattice,axiom,
! [T_2,T_1] :
( class_Lattices_Odistrib__lattice(T_1)
=> class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(T_1)
=> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [T_2,T_1] :
( class_Orderings_Opreorder(T_1)
=> class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [T_1,T_2] :
( ( class_Finite__Set_Ofinite(T_1)
& class_Finite__Set_Ofinite(T_2) )
=> class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(arity_fun__Lattices_Olattice,axiom,
! [T_2,T_1] :
( class_Lattices_Olattice(T_1)
=> class_Lattices_Olattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [T_2,T_1] :
( class_Orderings_Oorder(T_1)
=> class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Otop,axiom,
! [T_2,T_1] :
( class_Orderings_Otop(T_1)
=> class_Orderings_Otop(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(arity_fun__Orderings_Oord,axiom,
! [T_2,T_1] :
( class_Orderings_Oord(T_1)
=> class_Orderings_Oord(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Obot,axiom,
! [T_2,T_1] :
( class_Orderings_Obot(T_1)
=> class_Orderings_Obot(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [T_2,T_1] :
( class_Groups_Ouminus(T_1)
=> class_Groups_Ouminus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Groups_Ominus,axiom,
! [T_2,T_1] :
( class_Groups_Ominus(T_1)
=> class_Groups_Ominus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_fun__HOL_Oequal,axiom,
! [T_1,T_2] :
( ( class_HOL_Oequal(T_1)
& class_Enum_Oenum(T_2) )
=> class_HOL_Oequal(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__HOL_Oequal) ).
fof(arity_fun__Enum_Oenum,axiom,
! [T_1,T_2] :
( ( class_Enum_Oenum(T_1)
& class_Enum_Oenum(T_2) )
=> class_Enum_Oenum(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Enum_Oenum) ).
fof(arity_Com__Ocom__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Com_Ocom),
file('theBenchmark.p',arity_Com__Ocom__HOL_Oequal) ).
fof(arity_Com__Ocom__Nat_Osize,axiom,
class_Nat_Osize(tc_Com_Ocom),
file('theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lazy__Sequence_Osmall__lazy) ).
fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_Int__Oint__Groups_Osgn__if,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
fof(arity_Int__Oint__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Int__Oint__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Int__Oint__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__HOL_Oequal) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).
fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(arity_Nat__Onat__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Nat__Onat__Int_Onumber,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_Nat__Onat__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__HOL_Oequal) ).
fof(arity_Nat__Onat__Nat_Osize,axiom,
class_Nat_Osize(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).
fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(arity_HOL__Obool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_HOL__Obool__HOL_Oequal,axiom,
class_HOL_Oequal(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__HOL_Oequal) ).
fof(arity_HOL__Obool__Enum_Oenum,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
fof(arity_HOL__Obool__Nat_Osize,axiom,
class_Nat_Osize(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
fof(arity_Com__Ostate__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Com_Ostate),
file('theBenchmark.p',arity_Com__Ostate__HOL_Oequal) ).
fof(arity_Com__Ostate__Nat_Osize,axiom,
class_Nat_Osize(tc_Com_Ostate),
file('theBenchmark.p',arity_Com__Ostate__Nat_Osize) ).
fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
! [T_1] :
( class_Lazy__Sequence_Osmall__lazy(T_1)
=> class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ),
file('theBenchmark.p',arity_List__Olist__Lazy__Sequence_Osmall__lazy) ).
fof(arity_List__Olist__HOL_Oequal,axiom,
! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)),
file('theBenchmark.p',arity_List__Olist__HOL_Oequal) ).
fof(arity_List__Olist__Nat_Osize,axiom,
! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)),
file('theBenchmark.p',arity_List__Olist__Nat_Osize) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [T_1,T_2] :
( ( class_Finite__Set_Ofinite(T_1)
& class_Finite__Set_Ofinite(T_2) )
=> class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ),
file('theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(arity_sum__HOL_Oequal,axiom,
! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)),
file('theBenchmark.p',arity_sum__HOL_Oequal) ).
fof(arity_sum__Enum_Oenum,axiom,
! [T_1,T_2] :
( ( class_Enum_Oenum(T_1)
& class_Enum_Oenum(T_2) )
=> class_Enum_Oenum(tc_sum(T_2,T_1)) ),
file('theBenchmark.p',arity_sum__Enum_Oenum) ).
fof(arity_sum__Nat_Osize,axiom,
! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)),
file('theBenchmark.p',arity_sum__Nat_Osize) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [T_1] :
( class_Finite__Set_Ofinite(T_1)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ),
file('theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(arity_Option__Ooption__HOL_Oequal,axiom,
! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)),
file('theBenchmark.p',arity_Option__Ooption__HOL_Oequal) ).
fof(arity_Option__Ooption__Enum_Oenum,axiom,
! [T_1] :
( class_Enum_Oenum(T_1)
=> class_Enum_Oenum(tc_Option_Ooption(T_1)) ),
file('theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).
fof(arity_Option__Ooption__Nat_Osize,axiom,
! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)),
file('theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).
fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom,
! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)),
file('theBenchmark.p',arity_Nitpick__Opair____box__HOL_Oequal) ).
fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)),
file('theBenchmark.p',arity_Nitpick__Opair____box__Nat_Osize) ).
fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
! [T_1,T_2] :
( ( class_Lazy__Sequence_Osmall__lazy(T_1)
& class_Lazy__Sequence_Osmall__lazy(T_2) )
=> class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ),
file('theBenchmark.p',arity_prod__Lazy__Sequence_Osmall__lazy) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [T_1,T_2] :
( ( class_Finite__Set_Ofinite(T_1)
& class_Finite__Set_Ofinite(T_2) )
=> class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ),
file('theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(arity_prod__HOL_Oequal,axiom,
! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)),
file('theBenchmark.p',arity_prod__HOL_Oequal) ).
fof(arity_prod__Enum_Oenum,axiom,
! [T_1,T_2] :
( ( class_Enum_Oenum(T_1)
& class_Enum_Oenum(T_2) )
=> class_Enum_Oenum(tc_prod(T_2,T_1)) ),
file('theBenchmark.p',arity_prod__Enum_Oenum) ).
fof(arity_prod__Nat_Osize,axiom,
! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)),
file('theBenchmark.p',arity_prod__Nat_Osize) ).
fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__HOL_Oequal) ).
fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
class_Enum_Oenum(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).
fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
class_Nat_Osize(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).
fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Code__Evaluation_Oterm),
file('theBenchmark.p',arity_Code____Evaluation__Oterm__HOL_Oequal) ).
fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
file('theBenchmark.p',arity_Code____Evaluation__Oterm__Nat_Osize) ).
fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)),
file('theBenchmark.p',arity_Hoare____Mirabelle__Otriple__HOL_Oequal) ).
fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)),
file('theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).
fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__HOL_Oequal) ).
fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).
fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)),
file('theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal) ).
fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)),
file('theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).
fof(help_c__COMBI__1,axiom,
! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
file('theBenchmark.p',help_c__COMBI__1) ).
fof(help_c__COMBK__1,axiom,
! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
file('theBenchmark.p',help_c__COMBK__1) ).
fof(help_c__COMBB__1,axiom,
! [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)),
file('theBenchmark.p',help_c__COMBB__1) ).
fof(help_c__COMBC__1,axiom,
! [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),
file('theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBS__1,axiom,
! [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)),
file('theBenchmark.p',help_c__COMBS__1) ).
fof(help_c__fequal__1,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
file('theBenchmark.p',help_c__fequal__1) ).
fof(help_c__fequal__2,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
| V_x_2 != V_y_2 ),
file('theBenchmark.p',help_c__fequal__2) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('theBenchmark.p',help_c__fFalse__1) ).
fof(help_c__fTrue__1,axiom,
hBOOL(c_fTrue),
file('theBenchmark.p',help_c__fTrue__1) ).
fof(help_c__fNot__1,axiom,
! [V_Pa_2] :
( ~ hBOOL(V_Pa_2)
| ~ hBOOL(hAPP(c_fNot,V_Pa_2)) ),
file('theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [V_Pa_2] :
( hBOOL(hAPP(c_fNot,V_Pa_2))
| ~ ~ hBOOL(V_Pa_2) ),
file('theBenchmark.p',help_c__fNot__2) ).
fof(help_c__fconj__1,axiom,
! [V_Qa_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
| ~ hBOOL(V_Qa_2)
| ~ hBOOL(V_Pa_2) ),
file('theBenchmark.p',help_c__fconj__1) ).
fof(help_c__fconj__2,axiom,
! [V_Qa_2,V_Pa_2] :
( hBOOL(V_Pa_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
file('theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [V_Qa_2,V_Pa_2] :
( hBOOL(V_Qa_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
file('theBenchmark.p',help_c__fconj__3) ).
fof(help_c__fdisj__1,axiom,
! [V_Qa_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
| ~ hBOOL(V_Pa_2) ),
file('theBenchmark.p',help_c__fdisj__1) ).
fof(help_c__fdisj__2,axiom,
! [V_Pa_2,V_Qa_2] :
( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
| ~ hBOOL(V_Qa_2) ),
file('theBenchmark.p',help_c__fdisj__2) ).
fof(help_c__fdisj__3,axiom,
! [V_Qa_2,V_Pa_2] :
( hBOOL(V_Qa_2)
| hBOOL(V_Pa_2)
| ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ),
file('theBenchmark.p',help_c__fdisj__3) ).
fof(help_c__fimplies__1,axiom,
! [V_Qa_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
| hBOOL(V_Pa_2) ),
file('theBenchmark.p',help_c__fimplies__1) ).
fof(help_c__fimplies__2,axiom,
! [V_Pa_2,V_Qa_2] :
( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
| ~ hBOOL(V_Qa_2) ),
file('theBenchmark.p',help_c__fimplies__2) ).
fof(help_c__fimplies__3,axiom,
! [V_Qa_2,V_Pa_2] :
( hBOOL(V_Qa_2)
| ~ hBOOL(V_Pa_2)
| ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ),
file('theBenchmark.p',help_c__fimplies__3) ).
fof(conj_0,hypothesis,
! [B_Z,B_s] :
( v_Q_H(B_Z,B_s)
=> v_Q(B_Z,B_s) ),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( ! [B_Z_H] :
( v_P(B_Z_H,B_s)
=> v_Q_H(B_Z_H,B_s_H) )
=> v_Q(B_Z,B_s_H) ) ),
file('theBenchmark.p',conj_1) ).
fof(f_1_1,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
inference(fof_nnf,[status(thm)],[fact_ext]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_1 = U_2
| ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
fof(f_1_4,plain,
! [U_2,U_1] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,plain,
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(T_b)),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(T_b)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_equal__triple__def]) ).
fof(f_2_2,plain,
! [U_5,U_4,U_3] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(U_3)),U_4),U_5))
| U_4 != U_5 )
& ( U_4 = U_5
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(U_3)),U_4),U_5)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_11,U_9] :
( ! [U_7] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(U_7)),U_9),U_11))
| U_9 != U_11 )
& ! [U_10,U_8] :
( ! [U_6] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(U_6)),U_8),U_10))
| U_8 = U_10 ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_11,U_7,U_9] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(U_7)),U_9),U_11))
| U_9 != U_11 )
& ! [U_6,U_8,U_10] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(U_6)),U_8),U_10))
| U_8 = U_10 ) ),
inference(definitional_conversion,[status(esa)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(U_6)),U_8),U_10))
| U_8 = U_10 ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(U_7)),U_9),U_11))
| U_9 != U_11 ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2) = hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2) != hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Rep__triple__inject]) ).
fof(f_3_2,plain,
! [U_14,U_13,U_12] :
( ( hAPP(c_Hoare__Mirabelle_ORep__triple(U_12),U_13) = hAPP(c_Hoare__Mirabelle_ORep__triple(U_12),U_14)
| U_13 != U_14 )
& ( U_13 = U_14
| hAPP(c_Hoare__Mirabelle_ORep__triple(U_12),U_13) != hAPP(c_Hoare__Mirabelle_ORep__triple(U_12),U_14) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_20,U_18] :
( ! [U_16] : hAPP(c_Hoare__Mirabelle_ORep__triple(U_16),U_18) = hAPP(c_Hoare__Mirabelle_ORep__triple(U_16),U_20)
| U_18 != U_20 )
& ! [U_19,U_17] :
( ! [U_15] : hAPP(c_Hoare__Mirabelle_ORep__triple(U_15),U_17) != hAPP(c_Hoare__Mirabelle_ORep__triple(U_15),U_19)
| U_17 = U_19 ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_20,U_16,U_18] :
( hAPP(c_Hoare__Mirabelle_ORep__triple(U_16),U_18) = hAPP(c_Hoare__Mirabelle_ORep__triple(U_16),U_20)
| U_18 != U_20 )
& ! [U_19,U_17,U_15] :
( hAPP(c_Hoare__Mirabelle_ORep__triple(U_15),U_17) != hAPP(c_Hoare__Mirabelle_ORep__triple(U_15),U_19)
| U_17 = U_19 ) ),
inference(definitional_conversion,[status(esa)],[f_3_3]) ).
cnf(f_3_5,plain,
( hAPP(c_Hoare__Mirabelle_ORep__triple(U_15),U_17) != hAPP(c_Hoare__Mirabelle_ORep__triple(U_15),U_19)
| U_17 = U_19 ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( hAPP(c_Hoare__Mirabelle_ORep__triple(U_16),U_18) = hAPP(c_Hoare__Mirabelle_ORep__triple(U_16),U_20)
| U_18 != U_20 ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [T_b] :
( c_HOL_Oequal__class_Oequal(T_b) = c_fequal
| ~ class_HOL_Oequal(T_b) ),
inference(fof_nnf,[status(thm)],[fact_equal]) ).
fof(f_4_2,plain,
! [U_21] :
( c_HOL_Oequal__class_Oequal(U_21) = c_fequal
| ~ class_HOL_Oequal(U_21) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_21] :
( c_HOL_Oequal__class_Oequal(U_21) = c_fequal
| ~ class_HOL_Oequal(U_21) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( c_HOL_Oequal__class_Oequal(U_21) = c_fequal
| ~ class_HOL_Oequal(U_21) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [V_x,T_a] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x))
| ~ class_HOL_Oequal(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equal__refl]) ).
fof(f_5_2,plain,
! [U_23,U_22] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_22),U_23),U_23))
| ~ class_HOL_Oequal(U_22) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_22,U_23] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_22),U_23),U_23))
| ~ class_HOL_Oequal(U_22) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_22),U_23),U_23))
| ~ class_HOL_Oequal(U_22) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2)) ) )
| ~ class_HOL_Oequal(T_b) ),
inference(fof_nnf,[status(thm)],[fact_equal__eq]) ).
fof(f_6_2,plain,
! [U_26,U_25,U_24] :
( ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_24),U_25),U_26))
| U_25 != U_26 )
& ( U_25 = U_26
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_24),U_25),U_26)) ) )
| ~ class_HOL_Oequal(U_24) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_24,U_25,U_26] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_24),U_25),U_26))
| U_25 != U_26
| ~ sP0(U_24,U_25,U_26) )
& ! [U_24,U_25,U_26] :
( U_25 = U_26
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_24),U_25),U_26))
| ~ sP0(U_24,U_25,U_26) )
& ! [U_24,U_25,U_26] :
( sP0(U_24,U_25,U_26)
| ~ class_HOL_Oequal(U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP0(U_24,U_25,U_26)
| ~ class_HOL_Oequal(U_24) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( U_25 = U_26
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_24),U_25),U_26))
| ~ sP0(U_24,U_25,U_26) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_24),U_25),U_26))
| U_25 != U_26
| ~ sP0(U_24,U_25,U_26) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [T_b] :
( c_fequal = c_HOL_Oequal__class_Oequal(T_b)
| ~ class_HOL_Oequal(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__equal]) ).
fof(f_7_2,plain,
! [U_27] :
( c_fequal = c_HOL_Oequal__class_Oequal(U_27)
| ~ class_HOL_Oequal(U_27) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_27] :
( c_fequal = c_HOL_Oequal__class_Oequal(U_27)
| ~ class_HOL_Oequal(U_27) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(U_27)
| ~ class_HOL_Oequal(U_27) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [V_x_2,T_b] : hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_Rep__triple__inverse]) ).
fof(f_8_2,plain,
! [U_29,U_28] : hAPP(c_Hoare__Mirabelle_OAbs__triple(U_28),hAPP(c_Hoare__Mirabelle_ORep__triple(U_28),U_29)) = U_29,
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_29,U_28] : hAPP(c_Hoare__Mirabelle_OAbs__triple(U_28),hAPP(c_Hoare__Mirabelle_ORep__triple(U_28),U_29)) = U_29,
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
hAPP(c_Hoare__Mirabelle_OAbs__triple(U_28),hAPP(c_Hoare__Mirabelle_ORep__triple(U_28),U_29)) = U_29,
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))),
inference(fof_nnf,[status(thm)],[fact_Rep__triple]) ).
fof(f_9_2,plain,
! [U_31,U_30] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_30,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_30)),tc_HOL_Obool)),hAPP(c_Hoare__Mirabelle_ORep__triple(U_30),U_31)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_30,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_30)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_30)))),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_30,U_31] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_30,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_30)),tc_HOL_Obool)),hAPP(c_Hoare__Mirabelle_ORep__triple(U_30),U_31)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_30,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_30)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_30)))),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_30,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_30)),tc_HOL_Obool)),hAPP(c_Hoare__Mirabelle_ORep__triple(U_30),U_31)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_30,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_30)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_30)))),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [T_b] : c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(T_b),tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool),c_Hoare__Mirabelle_ORep__triple(T_b),c_Hoare__Mirabelle_OAbs__triple(T_b),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))),
inference(fof_nnf,[status(thm)],[fact_type__definition__triple]) ).
fof(f_10_2,plain,
! [U_32] : c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(U_32),tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_32,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_32)),tc_HOL_Obool),c_Hoare__Mirabelle_ORep__triple(U_32),c_Hoare__Mirabelle_OAbs__triple(U_32),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_32,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_32)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_32))),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_32] : c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(U_32),tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_32,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_32)),tc_HOL_Obool),c_Hoare__Mirabelle_ORep__triple(U_32),c_Hoare__Mirabelle_OAbs__triple(U_32),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_32,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_32)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_32))),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(U_32),tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_32,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_32)),tc_HOL_Obool),c_Hoare__Mirabelle_ORep__triple(U_32),c_Hoare__Mirabelle_OAbs__triple(U_32),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_32,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_32)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_32))),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [V_y_2,T_b] :
( hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2)) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ),
inference(fof_nnf,[status(thm)],[fact_Abs__triple__inverse]) ).
fof(f_11_2,plain,
! [U_34,U_33] :
( hAPP(c_Hoare__Mirabelle_ORep__triple(U_33),hAPP(c_Hoare__Mirabelle_OAbs__triple(U_33),U_34)) = U_34
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_33,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_33)),tc_HOL_Obool)),U_34),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_33,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_33)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_33)))) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_33,U_34] :
( hAPP(c_Hoare__Mirabelle_ORep__triple(U_33),hAPP(c_Hoare__Mirabelle_OAbs__triple(U_33),U_34)) = U_34
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_33,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_33)),tc_HOL_Obool)),U_34),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_33,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_33)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_33)))) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( hAPP(c_Hoare__Mirabelle_ORep__triple(U_33),hAPP(c_Hoare__Mirabelle_OAbs__triple(U_33),U_34)) = U_34
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_33,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_33)),tc_HOL_Obool)),U_34),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_33,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_33)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_33)))) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_x_2) = hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_x_2) != hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_x_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ),
inference(fof_nnf,[status(thm)],[fact_Abs__triple__inject]) ).
fof(f_12_2,plain,
! [U_37,U_36,U_35] :
( ( ( hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_36) = hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_37)
| U_36 != U_37 )
& ( U_36 = U_37
| hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_36) != hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_37) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),U_37),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_35))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),U_36),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_35)))) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_35,U_36,U_37] :
( hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_36) = hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_37)
| U_36 != U_37
| ~ sP1(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( U_36 = U_37
| hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_36) != hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_37)
| ~ sP1(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( sP1(U_35,U_36,U_37)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),U_37),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_35))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),U_36),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_35)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP1(U_35,U_36,U_37)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),U_37),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_35))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),U_36),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_35,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_35)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_35)))) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( U_36 = U_37
| hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_36) != hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_37)
| ~ sP1(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_36) = hAPP(c_Hoare__Mirabelle_OAbs__triple(U_35),U_37)
| U_36 != U_37
| ~ sP1(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [V_ca_2,T_b,V_B_2,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
| ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).
fof(f_13_2,plain,
! [U_41,U_40,U_39,U_38] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_39))
& ~ hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_38)) )
| ( hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_39))
& hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_38)) )
| U_38 != U_39 ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_41,U_39,U_40,U_38] :
( ~ hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_39))
| ~ sP3(U_41,U_39,U_40,U_38) )
& ! [U_41,U_39,U_40,U_38] :
( ~ hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_38))
| ~ sP3(U_41,U_39,U_40,U_38) )
& ! [U_41,U_39,U_40,U_38] :
( hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_39))
| ~ sP2(U_41,U_39,U_40,U_38) )
& ! [U_41,U_39,U_40,U_38] :
( hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_38))
| ~ sP2(U_41,U_39,U_40,U_38) )
& ! [U_41,U_39,U_40,U_38] :
( sP3(U_41,U_39,U_40,U_38)
| sP2(U_41,U_39,U_40,U_38)
| U_38 != U_39 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP3(U_41,U_39,U_40,U_38)
| sP2(U_41,U_39,U_40,U_38)
| U_38 != U_39 ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_38))
| ~ sP2(U_41,U_39,U_40,U_38) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_39))
| ~ sP2(U_41,U_39,U_40,U_38) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_38))
| ~ sP3(U_41,U_39,U_40,U_38) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_40),U_41),U_39))
| ~ sP3(U_41,U_39,U_40,U_38) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( ( ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(V_Abs_2,V_x_2) != hAPP(V_Abs_2,V_y_2) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject]) ).
fof(f_14_2,plain,
! [U_48,U_47,U_46,U_45,U_44,U_43,U_42] :
( ( ( hAPP(U_45,U_47) = hAPP(U_45,U_48)
| U_47 != U_48 )
& ( U_47 = U_48
| hAPP(U_45,U_47) != hAPP(U_45,U_48) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_43),U_48),U_46))
| ~ hBOOL(hAPP(hAPP(c_member(U_43),U_47),U_46))
| ~ c_Typedef_Otype__definition(U_42,U_43,U_44,U_45,U_46) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_48,U_47,U_46,U_45,U_44,U_43] :
( ! [U_42] : ~ c_Typedef_Otype__definition(U_42,U_43,U_44,U_45,U_46)
| ( ( hAPP(U_45,U_47) = hAPP(U_45,U_48)
| U_47 != U_48 )
& ( U_47 = U_48
| hAPP(U_45,U_47) != hAPP(U_45,U_48) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_43),U_48),U_46))
| ~ hBOOL(hAPP(hAPP(c_member(U_43),U_47),U_46)) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_45,U_47,U_48] :
( hAPP(U_45,U_47) = hAPP(U_45,U_48)
| U_47 != U_48
| ~ sP4(U_45,U_47,U_48) )
& ! [U_45,U_47,U_48] :
( U_47 = U_48
| hAPP(U_45,U_47) != hAPP(U_45,U_48)
| ~ sP4(U_45,U_47,U_48) )
& ! [U_43,U_42,U_46,U_44,U_45,U_47,U_48] :
( ~ c_Typedef_Otype__definition(U_42,U_43,U_44,U_45,U_46)
| sP4(U_45,U_47,U_48)
| ~ hBOOL(hAPP(hAPP(c_member(U_43),U_48),U_46))
| ~ hBOOL(hAPP(hAPP(c_member(U_43),U_47),U_46)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_14_3]) ).
cnf(f_14_5,plain,
( ~ c_Typedef_Otype__definition(U_42,U_43,U_44,U_45,U_46)
| sP4(U_45,U_47,U_48)
| ~ hBOOL(hAPP(hAPP(c_member(U_43),U_48),U_46))
| ~ hBOOL(hAPP(hAPP(c_member(U_43),U_47),U_46)) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( U_47 = U_48
| hAPP(U_45,U_47) != hAPP(U_45,U_48)
| ~ sP4(U_45,U_47,U_48) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_7,plain,
( hAPP(U_45,U_47) = hAPP(U_45,U_48)
| U_47 != U_48
| ~ sP4(U_45,U_47,U_48) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse]) ).
fof(f_15_2,plain,
! [U_54,U_53,U_52,U_51,U_50,U_49] :
( hAPP(U_51,hAPP(U_52,U_54)) = U_54
| ~ hBOOL(hAPP(hAPP(c_member(U_50),U_54),U_53))
| ~ c_Typedef_Otype__definition(U_49,U_50,U_51,U_52,U_53) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_54,U_53,U_52,U_51,U_50] :
( ! [U_49] : ~ c_Typedef_Otype__definition(U_49,U_50,U_51,U_52,U_53)
| hAPP(U_51,hAPP(U_52,U_54)) = U_54
| ~ hBOOL(hAPP(hAPP(c_member(U_50),U_54),U_53)) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_50,U_53,U_52,U_49,U_54,U_51] :
( ~ c_Typedef_Otype__definition(U_49,U_50,U_51,U_52,U_53)
| hAPP(U_51,hAPP(U_52,U_54)) = U_54
| ~ hBOOL(hAPP(hAPP(c_member(U_50),U_54),U_53)) ),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
( ~ c_Typedef_Otype__definition(U_49,U_50,U_51,U_52,U_53)
| hAPP(U_51,hAPP(U_52,U_54)) = U_54
| ~ hBOOL(hAPP(hAPP(c_member(U_50),U_54),U_53)) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep]) ).
fof(f_16_2,plain,
! [U_60,U_59,U_58,U_57,U_56,U_55] :
( hBOOL(hAPP(hAPP(c_member(U_56),hAPP(U_57,U_60)),U_59))
| ~ c_Typedef_Otype__definition(U_55,U_56,U_57,U_58,U_59) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_60,U_59,U_58,U_57,U_56] :
( ! [U_55] : ~ c_Typedef_Otype__definition(U_55,U_56,U_57,U_58,U_59)
| hBOOL(hAPP(hAPP(c_member(U_56),hAPP(U_57,U_60)),U_59)) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_56,U_55,U_57,U_58,U_59,U_60] :
( ~ c_Typedef_Otype__definition(U_55,U_56,U_57,U_58,U_59)
| hBOOL(hAPP(hAPP(c_member(U_56),hAPP(U_57,U_60)),U_59)) ),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
( ~ c_Typedef_Otype__definition(U_55,U_56,U_57,U_58,U_59)
| hBOOL(hAPP(hAPP(c_member(U_56),hAPP(U_57,U_60)),U_59)) ),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
! [V_x_2,V_Pa_2,T_b] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
| ? [B_y] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),B_y)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),B_y),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ) ),
inference(fof_nnf,[status(thm)],[fact_Abs__triple__induct]) ).
fof(f_17_2,plain,
! [U_64,U_63,U_62] :
( hBOOL(hAPP(U_63,U_64))
| ? [U_61] :
( ~ hBOOL(hAPP(U_63,hAPP(c_Hoare__Mirabelle_OAbs__triple(U_62),U_61)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),U_61),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_62)))) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_64,U_63] :
( ! [U_62] :
? [U_61] :
( ~ hBOOL(hAPP(U_63,hAPP(c_Hoare__Mirabelle_OAbs__triple(U_62),U_61)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),U_61),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_62)))) )
| hBOOL(hAPP(U_63,U_64)) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_64,U_63] :
( ! [U_62] :
( ~ hBOOL(hAPP(U_63,hAPP(c_Hoare__Mirabelle_OAbs__triple(U_62),sK2(U_64,U_63,U_62))))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),sK2(U_64,U_63,U_62)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_62)))) )
| hBOOL(hAPP(U_63,U_64)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_61,sK2(U_64,U_63,U_62))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_62,U_63,U_64] :
( ~ hBOOL(hAPP(U_63,hAPP(c_Hoare__Mirabelle_OAbs__triple(U_62),sK2(U_64,U_63,U_62))))
| ~ sP5(U_62,U_63,U_64) )
& ! [U_62,U_63,U_64] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),sK2(U_64,U_63,U_62)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_62))))
| ~ sP5(U_62,U_63,U_64) )
& ! [U_62,U_63,U_64] :
( sP5(U_62,U_63,U_64)
| hBOOL(hAPP(U_63,U_64)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_17_4]) ).
cnf(f_17_6,plain,
( sP5(U_62,U_63,U_64)
| hBOOL(hAPP(U_63,U_64)) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),sK2(U_64,U_63,U_62)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_62,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_62)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_62))))
| ~ sP5(U_62,U_63,U_64) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( ~ hBOOL(hAPP(U_63,hAPP(c_Hoare__Mirabelle_OAbs__triple(U_62),sK2(U_64,U_63,U_62))))
| ~ sP5(U_62,U_63,U_64) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_1,plain,
! [T_b,V_x_2] :
? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),B_y),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
& V_x_2 = hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),B_y) ),
inference(fof_nnf,[status(thm)],[fact_Abs__triple__cases]) ).
fof(f_18_2,plain,
! [U_67,U_66] :
? [U_65] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_67,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_67)),tc_HOL_Obool)),U_65),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_67,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_67)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_67))))
& U_66 = hAPP(c_Hoare__Mirabelle_OAbs__triple(U_67),U_65) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_67,U_66] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_67,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_67)),tc_HOL_Obool)),sK3(U_67,U_66)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_67,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_67)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_67))))
& U_66 = hAPP(c_Hoare__Mirabelle_OAbs__triple(U_67),sK3(U_67,U_66)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_65,sK3(U_67,U_66))],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_67,U_66] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_67,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_67)),tc_HOL_Obool)),sK3(U_67,U_66)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_67,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_67)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_67))))
& ! [U_67,U_66] : U_66 = hAPP(c_Hoare__Mirabelle_OAbs__triple(U_67),sK3(U_67,U_66)) ),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
U_66 = hAPP(c_Hoare__Mirabelle_OAbs__triple(U_67),sK3(U_67,U_66)),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_67,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_67)),tc_HOL_Obool)),sK3(U_67,U_66)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_67,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_67)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_67)))),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [V_Pa_2,V_y_2,T_b] :
( hBOOL(hAPP(V_Pa_2,V_y_2))
| ? [B_x] : ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ),
inference(fof_nnf,[status(thm)],[fact_Rep__triple__induct]) ).
fof(f_19_2,plain,
! [U_71,U_70,U_69] :
( hBOOL(hAPP(U_71,U_70))
| ? [U_68] : ~ hBOOL(hAPP(U_71,hAPP(c_Hoare__Mirabelle_ORep__triple(U_69),U_68)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_69,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_69)),tc_HOL_Obool)),U_70),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_69,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_69)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_69)))) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_71,U_70,U_69] :
( hBOOL(hAPP(U_71,U_70))
| ~ hBOOL(hAPP(U_71,hAPP(c_Hoare__Mirabelle_ORep__triple(U_69),sK4(U_71,U_70,U_69))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_69,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_69)),tc_HOL_Obool)),U_70),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_69,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_69)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_69)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_68,sK4(U_71,U_70,U_69))],[f_19_2]) ).
fof(f_19_4,plain,
! [U_69,U_70,U_71] :
( hBOOL(hAPP(U_71,U_70))
| ~ hBOOL(hAPP(U_71,hAPP(c_Hoare__Mirabelle_ORep__triple(U_69),sK4(U_71,U_70,U_69))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_69,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_69)),tc_HOL_Obool)),U_70),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_69,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_69)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_69)))) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
( hBOOL(hAPP(U_71,U_70))
| ~ hBOOL(hAPP(U_71,hAPP(c_Hoare__Mirabelle_ORep__triple(U_69),sK4(U_71,U_70,U_69))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_69,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_69)),tc_HOL_Obool)),U_70),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_69,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_69)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_69)))) ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [V_y_2,T_b] :
( ? [B_x] : V_y_2 = hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ),
inference(fof_nnf,[status(thm)],[fact_Rep__triple__cases]) ).
fof(f_20_2,plain,
! [U_74,U_73] :
( ? [U_72] : U_74 = hAPP(c_Hoare__Mirabelle_ORep__triple(U_73),U_72)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_73,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_73)),tc_HOL_Obool)),U_74),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_73,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_73)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_73)))) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_74,U_73] :
( U_74 = hAPP(c_Hoare__Mirabelle_ORep__triple(U_73),sK5(U_74,U_73))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_73,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_73)),tc_HOL_Obool)),U_74),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_73,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_73)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_73)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_72,sK5(U_74,U_73))],[f_20_2]) ).
fof(f_20_4,plain,
! [U_73,U_74] :
( U_74 = hAPP(c_Hoare__Mirabelle_ORep__triple(U_73),sK5(U_74,U_73))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_73,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_73)),tc_HOL_Obool)),U_74),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_73,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_73)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_73)))) ),
inference(definitional_conversion,[status(esa)],[f_20_3]) ).
cnf(f_20_5,plain,
( U_74 = hAPP(c_Hoare__Mirabelle_ORep__triple(U_73),sK5(U_74,U_73))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_73,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_73)),tc_HOL_Obool)),U_74),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(U_73,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,U_73)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(U_73)))) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( ( ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(V_Rep_2,V_x_2) != hAPP(V_Rep_2,V_y_2) ) )
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject]) ).
fof(f_21_2,plain,
! [U_81,U_80,U_79,U_78,U_77,U_76,U_75] :
( ( ( hAPP(U_77,U_80) = hAPP(U_77,U_81)
| U_80 != U_81 )
& ( U_80 = U_81
| hAPP(U_77,U_80) != hAPP(U_77,U_81) ) )
| ~ c_Typedef_Otype__definition(U_75,U_76,U_77,U_78,U_79) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_81,U_80,U_79,U_78,U_77] :
( ! [U_76,U_75] : ~ c_Typedef_Otype__definition(U_75,U_76,U_77,U_78,U_79)
| ( ( hAPP(U_77,U_80) = hAPP(U_77,U_81)
| U_80 != U_81 )
& ( U_80 = U_81
| hAPP(U_77,U_80) != hAPP(U_77,U_81) ) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_77,U_80,U_81] :
( hAPP(U_77,U_80) = hAPP(U_77,U_81)
| U_80 != U_81
| ~ sP6(U_77,U_80,U_81) )
& ! [U_77,U_80,U_81] :
( U_80 = U_81
| hAPP(U_77,U_80) != hAPP(U_77,U_81)
| ~ sP6(U_77,U_80,U_81) )
& ! [U_75,U_77,U_76,U_78,U_79,U_80,U_81] :
( ~ c_Typedef_Otype__definition(U_75,U_76,U_77,U_78,U_79)
| sP6(U_77,U_80,U_81) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_21_3]) ).
cnf(f_21_5,plain,
( ~ c_Typedef_Otype__definition(U_75,U_76,U_77,U_78,U_79)
| sP6(U_77,U_80,U_81) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
( U_80 = U_81
| hAPP(U_77,U_80) != hAPP(U_77,U_81)
| ~ sP6(U_77,U_80,U_81) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_7,plain,
( hAPP(U_77,U_80) = hAPP(U_77,U_81)
| U_80 != U_81
| ~ sP6(U_77,U_80,U_81) ),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse]) ).
fof(f_22_2,plain,
! [U_87,U_86,U_85,U_84,U_83,U_82] :
( hAPP(U_85,hAPP(U_84,U_87)) = U_87
| ~ c_Typedef_Otype__definition(U_82,U_83,U_84,U_85,U_86) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_87,U_86,U_85,U_84] :
( ! [U_83,U_82] : ~ c_Typedef_Otype__definition(U_82,U_83,U_84,U_85,U_86)
| hAPP(U_85,hAPP(U_84,U_87)) = U_87 ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_85,U_86,U_87,U_84,U_82,U_83] :
( ~ c_Typedef_Otype__definition(U_82,U_83,U_84,U_85,U_86)
| hAPP(U_85,hAPP(U_84,U_87)) = U_87 ),
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
( ~ c_Typedef_Otype__definition(U_82,U_83,U_84,U_85,U_86)
| hAPP(U_85,hAPP(U_84,U_87)) = U_87 ),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2,
inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).
fof(f_23_2,plain,
! [U_89,U_88] : hAPP(c_Set_OCollect(U_88),U_89) = U_89,
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_88,U_89] : hAPP(c_Set_OCollect(U_88),U_89) = U_89,
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
hAPP(c_Set_OCollect(U_88),U_89) = U_89,
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [V_A_2,T_b,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
| V_a_2 != V_b_2 ),
inference(fof_nnf,[status(thm)],[fact_eq__mem__trans]) ).
fof(f_24_2,plain,
! [U_93,U_92,U_91,U_90] :
( hBOOL(hAPP(hAPP(c_member(U_92),U_90),U_93))
| ~ hBOOL(hAPP(hAPP(c_member(U_92),U_91),U_93))
| U_90 != U_91 ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_90,U_91,U_92,U_93] :
( hBOOL(hAPP(hAPP(c_member(U_92),U_90),U_93))
| ~ hBOOL(hAPP(hAPP(c_member(U_92),U_91),U_93))
| U_90 != U_91 ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_92),U_90),U_93))
| ~ hBOOL(hAPP(hAPP(c_member(U_92),U_91),U_93))
| U_90 != U_91 ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [V_A_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(V_A_2,V_x_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__def]) ).
fof(f_25_2,plain,
! [U_96,U_95,U_94] :
( ( hBOOL(hAPP(hAPP(c_member(U_94),U_95),U_96))
| ~ hBOOL(hAPP(U_96,U_95)) )
& ( hBOOL(hAPP(U_96,U_95))
| ~ hBOOL(hAPP(hAPP(c_member(U_94),U_95),U_96)) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_102,U_100] :
( ! [U_98] : hBOOL(hAPP(hAPP(c_member(U_98),U_100),U_102))
| ~ hBOOL(hAPP(U_102,U_100)) )
& ! [U_101,U_99] :
( ! [U_97] : ~ hBOOL(hAPP(hAPP(c_member(U_97),U_99),U_101))
| hBOOL(hAPP(U_101,U_99)) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_102,U_98,U_100] :
( hBOOL(hAPP(hAPP(c_member(U_98),U_100),U_102))
| ~ hBOOL(hAPP(U_102,U_100)) )
& ! [U_101,U_99,U_97] :
( ~ hBOOL(hAPP(hAPP(c_member(U_97),U_99),U_101))
| hBOOL(hAPP(U_101,U_99)) ) ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_97),U_99),U_101))
| hBOOL(hAPP(U_101,U_99)) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_98),U_100),U_102))
| ~ hBOOL(hAPP(U_102,U_100)) ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [V_x_2,T_b,V_B_2,V_A_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_eqset__imp__iff]) ).
fof(f_26_2,plain,
! [U_106,U_105,U_104,U_103] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_103))
| ~ hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_104)) )
& ( hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_104))
| ~ hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_103)) ) )
| U_103 != U_104 ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_103,U_105,U_104,U_106] :
( hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_103))
| ~ hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_104))
| ~ sP7(U_103,U_105,U_104,U_106) )
& ! [U_103,U_105,U_104,U_106] :
( hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_104))
| ~ hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_103))
| ~ sP7(U_103,U_105,U_104,U_106) )
& ! [U_103,U_105,U_104,U_106] :
( sP7(U_103,U_105,U_104,U_106)
| U_103 != U_104 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_26_2]) ).
cnf(f_26_4,plain,
( sP7(U_103,U_105,U_104,U_106)
| U_103 != U_104 ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_104))
| ~ hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_103))
| ~ sP7(U_103,U_105,U_104,U_106) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_103))
| ~ hBOOL(hAPP(hAPP(c_member(U_105),U_106),U_104))
| ~ sP7(U_103,U_105,U_104,U_106) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [V_A_2,T_b,V_y_2,V_x_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| V_x_2 != V_y_2 ),
inference(fof_nnf,[status(thm)],[fact_eqelem__imp__iff]) ).
fof(f_27_2,plain,
! [U_110,U_109,U_108,U_107] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_109),U_107),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_109),U_108),U_110)) )
& ( hBOOL(hAPP(hAPP(c_member(U_109),U_108),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_109),U_107),U_110)) ) )
| U_107 != U_108 ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_110,U_108,U_107,U_109] :
( hBOOL(hAPP(hAPP(c_member(U_109),U_107),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_109),U_108),U_110))
| ~ sP8(U_110,U_108,U_107,U_109) )
& ! [U_110,U_108,U_107,U_109] :
( hBOOL(hAPP(hAPP(c_member(U_109),U_108),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_109),U_107),U_110))
| ~ sP8(U_110,U_108,U_107,U_109) )
& ! [U_110,U_108,U_107,U_109] :
( sP8(U_110,U_108,U_107,U_109)
| U_107 != U_108 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP8(U_110,U_108,U_107,U_109)
| U_107 != U_108 ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_109),U_108),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_109),U_107),U_110))
| ~ sP8(U_110,U_108,U_107,U_109) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_109),U_107),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_109),U_108),U_110))
| ~ sP8(U_110,U_108,U_107,U_109) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__mem]) ).
fof(f_28_2,plain,
! [U_113,U_112,U_111] :
( ( hBOOL(hAPP(hAPP(c_member(U_111),U_112),hAPP(c_fequal,U_113)))
| U_112 != U_113 )
& ( U_112 = U_113
| ~ hBOOL(hAPP(hAPP(c_member(U_111),U_112),hAPP(c_fequal,U_113))) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_119,U_117] :
( ! [U_115] : hBOOL(hAPP(hAPP(c_member(U_115),U_117),hAPP(c_fequal,U_119)))
| U_117 != U_119 )
& ! [U_118,U_116] :
( ! [U_114] : ~ hBOOL(hAPP(hAPP(c_member(U_114),U_116),hAPP(c_fequal,U_118)))
| U_116 = U_118 ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_119,U_115,U_117] :
( hBOOL(hAPP(hAPP(c_member(U_115),U_117),hAPP(c_fequal,U_119)))
| U_117 != U_119 )
& ! [U_116,U_118,U_114] :
( ~ hBOOL(hAPP(hAPP(c_member(U_114),U_116),hAPP(c_fequal,U_118)))
| U_116 = U_118 ) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_114),U_116),hAPP(c_fequal,U_118)))
| U_116 = U_118 ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_115),U_117),hAPP(c_fequal,U_119)))
| U_117 != U_119 ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2))
& V_x_2 = hAPP(V_Abs_2,B_y) )
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__cases]) ).
fof(f_29_2,plain,
! [U_126,U_125,U_124,U_123,U_122,U_121] :
( ? [U_120] :
( hBOOL(hAPP(hAPP(c_member(U_122),U_120),U_125))
& U_126 = hAPP(U_124,U_120) )
| ~ c_Typedef_Otype__definition(U_121,U_122,U_123,U_124,U_125) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_126,U_125,U_124,U_123,U_122] :
( ! [U_121] : ~ c_Typedef_Otype__definition(U_121,U_122,U_123,U_124,U_125)
| ? [U_120] :
( hBOOL(hAPP(hAPP(c_member(U_122),U_120),U_125))
& U_126 = hAPP(U_124,U_120) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_126,U_125,U_124,U_123,U_122] :
( ! [U_121] : ~ c_Typedef_Otype__definition(U_121,U_122,U_123,U_124,U_125)
| ( hBOOL(hAPP(hAPP(c_member(U_122),sK6(U_126,U_125,U_124,U_123,U_122)),U_125))
& U_126 = hAPP(U_124,sK6(U_126,U_125,U_124,U_123,U_122)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_120,sK6(U_126,U_125,U_124,U_123,U_122))],[f_29_3]) ).
fof(f_29_5,plain,
( ! [U_122,U_123,U_124,U_125,U_126] :
( hBOOL(hAPP(hAPP(c_member(U_122),sK6(U_126,U_125,U_124,U_123,U_122)),U_125))
| ~ sP9(U_122,U_123,U_124,U_125,U_126) )
& ! [U_122,U_123,U_124,U_125,U_126] :
( U_126 = hAPP(U_124,sK6(U_126,U_125,U_124,U_123,U_122))
| ~ sP9(U_122,U_123,U_124,U_125,U_126) )
& ! [U_121,U_122,U_123,U_124,U_125,U_126] :
( ~ c_Typedef_Otype__definition(U_121,U_122,U_123,U_124,U_125)
| sP9(U_122,U_123,U_124,U_125,U_126) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_29_4]) ).
cnf(f_29_6,plain,
( ~ c_Typedef_Otype__definition(U_121,U_122,U_123,U_124,U_125)
| sP9(U_122,U_123,U_124,U_125,U_126) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_7,plain,
( U_126 = hAPP(U_124,sK6(U_126,U_125,U_124,U_123,U_122))
| ~ sP9(U_122,U_123,U_124,U_125,U_126) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_122),sK6(U_126,U_125,U_124,U_123,U_122)),U_125))
| ~ sP9(U_122,U_123,U_124,U_125,U_126) ),
inference(clausify,[status(thm)],[f_29_5]) ).
fof(f_30_1,plain,
! [V_x_2,V_Pa_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
| ? [B_y] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(V_Abs_2,B_y)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) )
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__induct]) ).
fof(f_30_2,plain,
! [U_134,U_133,U_132,U_131,U_130,U_129,U_128] :
( hBOOL(hAPP(U_133,U_134))
| ? [U_127] :
( ~ hBOOL(hAPP(U_133,hAPP(U_131,U_127)))
& hBOOL(hAPP(hAPP(c_member(U_129),U_127),U_132)) )
| ~ c_Typedef_Otype__definition(U_128,U_129,U_130,U_131,U_132) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_134,U_133,U_132,U_131,U_130,U_129] :
( ! [U_128] : ~ c_Typedef_Otype__definition(U_128,U_129,U_130,U_131,U_132)
| hBOOL(hAPP(U_133,U_134))
| ? [U_127] :
( ~ hBOOL(hAPP(U_133,hAPP(U_131,U_127)))
& hBOOL(hAPP(hAPP(c_member(U_129),U_127),U_132)) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_134,U_133,U_132,U_131,U_130,U_129] :
( ! [U_128] : ~ c_Typedef_Otype__definition(U_128,U_129,U_130,U_131,U_132)
| hBOOL(hAPP(U_133,U_134))
| ( ~ hBOOL(hAPP(U_133,hAPP(U_131,sK7(U_134,U_133,U_132,U_131,U_130,U_129))))
& hBOOL(hAPP(hAPP(c_member(U_129),sK7(U_134,U_133,U_132,U_131,U_130,U_129)),U_132)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_127,sK7(U_134,U_133,U_132,U_131,U_130,U_129))],[f_30_3]) ).
fof(f_30_5,plain,
( ! [U_132,U_131,U_130,U_129,U_133,U_134] :
( ~ hBOOL(hAPP(U_133,hAPP(U_131,sK7(U_134,U_133,U_132,U_131,U_130,U_129))))
| ~ sP10(U_132,U_131,U_130,U_129,U_133,U_134) )
& ! [U_132,U_131,U_130,U_129,U_133,U_134] :
( hBOOL(hAPP(hAPP(c_member(U_129),sK7(U_134,U_133,U_132,U_131,U_130,U_129)),U_132))
| ~ sP10(U_132,U_131,U_130,U_129,U_133,U_134) )
& ! [U_132,U_131,U_130,U_128,U_129,U_133,U_134] :
( ~ c_Typedef_Otype__definition(U_128,U_129,U_130,U_131,U_132)
| hBOOL(hAPP(U_133,U_134))
| sP10(U_132,U_131,U_130,U_129,U_133,U_134) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_30_4]) ).
cnf(f_30_6,plain,
( ~ c_Typedef_Otype__definition(U_128,U_129,U_130,U_131,U_132)
| hBOOL(hAPP(U_133,U_134))
| sP10(U_132,U_131,U_130,U_129,U_133,U_134) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_129),sK7(U_134,U_133,U_132,U_131,U_130,U_129)),U_132))
| ~ sP10(U_132,U_131,U_130,U_129,U_133,U_134) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_8,plain,
( ~ hBOOL(hAPP(U_133,hAPP(U_131,sK7(U_134,U_133,U_132,U_131,U_130,U_129))))
| ~ sP10(U_132,U_131,U_130,U_129,U_133,U_134) ),
inference(clausify,[status(thm)],[f_30_5]) ).
fof(f_31_1,plain,
! [V_Pa_2,V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hBOOL(hAPP(V_Pa_2,V_y_2))
| ? [B_x] : ~ hBOOL(hAPP(V_Pa_2,hAPP(V_Rep_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__induct]) ).
fof(f_31_2,plain,
! [U_142,U_141,U_140,U_139,U_138,U_137,U_136] :
( hBOOL(hAPP(U_142,U_141))
| ? [U_135] : ~ hBOOL(hAPP(U_142,hAPP(U_138,U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(U_137),U_141),U_140))
| ~ c_Typedef_Otype__definition(U_136,U_137,U_138,U_139,U_140) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_142,U_141,U_140,U_139,U_138,U_137] :
( ! [U_136] : ~ c_Typedef_Otype__definition(U_136,U_137,U_138,U_139,U_140)
| hBOOL(hAPP(U_142,U_141))
| ? [U_135] : ~ hBOOL(hAPP(U_142,hAPP(U_138,U_135)))
| ~ hBOOL(hAPP(hAPP(c_member(U_137),U_141),U_140)) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_142,U_141,U_140,U_139,U_138,U_137] :
( ! [U_136] : ~ c_Typedef_Otype__definition(U_136,U_137,U_138,U_139,U_140)
| hBOOL(hAPP(U_142,U_141))
| ~ hBOOL(hAPP(U_142,hAPP(U_138,sK8(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ hBOOL(hAPP(hAPP(c_member(U_137),U_141),U_140)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_135,sK8(U_142,U_141,U_140,U_139,U_138,U_137))],[f_31_3]) ).
fof(f_31_5,plain,
! [U_139,U_136,U_137,U_142,U_138,U_141,U_140] :
( ~ c_Typedef_Otype__definition(U_136,U_137,U_138,U_139,U_140)
| hBOOL(hAPP(U_142,U_141))
| ~ hBOOL(hAPP(U_142,hAPP(U_138,sK8(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ hBOOL(hAPP(hAPP(c_member(U_137),U_141),U_140)) ),
inference(definitional_conversion,[status(esa)],[f_31_4]) ).
cnf(f_31_6,plain,
( ~ c_Typedef_Otype__definition(U_136,U_137,U_138,U_139,U_140)
| hBOOL(hAPP(U_142,U_141))
| ~ hBOOL(hAPP(U_142,hAPP(U_138,sK8(U_142,U_141,U_140,U_139,U_138,U_137))))
| ~ hBOOL(hAPP(hAPP(c_member(U_137),U_141),U_140)) ),
inference(clausify,[status(thm)],[f_31_5]) ).
fof(f_32_1,plain,
! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( ? [B_x] : V_y_2 = hAPP(V_Rep_2,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__cases]) ).
fof(f_32_2,plain,
! [U_149,U_148,U_147,U_146,U_145,U_144] :
( ? [U_143] : U_149 = hAPP(U_146,U_143)
| ~ hBOOL(hAPP(hAPP(c_member(U_145),U_149),U_148))
| ~ c_Typedef_Otype__definition(U_144,U_145,U_146,U_147,U_148) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_149,U_148,U_147,U_146,U_145] :
( ! [U_144] : ~ c_Typedef_Otype__definition(U_144,U_145,U_146,U_147,U_148)
| ? [U_143] : U_149 = hAPP(U_146,U_143)
| ~ hBOOL(hAPP(hAPP(c_member(U_145),U_149),U_148)) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_149,U_148,U_147,U_146,U_145] :
( ! [U_144] : ~ c_Typedef_Otype__definition(U_144,U_145,U_146,U_147,U_148)
| U_149 = hAPP(U_146,sK9(U_149,U_148,U_147,U_146,U_145))
| ~ hBOOL(hAPP(hAPP(c_member(U_145),U_149),U_148)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_143,sK9(U_149,U_148,U_147,U_146,U_145))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_145,U_149,U_148,U_146,U_144,U_147] :
( ~ c_Typedef_Otype__definition(U_144,U_145,U_146,U_147,U_148)
| U_149 = hAPP(U_146,sK9(U_149,U_148,U_147,U_146,U_145))
| ~ hBOOL(hAPP(hAPP(c_member(U_145),U_149),U_148)) ),
inference(definitional_conversion,[status(esa)],[f_32_4]) ).
cnf(f_32_6,plain,
( ~ c_Typedef_Otype__definition(U_144,U_145,U_146,U_147,U_148)
| U_149 = hAPP(U_146,sK9(U_149,U_148,U_147,U_146,U_145))
| ~ hBOOL(hAPP(hAPP(c_member(U_145),U_149),U_148)) ),
inference(clausify,[status(thm)],[f_32_5]) ).
fof(f_33_1,plain,
~ c_HOL_Oinduct__false,
inference(fof_nnf,[status(thm)],[fact_induct__false__def]) ).
fof(f_33_2,plain,
~ c_HOL_Oinduct__false,
inference(definitional_conversion,[status(esa)],[f_33_1]) ).
cnf(f_33_3,plain,
~ c_HOL_Oinduct__false,
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff]) ).
fof(f_34_2,plain,
! [U_153,U_152,U_151,U_150] :
( ( hBOOL(hAPP(hAPP(c_member(U_150),U_151),c_SetInterval_Oord_OatMost(U_150,U_152,U_153)))
| ~ hBOOL(hAPP(hAPP(U_152,U_151),U_153)) )
& ( hBOOL(hAPP(hAPP(U_152,U_151),U_153))
| ~ hBOOL(hAPP(hAPP(c_member(U_150),U_151),c_SetInterval_Oord_OatMost(U_150,U_152,U_153))) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_161,U_159,U_157] :
( ! [U_155] : hBOOL(hAPP(hAPP(c_member(U_155),U_157),c_SetInterval_Oord_OatMost(U_155,U_159,U_161)))
| ~ hBOOL(hAPP(hAPP(U_159,U_157),U_161)) )
& ! [U_160,U_158,U_156] :
( ! [U_154] : ~ hBOOL(hAPP(hAPP(c_member(U_154),U_156),c_SetInterval_Oord_OatMost(U_154,U_158,U_160)))
| hBOOL(hAPP(hAPP(U_158,U_156),U_160)) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_155,U_161,U_157,U_159] :
( hBOOL(hAPP(hAPP(c_member(U_155),U_157),c_SetInterval_Oord_OatMost(U_155,U_159,U_161)))
| ~ hBOOL(hAPP(hAPP(U_159,U_157),U_161)) )
& ! [U_156,U_160,U_154,U_158] :
( ~ hBOOL(hAPP(hAPP(c_member(U_154),U_156),c_SetInterval_Oord_OatMost(U_154,U_158,U_160)))
| hBOOL(hAPP(hAPP(U_158,U_156),U_160)) ) ),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_154),U_156),c_SetInterval_Oord_OatMost(U_154,U_158,U_160)))
| hBOOL(hAPP(hAPP(U_158,U_156),U_160)) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_155),U_157),c_SetInterval_Oord_OatMost(U_155,U_159,U_161)))
| ~ hBOOL(hAPP(hAPP(U_159,U_157),U_161)) ),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff]) ).
fof(f_35_2,plain,
! [U_165,U_164,U_163,U_162] :
( ( hBOOL(hAPP(hAPP(c_member(U_162),U_163),c_SetInterval_Oord_OatLeast(U_162,U_164,U_165)))
| ~ hBOOL(hAPP(hAPP(U_164,U_165),U_163)) )
& ( hBOOL(hAPP(hAPP(U_164,U_165),U_163))
| ~ hBOOL(hAPP(hAPP(c_member(U_162),U_163),c_SetInterval_Oord_OatLeast(U_162,U_164,U_165))) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_173,U_171,U_169] :
( ! [U_167] : hBOOL(hAPP(hAPP(c_member(U_167),U_169),c_SetInterval_Oord_OatLeast(U_167,U_171,U_173)))
| ~ hBOOL(hAPP(hAPP(U_171,U_173),U_169)) )
& ! [U_172,U_170,U_168] :
( ! [U_166] : ~ hBOOL(hAPP(hAPP(c_member(U_166),U_168),c_SetInterval_Oord_OatLeast(U_166,U_170,U_172)))
| hBOOL(hAPP(hAPP(U_170,U_172),U_168)) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_167,U_169,U_171,U_173] :
( hBOOL(hAPP(hAPP(c_member(U_167),U_169),c_SetInterval_Oord_OatLeast(U_167,U_171,U_173)))
| ~ hBOOL(hAPP(hAPP(U_171,U_173),U_169)) )
& ! [U_170,U_168,U_166,U_172] :
( ~ hBOOL(hAPP(hAPP(c_member(U_166),U_168),c_SetInterval_Oord_OatLeast(U_166,U_170,U_172)))
| hBOOL(hAPP(hAPP(U_170,U_172),U_168)) ) ),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_166),U_168),c_SetInterval_Oord_OatLeast(U_166,U_170,U_172)))
| hBOOL(hAPP(hAPP(U_170,U_172),U_168)) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_167),U_169),c_SetInterval_Oord_OatLeast(U_167,U_171,U_173)))
| ~ hBOOL(hAPP(hAPP(U_171,U_173),U_169)) ),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
! [V_k_2,V_less_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff]) ).
fof(f_36_2,plain,
! [U_177,U_176,U_175,U_174] :
( ( hBOOL(hAPP(hAPP(c_member(U_174),U_175),c_SetInterval_Oord_OlessThan(U_174,U_176,U_177)))
| ~ hBOOL(hAPP(hAPP(U_176,U_175),U_177)) )
& ( hBOOL(hAPP(hAPP(U_176,U_175),U_177))
| ~ hBOOL(hAPP(hAPP(c_member(U_174),U_175),c_SetInterval_Oord_OlessThan(U_174,U_176,U_177))) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_185,U_183,U_181] :
( ! [U_179] : hBOOL(hAPP(hAPP(c_member(U_179),U_181),c_SetInterval_Oord_OlessThan(U_179,U_183,U_185)))
| ~ hBOOL(hAPP(hAPP(U_183,U_181),U_185)) )
& ! [U_184,U_182,U_180] :
( ! [U_178] : ~ hBOOL(hAPP(hAPP(c_member(U_178),U_180),c_SetInterval_Oord_OlessThan(U_178,U_182,U_184)))
| hBOOL(hAPP(hAPP(U_182,U_180),U_184)) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_185,U_179,U_181,U_183] :
( hBOOL(hAPP(hAPP(c_member(U_179),U_181),c_SetInterval_Oord_OlessThan(U_179,U_183,U_185)))
| ~ hBOOL(hAPP(hAPP(U_183,U_181),U_185)) )
& ! [U_182,U_180,U_178,U_184] :
( ~ hBOOL(hAPP(hAPP(c_member(U_178),U_180),c_SetInterval_Oord_OlessThan(U_178,U_182,U_184)))
| hBOOL(hAPP(hAPP(U_182,U_180),U_184)) ) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_178),U_180),c_SetInterval_Oord_OlessThan(U_178,U_182,U_184)))
| hBOOL(hAPP(hAPP(U_182,U_180),U_184)) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_179),U_181),c_SetInterval_Oord_OlessThan(U_179,U_183,U_185)))
| ~ hBOOL(hAPP(hAPP(U_183,U_181),U_185)) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
! [V_k_2,V_less_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff]) ).
fof(f_37_2,plain,
! [U_189,U_188,U_187,U_186] :
( ( hBOOL(hAPP(hAPP(c_member(U_186),U_187),c_SetInterval_Oord_OgreaterThan(U_186,U_188,U_189)))
| ~ hBOOL(hAPP(hAPP(U_188,U_189),U_187)) )
& ( hBOOL(hAPP(hAPP(U_188,U_189),U_187))
| ~ hBOOL(hAPP(hAPP(c_member(U_186),U_187),c_SetInterval_Oord_OgreaterThan(U_186,U_188,U_189))) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_197,U_195,U_193] :
( ! [U_191] : hBOOL(hAPP(hAPP(c_member(U_191),U_193),c_SetInterval_Oord_OgreaterThan(U_191,U_195,U_197)))
| ~ hBOOL(hAPP(hAPP(U_195,U_197),U_193)) )
& ! [U_196,U_194,U_192] :
( ! [U_190] : ~ hBOOL(hAPP(hAPP(c_member(U_190),U_192),c_SetInterval_Oord_OgreaterThan(U_190,U_194,U_196)))
| hBOOL(hAPP(hAPP(U_194,U_196),U_192)) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_191,U_193,U_195,U_197] :
( hBOOL(hAPP(hAPP(c_member(U_191),U_193),c_SetInterval_Oord_OgreaterThan(U_191,U_195,U_197)))
| ~ hBOOL(hAPP(hAPP(U_195,U_197),U_193)) )
& ! [U_194,U_192,U_190,U_196] :
( ~ hBOOL(hAPP(hAPP(c_member(U_190),U_192),c_SetInterval_Oord_OgreaterThan(U_190,U_194,U_196)))
| hBOOL(hAPP(hAPP(U_194,U_196),U_192)) ) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_190),U_192),c_SetInterval_Oord_OgreaterThan(U_190,U_194,U_196)))
| hBOOL(hAPP(hAPP(U_194,U_196),U_192)) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_191),U_193),c_SetInterval_Oord_OgreaterThan(U_191,U_195,U_197)))
| ~ hBOOL(hAPP(hAPP(U_195,U_197),U_193)) ),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
& ( ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff]) ).
fof(f_38_2,plain,
! [U_202,U_201,U_200,U_199,U_198] :
( ( hBOOL(hAPP(hAPP(c_member(U_198),U_199),c_SetInterval_Oord_OatLeastAtMost(U_198,U_200,U_201,U_202)))
| ~ hBOOL(hAPP(hAPP(U_200,U_199),U_202))
| ~ hBOOL(hAPP(hAPP(U_200,U_201),U_199)) )
& ( ( hBOOL(hAPP(hAPP(U_200,U_199),U_202))
& hBOOL(hAPP(hAPP(U_200,U_201),U_199)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_198),U_199),c_SetInterval_Oord_OatLeastAtMost(U_198,U_200,U_201,U_202))) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_212,U_210,U_208,U_206] :
( ! [U_204] : hBOOL(hAPP(hAPP(c_member(U_204),U_206),c_SetInterval_Oord_OatLeastAtMost(U_204,U_208,U_210,U_212)))
| ~ hBOOL(hAPP(hAPP(U_208,U_206),U_212))
| ~ hBOOL(hAPP(hAPP(U_208,U_210),U_206)) )
& ! [U_211,U_209,U_207,U_205] :
( ! [U_203] : ~ hBOOL(hAPP(hAPP(c_member(U_203),U_205),c_SetInterval_Oord_OatLeastAtMost(U_203,U_207,U_209,U_211)))
| ( hBOOL(hAPP(hAPP(U_207,U_205),U_211))
& hBOOL(hAPP(hAPP(U_207,U_209),U_205)) ) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_205,U_207,U_209,U_211] :
( hBOOL(hAPP(hAPP(U_207,U_205),U_211))
| ~ sP11(U_205,U_207,U_209,U_211) )
& ! [U_205,U_207,U_209,U_211] :
( hBOOL(hAPP(hAPP(U_207,U_209),U_205))
| ~ sP11(U_205,U_207,U_209,U_211) )
& ! [U_208,U_204,U_206,U_212,U_210] :
( hBOOL(hAPP(hAPP(c_member(U_204),U_206),c_SetInterval_Oord_OatLeastAtMost(U_204,U_208,U_210,U_212)))
| ~ hBOOL(hAPP(hAPP(U_208,U_206),U_212))
| ~ hBOOL(hAPP(hAPP(U_208,U_210),U_206)) )
& ! [U_203,U_205,U_207,U_209,U_211] :
( ~ hBOOL(hAPP(hAPP(c_member(U_203),U_205),c_SetInterval_Oord_OatLeastAtMost(U_203,U_207,U_209,U_211)))
| sP11(U_205,U_207,U_209,U_211) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_38_3]) ).
cnf(f_38_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_203),U_205),c_SetInterval_Oord_OatLeastAtMost(U_203,U_207,U_209,U_211)))
| sP11(U_205,U_207,U_209,U_211) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_204),U_206),c_SetInterval_Oord_OatLeastAtMost(U_204,U_208,U_210,U_212)))
| ~ hBOOL(hAPP(hAPP(U_208,U_206),U_212))
| ~ hBOOL(hAPP(hAPP(U_208,U_210),U_206)) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
( hBOOL(hAPP(hAPP(U_207,U_209),U_205))
| ~ sP11(U_205,U_207,U_209,U_211) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_8,plain,
( hBOOL(hAPP(hAPP(U_207,U_205),U_211))
| ~ sP11(U_205,U_207,U_209,U_211) ),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
& ( ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff]) ).
fof(f_39_2,plain,
! [U_217,U_216,U_215,U_214,U_213] :
( ( hBOOL(hAPP(hAPP(c_member(U_213),U_214),c_SetInterval_Oord_OgreaterThanLessThan(U_213,U_215,U_216,U_217)))
| ~ hBOOL(hAPP(hAPP(U_215,U_214),U_217))
| ~ hBOOL(hAPP(hAPP(U_215,U_216),U_214)) )
& ( ( hBOOL(hAPP(hAPP(U_215,U_214),U_217))
& hBOOL(hAPP(hAPP(U_215,U_216),U_214)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_213),U_214),c_SetInterval_Oord_OgreaterThanLessThan(U_213,U_215,U_216,U_217))) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_227,U_225,U_223,U_221] :
( ! [U_219] : hBOOL(hAPP(hAPP(c_member(U_219),U_221),c_SetInterval_Oord_OgreaterThanLessThan(U_219,U_223,U_225,U_227)))
| ~ hBOOL(hAPP(hAPP(U_223,U_221),U_227))
| ~ hBOOL(hAPP(hAPP(U_223,U_225),U_221)) )
& ! [U_226,U_224,U_222,U_220] :
( ! [U_218] : ~ hBOOL(hAPP(hAPP(c_member(U_218),U_220),c_SetInterval_Oord_OgreaterThanLessThan(U_218,U_222,U_224,U_226)))
| ( hBOOL(hAPP(hAPP(U_222,U_220),U_226))
& hBOOL(hAPP(hAPP(U_222,U_224),U_220)) ) ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
( ! [U_220,U_222,U_224,U_226] :
( hBOOL(hAPP(hAPP(U_222,U_220),U_226))
| ~ sP12(U_220,U_222,U_224,U_226) )
& ! [U_220,U_222,U_224,U_226] :
( hBOOL(hAPP(hAPP(U_222,U_224),U_220))
| ~ sP12(U_220,U_222,U_224,U_226) )
& ! [U_223,U_219,U_221,U_225,U_227] :
( hBOOL(hAPP(hAPP(c_member(U_219),U_221),c_SetInterval_Oord_OgreaterThanLessThan(U_219,U_223,U_225,U_227)))
| ~ hBOOL(hAPP(hAPP(U_223,U_221),U_227))
| ~ hBOOL(hAPP(hAPP(U_223,U_225),U_221)) )
& ! [U_218,U_220,U_222,U_224,U_226] :
( ~ hBOOL(hAPP(hAPP(c_member(U_218),U_220),c_SetInterval_Oord_OgreaterThanLessThan(U_218,U_222,U_224,U_226)))
| sP12(U_220,U_222,U_224,U_226) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_218),U_220),c_SetInterval_Oord_OgreaterThanLessThan(U_218,U_222,U_224,U_226)))
| sP12(U_220,U_222,U_224,U_226) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_219),U_221),c_SetInterval_Oord_OgreaterThanLessThan(U_219,U_223,U_225,U_227)))
| ~ hBOOL(hAPP(hAPP(U_223,U_221),U_227))
| ~ hBOOL(hAPP(hAPP(U_223,U_225),U_221)) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_7,plain,
( hBOOL(hAPP(hAPP(U_222,U_224),U_220))
| ~ sP12(U_220,U_222,U_224,U_226) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_8,plain,
( hBOOL(hAPP(hAPP(U_222,U_220),U_226))
| ~ sP12(U_220,U_222,U_224,U_226) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
& ( ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff]) ).
fof(f_40_2,plain,
! [U_233,U_232,U_231,U_230,U_229,U_228] :
( ( hBOOL(hAPP(hAPP(c_member(U_228),U_229),c_SetInterval_Oord_OgreaterThanAtMost(U_228,U_230,U_231,U_232,U_233)))
| ~ hBOOL(hAPP(hAPP(U_230,U_229),U_233))
| ~ hBOOL(hAPP(hAPP(U_231,U_232),U_229)) )
& ( ( hBOOL(hAPP(hAPP(U_230,U_229),U_233))
& hBOOL(hAPP(hAPP(U_231,U_232),U_229)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_228),U_229),c_SetInterval_Oord_OgreaterThanAtMost(U_228,U_230,U_231,U_232,U_233))) ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_245,U_243,U_241,U_239,U_237] :
( ! [U_235] : hBOOL(hAPP(hAPP(c_member(U_235),U_237),c_SetInterval_Oord_OgreaterThanAtMost(U_235,U_239,U_241,U_243,U_245)))
| ~ hBOOL(hAPP(hAPP(U_239,U_237),U_245))
| ~ hBOOL(hAPP(hAPP(U_241,U_243),U_237)) )
& ! [U_244,U_242,U_240,U_238,U_236] :
( ! [U_234] : ~ hBOOL(hAPP(hAPP(c_member(U_234),U_236),c_SetInterval_Oord_OgreaterThanAtMost(U_234,U_238,U_240,U_242,U_244)))
| ( hBOOL(hAPP(hAPP(U_238,U_236),U_244))
& hBOOL(hAPP(hAPP(U_240,U_242),U_236)) ) ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_240,U_236,U_238,U_242,U_244] :
( hBOOL(hAPP(hAPP(U_238,U_236),U_244))
| ~ sP13(U_240,U_236,U_238,U_242,U_244) )
& ! [U_240,U_236,U_238,U_242,U_244] :
( hBOOL(hAPP(hAPP(U_240,U_242),U_236))
| ~ sP13(U_240,U_236,U_238,U_242,U_244) )
& ! [U_239,U_235,U_241,U_237,U_245,U_243] :
( hBOOL(hAPP(hAPP(c_member(U_235),U_237),c_SetInterval_Oord_OgreaterThanAtMost(U_235,U_239,U_241,U_243,U_245)))
| ~ hBOOL(hAPP(hAPP(U_239,U_237),U_245))
| ~ hBOOL(hAPP(hAPP(U_241,U_243),U_237)) )
& ! [U_240,U_234,U_236,U_238,U_242,U_244] :
( ~ hBOOL(hAPP(hAPP(c_member(U_234),U_236),c_SetInterval_Oord_OgreaterThanAtMost(U_234,U_238,U_240,U_242,U_244)))
| sP13(U_240,U_236,U_238,U_242,U_244) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_40_3]) ).
cnf(f_40_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_234),U_236),c_SetInterval_Oord_OgreaterThanAtMost(U_234,U_238,U_240,U_242,U_244)))
| sP13(U_240,U_236,U_238,U_242,U_244) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_235),U_237),c_SetInterval_Oord_OgreaterThanAtMost(U_235,U_239,U_241,U_243,U_245)))
| ~ hBOOL(hAPP(hAPP(U_239,U_237),U_245))
| ~ hBOOL(hAPP(hAPP(U_241,U_243),U_237)) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_7,plain,
( hBOOL(hAPP(hAPP(U_240,U_242),U_236))
| ~ sP13(U_240,U_236,U_238,U_242,U_244) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_8,plain,
( hBOOL(hAPP(hAPP(U_238,U_236),U_244))
| ~ sP13(U_240,U_236,U_238,U_242,U_244) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
& ( ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff]) ).
fof(f_41_2,plain,
! [U_251,U_250,U_249,U_248,U_247,U_246] :
( ( hBOOL(hAPP(hAPP(c_member(U_246),U_247),c_SetInterval_Oord_OatLeastLessThan(U_246,U_248,U_249,U_250,U_251)))
| ~ hBOOL(hAPP(hAPP(U_249,U_247),U_251))
| ~ hBOOL(hAPP(hAPP(U_248,U_250),U_247)) )
& ( ( hBOOL(hAPP(hAPP(U_249,U_247),U_251))
& hBOOL(hAPP(hAPP(U_248,U_250),U_247)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_246),U_247),c_SetInterval_Oord_OatLeastLessThan(U_246,U_248,U_249,U_250,U_251))) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_263,U_261,U_259,U_257,U_255] :
( ! [U_253] : hBOOL(hAPP(hAPP(c_member(U_253),U_255),c_SetInterval_Oord_OatLeastLessThan(U_253,U_257,U_259,U_261,U_263)))
| ~ hBOOL(hAPP(hAPP(U_259,U_255),U_263))
| ~ hBOOL(hAPP(hAPP(U_257,U_261),U_255)) )
& ! [U_262,U_260,U_258,U_256,U_254] :
( ! [U_252] : ~ hBOOL(hAPP(hAPP(c_member(U_252),U_254),c_SetInterval_Oord_OatLeastLessThan(U_252,U_256,U_258,U_260,U_262)))
| ( hBOOL(hAPP(hAPP(U_258,U_254),U_262))
& hBOOL(hAPP(hAPP(U_256,U_260),U_254)) ) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
( ! [U_260,U_262,U_258,U_254,U_256] :
( hBOOL(hAPP(hAPP(U_258,U_254),U_262))
| ~ sP14(U_260,U_262,U_258,U_254,U_256) )
& ! [U_260,U_262,U_258,U_254,U_256] :
( hBOOL(hAPP(hAPP(U_256,U_260),U_254))
| ~ sP14(U_260,U_262,U_258,U_254,U_256) )
& ! [U_253,U_257,U_259,U_255,U_263,U_261] :
( hBOOL(hAPP(hAPP(c_member(U_253),U_255),c_SetInterval_Oord_OatLeastLessThan(U_253,U_257,U_259,U_261,U_263)))
| ~ hBOOL(hAPP(hAPP(U_259,U_255),U_263))
| ~ hBOOL(hAPP(hAPP(U_257,U_261),U_255)) )
& ! [U_260,U_262,U_258,U_252,U_254,U_256] :
( ~ hBOOL(hAPP(hAPP(c_member(U_252),U_254),c_SetInterval_Oord_OatLeastLessThan(U_252,U_256,U_258,U_260,U_262)))
| sP14(U_260,U_262,U_258,U_254,U_256) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_41_3]) ).
cnf(f_41_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_252),U_254),c_SetInterval_Oord_OatLeastLessThan(U_252,U_256,U_258,U_260,U_262)))
| sP14(U_260,U_262,U_258,U_254,U_256) ),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_253),U_255),c_SetInterval_Oord_OatLeastLessThan(U_253,U_257,U_259,U_261,U_263)))
| ~ hBOOL(hAPP(hAPP(U_259,U_255),U_263))
| ~ hBOOL(hAPP(hAPP(U_257,U_261),U_255)) ),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_7,plain,
( hBOOL(hAPP(hAPP(U_256,U_260),U_254))
| ~ sP14(U_260,U_262,U_258,U_254,U_256) ),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_8,plain,
( hBOOL(hAPP(hAPP(U_258,U_254),U_262))
| ~ sP14(U_260,U_262,U_258,U_254,U_256) ),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
! [V_x_2,V_Pa_2,V_A_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| hBOOL(hAPP(V_Pa_2,V_x_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_ballE]) ).
fof(f_42_2,plain,
! [U_268,U_267,U_266,U_265] :
( ~ hBOOL(hAPP(hAPP(c_member(U_265),U_268),U_266))
| hBOOL(hAPP(U_267,U_268))
| ? [U_264] :
( ~ hBOOL(hAPP(U_267,U_264))
& hBOOL(hAPP(hAPP(c_member(U_265),U_264),U_266)) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_268,U_267,U_266,U_265] :
( ~ hBOOL(hAPP(hAPP(c_member(U_265),U_268),U_266))
| hBOOL(hAPP(U_267,U_268))
| ( ~ hBOOL(hAPP(U_267,sK10(U_268,U_267,U_266,U_265)))
& hBOOL(hAPP(hAPP(c_member(U_265),sK10(U_268,U_267,U_266,U_265)),U_266)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_264,sK10(U_268,U_267,U_266,U_265))],[f_42_2]) ).
fof(f_42_4,plain,
( ! [U_267,U_266,U_265,U_268] :
( ~ hBOOL(hAPP(U_267,sK10(U_268,U_267,U_266,U_265)))
| ~ sP15(U_267,U_266,U_265,U_268) )
& ! [U_267,U_266,U_265,U_268] :
( hBOOL(hAPP(hAPP(c_member(U_265),sK10(U_268,U_267,U_266,U_265)),U_266))
| ~ sP15(U_267,U_266,U_265,U_268) )
& ! [U_267,U_266,U_265,U_268] :
( ~ hBOOL(hAPP(hAPP(c_member(U_265),U_268),U_266))
| hBOOL(hAPP(U_267,U_268))
| sP15(U_267,U_266,U_265,U_268) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_42_3]) ).
cnf(f_42_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_265),U_268),U_266))
| hBOOL(hAPP(U_267,U_268))
| sP15(U_267,U_266,U_265,U_268) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_265),sK10(U_268,U_267,U_266,U_265)),U_266))
| ~ sP15(U_267,U_266,U_265,U_268) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_7,plain,
( ~ hBOOL(hAPP(U_267,sK10(U_268,U_267,U_266,U_265)))
| ~ sP15(U_267,U_266,U_265,U_268) ),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
! [V_Pa_2,V_A_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_bexE]) ).
fof(f_43_2,plain,
! [U_273,U_272,U_271] :
( ? [U_270] :
( hBOOL(hAPP(U_273,U_270))
& hBOOL(hAPP(hAPP(c_member(U_271),U_270),U_272)) )
| ! [U_269] :
( ~ hBOOL(hAPP(U_273,U_269))
| ~ hBOOL(hAPP(hAPP(c_member(U_271),U_269),U_272)) ) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_273,U_272,U_271] :
( ( hBOOL(hAPP(U_273,sK11(U_273,U_272,U_271)))
& hBOOL(hAPP(hAPP(c_member(U_271),sK11(U_273,U_272,U_271)),U_272)) )
| ! [U_269] :
( ~ hBOOL(hAPP(U_273,U_269))
| ~ hBOOL(hAPP(hAPP(c_member(U_271),U_269),U_272)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_270,sK11(U_273,U_272,U_271))],[f_43_2]) ).
fof(f_43_4,plain,
( ! [U_271,U_272,U_273] :
( hBOOL(hAPP(U_273,sK11(U_273,U_272,U_271)))
| ~ sP16(U_271,U_272,U_273) )
& ! [U_271,U_272,U_273] :
( hBOOL(hAPP(hAPP(c_member(U_271),sK11(U_273,U_272,U_271)),U_272))
| ~ sP16(U_271,U_272,U_273) )
& ! [U_271,U_269,U_272,U_273] :
( sP16(U_271,U_272,U_273)
| ~ hBOOL(hAPP(U_273,U_269))
| ~ hBOOL(hAPP(hAPP(c_member(U_271),U_269),U_272)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_43_3]) ).
cnf(f_43_5,plain,
( sP16(U_271,U_272,U_273)
| ~ hBOOL(hAPP(U_273,U_269))
| ~ hBOOL(hAPP(hAPP(c_member(U_271),U_269),U_272)) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_271),sK11(U_273,U_272,U_271)),U_272))
| ~ sP16(U_271,U_272,U_273) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_7,plain,
( hBOOL(hAPP(U_273,sK11(U_273,U_272,U_271)))
| ~ sP16(U_271,U_272,U_273) ),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
! [V_A_2,T_b,V_x_2,V_Pa_2] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_bexI]) ).
fof(f_44_2,plain,
! [U_278,U_277,U_276,U_275] :
( ? [U_274] :
( hBOOL(hAPP(U_275,U_274))
& hBOOL(hAPP(hAPP(c_member(U_277),U_274),U_278)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_277),U_276),U_278))
| ~ hBOOL(hAPP(U_275,U_276)) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_278,U_277,U_276,U_275] :
( ( hBOOL(hAPP(U_275,sK12(U_278,U_277,U_276,U_275)))
& hBOOL(hAPP(hAPP(c_member(U_277),sK12(U_278,U_277,U_276,U_275)),U_278)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_277),U_276),U_278))
| ~ hBOOL(hAPP(U_275,U_276)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_274,sK12(U_278,U_277,U_276,U_275))],[f_44_2]) ).
fof(f_44_4,plain,
( ! [U_276,U_275,U_277,U_278] :
( hBOOL(hAPP(U_275,sK12(U_278,U_277,U_276,U_275)))
| ~ sP17(U_276,U_275,U_277,U_278) )
& ! [U_276,U_275,U_277,U_278] :
( hBOOL(hAPP(hAPP(c_member(U_277),sK12(U_278,U_277,U_276,U_275)),U_278))
| ~ sP17(U_276,U_275,U_277,U_278) )
& ! [U_276,U_275,U_277,U_278] :
( sP17(U_276,U_275,U_277,U_278)
| ~ hBOOL(hAPP(hAPP(c_member(U_277),U_276),U_278))
| ~ hBOOL(hAPP(U_275,U_276)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_44_3]) ).
cnf(f_44_5,plain,
( sP17(U_276,U_275,U_277,U_278)
| ~ hBOOL(hAPP(hAPP(c_member(U_277),U_276),U_278))
| ~ hBOOL(hAPP(U_275,U_276)) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_277),sK12(U_278,U_277,U_276,U_275)),U_278))
| ~ sP17(U_276,U_275,U_277,U_278) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_7,plain,
( hBOOL(hAPP(U_275,sK12(U_278,U_277,U_276,U_275)))
| ~ sP17(U_276,U_275,U_277,U_278) ),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_1,plain,
! [V_X_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_InterE]) ).
fof(f_45_2,plain,
! [U_282,U_281,U_280,U_279] :
( hBOOL(hAPP(hAPP(c_member(U_279),U_280),U_282))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_279,tc_HOL_Obool)),U_282),U_281))
| ~ hBOOL(hAPP(hAPP(c_member(U_279),U_280),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_279,tc_HOL_Obool),U_281))) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_280,U_279,U_281,U_282] :
( hBOOL(hAPP(hAPP(c_member(U_279),U_280),U_282))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_279,tc_HOL_Obool)),U_282),U_281))
| ~ hBOOL(hAPP(hAPP(c_member(U_279),U_280),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_279,tc_HOL_Obool),U_281))) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_279),U_280),U_282))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_279,tc_HOL_Obool)),U_282),U_281))
| ~ hBOOL(hAPP(hAPP(c_member(U_279),U_280),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_279,tc_HOL_Obool),U_281))) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [V_X_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_InterD]) ).
fof(f_46_2,plain,
! [U_286,U_285,U_284,U_283] :
( hBOOL(hAPP(hAPP(c_member(U_283),U_284),U_286))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_283,tc_HOL_Obool)),U_286),U_285))
| ~ hBOOL(hAPP(hAPP(c_member(U_283),U_284),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_283,tc_HOL_Obool),U_285))) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_283,U_284,U_285,U_286] :
( hBOOL(hAPP(hAPP(c_member(U_283),U_284),U_286))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_283,tc_HOL_Obool)),U_286),U_285))
| ~ hBOOL(hAPP(hAPP(c_member(U_283),U_284),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_283,tc_HOL_Obool),U_285))) ),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_283),U_284),U_286))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_283,tc_HOL_Obool)),U_286),U_285))
| ~ hBOOL(hAPP(hAPP(c_member(U_283),U_284),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_283,tc_HOL_Obool),U_285))) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [V_A_2,V_C_2,V_X_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnionI]) ).
fof(f_47_2,plain,
! [U_290,U_289,U_288,U_287] :
( hBOOL(hAPP(hAPP(c_member(U_287),U_290),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_287,tc_HOL_Obool),U_289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_287),U_290),U_288))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_287,tc_HOL_Obool)),U_288),U_289)) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_288,U_287,U_289,U_290] :
( hBOOL(hAPP(hAPP(c_member(U_287),U_290),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_287,tc_HOL_Obool),U_289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_287),U_290),U_288))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_287,tc_HOL_Obool)),U_288),U_289)) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_287),U_290),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_287,tc_HOL_Obool),U_289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_287),U_290),U_288))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_287,tc_HOL_Obool)),U_288),U_289)) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_emptyE]) ).
fof(f_48_2,plain,
! [U_292,U_291] : ~ hBOOL(hAPP(hAPP(c_member(U_291),U_292),c_Orderings_Obot__class_Obot(tc_fun(U_291,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_291,U_292] : ~ hBOOL(hAPP(hAPP(c_member(U_291),U_292),c_Orderings_Obot__class_Obot(tc_fun(U_291,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
~ hBOOL(hAPP(hAPP(c_member(U_291),U_292),c_Orderings_Obot__class_Obot(tc_fun(U_291,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_UNIV__I]) ).
fof(f_49_2,plain,
! [U_294,U_293] : hBOOL(hAPP(hAPP(c_member(U_293),U_294),c_Orderings_Otop__class_Otop(tc_fun(U_293,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_293,U_294] : hBOOL(hAPP(hAPP(c_member(U_293),U_294),c_Orderings_Otop__class_Otop(tc_fun(U_293,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
hBOOL(hAPP(hAPP(c_member(U_293),U_294),c_Orderings_Otop__class_Otop(tc_fun(U_293,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [V_ca_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subsetD]) ).
fof(f_50_2,plain,
! [U_298,U_297,U_296,U_295] :
( hBOOL(hAPP(hAPP(c_member(U_295),U_298),U_297))
| ~ hBOOL(hAPP(hAPP(c_member(U_295),U_298),U_296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_295,tc_HOL_Obool)),U_296),U_297)) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_295,U_296,U_297,U_298] :
( hBOOL(hAPP(hAPP(c_member(U_295),U_298),U_297))
| ~ hBOOL(hAPP(hAPP(c_member(U_295),U_298),U_296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_295,tc_HOL_Obool)),U_296),U_297)) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_295),U_298),U_297))
| ~ hBOOL(hAPP(hAPP(c_member(U_295),U_298),U_296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_295,tc_HOL_Obool)),U_296),U_297)) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [V_B_2,V_A_2,T_b] :
( V_A_2 = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_equalityI]) ).
fof(f_51_2,plain,
! [U_301,U_300,U_299] :
( U_300 = U_301
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_299,tc_HOL_Obool)),U_301),U_300))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_299,tc_HOL_Obool)),U_300),U_301)) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_299,U_300,U_301] :
( U_300 = U_301
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_299,tc_HOL_Obool)),U_301),U_300))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_299,tc_HOL_Obool)),U_300),U_301)) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( U_300 = U_301
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_299,tc_HOL_Obool)),U_301),U_300))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_299,tc_HOL_Obool)),U_300),U_301)) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_top1I]) ).
fof(f_52_2,plain,
! [U_303,U_302] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_302,tc_HOL_Obool)),U_303)),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_303,U_302] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_302,tc_HOL_Obool)),U_303)),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_302,tc_HOL_Obool)),U_303)),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_empty__subsetI]) ).
fof(f_53_2,plain,
! [U_305,U_304] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_304,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_304,tc_HOL_Obool))),U_305)),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_304,U_305] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_304,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_304,tc_HOL_Obool))),U_305)),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_304,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_304,tc_HOL_Obool))),U_305)),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
( hBOOL(hAPP(V_Qa_2,V_x_2))
| ~ hBOOL(hAPP(V_Pa_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) ),
inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).
fof(f_54_2,plain,
! [U_309,U_308,U_307,U_306] :
( hBOOL(hAPP(U_308,U_309))
| ~ hBOOL(hAPP(U_307,U_309))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_306,tc_HOL_Obool)),U_307),U_308)) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_309,U_308,U_307] :
( ! [U_306] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_306,tc_HOL_Obool)),U_307),U_308))
| hBOOL(hAPP(U_308,U_309))
| ~ hBOOL(hAPP(U_307,U_309)) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
! [U_306,U_307,U_308,U_309] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_306,tc_HOL_Obool)),U_307),U_308))
| hBOOL(hAPP(U_308,U_309))
| ~ hBOOL(hAPP(U_307,U_309)) ),
inference(definitional_conversion,[status(esa)],[f_54_3]) ).
cnf(f_54_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_306,tc_HOL_Obool)),U_307),U_308))
| hBOOL(hAPP(U_308,U_309))
| ~ hBOOL(hAPP(U_307,U_309)) ),
inference(clausify,[status(thm)],[f_54_4]) ).
fof(f_55_1,plain,
! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Qa_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
| ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).
fof(f_55_2,plain,
! [U_313,U_312,U_311,U_310] :
( hBOOL(hAPP(U_313,U_311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_312,tc_HOL_Obool)),U_310),U_313))
| ~ hBOOL(hAPP(U_310,U_311)) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_311,U_310,U_312,U_313] :
( hBOOL(hAPP(U_313,U_311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_312,tc_HOL_Obool)),U_310),U_313))
| ~ hBOOL(hAPP(U_310,U_311)) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( hBOOL(hAPP(U_313,U_311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_312,tc_HOL_Obool)),U_310),U_313))
| ~ hBOOL(hAPP(U_310,U_311)) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [T_b] :
( 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)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__empty]) ).
fof(f_56_2,plain,
! [U_314] :
( c_Complete__Lattice_OInf__class_OInf(U_314,c_Orderings_Obot__class_Obot(tc_fun(U_314,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_314)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_314) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_314] :
( c_Complete__Lattice_OInf__class_OInf(U_314,c_Orderings_Obot__class_Obot(tc_fun(U_314,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_314)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_314) ),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_314,c_Orderings_Obot__class_Obot(tc_fun(U_314,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_314)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_314) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Inter__empty]) ).
fof(f_57_2,plain,
! [U_315] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_315,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_315,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_315,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_315] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_315,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_315,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_315,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_315,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_315,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_315,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [T_b] :
( 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)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__UNIV]) ).
fof(f_58_2,plain,
! [U_316] :
( c_Complete__Lattice_OInf__class_OInf(U_316,c_Orderings_Otop__class_Otop(tc_fun(U_316,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_316)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_316) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_316] :
( c_Complete__Lattice_OInf__class_OInf(U_316,c_Orderings_Otop__class_Otop(tc_fun(U_316,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_316)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_316) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_316,c_Orderings_Otop__class_Otop(tc_fun(U_316,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_316)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_316) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Inter__UNIV]) ).
fof(f_59_2,plain,
! [U_317] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_317,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_317,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_317,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_317] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_317,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_317,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_317,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_317,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_317,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_317,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [T_b] :
( 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)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__empty]) ).
fof(f_60_2,plain,
! [U_318] :
( c_Complete__Lattice_OSup__class_OSup(U_318,c_Orderings_Obot__class_Obot(tc_fun(U_318,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_318)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_318) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_318] :
( c_Complete__Lattice_OSup__class_OSup(U_318,c_Orderings_Obot__class_Obot(tc_fun(U_318,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_318)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_318) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_318,c_Orderings_Obot__class_Obot(tc_fun(U_318,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_318)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_318) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Union__empty]) ).
fof(f_61_2,plain,
! [U_319] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_319,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_319,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_319,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_319] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_319,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_319,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_319,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_319,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_319,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_319,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [T_b] :
( 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)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__UNIV]) ).
fof(f_62_2,plain,
! [U_320] :
( c_Complete__Lattice_OSup__class_OSup(U_320,c_Orderings_Otop__class_Otop(tc_fun(U_320,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_320)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_320) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_320] :
( c_Complete__Lattice_OSup__class_OSup(U_320,c_Orderings_Otop__class_Otop(tc_fun(U_320,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_320)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_320) ),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_320,c_Orderings_Otop__class_Otop(tc_fun(U_320,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_320)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_320) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Union__UNIV]) ).
fof(f_63_2,plain,
! [U_321] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_321,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_321,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_321,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_321] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_321,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_321,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_321,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_321,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_321,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_321,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [V_A_2,V_b_2,T_b] :
( ( ( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__Inf__iff]) ).
fof(f_64_2,plain,
! [U_326,U_325,U_324] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),c_Complete__Lattice_OInf__class_OInf(U_324,U_326)))
| ? [U_323] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),U_323))
& hBOOL(hAPP(hAPP(c_member(U_324),U_323),U_326)) ) )
& ( ! [U_322] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),U_322))
| ~ hBOOL(hAPP(hAPP(c_member(U_324),U_322),U_326)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),c_Complete__Lattice_OInf__class_OInf(U_324,U_326))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_324) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_326,U_325,U_324] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),c_Complete__Lattice_OInf__class_OInf(U_324,U_326)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),sK13(U_326,U_325,U_324)))
& hBOOL(hAPP(hAPP(c_member(U_324),sK13(U_326,U_325,U_324)),U_326)) ) )
& ( ! [U_322] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),U_322))
| ~ hBOOL(hAPP(hAPP(c_member(U_324),U_322),U_326)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),c_Complete__Lattice_OInf__class_OInf(U_324,U_326))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_323,sK13(U_326,U_325,U_324))],[f_64_2]) ).
fof(f_64_4,plain,
( ! [U_324,U_325,U_326] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),sK13(U_326,U_325,U_324)))
| ~ sP18(U_324,U_325,U_326) )
& ! [U_324,U_325,U_326] :
( hBOOL(hAPP(hAPP(c_member(U_324),sK13(U_326,U_325,U_324)),U_326))
| ~ sP18(U_324,U_325,U_326) )
& ! [U_322,U_324,U_325,U_326] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),c_Complete__Lattice_OInf__class_OInf(U_324,U_326)))
| sP18(U_324,U_325,U_326)
| ~ sP19(U_322,U_324,U_325,U_326) )
& ! [U_322,U_324,U_325,U_326] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),U_322))
| ~ hBOOL(hAPP(hAPP(c_member(U_324),U_322),U_326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),c_Complete__Lattice_OInf__class_OInf(U_324,U_326)))
| ~ sP19(U_322,U_324,U_325,U_326) )
& ! [U_322,U_324,U_325,U_326] :
( sP19(U_322,U_324,U_325,U_326)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_324) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18,sP19])],[f_64_3]) ).
cnf(f_64_5,plain,
( sP19(U_322,U_324,U_325,U_326)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_324) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),U_322))
| ~ hBOOL(hAPP(hAPP(c_member(U_324),U_322),U_326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),c_Complete__Lattice_OInf__class_OInf(U_324,U_326)))
| ~ sP19(U_322,U_324,U_325,U_326) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),c_Complete__Lattice_OInf__class_OInf(U_324,U_326)))
| sP18(U_324,U_325,U_326)
| ~ sP19(U_322,U_324,U_325,U_326) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_324),sK13(U_326,U_325,U_324)),U_326))
| ~ sP18(U_324,U_325,U_326) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_324),U_325),sK13(U_326,U_325,U_324)))
| ~ sP18(U_324,U_325,U_326) ),
inference(clausify,[status(thm)],[f_64_4]) ).
fof(f_65_1,plain,
! [V_b_2,V_A_2,T_b] :
( ( ( 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))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__le__iff]) ).
fof(f_65_2,plain,
! [U_331,U_330,U_329] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),c_Complete__Lattice_OSup__class_OSup(U_329,U_330)),U_331))
| ? [U_328] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),U_328),U_331))
& hBOOL(hAPP(hAPP(c_member(U_329),U_328),U_330)) ) )
& ( ! [U_327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),U_327),U_331))
| ~ hBOOL(hAPP(hAPP(c_member(U_329),U_327),U_330)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),c_Complete__Lattice_OSup__class_OSup(U_329,U_330)),U_331)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_329) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_331,U_330,U_329] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),c_Complete__Lattice_OSup__class_OSup(U_329,U_330)),U_331))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),sK14(U_331,U_330,U_329)),U_331))
& hBOOL(hAPP(hAPP(c_member(U_329),sK14(U_331,U_330,U_329)),U_330)) ) )
& ( ! [U_327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),U_327),U_331))
| ~ hBOOL(hAPP(hAPP(c_member(U_329),U_327),U_330)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),c_Complete__Lattice_OSup__class_OSup(U_329,U_330)),U_331)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_329) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_328,sK14(U_331,U_330,U_329))],[f_65_2]) ).
fof(f_65_4,plain,
( ! [U_329,U_330,U_331] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),sK14(U_331,U_330,U_329)),U_331))
| ~ sP20(U_329,U_330,U_331) )
& ! [U_329,U_330,U_331] :
( hBOOL(hAPP(hAPP(c_member(U_329),sK14(U_331,U_330,U_329)),U_330))
| ~ sP20(U_329,U_330,U_331) )
& ! [U_329,U_330,U_327,U_331] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),c_Complete__Lattice_OSup__class_OSup(U_329,U_330)),U_331))
| sP20(U_329,U_330,U_331)
| ~ sP21(U_329,U_330,U_327,U_331) )
& ! [U_329,U_330,U_327,U_331] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),U_327),U_331))
| ~ hBOOL(hAPP(hAPP(c_member(U_329),U_327),U_330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),c_Complete__Lattice_OSup__class_OSup(U_329,U_330)),U_331))
| ~ sP21(U_329,U_330,U_327,U_331) )
& ! [U_329,U_330,U_327,U_331] :
( sP21(U_329,U_330,U_327,U_331)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_329) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20,sP21])],[f_65_3]) ).
cnf(f_65_5,plain,
( sP21(U_329,U_330,U_327,U_331)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_329) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),U_327),U_331))
| ~ hBOOL(hAPP(hAPP(c_member(U_329),U_327),U_330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),c_Complete__Lattice_OSup__class_OSup(U_329,U_330)),U_331))
| ~ sP21(U_329,U_330,U_327,U_331) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),c_Complete__Lattice_OSup__class_OSup(U_329,U_330)),U_331))
| sP20(U_329,U_330,U_331)
| ~ sP21(U_329,U_330,U_327,U_331) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_329),sK14(U_331,U_330,U_329)),U_330))
| ~ sP20(U_329,U_330,U_331) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_329),sK14(U_331,U_330,U_329)),U_331))
| ~ sP20(U_329,U_330,U_331) ),
inference(clausify,[status(thm)],[f_65_4]) ).
fof(f_66_1,plain,
! [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),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_Union__mono]) ).
fof(f_66_2,plain,
! [U_334,U_333,U_332] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_332,tc_HOL_Obool),U_333)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_332,tc_HOL_Obool),U_334)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_332,tc_HOL_Obool),tc_HOL_Obool)),U_333),U_334)) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_334,U_333,U_332] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_332,tc_HOL_Obool),U_333)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_332,tc_HOL_Obool),U_334)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_332,tc_HOL_Obool),tc_HOL_Obool)),U_333),U_334)) ),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_332,tc_HOL_Obool),U_333)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_332,tc_HOL_Obool),U_334)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_332,tc_HOL_Obool),tc_HOL_Obool)),U_333),U_334)) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [V_A_2,V_B_2,T_b] :
( 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)))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono]) ).
fof(f_67_2,plain,
! [U_337,U_336,U_335] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_335,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_335,tc_HOL_Obool),U_337)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_335,tc_HOL_Obool),U_336)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_335,tc_HOL_Obool),tc_HOL_Obool)),U_336),U_337)) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_336,U_335,U_337] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_335,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_335,tc_HOL_Obool),U_337)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_335,tc_HOL_Obool),U_336)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_335,tc_HOL_Obool),tc_HOL_Obool)),U_336),U_337)) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_335,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_335,tc_HOL_Obool),U_337)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_335,tc_HOL_Obool),U_336)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_335,tc_HOL_Obool),tc_HOL_Obool)),U_336),U_337)) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [T_b,V_B_2,V_A_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityE]) ).
fof(f_68_2,plain,
! [U_340,U_339,U_338] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_340,tc_HOL_Obool)),U_339),U_338))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_340,tc_HOL_Obool)),U_338),U_339)) )
| U_338 != U_339 ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( ! [U_338,U_339,U_340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_340,tc_HOL_Obool)),U_339),U_338))
| ~ sP22(U_338,U_339,U_340) )
& ! [U_338,U_339,U_340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_340,tc_HOL_Obool)),U_338),U_339))
| ~ sP22(U_338,U_339,U_340) )
& ! [U_338,U_339,U_340] :
( sP22(U_338,U_339,U_340)
| U_338 != U_339 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_68_2]) ).
cnf(f_68_4,plain,
( sP22(U_338,U_339,U_340)
| U_338 != U_339 ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_340,tc_HOL_Obool)),U_338),U_339))
| ~ sP22(U_338,U_339,U_340) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_340,tc_HOL_Obool)),U_339),U_338))
| ~ sP22(U_338,U_339,U_340) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [V_C_2,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),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__trans]) ).
fof(f_69_2,plain,
! [U_344,U_343,U_342,U_341] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_342),U_344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_343),U_344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_342),U_343)) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_342,U_341,U_343,U_344] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_342),U_344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_343),U_344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_342),U_343)) ),
inference(definitional_conversion,[status(esa)],[f_69_2]) ).
cnf(f_69_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_342),U_344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_343),U_344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_341,tc_HOL_Obool)),U_342),U_343)) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_1,plain,
! [T_b,V_B_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityD2]) ).
fof(f_70_2,plain,
! [U_347,U_346,U_345] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_347,tc_HOL_Obool)),U_346),U_345))
| U_345 != U_346 ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_346,U_345,U_347] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_347,tc_HOL_Obool)),U_346),U_345))
| U_345 != U_346 ),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_347,tc_HOL_Obool)),U_346),U_345))
| U_345 != U_346 ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [T_b,V_B_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityD1]) ).
fof(f_71_2,plain,
! [U_350,U_349,U_348] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_350,tc_HOL_Obool)),U_348),U_349))
| U_348 != U_349 ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_348,U_349,U_350] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_350,tc_HOL_Obool)),U_348),U_349))
| U_348 != U_349 ),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_350,tc_HOL_Obool)),U_348),U_349))
| U_348 != U_349 ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
! [T_b,V_B_2,V_A_2] :
( ( V_A_2 = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| V_A_2 != V_B_2 ) ),
inference(fof_nnf,[status(thm)],[fact_set__eq__subset]) ).
fof(f_72_2,plain,
! [U_353,U_352,U_351] :
( ( U_351 = U_352
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_353,tc_HOL_Obool)),U_352),U_351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_353,tc_HOL_Obool)),U_351),U_352)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_353,tc_HOL_Obool)),U_352),U_351))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_353,tc_HOL_Obool)),U_351),U_352)) )
| U_351 != U_352 ) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ! [U_359,U_357,U_355] :
( U_355 = U_357
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_359,tc_HOL_Obool)),U_357),U_355))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_359,tc_HOL_Obool)),U_355),U_357)) )
& ! [U_358,U_356,U_354] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_358,tc_HOL_Obool)),U_356),U_354))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_358,tc_HOL_Obool)),U_354),U_356)) )
| U_354 != U_356 ) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
( ! [U_356,U_354,U_358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_358,tc_HOL_Obool)),U_356),U_354))
| ~ sP23(U_356,U_354,U_358) )
& ! [U_356,U_354,U_358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_358,tc_HOL_Obool)),U_354),U_356))
| ~ sP23(U_356,U_354,U_358) )
& ! [U_357,U_355,U_359] :
( U_355 = U_357
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_359,tc_HOL_Obool)),U_357),U_355))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_359,tc_HOL_Obool)),U_355),U_357)) )
& ! [U_356,U_354,U_358] :
( sP23(U_356,U_354,U_358)
| U_354 != U_356 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_72_3]) ).
cnf(f_72_5,plain,
( sP23(U_356,U_354,U_358)
| U_354 != U_356 ),
inference(clausify,[status(thm)],[f_72_4]) ).
cnf(f_72_6,plain,
( U_355 = U_357
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_359,tc_HOL_Obool)),U_357),U_355))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_359,tc_HOL_Obool)),U_355),U_357)) ),
inference(clausify,[status(thm)],[f_72_4]) ).
cnf(f_72_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_358,tc_HOL_Obool)),U_354),U_356))
| ~ sP23(U_356,U_354,U_358) ),
inference(clausify,[status(thm)],[f_72_4]) ).
cnf(f_72_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_358,tc_HOL_Obool)),U_356),U_354))
| ~ sP23(U_356,U_354,U_358) ),
inference(clausify,[status(thm)],[f_72_4]) ).
fof(f_73_1,plain,
! [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_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)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__empty]) ).
fof(f_73_2,plain,
! [U_361,U_360] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_360,tc_HOL_Obool)),U_361),c_Orderings_Obot__class_Obot(tc_fun(U_360,tc_HOL_Obool))))
| U_361 != c_Orderings_Obot__class_Obot(tc_fun(U_360,tc_HOL_Obool)) )
& ( U_361 = c_Orderings_Obot__class_Obot(tc_fun(U_360,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_360,tc_HOL_Obool)),U_361),c_Orderings_Obot__class_Obot(tc_fun(U_360,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_365,U_363] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_363,tc_HOL_Obool)),U_365),c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool))))
| U_365 != c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool)) )
& ! [U_364,U_362] :
( U_364 = c_Orderings_Obot__class_Obot(tc_fun(U_362,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_362,tc_HOL_Obool)),U_364),c_Orderings_Obot__class_Obot(tc_fun(U_362,tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
( ! [U_363,U_365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_363,tc_HOL_Obool)),U_365),c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool))))
| U_365 != c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool)) )
& ! [U_364,U_362] :
( U_364 = c_Orderings_Obot__class_Obot(tc_fun(U_362,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_362,tc_HOL_Obool)),U_364),c_Orderings_Obot__class_Obot(tc_fun(U_362,tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa)],[f_73_3]) ).
cnf(f_73_5,plain,
( U_364 = c_Orderings_Obot__class_Obot(tc_fun(U_362,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_362,tc_HOL_Obool)),U_364),c_Orderings_Obot__class_Obot(tc_fun(U_362,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_363,tc_HOL_Obool)),U_365),c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool))))
| U_365 != c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_subset__refl]) ).
fof(f_74_2,plain,
! [U_367,U_366] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_366,tc_HOL_Obool)),U_367),U_367)),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_366,U_367] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_366,tc_HOL_Obool)),U_367),U_367)),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_366,tc_HOL_Obool)),U_367),U_367)),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_subset__UNIV]) ).
fof(f_75_2,plain,
! [U_369,U_368] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_368,tc_HOL_Obool)),U_369),c_Orderings_Otop__class_Otop(tc_fun(U_368,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_368,U_369] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_368,tc_HOL_Obool)),U_369),c_Orderings_Otop__class_Otop(tc_fun(U_368,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_75_2]) ).
cnf(f_75_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_368,tc_HOL_Obool)),U_369),c_Orderings_Otop__class_Otop(tc_fun(U_368,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UNIV__not__empty]) ).
fof(f_76_2,plain,
! [U_370] : c_Orderings_Otop__class_Otop(tc_fun(U_370,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_370,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_370] : c_Orderings_Otop__class_Otop(tc_fun(U_370,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_370,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_76_2]) ).
cnf(f_76_4,plain,
c_Orderings_Otop__class_Otop(tc_fun(U_370,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_370,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [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),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Union__upper]) ).
fof(f_77_2,plain,
! [U_373,U_372,U_371] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_371,tc_HOL_Obool)),U_372),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_371,tc_HOL_Obool),U_373)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_371,tc_HOL_Obool)),U_372),U_373)) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_371,U_372,U_373] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_371,tc_HOL_Obool)),U_372),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_371,tc_HOL_Obool),U_373)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_371,tc_HOL_Obool)),U_372),U_373)) ),
inference(definitional_conversion,[status(esa)],[f_77_2]) ).
cnf(f_77_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_371,tc_HOL_Obool)),U_372),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_371,tc_HOL_Obool),U_373)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_371,tc_HOL_Obool)),U_372),U_373)) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [V_A_2,V_x_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__upper]) ).
fof(f_78_2,plain,
! [U_376,U_375,U_374] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_374),U_375),c_Complete__Lattice_OSup__class_OSup(U_374,U_376)))
| ~ hBOOL(hAPP(hAPP(c_member(U_374),U_375),U_376))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_374) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_374,U_375,U_376] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_374),U_375),c_Complete__Lattice_OSup__class_OSup(U_374,U_376)))
| ~ hBOOL(hAPP(hAPP(c_member(U_374),U_375),U_376))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_374) ),
inference(definitional_conversion,[status(esa)],[f_78_2]) ).
cnf(f_78_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_374),U_375),c_Complete__Lattice_OSup__class_OSup(U_374,U_376)))
| ~ hBOOL(hAPP(hAPP(c_member(U_374),U_375),U_376))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_374) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [V_A_2,V_B_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Inter__lower]) ).
fof(f_79_2,plain,
! [U_379,U_378,U_377] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_377,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_377,tc_HOL_Obool),U_379)),U_378))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_377,tc_HOL_Obool)),U_378),U_379)) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_377,U_378,U_379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_377,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_377,tc_HOL_Obool),U_379)),U_378))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_377,tc_HOL_Obool)),U_378),U_379)) ),
inference(definitional_conversion,[status(esa)],[f_79_2]) ).
cnf(f_79_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_377,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_377,tc_HOL_Obool),U_379)),U_378))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_377,tc_HOL_Obool)),U_378),U_379)) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_1,plain,
! [V_A_2,V_x_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__lower]) ).
fof(f_80_2,plain,
! [U_382,U_381,U_380] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_380),c_Complete__Lattice_OInf__class_OInf(U_380,U_382)),U_381))
| ~ hBOOL(hAPP(hAPP(c_member(U_380),U_381),U_382))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_380) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_380,U_381,U_382] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_380),c_Complete__Lattice_OInf__class_OInf(U_380,U_382)),U_381))
| ~ hBOOL(hAPP(hAPP(c_member(U_380),U_381),U_382))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_380) ),
inference(definitional_conversion,[status(esa)],[f_80_2]) ).
cnf(f_80_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_380),c_Complete__Lattice_OInf__class_OInf(U_380,U_382)),U_381))
| ~ hBOOL(hAPP(hAPP(c_member(U_380),U_381),U_382))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_380) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_in__mono]) ).
fof(f_81_2,plain,
! [U_386,U_385,U_384,U_383] :
( hBOOL(hAPP(hAPP(c_member(U_383),U_386),U_385))
| ~ hBOOL(hAPP(hAPP(c_member(U_383),U_386),U_384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_383,tc_HOL_Obool)),U_384),U_385)) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_383,U_384,U_385,U_386] :
( hBOOL(hAPP(hAPP(c_member(U_383),U_386),U_385))
| ~ hBOOL(hAPP(hAPP(c_member(U_383),U_386),U_384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_383,tc_HOL_Obool)),U_384),U_385)) ),
inference(definitional_conversion,[status(esa)],[f_81_2]) ).
cnf(f_81_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_383),U_386),U_385))
| ~ hBOOL(hAPP(hAPP(c_member(U_383),U_386),U_384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_383,tc_HOL_Obool)),U_384),U_385)) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_set__rev__mp]) ).
fof(f_82_2,plain,
! [U_390,U_389,U_388,U_387] :
( hBOOL(hAPP(hAPP(c_member(U_387),U_388),U_390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_387,tc_HOL_Obool)),U_389),U_390))
| ~ hBOOL(hAPP(hAPP(c_member(U_387),U_388),U_389)) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_387,U_388,U_389,U_390] :
( hBOOL(hAPP(hAPP(c_member(U_387),U_388),U_390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_387,tc_HOL_Obool)),U_389),U_390))
| ~ hBOOL(hAPP(hAPP(c_member(U_387),U_388),U_389)) ),
inference(definitional_conversion,[status(esa)],[f_82_2]) ).
cnf(f_82_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_387),U_388),U_390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_387,tc_HOL_Obool)),U_389),U_390))
| ~ hBOOL(hAPP(hAPP(c_member(U_387),U_388),U_389)) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_set__mp]) ).
fof(f_83_2,plain,
! [U_394,U_393,U_392,U_391] :
( hBOOL(hAPP(hAPP(c_member(U_391),U_394),U_393))
| ~ hBOOL(hAPP(hAPP(c_member(U_391),U_394),U_392))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_391,tc_HOL_Obool)),U_392),U_393)) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_391,U_392,U_393,U_394] :
( hBOOL(hAPP(hAPP(c_member(U_391),U_394),U_393))
| ~ hBOOL(hAPP(hAPP(c_member(U_391),U_394),U_392))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_391,tc_HOL_Obool)),U_392),U_393)) ),
inference(definitional_conversion,[status(esa)],[f_83_2]) ).
cnf(f_83_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_391),U_394),U_393))
| ~ hBOOL(hAPP(hAPP(c_member(U_391),U_394),U_392))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_391,tc_HOL_Obool)),U_392),U_393)) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [V_A_2,T_b] :
( ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
| V_A_2 != 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))
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_all__not__in__conv]) ).
fof(f_84_2,plain,
! [U_398,U_397] :
( ( ! [U_396] : ~ hBOOL(hAPP(hAPP(c_member(U_397),U_396),U_398))
| U_398 != c_Orderings_Obot__class_Obot(tc_fun(U_397,tc_HOL_Obool)) )
& ( U_398 = c_Orderings_Obot__class_Obot(tc_fun(U_397,tc_HOL_Obool))
| ? [U_395] : hBOOL(hAPP(hAPP(c_member(U_397),U_395),U_398)) ) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_402,U_400] :
( ! [U_396] : ~ hBOOL(hAPP(hAPP(c_member(U_400),U_396),U_402))
| U_402 != c_Orderings_Obot__class_Obot(tc_fun(U_400,tc_HOL_Obool)) )
& ! [U_401,U_399] :
( U_401 = c_Orderings_Obot__class_Obot(tc_fun(U_399,tc_HOL_Obool))
| ? [U_395] : hBOOL(hAPP(hAPP(c_member(U_399),U_395),U_401)) ) ),
inference(miniscope,[status(thm)],[f_84_2]) ).
fof(f_84_4,plain,
( ! [U_402,U_400] :
( ! [U_396] : ~ hBOOL(hAPP(hAPP(c_member(U_400),U_396),U_402))
| U_402 != c_Orderings_Obot__class_Obot(tc_fun(U_400,tc_HOL_Obool)) )
& ! [U_401,U_399] :
( U_401 = c_Orderings_Obot__class_Obot(tc_fun(U_399,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_399),sK15(U_401,U_399)),U_401)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_395,sK15(U_401,U_399))],[f_84_3]) ).
fof(f_84_5,plain,
( ! [U_396,U_400,U_402] :
( ~ hBOOL(hAPP(hAPP(c_member(U_400),U_396),U_402))
| U_402 != c_Orderings_Obot__class_Obot(tc_fun(U_400,tc_HOL_Obool)) )
& ! [U_401,U_399] :
( U_401 = c_Orderings_Obot__class_Obot(tc_fun(U_399,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_399),sK15(U_401,U_399)),U_401)) ) ),
inference(definitional_conversion,[status(esa)],[f_84_4]) ).
cnf(f_84_6,plain,
( U_401 = c_Orderings_Obot__class_Obot(tc_fun(U_399,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_399),sK15(U_401,U_399)),U_401)) ),
inference(clausify,[status(thm)],[f_84_5]) ).
cnf(f_84_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_400),U_396),U_402))
| U_402 != c_Orderings_Obot__class_Obot(tc_fun(U_400,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_84_5]) ).
fof(f_85_1,plain,
! [V_A_2,T_b] :
( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
| V_A_2 = 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))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__in__conv]) ).
fof(f_85_2,plain,
! [U_406,U_405] :
( ( ? [U_404] : hBOOL(hAPP(hAPP(c_member(U_405),U_404),U_406))
| U_406 = c_Orderings_Obot__class_Obot(tc_fun(U_405,tc_HOL_Obool)) )
& ( U_406 != c_Orderings_Obot__class_Obot(tc_fun(U_405,tc_HOL_Obool))
| ! [U_403] : ~ hBOOL(hAPP(hAPP(c_member(U_405),U_403),U_406)) ) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
( ! [U_410,U_408] :
( ? [U_404] : hBOOL(hAPP(hAPP(c_member(U_408),U_404),U_410))
| U_410 = c_Orderings_Obot__class_Obot(tc_fun(U_408,tc_HOL_Obool)) )
& ! [U_409,U_407] :
( U_409 != c_Orderings_Obot__class_Obot(tc_fun(U_407,tc_HOL_Obool))
| ! [U_403] : ~ hBOOL(hAPP(hAPP(c_member(U_407),U_403),U_409)) ) ),
inference(miniscope,[status(thm)],[f_85_2]) ).
fof(f_85_4,plain,
( ! [U_410,U_408] :
( hBOOL(hAPP(hAPP(c_member(U_408),sK16(U_410,U_408)),U_410))
| U_410 = c_Orderings_Obot__class_Obot(tc_fun(U_408,tc_HOL_Obool)) )
& ! [U_409,U_407] :
( U_409 != c_Orderings_Obot__class_Obot(tc_fun(U_407,tc_HOL_Obool))
| ! [U_403] : ~ hBOOL(hAPP(hAPP(c_member(U_407),U_403),U_409)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_404,sK16(U_410,U_408))],[f_85_3]) ).
fof(f_85_5,plain,
( ! [U_408,U_410] :
( hBOOL(hAPP(hAPP(c_member(U_408),sK16(U_410,U_408)),U_410))
| U_410 = c_Orderings_Obot__class_Obot(tc_fun(U_408,tc_HOL_Obool)) )
& ! [U_403,U_409,U_407] :
( U_409 != c_Orderings_Obot__class_Obot(tc_fun(U_407,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_407),U_403),U_409)) ) ),
inference(definitional_conversion,[status(esa)],[f_85_4]) ).
cnf(f_85_6,plain,
( U_409 != c_Orderings_Obot__class_Obot(tc_fun(U_407,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_407),U_403),U_409)) ),
inference(clausify,[status(thm)],[f_85_5]) ).
cnf(f_85_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_408),sK16(U_410,U_408)),U_410))
| U_410 = c_Orderings_Obot__class_Obot(tc_fun(U_408,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_85_5]) ).
fof(f_86_1,plain,
! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_empty__iff]) ).
fof(f_86_2,plain,
! [U_412,U_411] : ~ hBOOL(hAPP(hAPP(c_member(U_411),U_412),c_Orderings_Obot__class_Obot(tc_fun(U_411,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_411,U_412] : ~ hBOOL(hAPP(hAPP(c_member(U_411),U_412),c_Orderings_Obot__class_Obot(tc_fun(U_411,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
~ hBOOL(hAPP(hAPP(c_member(U_411),U_412),c_Orderings_Obot__class_Obot(tc_fun(U_411,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
! [V_a_2,T_b,V_A_2] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_equals0D]) ).
fof(f_87_2,plain,
! [U_415,U_414,U_413] :
( ~ hBOOL(hAPP(hAPP(c_member(U_414),U_415),U_413))
| U_413 != c_Orderings_Obot__class_Obot(tc_fun(U_414,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_413,U_414,U_415] :
( ~ hBOOL(hAPP(hAPP(c_member(U_414),U_415),U_413))
| U_413 != c_Orderings_Obot__class_Obot(tc_fun(U_414,tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_414),U_415),U_413))
| U_413 != c_Orderings_Obot__class_Obot(tc_fun(U_414,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [V_Pa_2,T_b] :
( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
| ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x)) )
& ( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_Pa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).
fof(f_88_2,plain,
! [U_419,U_418] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_418,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_418),U_419)
| ? [U_417] : hBOOL(hAPP(U_419,U_417)) )
& ( ! [U_416] : ~ hBOOL(hAPP(U_419,U_416))
| c_Orderings_Obot__class_Obot(tc_fun(U_418,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_418),U_419) ) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
( ! [U_423] :
( ! [U_421] : c_Orderings_Obot__class_Obot(tc_fun(U_421,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_421),U_423)
| ? [U_417] : hBOOL(hAPP(U_423,U_417)) )
& ! [U_422] :
( ! [U_420] : c_Orderings_Obot__class_Obot(tc_fun(U_420,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_420),U_422)
| ! [U_416] : ~ hBOOL(hAPP(U_422,U_416)) ) ),
inference(miniscope,[status(thm)],[f_88_2]) ).
fof(f_88_4,plain,
( ! [U_423] :
( ! [U_421] : c_Orderings_Obot__class_Obot(tc_fun(U_421,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_421),U_423)
| hBOOL(hAPP(U_423,sK17(U_423))) )
& ! [U_422] :
( ! [U_420] : c_Orderings_Obot__class_Obot(tc_fun(U_420,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_420),U_422)
| ! [U_416] : ~ hBOOL(hAPP(U_422,U_416)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_417,sK17(U_423))],[f_88_3]) ).
fof(f_88_5,plain,
( ! [U_421,U_423] :
( c_Orderings_Obot__class_Obot(tc_fun(U_421,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_421),U_423)
| hBOOL(hAPP(U_423,sK17(U_423))) )
& ! [U_416,U_420,U_422] :
( c_Orderings_Obot__class_Obot(tc_fun(U_420,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_420),U_422)
| ~ hBOOL(hAPP(U_422,U_416)) ) ),
inference(definitional_conversion,[status(esa)],[f_88_4]) ).
cnf(f_88_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_420,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_420),U_422)
| ~ hBOOL(hAPP(U_422,U_416)) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_7,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_421,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_421),U_423)
| hBOOL(hAPP(U_423,sK17(U_423))) ),
inference(clausify,[status(thm)],[f_88_5]) ).
fof(f_89_1,plain,
! [V_Pa_2,T_b] :
( ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x)) )
& ( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
| hAPP(c_Set_OCollect(T_b),V_Pa_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).
fof(f_89_2,plain,
! [U_427,U_426] :
( ( hAPP(c_Set_OCollect(U_426),U_427) = c_Orderings_Obot__class_Obot(tc_fun(U_426,tc_HOL_Obool))
| ? [U_425] : hBOOL(hAPP(U_427,U_425)) )
& ( ! [U_424] : ~ hBOOL(hAPP(U_427,U_424))
| hAPP(c_Set_OCollect(U_426),U_427) != c_Orderings_Obot__class_Obot(tc_fun(U_426,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_431] :
( ! [U_429] : hAPP(c_Set_OCollect(U_429),U_431) = c_Orderings_Obot__class_Obot(tc_fun(U_429,tc_HOL_Obool))
| ? [U_425] : hBOOL(hAPP(U_431,U_425)) )
& ! [U_430] :
( ! [U_428] : hAPP(c_Set_OCollect(U_428),U_430) != c_Orderings_Obot__class_Obot(tc_fun(U_428,tc_HOL_Obool))
| ! [U_424] : ~ hBOOL(hAPP(U_430,U_424)) ) ),
inference(miniscope,[status(thm)],[f_89_2]) ).
fof(f_89_4,plain,
( ! [U_431] :
( ! [U_429] : hAPP(c_Set_OCollect(U_429),U_431) = c_Orderings_Obot__class_Obot(tc_fun(U_429,tc_HOL_Obool))
| hBOOL(hAPP(U_431,sK18(U_431))) )
& ! [U_430] :
( ! [U_428] : hAPP(c_Set_OCollect(U_428),U_430) != c_Orderings_Obot__class_Obot(tc_fun(U_428,tc_HOL_Obool))
| ! [U_424] : ~ hBOOL(hAPP(U_430,U_424)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_425,sK18(U_431))],[f_89_3]) ).
fof(f_89_5,plain,
( ! [U_429,U_431] :
( hAPP(c_Set_OCollect(U_429),U_431) = c_Orderings_Obot__class_Obot(tc_fun(U_429,tc_HOL_Obool))
| hBOOL(hAPP(U_431,sK18(U_431))) )
& ! [U_424,U_430,U_428] :
( hAPP(c_Set_OCollect(U_428),U_430) != c_Orderings_Obot__class_Obot(tc_fun(U_428,tc_HOL_Obool))
| ~ hBOOL(hAPP(U_430,U_424)) ) ),
inference(definitional_conversion,[status(esa)],[f_89_4]) ).
cnf(f_89_6,plain,
( hAPP(c_Set_OCollect(U_428),U_430) != c_Orderings_Obot__class_Obot(tc_fun(U_428,tc_HOL_Obool))
| ~ hBOOL(hAPP(U_430,U_424)) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_7,plain,
( hAPP(c_Set_OCollect(U_429),U_431) = c_Orderings_Obot__class_Obot(tc_fun(U_429,tc_HOL_Obool))
| hBOOL(hAPP(U_431,sK18(U_431))) ),
inference(clausify,[status(thm)],[f_89_5]) ).
fof(f_90_1,plain,
! [V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__refl]) ).
fof(f_90_2,plain,
! [U_433,U_432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_432),U_433),U_433))
| ~ class_Orderings_Opreorder(U_432) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_432,U_433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_432),U_433),U_433))
| ~ class_Orderings_Opreorder(U_432) ),
inference(definitional_conversion,[status(esa)],[f_90_2]) ).
cnf(f_90_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_432),U_433),U_433))
| ~ class_Orderings_Opreorder(U_432) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
! [V_x_2,T_c,T_b] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b)
| ~ class_Orderings_Otop(T_b) ),
inference(fof_nnf,[status(thm)],[fact_top__apply]) ).
fof(f_91_2,plain,
! [U_436,U_435,U_434] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_435,U_434)),U_436) = c_Orderings_Otop__class_Otop(U_434)
| ~ class_Orderings_Otop(U_434) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_434,U_435,U_436] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_435,U_434)),U_436) = c_Orderings_Otop__class_Otop(U_434)
| ~ class_Orderings_Otop(U_434) ),
inference(definitional_conversion,[status(esa)],[f_91_2]) ).
cnf(f_91_4,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_435,U_434)),U_436) = c_Orderings_Otop__class_Otop(U_434)
| ~ class_Orderings_Otop(U_434) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [V_x_2,T_c,T_b] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
| ~ class_Orderings_Obot(T_b) ),
inference(fof_nnf,[status(thm)],[fact_bot__apply]) ).
fof(f_92_2,plain,
! [U_439,U_438,U_437] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_438,U_437)),U_439) = c_Orderings_Obot__class_Obot(U_437)
| ~ class_Orderings_Obot(U_437) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_437,U_438,U_439] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_438,U_437)),U_439) = c_Orderings_Obot__class_Obot(U_437)
| ~ class_Orderings_Obot(U_437) ),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_438,U_437)),U_439) = c_Orderings_Obot__class_Obot(U_437)
| ~ class_Orderings_Obot(U_437) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(f_93_2,plain,
! [U_441,U_440] : hBOOL(hAPP(hAPP(c_member(U_440),U_441),c_Orderings_Otop__class_Otop(tc_fun(U_440,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_440,U_441] : hBOOL(hAPP(hAPP(c_member(U_440),U_441),c_Orderings_Otop__class_Otop(tc_fun(U_440,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_93_2]) ).
cnf(f_93_4,plain,
hBOOL(hAPP(hAPP(c_member(U_440),U_441),c_Orderings_Otop__class_Otop(tc_fun(U_440,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)))
| ~ class_Orderings_Otop(T_a) ),
inference(fof_nnf,[status(thm)],[fact_top__greatest]) ).
fof(f_94_2,plain,
! [U_443,U_442] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_442),U_443),c_Orderings_Otop__class_Otop(U_442)))
| ~ class_Orderings_Otop(U_442) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_442,U_443] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_442),U_443),c_Orderings_Otop__class_Otop(U_442)))
| ~ class_Orderings_Otop(U_442) ),
inference(definitional_conversion,[status(esa)],[f_94_2]) ).
cnf(f_94_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_442),U_443),c_Orderings_Otop__class_Otop(U_442)))
| ~ class_Orderings_Otop(U_442) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [V_g_2,V_f_2,T_b,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| ? [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))) )
& ( ! [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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_95_2,plain,
! [U_449,U_448,U_447,U_446] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_447,U_446)),U_448),U_449))
| ? [U_445] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_446),hAPP(U_448,U_445)),hAPP(U_449,U_445))) )
& ( ! [U_444] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_446),hAPP(U_448,U_444)),hAPP(U_449,U_444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_447,U_446)),U_448),U_449)) ) )
| ~ class_Orderings_Oord(U_446) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_449,U_448,U_447,U_446] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_447,U_446)),U_448),U_449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_446),hAPP(U_448,sK19(U_449,U_448,U_447,U_446))),hAPP(U_449,sK19(U_449,U_448,U_447,U_446)))) )
& ( ! [U_444] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_446),hAPP(U_448,U_444)),hAPP(U_449,U_444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_447,U_446)),U_448),U_449)) ) )
| ~ class_Orderings_Oord(U_446) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_445,sK19(U_449,U_448,U_447,U_446))],[f_95_2]) ).
fof(f_95_4,plain,
( ! [U_444,U_446,U_447,U_448,U_449] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_447,U_446)),U_448),U_449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_446),hAPP(U_448,sK19(U_449,U_448,U_447,U_446))),hAPP(U_449,sK19(U_449,U_448,U_447,U_446))))
| ~ sP24(U_444,U_446,U_447,U_448,U_449) )
& ! [U_444,U_446,U_447,U_448,U_449] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_446),hAPP(U_448,U_444)),hAPP(U_449,U_444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_447,U_446)),U_448),U_449))
| ~ sP24(U_444,U_446,U_447,U_448,U_449) )
& ! [U_444,U_446,U_447,U_448,U_449] :
( sP24(U_444,U_446,U_447,U_448,U_449)
| ~ class_Orderings_Oord(U_446) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_95_3]) ).
cnf(f_95_5,plain,
( sP24(U_444,U_446,U_447,U_448,U_449)
| ~ class_Orderings_Oord(U_446) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_446),hAPP(U_448,U_444)),hAPP(U_449,U_444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_447,U_446)),U_448),U_449))
| ~ sP24(U_444,U_446,U_447,U_448,U_449) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_447,U_446)),U_448),U_449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_446),hAPP(U_448,sK19(U_449,U_448,U_447,U_446))),hAPP(U_449,sK19(U_449,U_448,U_447,U_446))))
| ~ sP24(U_444,U_446,U_447,U_448,U_449) ),
inference(clausify,[status(thm)],[f_95_4]) ).
fof(f_96_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_96_2,plain,
! [U_454,U_453,U_452,U_451,U_450] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),hAPP(U_452,U_454)),hAPP(U_453,U_454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_451,U_450)),U_452),U_453))
| ~ class_Orderings_Oord(U_450) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_451,U_452,U_450,U_453,U_454] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),hAPP(U_452,U_454)),hAPP(U_453,U_454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_451,U_450)),U_452),U_453))
| ~ class_Orderings_Oord(U_450) ),
inference(definitional_conversion,[status(esa)],[f_96_2]) ).
cnf(f_96_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),hAPP(U_452,U_454)),hAPP(U_453,U_454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_451,U_450)),U_452),U_453))
| ~ class_Orderings_Oord(U_450) ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_97_2,plain,
! [U_459,U_458,U_457,U_456,U_455] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_455),hAPP(U_457,U_459)),hAPP(U_458,U_459)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_456,U_455)),U_457),U_458))
| ~ class_Orderings_Oord(U_455) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_455,U_456,U_457,U_458,U_459] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_455),hAPP(U_457,U_459)),hAPP(U_458,U_459)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_456,U_455)),U_457),U_458))
| ~ class_Orderings_Oord(U_455) ),
inference(definitional_conversion,[status(esa)],[f_97_2]) ).
cnf(f_97_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_455),hAPP(U_457,U_459)),hAPP(U_458,U_459)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_456,U_455)),U_457),U_458))
| ~ class_Orderings_Oord(U_455) ),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x))
| ~ class_Orderings_Obot(T_a) ),
inference(fof_nnf,[status(thm)],[fact_bot__least]) ).
fof(f_98_2,plain,
! [U_461,U_460] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_460),c_Orderings_Obot__class_Obot(U_460)),U_461))
| ~ class_Orderings_Obot(U_460) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_461,U_460] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_460),c_Orderings_Obot__class_Obot(U_460)),U_461))
| ~ class_Orderings_Obot(U_460) ),
inference(definitional_conversion,[status(esa)],[f_98_2]) ).
cnf(f_98_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_460),c_Orderings_Obot__class_Obot(U_460)),U_461))
| ~ class_Orderings_Obot(U_460) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
! [V_A_2,V_C_2,T_b] :
( 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)))
| ? [B_X] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_InterI]) ).
fof(f_99_2,plain,
! [U_465,U_464,U_463] :
( hBOOL(hAPP(hAPP(c_member(U_463),U_465),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_463,tc_HOL_Obool),U_464)))
| ? [U_462] :
( ~ hBOOL(hAPP(hAPP(c_member(U_463),U_465),U_462))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_463,tc_HOL_Obool)),U_462),U_464)) ) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_465,U_464,U_463] :
( hBOOL(hAPP(hAPP(c_member(U_463),U_465),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_463,tc_HOL_Obool),U_464)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_463),U_465),sK20(U_465,U_464,U_463)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_463,tc_HOL_Obool)),sK20(U_465,U_464,U_463)),U_464)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_462,sK20(U_465,U_464,U_463))],[f_99_2]) ).
fof(f_99_4,plain,
( ! [U_463,U_464,U_465] :
( ~ hBOOL(hAPP(hAPP(c_member(U_463),U_465),sK20(U_465,U_464,U_463)))
| ~ sP25(U_463,U_464,U_465) )
& ! [U_463,U_464,U_465] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_463,tc_HOL_Obool)),sK20(U_465,U_464,U_463)),U_464))
| ~ sP25(U_463,U_464,U_465) )
& ! [U_463,U_464,U_465] :
( hBOOL(hAPP(hAPP(c_member(U_463),U_465),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_463,tc_HOL_Obool),U_464)))
| sP25(U_463,U_464,U_465) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_99_3]) ).
cnf(f_99_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_463),U_465),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_463,tc_HOL_Obool),U_464)))
| sP25(U_463,U_464,U_465) ),
inference(clausify,[status(thm)],[f_99_4]) ).
cnf(f_99_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_463,tc_HOL_Obool)),sK20(U_465,U_464,U_463)),U_464))
| ~ sP25(U_463,U_464,U_465) ),
inference(clausify,[status(thm)],[f_99_4]) ).
cnf(f_99_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_463),U_465),sK20(U_465,U_464,U_463)))
| ~ sP25(U_463,U_464,U_465) ),
inference(clausify,[status(thm)],[f_99_4]) ).
fof(f_100_1,plain,
! [V_C_2,V_A_2,T_b] :
( ? [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_UnionE]) ).
fof(f_100_2,plain,
! [U_469,U_468,U_467] :
( ? [U_466] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_467,tc_HOL_Obool)),U_466),U_469))
& hBOOL(hAPP(hAPP(c_member(U_467),U_468),U_466)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_467),U_468),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_467,tc_HOL_Obool),U_469))) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_469,U_468,U_467] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_467,tc_HOL_Obool)),sK21(U_469,U_468,U_467)),U_469))
& hBOOL(hAPP(hAPP(c_member(U_467),U_468),sK21(U_469,U_468,U_467))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_467),U_468),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_467,tc_HOL_Obool),U_469))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_466,sK21(U_469,U_468,U_467))],[f_100_2]) ).
fof(f_100_4,plain,
( ! [U_467,U_468,U_469] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_467,tc_HOL_Obool)),sK21(U_469,U_468,U_467)),U_469))
| ~ sP26(U_467,U_468,U_469) )
& ! [U_467,U_468,U_469] :
( hBOOL(hAPP(hAPP(c_member(U_467),U_468),sK21(U_469,U_468,U_467)))
| ~ sP26(U_467,U_468,U_469) )
& ! [U_467,U_468,U_469] :
( sP26(U_467,U_468,U_469)
| ~ hBOOL(hAPP(hAPP(c_member(U_467),U_468),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_467,tc_HOL_Obool),U_469))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_100_3]) ).
cnf(f_100_5,plain,
( sP26(U_467,U_468,U_469)
| ~ hBOOL(hAPP(hAPP(c_member(U_467),U_468),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_467,tc_HOL_Obool),U_469))) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_467),U_468),sK21(U_469,U_468,U_467)))
| ~ sP26(U_467,U_468,U_469) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_467,tc_HOL_Obool)),sK21(U_469,U_468,U_467)),U_469))
| ~ sP26(U_467,U_468,U_469) ),
inference(clausify,[status(thm)],[f_100_4]) ).
fof(f_101_1,plain,
! [V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
| ? [B_X] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),B_X))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Inter__greatest]) ).
fof(f_101_2,plain,
! [U_473,U_472,U_471] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_471,tc_HOL_Obool)),U_473),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_471,tc_HOL_Obool),U_472)))
| ? [U_470] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_471,tc_HOL_Obool)),U_473),U_470))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_471,tc_HOL_Obool)),U_470),U_472)) ) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_473,U_472,U_471] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_471,tc_HOL_Obool)),U_473),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_471,tc_HOL_Obool),U_472)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_471,tc_HOL_Obool)),U_473),sK22(U_473,U_472,U_471)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_471,tc_HOL_Obool)),sK22(U_473,U_472,U_471)),U_472)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_470,sK22(U_473,U_472,U_471))],[f_101_2]) ).
fof(f_101_4,plain,
( ! [U_471,U_472,U_473] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_471,tc_HOL_Obool)),U_473),sK22(U_473,U_472,U_471)))
| ~ sP27(U_471,U_472,U_473) )
& ! [U_471,U_472,U_473] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_471,tc_HOL_Obool)),sK22(U_473,U_472,U_471)),U_472))
| ~ sP27(U_471,U_472,U_473) )
& ! [U_471,U_472,U_473] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_471,tc_HOL_Obool)),U_473),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_471,tc_HOL_Obool),U_472)))
| sP27(U_471,U_472,U_473) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_101_3]) ).
cnf(f_101_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_471,tc_HOL_Obool)),U_473),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_471,tc_HOL_Obool),U_472)))
| sP27(U_471,U_472,U_473) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_471,tc_HOL_Obool)),sK22(U_473,U_472,U_471)),U_472))
| ~ sP27(U_471,U_472,U_473) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_471,tc_HOL_Obool)),U_473),sK22(U_473,U_472,U_471)))
| ~ sP27(U_471,U_472,U_473) ),
inference(clausify,[status(thm)],[f_101_4]) ).
fof(f_102_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__le__cases]) ).
fof(f_102_2,plain,
! [U_476,U_475,U_474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_474),U_476),U_475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_474),U_475),U_476))
| ~ class_Orderings_Olinorder(U_474) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_474,U_475,U_476] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_474),U_476),U_475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_474),U_475),U_476))
| ~ class_Orderings_Olinorder(U_474) ),
inference(definitional_conversion,[status(esa)],[f_102_2]) ).
cnf(f_102_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_474),U_476),U_475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_474),U_475),U_476))
| ~ class_Orderings_Olinorder(U_474) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I6_J]) ).
fof(f_103_2,plain,
! [U_480,U_479,U_478,U_477] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_480),U_479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_480),U_478))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_478),U_479))
| ~ class_Orderings_Oorder(U_477) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_477,U_478,U_479,U_480] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_480),U_479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_480),U_478))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_478),U_479))
| ~ class_Orderings_Oorder(U_477) ),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_480),U_479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_480),U_478))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_478),U_479))
| ~ class_Orderings_Oorder(U_477) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
! [V_x,V_y,T_a] :
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I5_J]) ).
fof(f_104_2,plain,
! [U_483,U_482,U_481] :
( U_483 = U_482
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_483),U_482))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_482),U_483))
| ~ class_Orderings_Oorder(U_481) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_481,U_482,U_483] :
( U_483 = U_482
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_483),U_482))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_482),U_483))
| ~ class_Orderings_Oorder(U_481) ),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
( U_483 = U_482
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_483),U_482))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_482),U_483))
| ~ class_Orderings_Oorder(U_481) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__trans]) ).
fof(f_105_2,plain,
! [U_487,U_486,U_485,U_484] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_485),U_487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_486),U_487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_485),U_486))
| ~ class_Orderings_Opreorder(U_484) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_484,U_485,U_486,U_487] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_485),U_487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_486),U_487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_485),U_486))
| ~ class_Orderings_Opreorder(U_484) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_485),U_487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_486),U_487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_484),U_485),U_486))
| ~ class_Orderings_Opreorder(U_484) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym]) ).
fof(f_106_2,plain,
! [U_490,U_489,U_488] :
( U_489 = U_490
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_490),U_489))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_489),U_490))
| ~ class_Orderings_Oorder(U_488) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_490,U_489,U_488] :
( U_489 = U_490
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_490),U_489))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_489),U_490))
| ~ class_Orderings_Oorder(U_488) ),
inference(definitional_conversion,[status(esa)],[f_106_2]) ).
cnf(f_106_4,plain,
( U_489 = U_490
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_490),U_489))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_489),U_490))
| ~ class_Orderings_Oorder(U_488) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a))
| V_b != V_c
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I4_J]) ).
fof(f_107_2,plain,
! [U_494,U_493,U_492,U_491] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_491),U_494),U_493))
| U_492 != U_494
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_491),U_492),U_493))
| ~ class_Orderings_Oorder(U_491) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_493,U_492,U_491,U_494] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_491),U_494),U_493))
| U_492 != U_494
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_491),U_492),U_493))
| ~ class_Orderings_Oorder(U_491) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_491),U_494),U_493))
| U_492 != U_494
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_491),U_492),U_493))
| ~ class_Orderings_Oorder(U_491) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
| V_b != V_c
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__le__eq__trans]) ).
fof(f_108_2,plain,
! [U_498,U_497,U_496,U_495] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_495),U_496),U_498))
| U_497 != U_498
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_495),U_496),U_497))
| ~ class_Orderings_Oord(U_495) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_498,U_496,U_497,U_495] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_495),U_496),U_498))
| U_497 != U_498
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_495),U_496),U_497))
| ~ class_Orderings_Oord(U_495) ),
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_495),U_496),U_498))
| U_497 != U_498
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_495),U_496),U_497))
| ~ class_Orderings_Oord(U_495) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
| V_a != V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I3_J]) ).
fof(f_109_2,plain,
! [U_502,U_501,U_500,U_499] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_499),U_502),U_500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_499),U_502),U_501))
| U_500 != U_501
| ~ class_Orderings_Oorder(U_499) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_502,U_501,U_500,U_499] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_499),U_502),U_500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_499),U_502),U_501))
| U_500 != U_501
| ~ class_Orderings_Oorder(U_499) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_499),U_502),U_500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_499),U_502),U_501))
| U_500 != U_501
| ~ class_Orderings_Oorder(U_499) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
| V_a != V_b
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__eq__le__trans]) ).
fof(f_110_2,plain,
! [U_506,U_505,U_504,U_503] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_503),U_504),U_506))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_503),U_505),U_506))
| U_504 != U_505
| ~ class_Orderings_Oord(U_503) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_504,U_505,U_503,U_506] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_503),U_504),U_506))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_503),U_505),U_506))
| U_504 != U_505
| ~ class_Orderings_Oord(U_503) ),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_503),U_504),U_506))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_503),U_505),U_506))
| U_504 != U_505
| ~ class_Orderings_Oord(U_503) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [V_x_2,V_y_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_111_2,plain,
! [U_509,U_508,U_507] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_509),U_508))
| U_509 != U_508 )
& ( U_509 = U_508
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_509),U_508)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_508),U_509))
| ~ class_Orderings_Oorder(U_507) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
( ! [U_509,U_508,U_507] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_509),U_508))
| U_509 != U_508
| ~ sP28(U_509,U_508,U_507) )
& ! [U_509,U_508,U_507] :
( U_509 = U_508
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_509),U_508))
| ~ sP28(U_509,U_508,U_507) )
& ! [U_509,U_508,U_507] :
( sP28(U_509,U_508,U_507)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_508),U_509))
| ~ class_Orderings_Oorder(U_507) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_111_2]) ).
cnf(f_111_4,plain,
( sP28(U_509,U_508,U_507)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_508),U_509))
| ~ class_Orderings_Oorder(U_507) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_5,plain,
( U_509 = U_508
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_509),U_508))
| ~ sP28(U_509,U_508,U_507) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_507),U_509),U_508))
| U_509 != U_508
| ~ sP28(U_509,U_508,U_507) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| V_x != V_y
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__refl]) ).
fof(f_112_2,plain,
! [U_512,U_511,U_510] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_510),U_511),U_512))
| U_511 != U_512
| ~ class_Orderings_Opreorder(U_510) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_511,U_512,U_510] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_510),U_511),U_512))
| U_511 != U_512
| ~ class_Orderings_Opreorder(U_510) ),
inference(definitional_conversion,[status(esa)],[f_112_2]) ).
cnf(f_112_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_510),U_511),U_512))
| U_511 != U_512
| ~ class_Orderings_Opreorder(U_510) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| V_x_2 != V_y_2 ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_113_2,plain,
! [U_515,U_514,U_513] :
( ( ( U_514 = U_515
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_515),U_514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_514),U_515)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_515),U_514))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_514),U_515)) )
| U_514 != U_515 ) )
| ~ class_Orderings_Oorder(U_513) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_513,U_514,U_515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_515),U_514))
| ~ sP29(U_513,U_514,U_515) )
& ! [U_513,U_514,U_515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_514),U_515))
| ~ sP29(U_513,U_514,U_515) )
& ! [U_513,U_514,U_515] :
( U_514 = U_515
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_515),U_514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_514),U_515))
| ~ sP30(U_513,U_514,U_515) )
& ! [U_513,U_514,U_515] :
( sP29(U_513,U_514,U_515)
| U_514 != U_515
| ~ sP30(U_513,U_514,U_515) )
& ! [U_513,U_514,U_515] :
( sP30(U_513,U_514,U_515)
| ~ class_Orderings_Oorder(U_513) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29,sP30])],[f_113_2]) ).
cnf(f_113_4,plain,
( sP30(U_513,U_514,U_515)
| ~ class_Orderings_Oorder(U_513) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
( sP29(U_513,U_514,U_515)
| U_514 != U_515
| ~ sP30(U_513,U_514,U_515) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_6,plain,
( U_514 = U_515
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_515),U_514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_514),U_515))
| ~ sP30(U_513,U_514,U_515) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_514),U_515))
| ~ sP29(U_513,U_514,U_515) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_513),U_515),U_514))
| ~ sP29(U_513,U_514,U_515) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__linear]) ).
fof(f_114_2,plain,
! [U_518,U_517,U_516] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_516),U_518),U_517))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_516),U_517),U_518))
| ~ class_Orderings_Olinorder(U_516) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_516,U_517,U_518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_516),U_518),U_517))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_516),U_517),U_518))
| ~ class_Orderings_Olinorder(U_516) ),
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_516),U_518),U_517))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_516),U_517),U_518))
| ~ class_Orderings_Olinorder(U_516) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
! [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)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Powp__mono]) ).
fof(f_115_2,plain,
! [U_521,U_520,U_519] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_519,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_519,U_520)),c_Predicate_OPowp(U_519,U_521)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_519,tc_HOL_Obool)),U_520),U_521)) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_519,U_520,U_521] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_519,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_519,U_520)),c_Predicate_OPowp(U_519,U_521)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_519,tc_HOL_Obool)),U_520),U_521)) ),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_519,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_519,U_520)),c_Predicate_OPowp(U_519,U_521)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_519,tc_HOL_Obool)),U_520),U_521)) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
! [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_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
| ? [B_X] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Inter__subset]) ).
fof(f_116_2,plain,
! [U_525,U_524,U_523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_523,tc_HOL_Obool),U_524)),U_525))
| U_524 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_523,tc_HOL_Obool),tc_HOL_Obool))
| ? [U_522] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),U_522),U_525))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_523,tc_HOL_Obool)),U_522),U_524)) ) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_525,U_524,U_523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_523,tc_HOL_Obool),U_524)),U_525))
| U_524 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_523,tc_HOL_Obool),tc_HOL_Obool))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),sK23(U_525,U_524,U_523)),U_525))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_523,tc_HOL_Obool)),sK23(U_525,U_524,U_523)),U_524)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_522,sK23(U_525,U_524,U_523))],[f_116_2]) ).
fof(f_116_4,plain,
( ! [U_523,U_524,U_525] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),sK23(U_525,U_524,U_523)),U_525))
| ~ sP31(U_523,U_524,U_525) )
& ! [U_523,U_524,U_525] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_523,tc_HOL_Obool)),sK23(U_525,U_524,U_523)),U_524))
| ~ sP31(U_523,U_524,U_525) )
& ! [U_523,U_524,U_525] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_523,tc_HOL_Obool),U_524)),U_525))
| U_524 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_523,tc_HOL_Obool),tc_HOL_Obool))
| sP31(U_523,U_524,U_525) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_116_3]) ).
cnf(f_116_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_523,tc_HOL_Obool),U_524)),U_525))
| U_524 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_523,tc_HOL_Obool),tc_HOL_Obool))
| sP31(U_523,U_524,U_525) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_523,tc_HOL_Obool)),sK23(U_525,U_524,U_523)),U_524))
| ~ sP31(U_523,U_524,U_525) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),sK23(U_525,U_524,U_523)),U_525))
| ~ sP31(U_523,U_524,U_525) ),
inference(clausify,[status(thm)],[f_116_4]) ).
fof(f_117_1,plain,
! [V_C_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),V_A_2)),V_C_2))
| ? [B_X] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Union__least]) ).
fof(f_117_2,plain,
! [U_529,U_528,U_527] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_527,tc_HOL_Obool),U_528)),U_529))
| ? [U_526] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),U_526),U_529))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_527,tc_HOL_Obool)),U_526),U_528)) ) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_529,U_528,U_527] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_527,tc_HOL_Obool),U_528)),U_529))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),sK24(U_529,U_528,U_527)),U_529))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_527,tc_HOL_Obool)),sK24(U_529,U_528,U_527)),U_528)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_526,sK24(U_529,U_528,U_527))],[f_117_2]) ).
fof(f_117_4,plain,
( ! [U_529,U_528,U_527] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),sK24(U_529,U_528,U_527)),U_529))
| ~ sP32(U_529,U_528,U_527) )
& ! [U_529,U_528,U_527] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_527,tc_HOL_Obool)),sK24(U_529,U_528,U_527)),U_528))
| ~ sP32(U_529,U_528,U_527) )
& ! [U_529,U_528,U_527] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_527,tc_HOL_Obool),U_528)),U_529))
| sP32(U_529,U_528,U_527) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_117_3]) ).
cnf(f_117_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_527,tc_HOL_Obool),U_528)),U_529))
| sP32(U_529,U_528,U_527) ),
inference(clausify,[status(thm)],[f_117_4]) ).
cnf(f_117_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_527,tc_HOL_Obool)),sK24(U_529,U_528,U_527)),U_528))
| ~ sP32(U_529,U_528,U_527) ),
inference(clausify,[status(thm)],[f_117_4]) ).
cnf(f_117_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),sK24(U_529,U_528,U_527)),U_529))
| ~ sP32(U_529,U_528,U_527) ),
inference(clausify,[status(thm)],[f_117_4]) ).
fof(f_118_1,plain,
! [V_z_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__greatest]) ).
fof(f_118_2,plain,
! [U_533,U_532,U_531] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_531),U_533),c_Complete__Lattice_OInf__class_OInf(U_531,U_532)))
| ? [U_530] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_531),U_533),U_530))
& hBOOL(hAPP(hAPP(c_member(U_531),U_530),U_532)) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_531) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_533,U_532,U_531] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_531),U_533),c_Complete__Lattice_OInf__class_OInf(U_531,U_532)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_531),U_533),sK25(U_533,U_532,U_531)))
& hBOOL(hAPP(hAPP(c_member(U_531),sK25(U_533,U_532,U_531)),U_532)) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_531) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_530,sK25(U_533,U_532,U_531))],[f_118_2]) ).
fof(f_118_4,plain,
( ! [U_531,U_532,U_533] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_531),U_533),sK25(U_533,U_532,U_531)))
| ~ sP33(U_531,U_532,U_533) )
& ! [U_531,U_532,U_533] :
( hBOOL(hAPP(hAPP(c_member(U_531),sK25(U_533,U_532,U_531)),U_532))
| ~ sP33(U_531,U_532,U_533) )
& ! [U_531,U_532,U_533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_531),U_533),c_Complete__Lattice_OInf__class_OInf(U_531,U_532)))
| sP33(U_531,U_532,U_533)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_531) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33])],[f_118_3]) ).
cnf(f_118_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_531),U_533),c_Complete__Lattice_OInf__class_OInf(U_531,U_532)))
| sP33(U_531,U_532,U_533)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_531) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_531),sK25(U_533,U_532,U_531)),U_532))
| ~ sP33(U_531,U_532,U_533) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_531),U_533),sK25(U_533,U_532,U_531)))
| ~ sP33(U_531,U_532,U_533) ),
inference(clausify,[status(thm)],[f_118_4]) ).
fof(f_119_1,plain,
! [V_z_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_z_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_z_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__least]) ).
fof(f_119_2,plain,
! [U_537,U_536,U_535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_535),c_Complete__Lattice_OSup__class_OSup(U_535,U_536)),U_537))
| ? [U_534] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_535),U_534),U_537))
& hBOOL(hAPP(hAPP(c_member(U_535),U_534),U_536)) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_535) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_537,U_536,U_535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_535),c_Complete__Lattice_OSup__class_OSup(U_535,U_536)),U_537))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_535),sK26(U_537,U_536,U_535)),U_537))
& hBOOL(hAPP(hAPP(c_member(U_535),sK26(U_537,U_536,U_535)),U_536)) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_535) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_534,sK26(U_537,U_536,U_535))],[f_119_2]) ).
fof(f_119_4,plain,
( ! [U_535,U_536,U_537] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_535),sK26(U_537,U_536,U_535)),U_537))
| ~ sP34(U_535,U_536,U_537) )
& ! [U_535,U_536,U_537] :
( hBOOL(hAPP(hAPP(c_member(U_535),sK26(U_537,U_536,U_535)),U_536))
| ~ sP34(U_535,U_536,U_537) )
& ! [U_535,U_536,U_537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_535),c_Complete__Lattice_OSup__class_OSup(U_535,U_536)),U_537))
| sP34(U_535,U_536,U_537)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_535) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_119_3]) ).
cnf(f_119_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_535),c_Complete__Lattice_OSup__class_OSup(U_535,U_536)),U_537))
| sP34(U_535,U_536,U_537)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_535) ),
inference(clausify,[status(thm)],[f_119_4]) ).
cnf(f_119_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_535),sK26(U_537,U_536,U_535)),U_536))
| ~ sP34(U_535,U_536,U_537) ),
inference(clausify,[status(thm)],[f_119_4]) ).
cnf(f_119_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_535),sK26(U_537,U_536,U_535)),U_537))
| ~ sP34(U_535,U_536,U_537) ),
inference(clausify,[status(thm)],[f_119_4]) ).
fof(f_120_1,plain,
! [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),V_B_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_subsetI]) ).
fof(f_120_2,plain,
! [U_541,U_540,U_539] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_539,tc_HOL_Obool)),U_540),U_541))
| ? [U_538] :
( ~ hBOOL(hAPP(hAPP(c_member(U_539),U_538),U_541))
& hBOOL(hAPP(hAPP(c_member(U_539),U_538),U_540)) ) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_541,U_540,U_539] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_539,tc_HOL_Obool)),U_540),U_541))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_539),sK27(U_541,U_540,U_539)),U_541))
& hBOOL(hAPP(hAPP(c_member(U_539),sK27(U_541,U_540,U_539)),U_540)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_538,sK27(U_541,U_540,U_539))],[f_120_2]) ).
fof(f_120_4,plain,
( ! [U_539,U_540,U_541] :
( ~ hBOOL(hAPP(hAPP(c_member(U_539),sK27(U_541,U_540,U_539)),U_541))
| ~ sP35(U_539,U_540,U_541) )
& ! [U_539,U_540,U_541] :
( hBOOL(hAPP(hAPP(c_member(U_539),sK27(U_541,U_540,U_539)),U_540))
| ~ sP35(U_539,U_540,U_541) )
& ! [U_539,U_540,U_541] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_539,tc_HOL_Obool)),U_540),U_541))
| sP35(U_539,U_540,U_541) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_120_3]) ).
cnf(f_120_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_539,tc_HOL_Obool)),U_540),U_541))
| sP35(U_539,U_540,U_541) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_539),sK27(U_541,U_540,U_539)),U_540))
| ~ sP35(U_539,U_540,U_541) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_539),sK27(U_541,U_540,U_539)),U_541))
| ~ sP35(U_539,U_540,U_541) ),
inference(clausify,[status(thm)],[f_120_4]) ).
fof(f_121_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff]) ).
fof(f_121_2,plain,
! [U_544,U_543,U_542] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_542,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_543)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_544)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_542),U_544),U_543)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_542),U_544),U_543))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_542,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_543)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_544))) ) )
| ~ class_Orderings_Olinorder(U_542) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
( ! [U_542,U_543,U_544] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_542,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_543)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_544)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_542),U_544),U_543))
| ~ sP36(U_542,U_543,U_544) )
& ! [U_542,U_543,U_544] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_542),U_544),U_543))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_542,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_543)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_544)))
| ~ sP36(U_542,U_543,U_544) )
& ! [U_542,U_543,U_544] :
( sP36(U_542,U_543,U_544)
| ~ class_Orderings_Olinorder(U_542) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_121_2]) ).
cnf(f_121_4,plain,
( sP36(U_542,U_543,U_544)
| ~ class_Orderings_Olinorder(U_542) ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_542),U_544),U_543))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_542,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_543)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_544)))
| ~ sP36(U_542,U_543,U_544) ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_542,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_543)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_542),U_544)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_542),U_544),U_543))
| ~ sP36(U_542,U_543,U_544) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Pow__UNIV]) ).
fof(f_122_2,plain,
! [U_545] : hAPP(c_Set_OPow(U_545),c_Orderings_Otop__class_Otop(tc_fun(U_545,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_545,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_545] : hAPP(c_Set_OPow(U_545),c_Orderings_Otop__class_Otop(tc_fun(U_545,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_545,tc_HOL_Obool),tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
hAPP(c_Set_OPow(U_545),c_Orderings_Otop__class_Otop(tc_fun(U_545,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_545,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [V_B_2,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_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_PowI]) ).
fof(f_123_2,plain,
! [U_548,U_547,U_546] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_546,tc_HOL_Obool)),U_547),hAPP(c_Set_OPow(U_546),U_548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_546,tc_HOL_Obool)),U_547),U_548)) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_546,U_547,U_548] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_546,tc_HOL_Obool)),U_547),hAPP(c_Set_OPow(U_546),U_548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_546,tc_HOL_Obool)),U_547),U_548)) ),
inference(definitional_conversion,[status(esa)],[f_123_2]) ).
cnf(f_123_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_546,tc_HOL_Obool)),U_547),hAPP(c_Set_OPow(U_546),U_548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_546,tc_HOL_Obool)),U_547),U_548)) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ 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))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff]) ).
fof(f_124_2,plain,
! [U_551,U_550,U_549] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_549,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_550)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_551)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_549),U_550),U_551)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_549),U_550),U_551))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_549,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_550)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_551))) ) )
| ~ class_Orderings_Oorder(U_549) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
( ! [U_549,U_550,U_551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_549,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_550)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_551)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_549),U_550),U_551))
| ~ sP37(U_549,U_550,U_551) )
& ! [U_549,U_550,U_551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_549),U_550),U_551))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_549,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_550)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_551)))
| ~ sP37(U_549,U_550,U_551) )
& ! [U_549,U_550,U_551] :
( sP37(U_549,U_550,U_551)
| ~ class_Orderings_Oorder(U_549) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37])],[f_124_2]) ).
cnf(f_124_4,plain,
( sP37(U_549,U_550,U_551)
| ~ class_Orderings_Oorder(U_549) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_549),U_550),U_551))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_549,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_550)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_551)))
| ~ sP37(U_549,U_550,U_551) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_549,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_550)),hAPP(c_SetInterval_Oord__class_OatMost(U_549),U_551)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_549),U_550),U_551))
| ~ sP37(U_549,U_550,U_551) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ 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))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff]) ).
fof(f_125_2,plain,
! [U_554,U_553,U_552] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_552,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_553)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_552),U_554),U_553)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_552),U_554),U_553))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_552,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_553)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_554))) ) )
| ~ class_Orderings_Oorder(U_552) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
( ! [U_553,U_554,U_552] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_552,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_553)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_552),U_554),U_553))
| ~ sP38(U_553,U_554,U_552) )
& ! [U_553,U_554,U_552] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_552),U_554),U_553))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_552,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_553)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_554)))
| ~ sP38(U_553,U_554,U_552) )
& ! [U_553,U_554,U_552] :
( sP38(U_553,U_554,U_552)
| ~ class_Orderings_Oorder(U_552) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_125_2]) ).
cnf(f_125_4,plain,
( sP38(U_553,U_554,U_552)
| ~ class_Orderings_Oorder(U_552) ),
inference(clausify,[status(thm)],[f_125_3]) ).
cnf(f_125_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_552),U_554),U_553))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_552,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_553)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_554)))
| ~ sP38(U_553,U_554,U_552) ),
inference(clausify,[status(thm)],[f_125_3]) ).
cnf(f_125_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_552,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_553)),hAPP(c_SetInterval_Oord__class_OatLeast(U_552),U_554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_552),U_554),U_553))
| ~ sP38(U_553,U_554,U_552) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff]) ).
fof(f_126_2,plain,
! [U_557,U_556,U_555] :
( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_556) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_557)
| U_556 != U_557 )
& ( U_556 = U_557
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_556) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_557) ) )
| ~ class_Orderings_Olinorder(U_555) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
( ! [U_557,U_555,U_556] :
( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_556) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_557)
| U_556 != U_557
| ~ sP39(U_557,U_555,U_556) )
& ! [U_557,U_555,U_556] :
( U_556 = U_557
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_556) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_557)
| ~ sP39(U_557,U_555,U_556) )
& ! [U_557,U_555,U_556] :
( sP39(U_557,U_555,U_556)
| ~ class_Orderings_Olinorder(U_555) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_126_2]) ).
cnf(f_126_4,plain,
( sP39(U_557,U_555,U_556)
| ~ class_Orderings_Olinorder(U_555) ),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_5,plain,
( U_556 = U_557
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_556) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_557)
| ~ sP39(U_557,U_555,U_556) ),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_6,plain,
( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_556) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_555),U_557)
| U_556 != U_557
| ~ sP39(U_557,U_555,U_556) ),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff]) ).
fof(f_127_2,plain,
! [U_560,U_559,U_558] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_559) = hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_560)
| U_559 != U_560 )
& ( U_559 = U_560
| hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_559) != hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_560) ) )
| ~ class_Orderings_Olinorder(U_558) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( ! [U_559,U_560,U_558] :
( hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_559) = hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_560)
| U_559 != U_560
| ~ sP40(U_559,U_560,U_558) )
& ! [U_559,U_560,U_558] :
( U_559 = U_560
| hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_559) != hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_560)
| ~ sP40(U_559,U_560,U_558) )
& ! [U_559,U_560,U_558] :
( sP40(U_559,U_560,U_558)
| ~ class_Orderings_Olinorder(U_558) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_127_2]) ).
cnf(f_127_4,plain,
( sP40(U_559,U_560,U_558)
| ~ class_Orderings_Olinorder(U_558) ),
inference(clausify,[status(thm)],[f_127_3]) ).
cnf(f_127_5,plain,
( U_559 = U_560
| hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_559) != hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_560)
| ~ sP40(U_559,U_560,U_558) ),
inference(clausify,[status(thm)],[f_127_3]) ).
cnf(f_127_6,plain,
( hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_559) = hAPP(c_SetInterval_Oord__class_OatLeast(U_558),U_560)
| U_559 != U_560
| ~ sP40(U_559,U_560,U_558) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff]) ).
fof(f_128_2,plain,
! [U_563,U_562,U_561] :
( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_562) = hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_563)
| U_562 != U_563 )
& ( U_562 = U_563
| hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_562) != hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_563) ) )
| ~ class_Orderings_Olinorder(U_561) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_563,U_561,U_562] :
( hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_562) = hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_563)
| U_562 != U_563
| ~ sP41(U_563,U_561,U_562) )
& ! [U_563,U_561,U_562] :
( U_562 = U_563
| hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_562) != hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_563)
| ~ sP41(U_563,U_561,U_562) )
& ! [U_563,U_561,U_562] :
( sP41(U_563,U_561,U_562)
| ~ class_Orderings_Olinorder(U_561) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_128_2]) ).
cnf(f_128_4,plain,
( sP41(U_563,U_561,U_562)
| ~ class_Orderings_Olinorder(U_561) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_5,plain,
( U_562 = U_563
| hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_562) != hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_563)
| ~ sP41(U_563,U_561,U_562) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_6,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_562) = hAPP(c_SetInterval_Oord__class_OatMost(U_561),U_563)
| U_562 != U_563
| ~ sP41(U_563,U_561,U_562) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Pow__top]) ).
fof(f_129_2,plain,
! [U_565,U_564] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_564,tc_HOL_Obool)),U_565),hAPP(c_Set_OPow(U_564),U_565))),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_565,U_564] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_564,tc_HOL_Obool)),U_565),hAPP(c_Set_OPow(U_564),U_565))),
inference(definitional_conversion,[status(esa)],[f_129_2]) ).
cnf(f_129_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_564,tc_HOL_Obool)),U_565),hAPP(c_Set_OPow(U_564),U_565))),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Union__Pow__eq]) ).
fof(f_130_2,plain,
! [U_567,U_566] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_566,tc_HOL_Obool),hAPP(c_Set_OPow(U_566),U_567)) = U_567,
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_567,U_566] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_566,tc_HOL_Obool),hAPP(c_Set_OPow(U_566),U_567)) = U_567,
inference(definitional_conversion,[status(esa)],[f_130_2]) ).
cnf(f_130_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_566,tc_HOL_Obool),hAPP(c_Set_OPow(U_566),U_567)) = U_567,
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Pow__not__empty]) ).
fof(f_131_2,plain,
! [U_569,U_568] : hAPP(c_Set_OPow(U_568),U_569) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_568,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_569,U_568] : hAPP(c_Set_OPow(U_568),U_569) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_568,tc_HOL_Obool),tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_131_2]) ).
cnf(f_131_4,plain,
hAPP(c_Set_OPow(U_568),U_569) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_568,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Pow__bottom]) ).
fof(f_132_2,plain,
! [U_571,U_570] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_570,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_570,tc_HOL_Obool))),hAPP(c_Set_OPow(U_570),U_571))),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_570,U_571] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_570,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_570,tc_HOL_Obool))),hAPP(c_Set_OPow(U_570),U_571))),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_570,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_570,tc_HOL_Obool))),hAPP(c_Set_OPow(U_570),U_571))),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_1,plain,
! [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),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_PowD]) ).
fof(f_133_2,plain,
! [U_574,U_573,U_572] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_572,tc_HOL_Obool)),U_573),U_574))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_572,tc_HOL_Obool)),U_573),hAPP(c_Set_OPow(U_572),U_574))) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_572,U_573,U_574] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_572,tc_HOL_Obool)),U_573),U_574))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_572,tc_HOL_Obool)),U_573),hAPP(c_Set_OPow(U_572),U_574))) ),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_572,tc_HOL_Obool)),U_573),U_574))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_572,tc_HOL_Obool)),U_573),hAPP(c_Set_OPow(U_572),U_574))) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
! [V_B_2,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_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Pow__iff]) ).
fof(f_134_2,plain,
! [U_577,U_576,U_575] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_575,tc_HOL_Obool)),U_576),hAPP(c_Set_OPow(U_575),U_577)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_575,tc_HOL_Obool)),U_576),U_577)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_575,tc_HOL_Obool)),U_576),U_577))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_575,tc_HOL_Obool)),U_576),hAPP(c_Set_OPow(U_575),U_577))) ) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
( ! [U_583,U_581,U_579] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_579,tc_HOL_Obool)),U_581),hAPP(c_Set_OPow(U_579),U_583)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_579,tc_HOL_Obool)),U_581),U_583)) )
& ! [U_582,U_580,U_578] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_578,tc_HOL_Obool)),U_580),U_582))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_578,tc_HOL_Obool)),U_580),hAPP(c_Set_OPow(U_578),U_582))) ) ),
inference(miniscope,[status(thm)],[f_134_2]) ).
fof(f_134_4,plain,
( ! [U_579,U_581,U_583] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_579,tc_HOL_Obool)),U_581),hAPP(c_Set_OPow(U_579),U_583)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_579,tc_HOL_Obool)),U_581),U_583)) )
& ! [U_580,U_578,U_582] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_578,tc_HOL_Obool)),U_580),U_582))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_578,tc_HOL_Obool)),U_580),hAPP(c_Set_OPow(U_578),U_582))) ) ),
inference(definitional_conversion,[status(esa)],[f_134_3]) ).
cnf(f_134_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_578,tc_HOL_Obool)),U_580),U_582))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_578,tc_HOL_Obool)),U_580),hAPP(c_Set_OPow(U_578),U_582))) ),
inference(clausify,[status(thm)],[f_134_4]) ).
cnf(f_134_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_579,tc_HOL_Obool)),U_581),hAPP(c_Set_OPow(U_579),U_583)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_579,tc_HOL_Obool)),U_581),U_583)) ),
inference(clausify,[status(thm)],[f_134_4]) ).
fof(f_135_1,plain,
! [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(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Pow__mono]) ).
fof(f_135_2,plain,
! [U_586,U_585,U_584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_584,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_584),U_585)),hAPP(c_Set_OPow(U_584),U_586)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_584,tc_HOL_Obool)),U_585),U_586)) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_584,U_585,U_586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_584,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_584),U_585)),hAPP(c_Set_OPow(U_584),U_586)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_584,tc_HOL_Obool)),U_585),U_586)) ),
inference(definitional_conversion,[status(esa)],[f_135_2]) ).
cnf(f_135_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_584,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_584),U_585)),hAPP(c_Set_OPow(U_584),U_586)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_584,tc_HOL_Obool)),U_585),U_586)) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_1,plain,
! [V_k_2,V_i_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__iff]) ).
fof(f_136_2,plain,
! [U_589,U_588,U_587] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_587),U_588),hAPP(c_SetInterval_Oord__class_OatMost(U_587),U_589)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_587),U_588),U_589)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_587),U_588),U_589))
| ~ hBOOL(hAPP(hAPP(c_member(U_587),U_588),hAPP(c_SetInterval_Oord__class_OatMost(U_587),U_589))) ) )
| ~ class_Orderings_Oord(U_587) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( ! [U_587,U_588,U_589] :
( hBOOL(hAPP(hAPP(c_member(U_587),U_588),hAPP(c_SetInterval_Oord__class_OatMost(U_587),U_589)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_587),U_588),U_589))
| ~ sP42(U_587,U_588,U_589) )
& ! [U_587,U_588,U_589] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_587),U_588),U_589))
| ~ hBOOL(hAPP(hAPP(c_member(U_587),U_588),hAPP(c_SetInterval_Oord__class_OatMost(U_587),U_589)))
| ~ sP42(U_587,U_588,U_589) )
& ! [U_587,U_588,U_589] :
( sP42(U_587,U_588,U_589)
| ~ class_Orderings_Oord(U_587) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42])],[f_136_2]) ).
cnf(f_136_4,plain,
( sP42(U_587,U_588,U_589)
| ~ class_Orderings_Oord(U_587) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_587),U_588),U_589))
| ~ hBOOL(hAPP(hAPP(c_member(U_587),U_588),hAPP(c_SetInterval_Oord__class_OatMost(U_587),U_589)))
| ~ sP42(U_587,U_588,U_589) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_587),U_588),hAPP(c_SetInterval_Oord__class_OatMost(U_587),U_589)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_587),U_588),U_589))
| ~ sP42(U_587,U_588,U_589) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_1,plain,
! [V_k_2,V_i_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__iff]) ).
fof(f_137_2,plain,
! [U_592,U_591,U_590] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_590),U_591),hAPP(c_SetInterval_Oord__class_OatLeast(U_590),U_592)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_590),U_592),U_591)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_590),U_592),U_591))
| ~ hBOOL(hAPP(hAPP(c_member(U_590),U_591),hAPP(c_SetInterval_Oord__class_OatLeast(U_590),U_592))) ) )
| ~ class_Orderings_Oord(U_590) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
( ! [U_592,U_591,U_590] :
( hBOOL(hAPP(hAPP(c_member(U_590),U_591),hAPP(c_SetInterval_Oord__class_OatLeast(U_590),U_592)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_590),U_592),U_591))
| ~ sP43(U_592,U_591,U_590) )
& ! [U_592,U_591,U_590] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_590),U_592),U_591))
| ~ hBOOL(hAPP(hAPP(c_member(U_590),U_591),hAPP(c_SetInterval_Oord__class_OatLeast(U_590),U_592)))
| ~ sP43(U_592,U_591,U_590) )
& ! [U_592,U_591,U_590] :
( sP43(U_592,U_591,U_590)
| ~ class_Orderings_Oord(U_590) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_137_2]) ).
cnf(f_137_4,plain,
( sP43(U_592,U_591,U_590)
| ~ class_Orderings_Oord(U_590) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_590),U_592),U_591))
| ~ hBOOL(hAPP(hAPP(c_member(U_590),U_591),hAPP(c_SetInterval_Oord__class_OatLeast(U_590),U_592)))
| ~ sP43(U_592,U_591,U_590) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_590),U_591),hAPP(c_SetInterval_Oord__class_OatLeast(U_590),U_592)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_590),U_592),U_591))
| ~ sP43(U_592,U_591,U_590) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_subset__Pow__Union]) ).
fof(f_138_2,plain,
! [U_594,U_593] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_593,tc_HOL_Obool),tc_HOL_Obool)),U_594),hAPP(c_Set_OPow(U_593),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_593,tc_HOL_Obool),U_594)))),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_594,U_593] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_593,tc_HOL_Obool),tc_HOL_Obool)),U_594),hAPP(c_Set_OPow(U_593),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_593,tc_HOL_Obool),U_594)))),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_593,tc_HOL_Obool),tc_HOL_Obool)),U_594),hAPP(c_Set_OPow(U_593),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_593,tc_HOL_Obool),U_594)))),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Pow__empty]) ).
fof(f_139_2,plain,
! [U_595] : hAPP(c_Set_OPow(U_595),c_Orderings_Obot__class_Obot(tc_fun(U_595,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_595,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_595,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_595,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_595] : hAPP(c_Set_OPow(U_595),c_Orderings_Obot__class_Obot(tc_fun(U_595,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_595,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_595,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_595,tc_HOL_Obool),tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
hAPP(c_Set_OPow(U_595),c_Orderings_Obot__class_Obot(tc_fun(U_595,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_595,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_595,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_595,tc_HOL_Obool),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff]) ).
fof(f_140_2,plain,
! [U_598,U_597,U_596] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_596,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_597)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_598)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_596),U_597),U_598)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_596),U_597),U_598))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_596,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_597)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_598))) ) )
| ~ class_Orderings_Olinorder(U_596) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ! [U_596,U_597,U_598] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_596,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_597)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_598)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_596),U_597),U_598))
| ~ sP44(U_596,U_597,U_598) )
& ! [U_596,U_597,U_598] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_596),U_597),U_598))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_596,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_597)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_598)))
| ~ sP44(U_596,U_597,U_598) )
& ! [U_596,U_597,U_598] :
( sP44(U_596,U_597,U_598)
| ~ class_Orderings_Olinorder(U_596) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_140_2]) ).
cnf(f_140_4,plain,
( sP44(U_596,U_597,U_598)
| ~ class_Orderings_Olinorder(U_596) ),
inference(clausify,[status(thm)],[f_140_3]) ).
cnf(f_140_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_596),U_597),U_598))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_596,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_597)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_598)))
| ~ sP44(U_596,U_597,U_598) ),
inference(clausify,[status(thm)],[f_140_3]) ).
cnf(f_140_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_596,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_597)),hAPP(c_SetInterval_Oord__class_OlessThan(U_596),U_598)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_596),U_597),U_598))
| ~ sP44(U_596,U_597,U_598) ),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INF__subset]) ).
fof(f_141_2,plain,
! [U_603,U_602,U_601,U_600,U_599] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_599),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_600,U_599),U_602),U_603)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_600,U_599),U_601),U_603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_600,tc_HOL_Obool)),U_601),U_602))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_599) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_600,U_599,U_601,U_602,U_603] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_599),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_600,U_599),U_602),U_603)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_600,U_599),U_601),U_603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_600,tc_HOL_Obool)),U_601),U_602))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_599) ),
inference(definitional_conversion,[status(esa)],[f_141_2]) ).
cnf(f_141_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_599),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_600,U_599),U_602),U_603)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_600,U_599),U_601),U_603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_600,tc_HOL_Obool)),U_601),U_602))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_599) ),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUP__subset]) ).
fof(f_142_2,plain,
! [U_608,U_607,U_606,U_605,U_604] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_604),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_605,U_604),U_606),U_608)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_605,U_604),U_607),U_608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_605,tc_HOL_Obool)),U_606),U_607))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_604) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_604,U_605,U_606,U_607,U_608] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_604),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_605,U_604),U_606),U_608)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_605,U_604),U_607),U_608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_605,tc_HOL_Obool)),U_606),U_607))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_604) ),
inference(definitional_conversion,[status(esa)],[f_142_2]) ).
cnf(f_142_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_604),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_605,U_604),U_606),U_608)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_605,U_604),U_607),U_608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_605,tc_HOL_Obool)),U_606),U_607))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_604) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
! [V_k_2,V_l_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty]) ).
fof(f_143_2,plain,
! [U_611,U_610,U_609] :
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_609,U_611,U_610) = c_Orderings_Obot__class_Obot(tc_fun(U_609,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_609),U_610),U_611))
| ~ class_Orderings_Oorder(U_609) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_609,U_610,U_611] :
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_609,U_611,U_610) = c_Orderings_Obot__class_Obot(tc_fun(U_609,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_609),U_610),U_611))
| ~ class_Orderings_Oorder(U_609) ),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_609,U_611,U_610) = c_Orderings_Obot__class_Obot(tc_fun(U_609,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_609),U_610),U_611))
| ~ class_Orderings_Oorder(U_609) ),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_1,plain,
! [V_k_2,V_l_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty]) ).
fof(f_144_2,plain,
! [U_614,U_613,U_612] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_612,U_614,U_613) = c_Orderings_Obot__class_Obot(tc_fun(U_612,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_612),U_613),U_614))
| ~ class_Orderings_Oorder(U_612) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_612,U_613,U_614] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_612,U_614,U_613) = c_Orderings_Obot__class_Obot(tc_fun(U_612,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_612),U_613),U_614))
| ~ class_Orderings_Oorder(U_612) ),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_612,U_614,U_613) = c_Orderings_Obot__class_Obot(tc_fun(U_612,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_612),U_613),U_614))
| ~ class_Orderings_Oorder(U_612) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [T_b,V_Qa_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Qa_2,B_x))
& hBOOL(hAPP(V_Pa_2,B_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__mono]) ).
fof(f_145_2,plain,
! [U_618,U_617,U_616] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_618,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_618),U_616)),hAPP(c_Set_OCollect(U_618),U_617)))
| ? [U_615] :
( ~ hBOOL(hAPP(U_617,U_615))
& hBOOL(hAPP(U_616,U_615)) ) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_618,U_617,U_616] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_618,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_618),U_616)),hAPP(c_Set_OCollect(U_618),U_617)))
| ( ~ hBOOL(hAPP(U_617,sK28(U_618,U_617,U_616)))
& hBOOL(hAPP(U_616,sK28(U_618,U_617,U_616))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_615,sK28(U_618,U_617,U_616))],[f_145_2]) ).
fof(f_145_4,plain,
( ! [U_616,U_617,U_618] :
( ~ hBOOL(hAPP(U_617,sK28(U_618,U_617,U_616)))
| ~ sP45(U_616,U_617,U_618) )
& ! [U_616,U_617,U_618] :
( hBOOL(hAPP(U_616,sK28(U_618,U_617,U_616)))
| ~ sP45(U_616,U_617,U_618) )
& ! [U_616,U_617,U_618] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_618,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_618),U_616)),hAPP(c_Set_OCollect(U_618),U_617)))
| sP45(U_616,U_617,U_618) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_145_3]) ).
cnf(f_145_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_618,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_618),U_616)),hAPP(c_Set_OCollect(U_618),U_617)))
| sP45(U_616,U_617,U_618) ),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_6,plain,
( hBOOL(hAPP(U_616,sK28(U_618,U_617,U_616)))
| ~ sP45(U_616,U_617,U_618) ),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_7,plain,
( ~ hBOOL(hAPP(U_617,sK28(U_618,U_617,U_616)))
| ~ sP45(U_616,U_617,U_618) ),
inference(clausify,[status(thm)],[f_145_4]) ).
fof(f_146_1,plain,
! [V_A_2,T_b] :
( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = V_A_2
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UNIV__eq__I]) ).
fof(f_146_2,plain,
! [U_621,U_620] :
( c_Orderings_Otop__class_Otop(tc_fun(U_620,tc_HOL_Obool)) = U_621
| ? [U_619] : ~ hBOOL(hAPP(hAPP(c_member(U_620),U_619),U_621)) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_621,U_620] :
( c_Orderings_Otop__class_Otop(tc_fun(U_620,tc_HOL_Obool)) = U_621
| ~ hBOOL(hAPP(hAPP(c_member(U_620),sK29(U_621,U_620)),U_621)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_619,sK29(U_621,U_620))],[f_146_2]) ).
fof(f_146_4,plain,
! [U_620,U_621] :
( c_Orderings_Otop__class_Otop(tc_fun(U_620,tc_HOL_Obool)) = U_621
| ~ hBOOL(hAPP(hAPP(c_member(U_620),sK29(U_621,U_620)),U_621)) ),
inference(definitional_conversion,[status(esa)],[f_146_3]) ).
cnf(f_146_5,plain,
( c_Orderings_Otop__class_Otop(tc_fun(U_620,tc_HOL_Obool)) = U_621
| ~ hBOOL(hAPP(hAPP(c_member(U_620),sK29(U_621,U_620)),U_621)) ),
inference(clausify,[status(thm)],[f_146_4]) ).
fof(f_147_1,plain,
! [T_b] :
? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_UNIV__witness]) ).
fof(f_147_2,plain,
! [U_623] :
? [U_622] : hBOOL(hAPP(hAPP(c_member(U_623),U_622),c_Orderings_Otop__class_Otop(tc_fun(U_623,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_623] : hBOOL(hAPP(hAPP(c_member(U_623),sK30(U_623)),c_Orderings_Otop__class_Otop(tc_fun(U_623,tc_HOL_Obool)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_622,sK30(U_623))],[f_147_2]) ).
fof(f_147_4,plain,
! [U_623] : hBOOL(hAPP(hAPP(c_member(U_623),sK30(U_623)),c_Orderings_Otop__class_Otop(tc_fun(U_623,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_147_3]) ).
cnf(f_147_5,plain,
hBOOL(hAPP(hAPP(c_member(U_623),sK30(U_623)),c_Orderings_Otop__class_Otop(tc_fun(U_623,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_147_4]) ).
fof(f_148_1,plain,
! [T_b,V_g_2,V_f_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| ? [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)))
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__funI]) ).
fof(f_148_2,plain,
! [U_628,U_627,U_626,U_625] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_628,U_625)),U_626),U_627))
| ? [U_624] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_625),hAPP(U_626,U_624)),hAPP(U_627,U_624)))
| ~ class_Orderings_Oord(U_625) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_628,U_627,U_626,U_625] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_628,U_625)),U_626),U_627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_625),hAPP(U_626,sK31(U_628,U_627,U_626,U_625))),hAPP(U_627,sK31(U_628,U_627,U_626,U_625))))
| ~ class_Orderings_Oord(U_625) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_624,sK31(U_628,U_627,U_626,U_625))],[f_148_2]) ).
fof(f_148_4,plain,
! [U_625,U_626,U_627,U_628] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_628,U_625)),U_626),U_627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_625),hAPP(U_626,sK31(U_628,U_627,U_626,U_625))),hAPP(U_627,sK31(U_628,U_627,U_626,U_625))))
| ~ class_Orderings_Oord(U_625) ),
inference(definitional_conversion,[status(esa)],[f_148_3]) ).
cnf(f_148_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_628,U_625)),U_626),U_627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_625),hAPP(U_626,sK31(U_628,U_627,U_626,U_625))),hAPP(U_627,sK31(U_628,U_627,U_626,U_625))))
| ~ class_Orderings_Oord(U_625) ),
inference(clausify,[status(thm)],[f_148_4]) ).
fof(f_149_1,plain,
! [V_A_2,T_b] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_y] : hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_equals0I]) ).
fof(f_149_2,plain,
! [U_631,U_630] :
( U_631 = c_Orderings_Obot__class_Obot(tc_fun(U_630,tc_HOL_Obool))
| ? [U_629] : hBOOL(hAPP(hAPP(c_member(U_630),U_629),U_631)) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_631,U_630] :
( U_631 = c_Orderings_Obot__class_Obot(tc_fun(U_630,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_630),sK32(U_631,U_630)),U_631)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_629,sK32(U_631,U_630))],[f_149_2]) ).
fof(f_149_4,plain,
! [U_630,U_631] :
( U_631 = c_Orderings_Obot__class_Obot(tc_fun(U_630,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_630),sK32(U_631,U_630)),U_631)) ),
inference(definitional_conversion,[status(esa)],[f_149_3]) ).
cnf(f_149_5,plain,
( U_631 = c_Orderings_Obot__class_Obot(tc_fun(U_630,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_630),sK32(U_631,U_630)),U_631)) ),
inference(clausify,[status(thm)],[f_149_4]) ).
fof(f_150_1,plain,
! [V_b_2,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_b_2),V_B_2)))
| ( V_a_2 != V_b_2
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insertCI]) ).
fof(f_150_2,plain,
! [U_635,U_634,U_633,U_632] :
( hBOOL(hAPP(hAPP(c_member(U_632),U_633),hAPP(hAPP(c_Set_Oinsert(U_632),U_635),U_634)))
| ( U_633 != U_635
& ~ hBOOL(hAPP(hAPP(c_member(U_632),U_633),U_634)) ) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
( ! [U_632,U_633,U_634,U_635] :
( U_633 != U_635
| ~ sP46(U_632,U_633,U_634,U_635) )
& ! [U_632,U_633,U_634,U_635] :
( ~ hBOOL(hAPP(hAPP(c_member(U_632),U_633),U_634))
| ~ sP46(U_632,U_633,U_634,U_635) )
& ! [U_632,U_633,U_634,U_635] :
( hBOOL(hAPP(hAPP(c_member(U_632),U_633),hAPP(hAPP(c_Set_Oinsert(U_632),U_635),U_634)))
| sP46(U_632,U_633,U_634,U_635) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_150_2]) ).
cnf(f_150_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_632),U_633),hAPP(hAPP(c_Set_Oinsert(U_632),U_635),U_634)))
| sP46(U_632,U_633,U_634,U_635) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_632),U_633),U_634))
| ~ sP46(U_632,U_633,U_634,U_635) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_6,plain,
( U_633 != U_635
| ~ sP46(U_632,U_633,U_634,U_635) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [V_A_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_insertE]) ).
fof(f_151_2,plain,
! [U_639,U_638,U_637,U_636] :
( hBOOL(hAPP(hAPP(c_member(U_636),U_637),U_639))
| U_637 = U_638
| ~ hBOOL(hAPP(hAPP(c_member(U_636),U_637),hAPP(hAPP(c_Set_Oinsert(U_636),U_638),U_639))) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_636,U_637,U_638,U_639] :
( hBOOL(hAPP(hAPP(c_member(U_636),U_637),U_639))
| U_637 = U_638
| ~ hBOOL(hAPP(hAPP(c_member(U_636),U_637),hAPP(hAPP(c_Set_Oinsert(U_636),U_638),U_639))) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_636),U_637),U_639))
| U_637 = U_638
| ~ hBOOL(hAPP(hAPP(c_member(U_636),U_637),hAPP(hAPP(c_Set_Oinsert(U_636),U_638),U_639))) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_insert__absorb2]) ).
fof(f_152_2,plain,
! [U_642,U_641,U_640] : hAPP(hAPP(c_Set_Oinsert(U_640),U_641),hAPP(hAPP(c_Set_Oinsert(U_640),U_641),U_642)) = hAPP(hAPP(c_Set_Oinsert(U_640),U_641),U_642),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_640,U_641,U_642] : hAPP(hAPP(c_Set_Oinsert(U_640),U_641),hAPP(hAPP(c_Set_Oinsert(U_640),U_641),U_642)) = hAPP(hAPP(c_Set_Oinsert(U_640),U_641),U_642),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_640),U_641),hAPP(hAPP(c_Set_Oinsert(U_640),U_641),U_642)) = hAPP(hAPP(c_Set_Oinsert(U_640),U_641),U_642),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_insert__commute]) ).
fof(f_153_2,plain,
! [U_646,U_645,U_644,U_643] : hAPP(hAPP(c_Set_Oinsert(U_643),U_644),hAPP(hAPP(c_Set_Oinsert(U_643),U_645),U_646)) = hAPP(hAPP(c_Set_Oinsert(U_643),U_645),hAPP(hAPP(c_Set_Oinsert(U_643),U_644),U_646)),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_643,U_644,U_645,U_646] : hAPP(hAPP(c_Set_Oinsert(U_643),U_644),hAPP(hAPP(c_Set_Oinsert(U_643),U_645),U_646)) = hAPP(hAPP(c_Set_Oinsert(U_643),U_645),hAPP(hAPP(c_Set_Oinsert(U_643),U_644),U_646)),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_643),U_644),hAPP(hAPP(c_Set_Oinsert(U_643),U_645),U_646)) = hAPP(hAPP(c_Set_Oinsert(U_643),U_645),hAPP(hAPP(c_Set_Oinsert(U_643),U_644),U_646)),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [V_x_2,V_A_2,V_y_2,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
| ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& V_y_2 != V_x_2 ) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__code]) ).
fof(f_154_2,plain,
! [U_650,U_649,U_648,U_647] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_647),U_648),U_649),U_650))
| ( ~ hBOOL(hAPP(U_649,U_650))
& U_648 != U_650 ) )
& ( hBOOL(hAPP(U_649,U_650))
| U_648 = U_650
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_647),U_648),U_649),U_650)) ) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
( ! [U_658,U_656,U_654] :
( ! [U_652] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_652),U_654),U_656),U_658))
| ( ~ hBOOL(hAPP(U_656,U_658))
& U_654 != U_658 ) )
& ! [U_657,U_655,U_653] :
( ! [U_651] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_651),U_653),U_655),U_657))
| hBOOL(hAPP(U_655,U_657))
| U_653 = U_657 ) ),
inference(miniscope,[status(thm)],[f_154_2]) ).
fof(f_154_4,plain,
( ! [U_658,U_656,U_654] :
( ~ hBOOL(hAPP(U_656,U_658))
| ~ sP47(U_658,U_656,U_654) )
& ! [U_658,U_656,U_654] :
( U_654 != U_658
| ~ sP47(U_658,U_656,U_654) )
& ! [U_658,U_656,U_654,U_652] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_652),U_654),U_656),U_658))
| sP47(U_658,U_656,U_654) )
& ! [U_655,U_653,U_651,U_657] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_651),U_653),U_655),U_657))
| hBOOL(hAPP(U_655,U_657))
| U_653 = U_657 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_154_3]) ).
cnf(f_154_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_651),U_653),U_655),U_657))
| hBOOL(hAPP(U_655,U_657))
| U_653 = U_657 ),
inference(clausify,[status(thm)],[f_154_4]) ).
cnf(f_154_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_652),U_654),U_656),U_658))
| sP47(U_658,U_656,U_654) ),
inference(clausify,[status(thm)],[f_154_4]) ).
cnf(f_154_7,plain,
( U_654 != U_658
| ~ sP47(U_658,U_656,U_654) ),
inference(clausify,[status(thm)],[f_154_4]) ).
cnf(f_154_8,plain,
( ~ hBOOL(hAPP(U_656,U_658))
| ~ sP47(U_658,U_656,U_654) ),
inference(clausify,[status(thm)],[f_154_4]) ).
fof(f_155_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff]) ).
fof(f_155_2,plain,
! [U_661,U_660,U_659] :
( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_660) = hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_661)
| U_660 != U_661 )
& ( U_660 = U_661
| hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_660) != hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_661) ) )
| ~ class_Orderings_Olinorder(U_659) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( ! [U_660,U_661,U_659] :
( hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_660) = hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_661)
| U_660 != U_661
| ~ sP48(U_660,U_661,U_659) )
& ! [U_660,U_661,U_659] :
( U_660 = U_661
| hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_660) != hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_661)
| ~ sP48(U_660,U_661,U_659) )
& ! [U_660,U_661,U_659] :
( sP48(U_660,U_661,U_659)
| ~ class_Orderings_Olinorder(U_659) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_155_2]) ).
cnf(f_155_4,plain,
( sP48(U_660,U_661,U_659)
| ~ class_Orderings_Olinorder(U_659) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
( U_660 = U_661
| hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_660) != hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_661)
| ~ sP48(U_660,U_661,U_659) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_6,plain,
( hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_660) = hAPP(c_SetInterval_Oord__class_OlessThan(U_659),U_661)
| U_660 != U_661
| ~ sP48(U_660,U_661,U_659) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [V_A_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__absorb]) ).
fof(f_156_2,plain,
! [U_664,U_663,U_662] :
( hAPP(hAPP(c_Set_Oinsert(U_662),U_663),U_664) = U_664
| ~ hBOOL(hAPP(hAPP(c_member(U_662),U_663),U_664)) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_663,U_664,U_662] :
( hAPP(hAPP(c_Set_Oinsert(U_662),U_663),U_664) = U_664
| ~ hBOOL(hAPP(hAPP(c_member(U_662),U_663),U_664)) ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_662),U_663),U_664) = U_664
| ~ hBOOL(hAPP(hAPP(c_member(U_662),U_663),U_664)) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_1,plain,
! [V_b_2,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_b_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_insertI2]) ).
fof(f_157_2,plain,
! [U_668,U_667,U_666,U_665] :
( hBOOL(hAPP(hAPP(c_member(U_665),U_666),hAPP(hAPP(c_Set_Oinsert(U_665),U_668),U_667)))
| ~ hBOOL(hAPP(hAPP(c_member(U_665),U_666),U_667)) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
! [U_665,U_666,U_667,U_668] :
( hBOOL(hAPP(hAPP(c_member(U_665),U_666),hAPP(hAPP(c_Set_Oinsert(U_665),U_668),U_667)))
| ~ hBOOL(hAPP(hAPP(c_member(U_665),U_666),U_667)) ),
inference(definitional_conversion,[status(esa)],[f_157_2]) ).
cnf(f_157_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_665),U_666),hAPP(hAPP(c_Set_Oinsert(U_665),U_668),U_667)))
| ~ hBOOL(hAPP(hAPP(c_member(U_665),U_666),U_667)) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ( ( 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)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_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_B_2) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__ident]) ).
fof(f_158_2,plain,
! [U_672,U_671,U_670,U_669] :
( ( ( hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_671) = hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_672)
| U_671 != U_672 )
& ( U_671 = U_672
| hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_671) != hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_672) ) )
| hBOOL(hAPP(hAPP(c_member(U_669),U_670),U_672))
| hBOOL(hAPP(hAPP(c_member(U_669),U_670),U_671)) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
( ! [U_669,U_670,U_671,U_672] :
( hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_671) = hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_672)
| U_671 != U_672
| ~ sP49(U_669,U_670,U_671,U_672) )
& ! [U_669,U_670,U_671,U_672] :
( U_671 = U_672
| hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_671) != hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_672)
| ~ sP49(U_669,U_670,U_671,U_672) )
& ! [U_669,U_670,U_671,U_672] :
( sP49(U_669,U_670,U_671,U_672)
| hBOOL(hAPP(hAPP(c_member(U_669),U_670),U_672))
| hBOOL(hAPP(hAPP(c_member(U_669),U_670),U_671)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_158_2]) ).
cnf(f_158_4,plain,
( sP49(U_669,U_670,U_671,U_672)
| hBOOL(hAPP(hAPP(c_member(U_669),U_670),U_672))
| hBOOL(hAPP(hAPP(c_member(U_669),U_670),U_671)) ),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_5,plain,
( U_671 = U_672
| hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_671) != hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_672)
| ~ sP49(U_669,U_670,U_671,U_672) ),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_6,plain,
( hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_671) = hAPP(hAPP(c_Set_Oinsert(U_669),U_670),U_672)
| U_671 != U_672
| ~ sP49(U_669,U_670,U_671,U_672) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [V_A_2,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_b_2),V_A_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
& V_a_2 != V_b_2 ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__iff]) ).
fof(f_159_2,plain,
! [U_676,U_675,U_674,U_673] :
( ( hBOOL(hAPP(hAPP(c_member(U_673),U_674),hAPP(hAPP(c_Set_Oinsert(U_673),U_675),U_676)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_673),U_674),U_676))
& U_674 != U_675 ) )
& ( hBOOL(hAPP(hAPP(c_member(U_673),U_674),U_676))
| U_674 = U_675
| ~ hBOOL(hAPP(hAPP(c_member(U_673),U_674),hAPP(hAPP(c_Set_Oinsert(U_673),U_675),U_676))) ) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
( ! [U_684,U_682,U_680,U_678] :
( hBOOL(hAPP(hAPP(c_member(U_678),U_680),hAPP(hAPP(c_Set_Oinsert(U_678),U_682),U_684)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_678),U_680),U_684))
& U_680 != U_682 ) )
& ! [U_683,U_681,U_679,U_677] :
( hBOOL(hAPP(hAPP(c_member(U_677),U_679),U_683))
| U_679 = U_681
| ~ hBOOL(hAPP(hAPP(c_member(U_677),U_679),hAPP(hAPP(c_Set_Oinsert(U_677),U_681),U_683))) ) ),
inference(miniscope,[status(thm)],[f_159_2]) ).
fof(f_159_4,plain,
( ! [U_682,U_680,U_684,U_678] :
( ~ hBOOL(hAPP(hAPP(c_member(U_678),U_680),U_684))
| ~ sP50(U_682,U_680,U_684,U_678) )
& ! [U_682,U_680,U_684,U_678] :
( U_680 != U_682
| ~ sP50(U_682,U_680,U_684,U_678) )
& ! [U_682,U_680,U_684,U_678] :
( hBOOL(hAPP(hAPP(c_member(U_678),U_680),hAPP(hAPP(c_Set_Oinsert(U_678),U_682),U_684)))
| sP50(U_682,U_680,U_684,U_678) )
& ! [U_679,U_683,U_677,U_681] :
( hBOOL(hAPP(hAPP(c_member(U_677),U_679),U_683))
| U_679 = U_681
| ~ hBOOL(hAPP(hAPP(c_member(U_677),U_679),hAPP(hAPP(c_Set_Oinsert(U_677),U_681),U_683))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_159_3]) ).
cnf(f_159_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_677),U_679),U_683))
| U_679 = U_681
| ~ hBOOL(hAPP(hAPP(c_member(U_677),U_679),hAPP(hAPP(c_Set_Oinsert(U_677),U_681),U_683))) ),
inference(clausify,[status(thm)],[f_159_4]) ).
cnf(f_159_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_678),U_680),hAPP(hAPP(c_Set_Oinsert(U_678),U_682),U_684)))
| sP50(U_682,U_680,U_684,U_678) ),
inference(clausify,[status(thm)],[f_159_4]) ).
cnf(f_159_7,plain,
( U_680 != U_682
| ~ sP50(U_682,U_680,U_684,U_678) ),
inference(clausify,[status(thm)],[f_159_4]) ).
cnf(f_159_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_678),U_680),U_684))
| ~ sP50(U_682,U_680,U_684,U_678) ),
inference(clausify,[status(thm)],[f_159_4]) ).
fof(f_160_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_insertI1]) ).
fof(f_160_2,plain,
! [U_687,U_686,U_685] : hBOOL(hAPP(hAPP(c_member(U_685),U_686),hAPP(hAPP(c_Set_Oinsert(U_685),U_686),U_687))),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_686,U_685,U_687] : hBOOL(hAPP(hAPP(c_member(U_685),U_686),hAPP(hAPP(c_Set_Oinsert(U_685),U_686),U_687))),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
hBOOL(hAPP(hAPP(c_member(U_685),U_686),hAPP(hAPP(c_Set_Oinsert(U_685),U_686),U_687))),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_empty__not__insert]) ).
fof(f_161_2,plain,
! [U_690,U_689,U_688] : c_Orderings_Obot__class_Obot(tc_fun(U_688,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_688),U_689),U_690),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_688,U_689,U_690] : c_Orderings_Obot__class_Obot(tc_fun(U_688,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_688),U_689),U_690),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
c_Orderings_Obot__class_Obot(tc_fun(U_688,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_688),U_689),U_690),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_insert__not__empty]) ).
fof(f_162_2,plain,
! [U_693,U_692,U_691] : hAPP(hAPP(c_Set_Oinsert(U_691),U_692),U_693) != c_Orderings_Obot__class_Obot(tc_fun(U_691,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_691,U_692,U_693] : hAPP(hAPP(c_Set_Oinsert(U_691),U_692),U_693) != c_Orderings_Obot__class_Obot(tc_fun(U_691,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_691),U_692),U_693) != c_Orderings_Obot__class_Obot(tc_fun(U_691,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,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_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ( ( V_b_2 != V_ca_2
| V_a_2 != V_d_2 )
& ( V_b_2 != V_d_2
| V_a_2 != V_ca_2 ) ) )
& ( ( V_b_2 = V_ca_2
& V_a_2 = V_d_2 )
| ( V_b_2 = V_d_2
& V_a_2 = V_ca_2 )
| 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_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff]) ).
fof(f_163_2,plain,
! [U_698,U_697,U_696,U_695,U_694] :
( ( hAPP(hAPP(c_Set_Oinsert(U_694),U_695),hAPP(hAPP(c_Set_Oinsert(U_694),U_696),c_Orderings_Obot__class_Obot(tc_fun(U_694,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_694),U_697),hAPP(hAPP(c_Set_Oinsert(U_694),U_698),c_Orderings_Obot__class_Obot(tc_fun(U_694,tc_HOL_Obool))))
| ( ( U_696 != U_697
| U_695 != U_698 )
& ( U_696 != U_698
| U_695 != U_697 ) ) )
& ( ( U_696 = U_697
& U_695 = U_698 )
| ( U_696 = U_698
& U_695 = U_697 )
| hAPP(hAPP(c_Set_Oinsert(U_694),U_695),hAPP(hAPP(c_Set_Oinsert(U_694),U_696),c_Orderings_Obot__class_Obot(tc_fun(U_694,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_694),U_697),hAPP(hAPP(c_Set_Oinsert(U_694),U_698),c_Orderings_Obot__class_Obot(tc_fun(U_694,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
( ! [U_708,U_706,U_704,U_702] :
( ! [U_700] : hAPP(hAPP(c_Set_Oinsert(U_700),U_702),hAPP(hAPP(c_Set_Oinsert(U_700),U_704),c_Orderings_Obot__class_Obot(tc_fun(U_700,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_700),U_706),hAPP(hAPP(c_Set_Oinsert(U_700),U_708),c_Orderings_Obot__class_Obot(tc_fun(U_700,tc_HOL_Obool))))
| ( ( U_704 != U_706
| U_702 != U_708 )
& ( U_704 != U_708
| U_702 != U_706 ) ) )
& ! [U_707,U_705,U_703,U_701] :
( ! [U_699] : hAPP(hAPP(c_Set_Oinsert(U_699),U_701),hAPP(hAPP(c_Set_Oinsert(U_699),U_703),c_Orderings_Obot__class_Obot(tc_fun(U_699,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_699),U_705),hAPP(hAPP(c_Set_Oinsert(U_699),U_707),c_Orderings_Obot__class_Obot(tc_fun(U_699,tc_HOL_Obool))))
| ( U_703 = U_705
& U_701 = U_707 )
| ( U_703 = U_707
& U_701 = U_705 ) ) ),
inference(miniscope,[status(thm)],[f_163_2]) ).
fof(f_163_4,plain,
( ! [U_706,U_704,U_702,U_708] :
( U_704 != U_706
| U_702 != U_708
| ~ sP53(U_706,U_704,U_702,U_708) )
& ! [U_706,U_704,U_702,U_708] :
( U_704 != U_708
| U_702 != U_706
| ~ sP53(U_706,U_704,U_702,U_708) )
& ! [U_703,U_701,U_705,U_707] :
( U_703 = U_705
| ~ sP52(U_703,U_701,U_705,U_707) )
& ! [U_703,U_701,U_705,U_707] :
( U_701 = U_707
| ~ sP52(U_703,U_701,U_705,U_707) )
& ! [U_703,U_701,U_705,U_707] :
( U_703 = U_707
| ~ sP51(U_703,U_701,U_705,U_707) )
& ! [U_703,U_701,U_705,U_707] :
( U_701 = U_705
| ~ sP51(U_703,U_701,U_705,U_707) )
& ! [U_700,U_706,U_704,U_702,U_708] :
( hAPP(hAPP(c_Set_Oinsert(U_700),U_702),hAPP(hAPP(c_Set_Oinsert(U_700),U_704),c_Orderings_Obot__class_Obot(tc_fun(U_700,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_700),U_706),hAPP(hAPP(c_Set_Oinsert(U_700),U_708),c_Orderings_Obot__class_Obot(tc_fun(U_700,tc_HOL_Obool))))
| sP53(U_706,U_704,U_702,U_708) )
& ! [U_699,U_703,U_701,U_705,U_707] :
( hAPP(hAPP(c_Set_Oinsert(U_699),U_701),hAPP(hAPP(c_Set_Oinsert(U_699),U_703),c_Orderings_Obot__class_Obot(tc_fun(U_699,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_699),U_705),hAPP(hAPP(c_Set_Oinsert(U_699),U_707),c_Orderings_Obot__class_Obot(tc_fun(U_699,tc_HOL_Obool))))
| sP52(U_703,U_701,U_705,U_707)
| sP51(U_703,U_701,U_705,U_707) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51,sP52,sP53])],[f_163_3]) ).
cnf(f_163_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_699),U_701),hAPP(hAPP(c_Set_Oinsert(U_699),U_703),c_Orderings_Obot__class_Obot(tc_fun(U_699,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_699),U_705),hAPP(hAPP(c_Set_Oinsert(U_699),U_707),c_Orderings_Obot__class_Obot(tc_fun(U_699,tc_HOL_Obool))))
| sP52(U_703,U_701,U_705,U_707)
| sP51(U_703,U_701,U_705,U_707) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_6,plain,
( hAPP(hAPP(c_Set_Oinsert(U_700),U_702),hAPP(hAPP(c_Set_Oinsert(U_700),U_704),c_Orderings_Obot__class_Obot(tc_fun(U_700,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_700),U_706),hAPP(hAPP(c_Set_Oinsert(U_700),U_708),c_Orderings_Obot__class_Obot(tc_fun(U_700,tc_HOL_Obool))))
| sP53(U_706,U_704,U_702,U_708) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_7,plain,
( U_701 = U_705
| ~ sP51(U_703,U_701,U_705,U_707) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_8,plain,
( U_703 = U_707
| ~ sP51(U_703,U_701,U_705,U_707) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_9,plain,
( U_701 = U_707
| ~ sP52(U_703,U_701,U_705,U_707) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_10,plain,
( U_703 = U_705
| ~ sP52(U_703,U_701,U_705,U_707) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_11,plain,
( U_704 != U_708
| U_702 != U_706
| ~ sP53(U_706,U_704,U_702,U_708) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_12,plain,
( U_704 != U_706
| U_702 != U_708
| ~ sP53(U_706,U_704,U_702,U_708) ),
inference(clausify,[status(thm)],[f_163_4]) ).
fof(f_164_1,plain,
! [V_b_2,V_a_2,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))) != hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_singleton__inject]) ).
fof(f_164_2,plain,
! [U_711,U_710,U_709] :
( U_710 = U_711
| hAPP(hAPP(c_Set_Oinsert(U_709),U_710),c_Orderings_Obot__class_Obot(tc_fun(U_709,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_709),U_711),c_Orderings_Obot__class_Obot(tc_fun(U_709,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_711,U_710] :
( ! [U_709] : hAPP(hAPP(c_Set_Oinsert(U_709),U_710),c_Orderings_Obot__class_Obot(tc_fun(U_709,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_709),U_711),c_Orderings_Obot__class_Obot(tc_fun(U_709,tc_HOL_Obool)))
| U_710 = U_711 ),
inference(miniscope,[status(thm)],[f_164_2]) ).
fof(f_164_4,plain,
! [U_709,U_711,U_710] :
( hAPP(hAPP(c_Set_Oinsert(U_709),U_710),c_Orderings_Obot__class_Obot(tc_fun(U_709,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_709),U_711),c_Orderings_Obot__class_Obot(tc_fun(U_709,tc_HOL_Obool)))
| U_710 = U_711 ),
inference(definitional_conversion,[status(esa)],[f_164_3]) ).
cnf(f_164_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_709),U_710),c_Orderings_Obot__class_Obot(tc_fun(U_709,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_709),U_711),c_Orderings_Obot__class_Obot(tc_fun(U_709,tc_HOL_Obool)))
| U_710 = U_711 ),
inference(clausify,[status(thm)],[f_164_4]) ).
fof(f_165_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_subset__insertI]) ).
fof(f_165_2,plain,
! [U_714,U_713,U_712] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_712,tc_HOL_Obool)),U_713),hAPP(hAPP(c_Set_Oinsert(U_712),U_714),U_713))),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_713,U_712,U_714] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_712,tc_HOL_Obool)),U_713),hAPP(hAPP(c_Set_Oinsert(U_712),U_714),U_713))),
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_712,tc_HOL_Obool)),U_713),hAPP(hAPP(c_Set_Oinsert(U_712),U_714),U_713))),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [V_b_2,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_Set_Oinsert(T_b),V_b_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__insertI2]) ).
fof(f_166_2,plain,
! [U_718,U_717,U_716,U_715] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_715,tc_HOL_Obool)),U_716),hAPP(hAPP(c_Set_Oinsert(U_715),U_718),U_717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_715,tc_HOL_Obool)),U_716),U_717)) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_715,U_716,U_717,U_718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_715,tc_HOL_Obool)),U_716),hAPP(hAPP(c_Set_Oinsert(U_715),U_718),U_717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_715,tc_HOL_Obool)),U_716),U_717)) ),
inference(definitional_conversion,[status(esa)],[f_166_2]) ).
cnf(f_166_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_715,tc_HOL_Obool)),U_716),hAPP(hAPP(c_Set_Oinsert(U_715),U_718),U_717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_715,tc_HOL_Obool)),U_716),U_717)) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
! [V_a_2,V_D_2,V_C_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__mono]) ).
fof(f_167_2,plain,
! [U_722,U_721,U_720,U_719] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_719,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_719),U_722),U_720)),hAPP(hAPP(c_Set_Oinsert(U_719),U_722),U_721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_719,tc_HOL_Obool)),U_720),U_721)) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_719,U_720,U_721,U_722] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_719,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_719),U_722),U_720)),hAPP(hAPP(c_Set_Oinsert(U_719),U_722),U_721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_719,tc_HOL_Obool)),U_720),U_721)) ),
inference(definitional_conversion,[status(esa)],[f_167_2]) ).
cnf(f_167_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_719,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_719),U_722),U_720)),hAPP(hAPP(c_Set_Oinsert(U_719),U_722),U_721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_719,tc_HOL_Obool)),U_720),U_721)) ),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( 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)))))
| V_b_2 != V_a_2 )
& ( V_b_2 = V_a_2
| ~ 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))))) ) ),
inference(fof_nnf,[status(thm)],[fact_singleton__iff]) ).
fof(f_168_2,plain,
! [U_725,U_724,U_723] :
( ( hBOOL(hAPP(hAPP(c_member(U_723),U_724),hAPP(hAPP(c_Set_Oinsert(U_723),U_725),c_Orderings_Obot__class_Obot(tc_fun(U_723,tc_HOL_Obool)))))
| U_724 != U_725 )
& ( U_724 = U_725
| ~ hBOOL(hAPP(hAPP(c_member(U_723),U_724),hAPP(hAPP(c_Set_Oinsert(U_723),U_725),c_Orderings_Obot__class_Obot(tc_fun(U_723,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
( ! [U_731,U_729] :
( ! [U_727] : hBOOL(hAPP(hAPP(c_member(U_727),U_729),hAPP(hAPP(c_Set_Oinsert(U_727),U_731),c_Orderings_Obot__class_Obot(tc_fun(U_727,tc_HOL_Obool)))))
| U_729 != U_731 )
& ! [U_730,U_728] :
( ! [U_726] : ~ hBOOL(hAPP(hAPP(c_member(U_726),U_728),hAPP(hAPP(c_Set_Oinsert(U_726),U_730),c_Orderings_Obot__class_Obot(tc_fun(U_726,tc_HOL_Obool)))))
| U_728 = U_730 ) ),
inference(miniscope,[status(thm)],[f_168_2]) ).
fof(f_168_4,plain,
( ! [U_727,U_729,U_731] :
( hBOOL(hAPP(hAPP(c_member(U_727),U_729),hAPP(hAPP(c_Set_Oinsert(U_727),U_731),c_Orderings_Obot__class_Obot(tc_fun(U_727,tc_HOL_Obool)))))
| U_729 != U_731 )
& ! [U_730,U_726,U_728] :
( ~ hBOOL(hAPP(hAPP(c_member(U_726),U_728),hAPP(hAPP(c_Set_Oinsert(U_726),U_730),c_Orderings_Obot__class_Obot(tc_fun(U_726,tc_HOL_Obool)))))
| U_728 = U_730 ) ),
inference(definitional_conversion,[status(esa)],[f_168_3]) ).
cnf(f_168_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_726),U_728),hAPP(hAPP(c_Set_Oinsert(U_726),U_730),c_Orderings_Obot__class_Obot(tc_fun(U_726,tc_HOL_Obool)))))
| U_728 = U_730 ),
inference(clausify,[status(thm)],[f_168_4]) ).
cnf(f_168_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_727),U_729),hAPP(hAPP(c_Set_Oinsert(U_727),U_731),c_Orderings_Obot__class_Obot(tc_fun(U_727,tc_HOL_Obool)))))
| U_729 != U_731 ),
inference(clausify,[status(thm)],[f_168_4]) ).
fof(f_169_1,plain,
! [V_a_2,V_b_2,T_b] :
( V_b_2 = V_a_2
| ~ 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))))) ),
inference(fof_nnf,[status(thm)],[fact_singletonE]) ).
fof(f_169_2,plain,
! [U_734,U_733,U_732] :
( U_733 = U_734
| ~ hBOOL(hAPP(hAPP(c_member(U_732),U_733),hAPP(hAPP(c_Set_Oinsert(U_732),U_734),c_Orderings_Obot__class_Obot(tc_fun(U_732,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_734,U_733] :
( ! [U_732] : ~ hBOOL(hAPP(hAPP(c_member(U_732),U_733),hAPP(hAPP(c_Set_Oinsert(U_732),U_734),c_Orderings_Obot__class_Obot(tc_fun(U_732,tc_HOL_Obool)))))
| U_733 = U_734 ),
inference(miniscope,[status(thm)],[f_169_2]) ).
fof(f_169_4,plain,
! [U_732,U_733,U_734] :
( ~ hBOOL(hAPP(hAPP(c_member(U_732),U_733),hAPP(hAPP(c_Set_Oinsert(U_732),U_734),c_Orderings_Obot__class_Obot(tc_fun(U_732,tc_HOL_Obool)))))
| U_733 = U_734 ),
inference(definitional_conversion,[status(esa)],[f_169_3]) ).
cnf(f_169_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_732),U_733),hAPP(hAPP(c_Set_Oinsert(U_732),U_734),c_Orderings_Obot__class_Obot(tc_fun(U_732,tc_HOL_Obool)))))
| U_733 = U_734 ),
inference(clausify,[status(thm)],[f_169_4]) ).
fof(f_170_1,plain,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__subset]) ).
fof(f_170_2,plain,
! [U_738,U_737,U_736,U_735] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_735,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_735),U_736),U_737)),U_738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_735,tc_HOL_Obool)),U_737),U_738))
| ~ hBOOL(hAPP(hAPP(c_member(U_735),U_736),U_738)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_735,tc_HOL_Obool)),U_737),U_738))
& hBOOL(hAPP(hAPP(c_member(U_735),U_736),U_738)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_735,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_735),U_736),U_737)),U_738)) ) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
( ! [U_746,U_744,U_742,U_740] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_740,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_740),U_742),U_744)),U_746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_740,tc_HOL_Obool)),U_744),U_746))
| ~ hBOOL(hAPP(hAPP(c_member(U_740),U_742),U_746)) )
& ! [U_745,U_743,U_741,U_739] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_739,tc_HOL_Obool)),U_743),U_745))
& hBOOL(hAPP(hAPP(c_member(U_739),U_741),U_745)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_739,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_739),U_741),U_743)),U_745)) ) ),
inference(miniscope,[status(thm)],[f_170_2]) ).
fof(f_170_4,plain,
( ! [U_743,U_741,U_745,U_739] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_739,tc_HOL_Obool)),U_743),U_745))
| ~ sP54(U_743,U_741,U_745,U_739) )
& ! [U_743,U_741,U_745,U_739] :
( hBOOL(hAPP(hAPP(c_member(U_739),U_741),U_745))
| ~ sP54(U_743,U_741,U_745,U_739) )
& ! [U_740,U_744,U_746,U_742] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_740,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_740),U_742),U_744)),U_746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_740,tc_HOL_Obool)),U_744),U_746))
| ~ hBOOL(hAPP(hAPP(c_member(U_740),U_742),U_746)) )
& ! [U_743,U_741,U_745,U_739] :
( sP54(U_743,U_741,U_745,U_739)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_739,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_739),U_741),U_743)),U_745)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_170_3]) ).
cnf(f_170_5,plain,
( sP54(U_743,U_741,U_745,U_739)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_739,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_739),U_741),U_743)),U_745)) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_740,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_740),U_742),U_744)),U_746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_740,tc_HOL_Obool)),U_744),U_746))
| ~ hBOOL(hAPP(hAPP(c_member(U_740),U_742),U_746)) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_739),U_741),U_745))
| ~ sP54(U_743,U_741,U_745,U_739) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_739,tc_HOL_Obool)),U_743),U_745))
| ~ sP54(U_743,U_741,U_745,U_739) ),
inference(clausify,[status(thm)],[f_170_4]) ).
fof(f_171_1,plain,
! [V_B_2,V_A_2,V_x_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_Set_Oinsert(T_b),V_x_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ 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))) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__insert]) ).
fof(f_171_2,plain,
! [U_750,U_749,U_748,U_747] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),U_750)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),U_750)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),U_750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),U_750))) ) )
| hBOOL(hAPP(hAPP(c_member(U_747),U_748),U_749)) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
( ! [U_748,U_747,U_749,U_750] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),U_750)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),U_750))
| ~ sP55(U_748,U_747,U_749,U_750) )
& ! [U_748,U_747,U_749,U_750] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),U_750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),U_750)))
| ~ sP55(U_748,U_747,U_749,U_750) )
& ! [U_748,U_747,U_749,U_750] :
( sP55(U_748,U_747,U_749,U_750)
| hBOOL(hAPP(hAPP(c_member(U_747),U_748),U_749)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_171_2]) ).
cnf(f_171_4,plain,
( sP55(U_748,U_747,U_749,U_750)
| hBOOL(hAPP(hAPP(c_member(U_747),U_748),U_749)) ),
inference(clausify,[status(thm)],[f_171_3]) ).
cnf(f_171_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),U_750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),U_750)))
| ~ sP55(U_748,U_747,U_749,U_750) ),
inference(clausify,[status(thm)],[f_171_3]) ).
cnf(f_171_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),U_750)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_747,tc_HOL_Obool)),U_749),U_750))
| ~ sP55(U_748,U_747,U_749,U_750) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ 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))))) ),
inference(fof_nnf,[status(thm)],[fact_subset__singletonD]) ).
fof(f_172_2,plain,
! [U_753,U_752,U_751] :
( U_752 = hAPP(hAPP(c_Set_Oinsert(U_751),U_753),c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool)))
| U_752 = c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_751,tc_HOL_Obool)),U_752),hAPP(hAPP(c_Set_Oinsert(U_751),U_753),c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_753,U_752,U_751] :
( U_752 = hAPP(hAPP(c_Set_Oinsert(U_751),U_753),c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool)))
| U_752 = c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_751,tc_HOL_Obool)),U_752),hAPP(hAPP(c_Set_Oinsert(U_751),U_753),c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool))))) ),
inference(definitional_conversion,[status(esa)],[f_172_2]) ).
cnf(f_172_4,plain,
( U_752 = hAPP(hAPP(c_Set_Oinsert(U_751),U_753),c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool)))
| U_752 = c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_751,tc_HOL_Obool)),U_752),hAPP(hAPP(c_Set_Oinsert(U_751),U_753),c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_1,plain,
! [V_a_2,T_b] :
( 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
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__singleton]) ).
fof(f_173_2,plain,
! [U_755,U_754] :
( c_Complete__Lattice_OSup__class_OSup(U_754,hAPP(hAPP(c_Set_Oinsert(U_754),U_755),c_Orderings_Obot__class_Obot(tc_fun(U_754,tc_HOL_Obool)))) = U_755
| ~ class_Complete__Lattice_Ocomplete__lattice(U_754) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_754,U_755] :
( c_Complete__Lattice_OSup__class_OSup(U_754,hAPP(hAPP(c_Set_Oinsert(U_754),U_755),c_Orderings_Obot__class_Obot(tc_fun(U_754,tc_HOL_Obool)))) = U_755
| ~ class_Complete__Lattice_Ocomplete__lattice(U_754) ),
inference(definitional_conversion,[status(esa)],[f_173_2]) ).
cnf(f_173_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_754,hAPP(hAPP(c_Set_Oinsert(U_754),U_755),c_Orderings_Obot__class_Obot(tc_fun(U_754,tc_HOL_Obool)))) = U_755
| ~ class_Complete__Lattice_Ocomplete__lattice(U_754) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
! [V_a_2,T_b] :
( 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
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__singleton]) ).
fof(f_174_2,plain,
! [U_757,U_756] :
( c_Complete__Lattice_OInf__class_OInf(U_756,hAPP(hAPP(c_Set_Oinsert(U_756),U_757),c_Orderings_Obot__class_Obot(tc_fun(U_756,tc_HOL_Obool)))) = U_757
| ~ class_Complete__Lattice_Ocomplete__lattice(U_756) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_757,U_756] :
( c_Complete__Lattice_OInf__class_OInf(U_756,hAPP(hAPP(c_Set_Oinsert(U_756),U_757),c_Orderings_Obot__class_Obot(tc_fun(U_756,tc_HOL_Obool)))) = U_757
| ~ class_Complete__Lattice_Ocomplete__lattice(U_756) ),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_756,hAPP(hAPP(c_Set_Oinsert(U_756),U_757),c_Orderings_Obot__class_Obot(tc_fun(U_756,tc_HOL_Obool)))) = U_757
| ~ class_Complete__Lattice_Ocomplete__lattice(U_756) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_the__elem__eq]) ).
fof(f_175_2,plain,
! [U_759,U_758] : c_Set_Othe__elem(U_758,hAPP(hAPP(c_Set_Oinsert(U_758),U_759),c_Orderings_Obot__class_Obot(tc_fun(U_758,tc_HOL_Obool)))) = U_759,
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_758,U_759] : c_Set_Othe__elem(U_758,hAPP(hAPP(c_Set_Oinsert(U_758),U_759),c_Orderings_Obot__class_Obot(tc_fun(U_758,tc_HOL_Obool)))) = U_759,
inference(definitional_conversion,[status(esa)],[f_175_2]) ).
cnf(f_175_4,plain,
c_Set_Othe__elem(U_758,hAPP(hAPP(c_Set_Oinsert(U_758),U_759),c_Orderings_Obot__class_Obot(tc_fun(U_758,tc_HOL_Obool)))) = U_759,
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [V_l_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_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)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J]) ).
fof(f_176_2,plain,
! [U_761,U_760] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_760,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_760),U_761),c_Orderings_Obot__class_Obot(tc_fun(U_760,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_760),U_761)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_760),U_761)
| ~ class_Orderings_Olinorder(U_760) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_760,U_761] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_760,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_760),U_761),c_Orderings_Obot__class_Obot(tc_fun(U_760,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_760),U_761)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_760),U_761)
| ~ class_Orderings_Olinorder(U_760) ),
inference(definitional_conversion,[status(esa)],[f_176_2]) ).
cnf(f_176_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_760,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_760),U_761),c_Orderings_Obot__class_Obot(tc_fun(U_760,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_760),U_761)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_760),U_761)
| ~ class_Orderings_Olinorder(U_760) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [V_n_2,T_b] :
( 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)))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast]) ).
fof(f_177_2,plain,
! [U_763,U_762] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_762,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_762),U_763)),hAPP(c_SetInterval_Oord__class_OatLeast(U_762),U_763)) = hAPP(hAPP(c_Set_Oinsert(U_762),U_763),c_Orderings_Obot__class_Obot(tc_fun(U_762,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_762) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_762,U_763] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_762,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_762),U_763)),hAPP(c_SetInterval_Oord__class_OatLeast(U_762),U_763)) = hAPP(hAPP(c_Set_Oinsert(U_762),U_763),c_Orderings_Obot__class_Obot(tc_fun(U_762,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_762) ),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_762,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_762),U_763)),hAPP(c_SetInterval_Oord__class_OatLeast(U_762),U_763)) = hAPP(hAPP(c_Set_Oinsert(U_762),U_763),c_Orderings_Obot__class_Obot(tc_fun(U_762,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_762) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [V_u_2,T_b] :
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J]) ).
fof(f_178_2,plain,
! [U_765,U_764] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_764,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_764),U_765)),hAPP(hAPP(c_Set_Oinsert(U_764),U_765),c_Orderings_Obot__class_Obot(tc_fun(U_764,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_764),U_765)
| ~ class_Orderings_Olinorder(U_764) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_764,U_765] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_764,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_764),U_765)),hAPP(hAPP(c_Set_Oinsert(U_764),U_765),c_Orderings_Obot__class_Obot(tc_fun(U_764,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_764),U_765)
| ~ class_Orderings_Olinorder(U_764) ),
inference(definitional_conversion,[status(esa)],[f_178_2]) ).
cnf(f_178_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_764,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_764),U_765)),hAPP(hAPP(c_Set_Oinsert(U_764),U_765),c_Orderings_Obot__class_Obot(tc_fun(U_764,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_764),U_765)
| ~ class_Orderings_Olinorder(U_764) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [V_B_2,V_x_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_Set_Oinsert(T_b),V_x_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_diff__single__insert]) ).
fof(f_179_2,plain,
! [U_769,U_768,U_767,U_766] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_766,tc_HOL_Obool)),U_767),hAPP(hAPP(c_Set_Oinsert(U_766),U_768),U_769)))
| ~ hBOOL(hAPP(hAPP(c_member(U_766),U_768),U_767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_766,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_766,tc_HOL_Obool)),U_767),hAPP(hAPP(c_Set_Oinsert(U_766),U_768),c_Orderings_Obot__class_Obot(tc_fun(U_766,tc_HOL_Obool))))),U_769)) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_766,U_767,U_768,U_769] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_766,tc_HOL_Obool)),U_767),hAPP(hAPP(c_Set_Oinsert(U_766),U_768),U_769)))
| ~ hBOOL(hAPP(hAPP(c_member(U_766),U_768),U_767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_766,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_766,tc_HOL_Obool)),U_767),hAPP(hAPP(c_Set_Oinsert(U_766),U_768),c_Orderings_Obot__class_Obot(tc_fun(U_766,tc_HOL_Obool))))),U_769)) ),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_766,tc_HOL_Obool)),U_767),hAPP(hAPP(c_Set_Oinsert(U_766),U_768),U_769)))
| ~ hBOOL(hAPP(hAPP(c_member(U_766),U_768),U_767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_766,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_766,tc_HOL_Obool)),U_767),hAPP(hAPP(c_Set_Oinsert(U_766),U_768),c_Orderings_Obot__class_Obot(tc_fun(U_766,tc_HOL_Obool))))),U_769)) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [V_B_2,V_x_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_Set_Oinsert(T_b),V_x_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
| ( ~ 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))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__insert__iff]) ).
fof(f_180_2,plain,
! [U_773,U_772,U_771,U_770] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_770,tc_HOL_Obool)),U_771),hAPP(hAPP(c_Set_Oinsert(U_770),U_772),U_773)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_770,tc_HOL_Obool)),U_771),U_773))
& ~ hBOOL(hAPP(hAPP(c_member(U_770),U_772),U_771)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_770,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_770,tc_HOL_Obool)),U_771),hAPP(hAPP(c_Set_Oinsert(U_770),U_772),c_Orderings_Obot__class_Obot(tc_fun(U_770,tc_HOL_Obool))))),U_773))
& hBOOL(hAPP(hAPP(c_member(U_770),U_772),U_771)) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_770,tc_HOL_Obool)),U_771),U_773))
| hBOOL(hAPP(hAPP(c_member(U_770),U_772),U_771)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_770,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_770,tc_HOL_Obool)),U_771),hAPP(hAPP(c_Set_Oinsert(U_770),U_772),c_Orderings_Obot__class_Obot(tc_fun(U_770,tc_HOL_Obool))))),U_773))
| ~ hBOOL(hAPP(hAPP(c_member(U_770),U_772),U_771)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_770,tc_HOL_Obool)),U_771),hAPP(hAPP(c_Set_Oinsert(U_770),U_772),U_773))) ) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( ! [U_781,U_779,U_777,U_775] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),U_777),hAPP(hAPP(c_Set_Oinsert(U_775),U_779),U_781)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),U_777),U_781))
& ~ hBOOL(hAPP(hAPP(c_member(U_775),U_779),U_777)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_775,tc_HOL_Obool)),U_777),hAPP(hAPP(c_Set_Oinsert(U_775),U_779),c_Orderings_Obot__class_Obot(tc_fun(U_775,tc_HOL_Obool))))),U_781))
& hBOOL(hAPP(hAPP(c_member(U_775),U_779),U_777)) ) )
& ! [U_780,U_778,U_776,U_774] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),U_776),U_780))
| hBOOL(hAPP(hAPP(c_member(U_774),U_778),U_776)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_774,tc_HOL_Obool)),U_776),hAPP(hAPP(c_Set_Oinsert(U_774),U_778),c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool))))),U_780))
| ~ hBOOL(hAPP(hAPP(c_member(U_774),U_778),U_776)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),U_776),hAPP(hAPP(c_Set_Oinsert(U_774),U_778),U_780))) ) ),
inference(miniscope,[status(thm)],[f_180_2]) ).
fof(f_180_4,plain,
( ! [U_777,U_775,U_779,U_781] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),U_777),U_781))
| ~ sP58(U_777,U_775,U_779,U_781) )
& ! [U_777,U_775,U_779,U_781] :
( ~ hBOOL(hAPP(hAPP(c_member(U_775),U_779),U_777))
| ~ sP58(U_777,U_775,U_779,U_781) )
& ! [U_777,U_775,U_779,U_781] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_775,tc_HOL_Obool)),U_777),hAPP(hAPP(c_Set_Oinsert(U_775),U_779),c_Orderings_Obot__class_Obot(tc_fun(U_775,tc_HOL_Obool))))),U_781))
| ~ sP57(U_777,U_775,U_779,U_781) )
& ! [U_777,U_775,U_779,U_781] :
( hBOOL(hAPP(hAPP(c_member(U_775),U_779),U_777))
| ~ sP57(U_777,U_775,U_779,U_781) )
& ! [U_774,U_776,U_780,U_778] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),U_776),U_780))
| hBOOL(hAPP(hAPP(c_member(U_774),U_778),U_776))
| ~ sP56(U_774,U_776,U_780,U_778) )
& ! [U_774,U_776,U_780,U_778] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_774,tc_HOL_Obool)),U_776),hAPP(hAPP(c_Set_Oinsert(U_774),U_778),c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool))))),U_780))
| ~ hBOOL(hAPP(hAPP(c_member(U_774),U_778),U_776))
| ~ sP56(U_774,U_776,U_780,U_778) )
& ! [U_777,U_775,U_779,U_781] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),U_777),hAPP(hAPP(c_Set_Oinsert(U_775),U_779),U_781)))
| sP58(U_777,U_775,U_779,U_781)
| sP57(U_777,U_775,U_779,U_781) )
& ! [U_774,U_776,U_780,U_778] :
( sP56(U_774,U_776,U_780,U_778)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),U_776),hAPP(hAPP(c_Set_Oinsert(U_774),U_778),U_780))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56,sP57,sP58])],[f_180_3]) ).
cnf(f_180_5,plain,
( sP56(U_774,U_776,U_780,U_778)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),U_776),hAPP(hAPP(c_Set_Oinsert(U_774),U_778),U_780))) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),U_777),hAPP(hAPP(c_Set_Oinsert(U_775),U_779),U_781)))
| sP58(U_777,U_775,U_779,U_781)
| sP57(U_777,U_775,U_779,U_781) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_774,tc_HOL_Obool)),U_776),hAPP(hAPP(c_Set_Oinsert(U_774),U_778),c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool))))),U_780))
| ~ hBOOL(hAPP(hAPP(c_member(U_774),U_778),U_776))
| ~ sP56(U_774,U_776,U_780,U_778) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_774,tc_HOL_Obool)),U_776),U_780))
| hBOOL(hAPP(hAPP(c_member(U_774),U_778),U_776))
| ~ sP56(U_774,U_776,U_780,U_778) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_775),U_779),U_777))
| ~ sP57(U_777,U_775,U_779,U_781) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_775,tc_HOL_Obool)),U_777),hAPP(hAPP(c_Set_Oinsert(U_775),U_779),c_Orderings_Obot__class_Obot(tc_fun(U_775,tc_HOL_Obool))))),U_781))
| ~ sP57(U_777,U_775,U_779,U_781) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_775),U_779),U_777))
| ~ sP58(U_777,U_775,U_779,U_781) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_775,tc_HOL_Obool)),U_777),U_781))
| ~ sP58(U_777,U_775,U_779,U_781) ),
inference(clausify,[status(thm)],[f_180_4]) ).
fof(f_181_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_Int__eq__Inter]) ).
fof(f_181_2,plain,
! [U_784,U_783,U_782] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_782,tc_HOL_Obool)),U_783),U_784) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_782,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_782,tc_HOL_Obool)),U_783),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_782,tc_HOL_Obool)),U_784),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_782,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_783,U_784,U_782] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_782,tc_HOL_Obool)),U_783),U_784) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_782,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_782,tc_HOL_Obool)),U_783),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_782,tc_HOL_Obool)),U_784),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_782,tc_HOL_Obool),tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_181_2]) ).
cnf(f_181_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_782,tc_HOL_Obool)),U_783),U_784) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_782,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_782,tc_HOL_Obool)),U_783),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_782,tc_HOL_Obool)),U_784),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_782,tc_HOL_Obool),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_Un__eq__Union]) ).
fof(f_182_2,plain,
! [U_787,U_786,U_785] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_785,tc_HOL_Obool)),U_786),U_787) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_785,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_785,tc_HOL_Obool)),U_786),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_785,tc_HOL_Obool)),U_787),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_785,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_785,U_786,U_787] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_785,tc_HOL_Obool)),U_786),U_787) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_785,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_785,tc_HOL_Obool)),U_786),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_785,tc_HOL_Obool)),U_787),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_785,tc_HOL_Obool),tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_182_2]) ).
cnf(f_182_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_785,tc_HOL_Obool)),U_786),U_787) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_785,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_785,tc_HOL_Obool)),U_786),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_785,tc_HOL_Obool)),U_787),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_785,tc_HOL_Obool),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J]) ).
fof(f_183_2,plain,
! [U_790,U_789,U_788] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_788,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_788,U_789,U_790)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_788),U_790)) = c_Orderings_Obot__class_Obot(tc_fun(U_788,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_788) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_789,U_788,U_790] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_788,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_788,U_789,U_790)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_788),U_790)) = c_Orderings_Obot__class_Obot(tc_fun(U_788,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_788) ),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_788,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_788,U_789,U_790)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_788),U_790)) = c_Orderings_Obot__class_Obot(tc_fun(U_788,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_788) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J]) ).
fof(f_184_2,plain,
! [U_793,U_792,U_791] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_791,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_791,U_792,U_793)),hAPP(c_SetInterval_Oord__class_OatLeast(U_791),U_793)) = c_Orderings_Obot__class_Obot(tc_fun(U_791,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_791) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
! [U_791,U_792,U_793] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_791,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_791,U_792,U_793)),hAPP(c_SetInterval_Oord__class_OatLeast(U_791),U_793)) = c_Orderings_Obot__class_Obot(tc_fun(U_791,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_791) ),
inference(definitional_conversion,[status(esa)],[f_184_2]) ).
cnf(f_184_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_791,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_791,U_792,U_793)),hAPP(c_SetInterval_Oord__class_OatLeast(U_791),U_793)) = c_Orderings_Obot__class_Obot(tc_fun(U_791,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_791) ),
inference(clausify,[status(thm)],[f_184_3]) ).
fof(f_185_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J]) ).
fof(f_185_2,plain,
! [U_796,U_795,U_794] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_794,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_794,U_795,U_796)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_794),U_796)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_794),U_795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_794),U_795),U_796))
| ~ class_Orderings_Olinorder(U_794) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
! [U_794,U_795,U_796] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_794,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_794,U_795,U_796)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_794),U_796)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_794),U_795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_794),U_795),U_796))
| ~ class_Orderings_Olinorder(U_794) ),
inference(definitional_conversion,[status(esa)],[f_185_2]) ).
cnf(f_185_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_794,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_794,U_795,U_796)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_794),U_796)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_794),U_795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_794),U_795),U_796))
| ~ class_Orderings_Olinorder(U_794) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_1,plain,
! [T_b,V_A_2,V_x_2,V_B_2] :
( 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))
| ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup1CI]) ).
fof(f_186_2,plain,
! [U_800,U_799,U_798,U_797] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_800,tc_HOL_Obool)),U_799),U_797),U_798))
| ( ~ hBOOL(hAPP(U_799,U_798))
& ~ hBOOL(hAPP(U_797,U_798)) ) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
( ! [U_798,U_797,U_799] :
( ~ hBOOL(hAPP(U_799,U_798))
| ~ sP59(U_798,U_797,U_799) )
& ! [U_798,U_797,U_799] :
( ~ hBOOL(hAPP(U_797,U_798))
| ~ sP59(U_798,U_797,U_799) )
& ! [U_798,U_797,U_799,U_800] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_800,tc_HOL_Obool)),U_799),U_797),U_798))
| sP59(U_798,U_797,U_799) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_186_2]) ).
cnf(f_186_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_800,tc_HOL_Obool)),U_799),U_797),U_798))
| sP59(U_798,U_797,U_799) ),
inference(clausify,[status(thm)],[f_186_3]) ).
cnf(f_186_5,plain,
( ~ hBOOL(hAPP(U_797,U_798))
| ~ sP59(U_798,U_797,U_799) ),
inference(clausify,[status(thm)],[f_186_3]) ).
cnf(f_186_6,plain,
( ~ hBOOL(hAPP(U_799,U_798))
| ~ sP59(U_798,U_797,U_799) ),
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(V_B_2,V_x_2))
| hBOOL(hAPP(V_A_2,V_x_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_sup1E]) ).
fof(f_187_2,plain,
! [U_804,U_803,U_802,U_801] :
( hBOOL(hAPP(U_803,U_804))
| hBOOL(hAPP(U_802,U_804))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_801,tc_HOL_Obool)),U_802),U_803),U_804)) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_804,U_803,U_802] :
( ! [U_801] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_801,tc_HOL_Obool)),U_802),U_803),U_804))
| hBOOL(hAPP(U_803,U_804))
| hBOOL(hAPP(U_802,U_804)) ),
inference(miniscope,[status(thm)],[f_187_2]) ).
fof(f_187_4,plain,
! [U_802,U_801,U_803,U_804] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_801,tc_HOL_Obool)),U_802),U_803),U_804))
| hBOOL(hAPP(U_803,U_804))
| hBOOL(hAPP(U_802,U_804)) ),
inference(definitional_conversion,[status(esa)],[f_187_3]) ).
cnf(f_187_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_801,tc_HOL_Obool)),U_802),U_803),U_804))
| hBOOL(hAPP(U_803,U_804))
| hBOOL(hAPP(U_802,U_804)) ),
inference(clausify,[status(thm)],[f_187_4]) ).
fof(f_188_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(V_B_2,V_x_2))
& hBOOL(hAPP(V_A_2,V_x_2)) )
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_inf1E]) ).
fof(f_188_2,plain,
! [U_808,U_807,U_806,U_805] :
( ( hBOOL(hAPP(U_807,U_808))
& hBOOL(hAPP(U_806,U_808)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_805,tc_HOL_Obool)),U_806),U_807),U_808)) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
! [U_808,U_807,U_806] :
( ! [U_805] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_805,tc_HOL_Obool)),U_806),U_807),U_808))
| ( hBOOL(hAPP(U_807,U_808))
& hBOOL(hAPP(U_806,U_808)) ) ),
inference(miniscope,[status(thm)],[f_188_2]) ).
fof(f_188_4,plain,
( ! [U_806,U_807,U_808] :
( hBOOL(hAPP(U_807,U_808))
| ~ sP60(U_806,U_807,U_808) )
& ! [U_806,U_807,U_808] :
( hBOOL(hAPP(U_806,U_808))
| ~ sP60(U_806,U_807,U_808) )
& ! [U_806,U_805,U_807,U_808] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_805,tc_HOL_Obool)),U_806),U_807),U_808))
| sP60(U_806,U_807,U_808) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_188_3]) ).
cnf(f_188_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_805,tc_HOL_Obool)),U_806),U_807),U_808))
| sP60(U_806,U_807,U_808) ),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_6,plain,
( hBOOL(hAPP(U_806,U_808))
| ~ sP60(U_806,U_807,U_808) ),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_7,plain,
( hBOOL(hAPP(U_807,U_808))
| ~ sP60(U_806,U_807,U_808) ),
inference(clausify,[status(thm)],[f_188_4]) ).
fof(f_189_1,plain,
! [T_b,V_B_2,V_x_2,V_A_2] :
( 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))
| ~ hBOOL(hAPP(V_B_2,V_x_2))
| ~ hBOOL(hAPP(V_A_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1I]) ).
fof(f_189_2,plain,
! [U_812,U_811,U_810,U_809] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_812,tc_HOL_Obool)),U_809),U_811),U_810))
| ~ hBOOL(hAPP(U_811,U_810))
| ~ hBOOL(hAPP(U_809,U_810)) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_810,U_809,U_811,U_812] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_812,tc_HOL_Obool)),U_809),U_811),U_810))
| ~ hBOOL(hAPP(U_811,U_810))
| ~ hBOOL(hAPP(U_809,U_810)) ),
inference(definitional_conversion,[status(esa)],[f_189_2]) ).
cnf(f_189_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_812,tc_HOL_Obool)),U_809),U_811),U_810))
| ~ hBOOL(hAPP(U_811,U_810))
| ~ hBOOL(hAPP(U_809,U_810)) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_UnE]) ).
fof(f_190_2,plain,
! [U_816,U_815,U_814,U_813] :
( hBOOL(hAPP(hAPP(c_member(U_813),U_814),U_816))
| hBOOL(hAPP(hAPP(c_member(U_813),U_814),U_815))
| ~ hBOOL(hAPP(hAPP(c_member(U_813),U_814),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_813,tc_HOL_Obool)),U_815),U_816))) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_816,U_813,U_814,U_815] :
( hBOOL(hAPP(hAPP(c_member(U_813),U_814),U_816))
| hBOOL(hAPP(hAPP(c_member(U_813),U_814),U_815))
| ~ hBOOL(hAPP(hAPP(c_member(U_813),U_814),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_813,tc_HOL_Obool)),U_815),U_816))) ),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_813),U_814),U_816))
| hBOOL(hAPP(hAPP(c_member(U_813),U_814),U_815))
| ~ hBOOL(hAPP(hAPP(c_member(U_813),U_814),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_813,tc_HOL_Obool)),U_815),U_816))) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [V_A_2,V_B_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_UnCI]) ).
fof(f_191_2,plain,
! [U_820,U_819,U_818,U_817] :
( hBOOL(hAPP(hAPP(c_member(U_817),U_818),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_817,tc_HOL_Obool)),U_820),U_819)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_817),U_818),U_820))
& ~ hBOOL(hAPP(hAPP(c_member(U_817),U_818),U_819)) ) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
( ! [U_817,U_818,U_819,U_820] :
( ~ hBOOL(hAPP(hAPP(c_member(U_817),U_818),U_820))
| ~ sP61(U_817,U_818,U_819,U_820) )
& ! [U_817,U_818,U_819,U_820] :
( ~ hBOOL(hAPP(hAPP(c_member(U_817),U_818),U_819))
| ~ sP61(U_817,U_818,U_819,U_820) )
& ! [U_817,U_818,U_819,U_820] :
( hBOOL(hAPP(hAPP(c_member(U_817),U_818),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_817,tc_HOL_Obool)),U_820),U_819)))
| sP61(U_817,U_818,U_819,U_820) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_191_2]) ).
cnf(f_191_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_817),U_818),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_817,tc_HOL_Obool)),U_820),U_819)))
| sP61(U_817,U_818,U_819,U_820) ),
inference(clausify,[status(thm)],[f_191_3]) ).
cnf(f_191_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_817),U_818),U_819))
| ~ sP61(U_817,U_818,U_819,U_820) ),
inference(clausify,[status(thm)],[f_191_3]) ).
cnf(f_191_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_817),U_818),U_820))
| ~ sP61(U_817,U_818,U_819,U_820) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_IntI]) ).
fof(f_192_2,plain,
! [U_824,U_823,U_822,U_821] :
( hBOOL(hAPP(hAPP(c_member(U_821),U_822),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_821,tc_HOL_Obool)),U_823),U_824)))
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_822),U_824))
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_822),U_823)) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_824,U_821,U_822,U_823] :
( hBOOL(hAPP(hAPP(c_member(U_821),U_822),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_821,tc_HOL_Obool)),U_823),U_824)))
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_822),U_824))
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_822),U_823)) ),
inference(definitional_conversion,[status(esa)],[f_192_2]) ).
cnf(f_192_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_821),U_822),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_821,tc_HOL_Obool)),U_823),U_824)))
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_822),U_824))
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_822),U_823)) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntE]) ).
fof(f_193_2,plain,
! [U_828,U_827,U_826,U_825] :
( ( hBOOL(hAPP(hAPP(c_member(U_825),U_826),U_828))
& hBOOL(hAPP(hAPP(c_member(U_825),U_826),U_827)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_825),U_826),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_825,tc_HOL_Obool)),U_827),U_828))) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
( ! [U_825,U_826,U_827,U_828] :
( hBOOL(hAPP(hAPP(c_member(U_825),U_826),U_828))
| ~ sP62(U_825,U_826,U_827,U_828) )
& ! [U_825,U_826,U_827,U_828] :
( hBOOL(hAPP(hAPP(c_member(U_825),U_826),U_827))
| ~ sP62(U_825,U_826,U_827,U_828) )
& ! [U_825,U_826,U_827,U_828] :
( sP62(U_825,U_826,U_827,U_828)
| ~ hBOOL(hAPP(hAPP(c_member(U_825),U_826),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_825,tc_HOL_Obool)),U_827),U_828))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_193_2]) ).
cnf(f_193_4,plain,
( sP62(U_825,U_826,U_827,U_828)
| ~ hBOOL(hAPP(hAPP(c_member(U_825),U_826),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_825,tc_HOL_Obool)),U_827),U_828))) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_825),U_826),U_827))
| ~ sP62(U_825,U_826,U_827,U_828) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_825),U_826),U_828))
| ~ sP62(U_825,U_826,U_827,U_828) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_DiffI]) ).
fof(f_194_2,plain,
! [U_832,U_831,U_830,U_829] :
( hBOOL(hAPP(hAPP(c_member(U_829),U_830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_829,tc_HOL_Obool)),U_831),U_832)))
| hBOOL(hAPP(hAPP(c_member(U_829),U_830),U_832))
| ~ hBOOL(hAPP(hAPP(c_member(U_829),U_830),U_831)) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_829,U_830,U_831,U_832] :
( hBOOL(hAPP(hAPP(c_member(U_829),U_830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_829,tc_HOL_Obool)),U_831),U_832)))
| hBOOL(hAPP(hAPP(c_member(U_829),U_830),U_832))
| ~ hBOOL(hAPP(hAPP(c_member(U_829),U_830),U_831)) ),
inference(definitional_conversion,[status(esa)],[f_194_2]) ).
cnf(f_194_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_829),U_830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_829,tc_HOL_Obool)),U_831),U_832)))
| hBOOL(hAPP(hAPP(c_member(U_829),U_830),U_832))
| ~ hBOOL(hAPP(hAPP(c_member(U_829),U_830),U_831)) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffE]) ).
fof(f_195_2,plain,
! [U_836,U_835,U_834,U_833] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_833),U_834),U_836))
& hBOOL(hAPP(hAPP(c_member(U_833),U_834),U_835)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_833),U_834),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_833,tc_HOL_Obool)),U_835),U_836))) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
( ! [U_833,U_834,U_835,U_836] :
( ~ hBOOL(hAPP(hAPP(c_member(U_833),U_834),U_836))
| ~ sP63(U_833,U_834,U_835,U_836) )
& ! [U_833,U_834,U_835,U_836] :
( hBOOL(hAPP(hAPP(c_member(U_833),U_834),U_835))
| ~ sP63(U_833,U_834,U_835,U_836) )
& ! [U_833,U_834,U_835,U_836] :
( sP63(U_833,U_834,U_835,U_836)
| ~ hBOOL(hAPP(hAPP(c_member(U_833),U_834),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_833,tc_HOL_Obool)),U_835),U_836))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_195_2]) ).
cnf(f_195_4,plain,
( sP63(U_833,U_834,U_835,U_836)
| ~ hBOOL(hAPP(hAPP(c_member(U_833),U_834),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_833,tc_HOL_Obool)),U_835),U_836))) ),
inference(clausify,[status(thm)],[f_195_3]) ).
cnf(f_195_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_833),U_834),U_835))
| ~ sP63(U_833,U_834,U_835,U_836) ),
inference(clausify,[status(thm)],[f_195_3]) ).
cnf(f_195_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_833),U_834),U_836))
| ~ sP63(U_833,U_834,U_835,U_836) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(V_B_2,V_x_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_inf1D2]) ).
fof(f_196_2,plain,
! [U_840,U_839,U_838,U_837] :
( hBOOL(hAPP(U_839,U_840))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_837,tc_HOL_Obool)),U_838),U_839),U_840)) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
! [U_840,U_839] :
( ! [U_838,U_837] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_837,tc_HOL_Obool)),U_838),U_839),U_840))
| hBOOL(hAPP(U_839,U_840)) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
fof(f_196_4,plain,
! [U_840,U_839,U_837,U_838] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_837,tc_HOL_Obool)),U_838),U_839),U_840))
| hBOOL(hAPP(U_839,U_840)) ),
inference(definitional_conversion,[status(esa)],[f_196_3]) ).
cnf(f_196_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_837,tc_HOL_Obool)),U_838),U_839),U_840))
| hBOOL(hAPP(U_839,U_840)) ),
inference(clausify,[status(thm)],[f_196_4]) ).
fof(f_197_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_inf1D1]) ).
fof(f_197_2,plain,
! [U_844,U_843,U_842,U_841] :
( hBOOL(hAPP(U_842,U_844))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_841,tc_HOL_Obool)),U_842),U_843),U_844)) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_844,U_843,U_842] :
( ! [U_841] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_841,tc_HOL_Obool)),U_842),U_843),U_844))
| hBOOL(hAPP(U_842,U_844)) ),
inference(miniscope,[status(thm)],[f_197_2]) ).
fof(f_197_4,plain,
! [U_841,U_842,U_843,U_844] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_841,tc_HOL_Obool)),U_842),U_843),U_844))
| hBOOL(hAPP(U_842,U_844)) ),
inference(definitional_conversion,[status(esa)],[f_197_3]) ).
cnf(f_197_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_841,tc_HOL_Obool)),U_842),U_843),U_844))
| hBOOL(hAPP(U_842,U_844)) ),
inference(clausify,[status(thm)],[f_197_4]) ).
fof(f_198_1,plain,
! [V_A_2,T_b,V_x_2,V_B_2] :
( 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))
| ~ hBOOL(hAPP(V_B_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup1I2]) ).
fof(f_198_2,plain,
! [U_848,U_847,U_846,U_845] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_847,tc_HOL_Obool)),U_848),U_845),U_846))
| ~ hBOOL(hAPP(U_845,U_846)) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_845,U_846,U_847,U_848] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_847,tc_HOL_Obool)),U_848),U_845),U_846))
| ~ hBOOL(hAPP(U_845,U_846)) ),
inference(definitional_conversion,[status(esa)],[f_198_2]) ).
cnf(f_198_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_847,tc_HOL_Obool)),U_848),U_845),U_846))
| ~ hBOOL(hAPP(U_845,U_846)) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_1,plain,
! [V_B_2,T_b,V_x_2,V_A_2] :
( 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))
| ~ hBOOL(hAPP(V_A_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup1I1]) ).
fof(f_199_2,plain,
! [U_852,U_851,U_850,U_849] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_851,tc_HOL_Obool)),U_849),U_852),U_850))
| ~ hBOOL(hAPP(U_849,U_850)) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_849,U_850,U_851,U_852] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_851,tc_HOL_Obool)),U_849),U_852),U_850))
| ~ hBOOL(hAPP(U_849,U_850)) ),
inference(definitional_conversion,[status(esa)],[f_199_2]) ).
cnf(f_199_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_851,tc_HOL_Obool)),U_849),U_852),U_850))
| ~ hBOOL(hAPP(U_849,U_850)) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__crazy]) ).
fof(f_200_2,plain,
! [U_856,U_855,U_854,U_853] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_854),U_855)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_855),U_856))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_856),U_854)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_854),U_855)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_855),U_856))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_856),U_854)),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_853,U_854,U_855,U_856] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_854),U_855)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_855),U_856))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_856),U_854)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_854),U_855)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_855),U_856))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_856),U_854)),
inference(definitional_conversion,[status(esa)],[f_200_2]) ).
cnf(f_200_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_854),U_855)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_855),U_856))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),U_856),U_854)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_854),U_855)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_855),U_856))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_853,tc_HOL_Obool)),U_856),U_854)),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Diff__Int2]) ).
fof(f_201_2,plain,
! [U_860,U_859,U_858,U_857] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_857,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_858),U_859)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_860),U_859)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_857,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_858),U_859)),U_860),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_857,U_858,U_859,U_860] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_857,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_858),U_859)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_860),U_859)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_857,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_858),U_859)),U_860),
inference(definitional_conversion,[status(esa)],[f_201_2]) ).
cnf(f_201_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_857,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_858),U_859)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_860),U_859)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_857,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_858),U_859)),U_860),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Un__Diff__Int]) ).
fof(f_202_2,plain,
! [U_863,U_862,U_861] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_861,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_861,tc_HOL_Obool)),U_862),U_863)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_861,tc_HOL_Obool)),U_862),U_863)) = U_862,
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_861,U_862,U_863] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_861,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_861,tc_HOL_Obool)),U_862),U_863)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_861,tc_HOL_Obool)),U_862),U_863)) = U_862,
inference(definitional_conversion,[status(esa)],[f_202_2]) ).
cnf(f_202_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_861,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_861,tc_HOL_Obool)),U_862),U_863)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_861,tc_HOL_Obool)),U_862),U_863)) = U_862,
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_1,plain,
! [V_Pa_2,V_B_2,V_A_2,T_b] :
( ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ 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))) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
& ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& 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))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ball__Un]) ).
fof(f_203_2,plain,
! [U_873,U_872,U_871,U_870] :
( ( ! [U_869] :
( hBOOL(hAPP(U_873,U_869))
| ~ hBOOL(hAPP(hAPP(c_member(U_870),U_869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_870,tc_HOL_Obool)),U_871),U_872))) )
| ? [U_868] :
( ~ hBOOL(hAPP(U_873,U_868))
& hBOOL(hAPP(hAPP(c_member(U_870),U_868),U_872)) )
| ? [U_867] :
( ~ hBOOL(hAPP(U_873,U_867))
& hBOOL(hAPP(hAPP(c_member(U_870),U_867),U_871)) ) )
& ( ( ! [U_866] :
( hBOOL(hAPP(U_873,U_866))
| ~ hBOOL(hAPP(hAPP(c_member(U_870),U_866),U_872)) )
& ! [U_865] :
( hBOOL(hAPP(U_873,U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_870),U_865),U_871)) ) )
| ? [U_864] :
( ~ hBOOL(hAPP(U_873,U_864))
& hBOOL(hAPP(hAPP(c_member(U_870),U_864),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_870,tc_HOL_Obool)),U_871),U_872))) ) ) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
( ! [U_881,U_879,U_877,U_875] :
( ! [U_869] :
( hBOOL(hAPP(U_881,U_869))
| ~ hBOOL(hAPP(hAPP(c_member(U_875),U_869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_875,tc_HOL_Obool)),U_877),U_879))) )
| ? [U_868] :
( ~ hBOOL(hAPP(U_881,U_868))
& hBOOL(hAPP(hAPP(c_member(U_875),U_868),U_879)) )
| ? [U_867] :
( ~ hBOOL(hAPP(U_881,U_867))
& hBOOL(hAPP(hAPP(c_member(U_875),U_867),U_877)) ) )
& ! [U_880,U_878,U_876,U_874] :
( ( ! [U_866] :
( hBOOL(hAPP(U_880,U_866))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_866),U_878)) )
& ! [U_865] :
( hBOOL(hAPP(U_880,U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_865),U_876)) ) )
| ? [U_864] :
( ~ hBOOL(hAPP(U_880,U_864))
& hBOOL(hAPP(hAPP(c_member(U_874),U_864),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_874,tc_HOL_Obool)),U_876),U_878))) ) ) ),
inference(miniscope,[status(thm)],[f_203_2]) ).
fof(f_203_4,plain,
( ! [U_881,U_879,U_877,U_875] :
( ! [U_869] :
( hBOOL(hAPP(U_881,U_869))
| ~ hBOOL(hAPP(hAPP(c_member(U_875),U_869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_875,tc_HOL_Obool)),U_877),U_879))) )
| ? [U_868] :
( ~ hBOOL(hAPP(U_881,U_868))
& hBOOL(hAPP(hAPP(c_member(U_875),U_868),U_879)) )
| ? [U_867] :
( ~ hBOOL(hAPP(U_881,U_867))
& hBOOL(hAPP(hAPP(c_member(U_875),U_867),U_877)) ) )
& ! [U_880,U_878,U_876,U_874] :
( ( ! [U_866] :
( hBOOL(hAPP(U_880,U_866))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_866),U_878)) )
& ! [U_865] :
( hBOOL(hAPP(U_880,U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_865),U_876)) ) )
| ( ~ hBOOL(hAPP(U_880,sK33(U_880,U_878,U_876,U_874)))
& hBOOL(hAPP(hAPP(c_member(U_874),sK33(U_880,U_878,U_876,U_874)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_874,tc_HOL_Obool)),U_876),U_878))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_864,sK33(U_880,U_878,U_876,U_874))],[f_203_3]) ).
fof(f_203_5,plain,
( ! [U_881,U_879,U_877,U_875] :
( ! [U_869] :
( hBOOL(hAPP(U_881,U_869))
| ~ hBOOL(hAPP(hAPP(c_member(U_875),U_869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_875,tc_HOL_Obool)),U_877),U_879))) )
| ? [U_868] :
( ~ hBOOL(hAPP(U_881,U_868))
& hBOOL(hAPP(hAPP(c_member(U_875),U_868),U_879)) )
| ( ~ hBOOL(hAPP(U_881,sK34(U_881,U_879,U_877,U_875)))
& hBOOL(hAPP(hAPP(c_member(U_875),sK34(U_881,U_879,U_877,U_875)),U_877)) ) )
& ! [U_880,U_878,U_876,U_874] :
( ( ! [U_866] :
( hBOOL(hAPP(U_880,U_866))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_866),U_878)) )
& ! [U_865] :
( hBOOL(hAPP(U_880,U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_865),U_876)) ) )
| ( ~ hBOOL(hAPP(U_880,sK33(U_880,U_878,U_876,U_874)))
& hBOOL(hAPP(hAPP(c_member(U_874),sK33(U_880,U_878,U_876,U_874)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_874,tc_HOL_Obool)),U_876),U_878))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_867,sK34(U_881,U_879,U_877,U_875))],[f_203_4]) ).
fof(f_203_6,plain,
( ! [U_881,U_879,U_877,U_875] :
( ! [U_869] :
( hBOOL(hAPP(U_881,U_869))
| ~ hBOOL(hAPP(hAPP(c_member(U_875),U_869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_875,tc_HOL_Obool)),U_877),U_879))) )
| ( ~ hBOOL(hAPP(U_881,sK35(U_881,U_879,U_877,U_875)))
& hBOOL(hAPP(hAPP(c_member(U_875),sK35(U_881,U_879,U_877,U_875)),U_879)) )
| ( ~ hBOOL(hAPP(U_881,sK34(U_881,U_879,U_877,U_875)))
& hBOOL(hAPP(hAPP(c_member(U_875),sK34(U_881,U_879,U_877,U_875)),U_877)) ) )
& ! [U_880,U_878,U_876,U_874] :
( ( ! [U_866] :
( hBOOL(hAPP(U_880,U_866))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_866),U_878)) )
& ! [U_865] :
( hBOOL(hAPP(U_880,U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_865),U_876)) ) )
| ( ~ hBOOL(hAPP(U_880,sK33(U_880,U_878,U_876,U_874)))
& hBOOL(hAPP(hAPP(c_member(U_874),sK33(U_880,U_878,U_876,U_874)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_874,tc_HOL_Obool)),U_876),U_878))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_868,sK35(U_881,U_879,U_877,U_875))],[f_203_5]) ).
fof(f_203_7,plain,
( ! [U_875,U_881,U_879,U_877] :
( ~ hBOOL(hAPP(U_881,sK35(U_881,U_879,U_877,U_875)))
| ~ sP67(U_875,U_881,U_879,U_877) )
& ! [U_875,U_881,U_879,U_877] :
( hBOOL(hAPP(hAPP(c_member(U_875),sK35(U_881,U_879,U_877,U_875)),U_879))
| ~ sP67(U_875,U_881,U_879,U_877) )
& ! [U_875,U_881,U_879,U_877] :
( ~ hBOOL(hAPP(U_881,sK34(U_881,U_879,U_877,U_875)))
| ~ sP66(U_875,U_881,U_879,U_877) )
& ! [U_875,U_881,U_879,U_877] :
( hBOOL(hAPP(hAPP(c_member(U_875),sK34(U_881,U_879,U_877,U_875)),U_877))
| ~ sP66(U_875,U_881,U_879,U_877) )
& ! [U_878,U_865,U_866,U_874,U_876,U_880] :
( hBOOL(hAPP(U_880,U_866))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_866),U_878))
| ~ sP65(U_878,U_865,U_866,U_874,U_876,U_880) )
& ! [U_878,U_865,U_866,U_874,U_876,U_880] :
( hBOOL(hAPP(U_880,U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_865),U_876))
| ~ sP65(U_878,U_865,U_866,U_874,U_876,U_880) )
& ! [U_878,U_874,U_876,U_880] :
( ~ hBOOL(hAPP(U_880,sK33(U_880,U_878,U_876,U_874)))
| ~ sP64(U_878,U_874,U_876,U_880) )
& ! [U_878,U_874,U_876,U_880] :
( hBOOL(hAPP(hAPP(c_member(U_874),sK33(U_880,U_878,U_876,U_874)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_874,tc_HOL_Obool)),U_876),U_878)))
| ~ sP64(U_878,U_874,U_876,U_880) )
& ! [U_869,U_875,U_881,U_879,U_877] :
( hBOOL(hAPP(U_881,U_869))
| ~ hBOOL(hAPP(hAPP(c_member(U_875),U_869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_875,tc_HOL_Obool)),U_877),U_879)))
| sP67(U_875,U_881,U_879,U_877)
| sP66(U_875,U_881,U_879,U_877) )
& ! [U_878,U_865,U_866,U_874,U_876,U_880] :
( sP65(U_878,U_865,U_866,U_874,U_876,U_880)
| sP64(U_878,U_874,U_876,U_880) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64,sP65,sP66,sP67])],[f_203_6]) ).
cnf(f_203_8,plain,
( sP65(U_878,U_865,U_866,U_874,U_876,U_880)
| sP64(U_878,U_874,U_876,U_880) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_9,plain,
( hBOOL(hAPP(U_881,U_869))
| ~ hBOOL(hAPP(hAPP(c_member(U_875),U_869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_875,tc_HOL_Obool)),U_877),U_879)))
| sP67(U_875,U_881,U_879,U_877)
| sP66(U_875,U_881,U_879,U_877) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_874),sK33(U_880,U_878,U_876,U_874)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_874,tc_HOL_Obool)),U_876),U_878)))
| ~ sP64(U_878,U_874,U_876,U_880) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_11,plain,
( ~ hBOOL(hAPP(U_880,sK33(U_880,U_878,U_876,U_874)))
| ~ sP64(U_878,U_874,U_876,U_880) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_12,plain,
( hBOOL(hAPP(U_880,U_865))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_865),U_876))
| ~ sP65(U_878,U_865,U_866,U_874,U_876,U_880) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_13,plain,
( hBOOL(hAPP(U_880,U_866))
| ~ hBOOL(hAPP(hAPP(c_member(U_874),U_866),U_878))
| ~ sP65(U_878,U_865,U_866,U_874,U_876,U_880) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_14,plain,
( hBOOL(hAPP(hAPP(c_member(U_875),sK34(U_881,U_879,U_877,U_875)),U_877))
| ~ sP66(U_875,U_881,U_879,U_877) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_15,plain,
( ~ hBOOL(hAPP(U_881,sK34(U_881,U_879,U_877,U_875)))
| ~ sP66(U_875,U_881,U_879,U_877) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_16,plain,
( hBOOL(hAPP(hAPP(c_member(U_875),sK35(U_881,U_879,U_877,U_875)),U_879))
| ~ sP67(U_875,U_881,U_879,U_877) ),
inference(clausify,[status(thm)],[f_203_7]) ).
cnf(f_203_17,plain,
( ~ hBOOL(hAPP(U_881,sK35(U_881,U_879,U_877,U_875)))
| ~ sP67(U_875,U_881,U_879,U_877) ),
inference(clausify,[status(thm)],[f_203_7]) ).
fof(f_204_1,plain,
! [V_Pa_2,V_B_2,V_A_2,T_b] :
( ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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))) )
| ( ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
& ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ 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))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_bex__Un]) ).
fof(f_204_2,plain,
! [U_891,U_890,U_889,U_888] :
( ( ? [U_887] :
( hBOOL(hAPP(U_891,U_887))
& hBOOL(hAPP(hAPP(c_member(U_888),U_887),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_888,tc_HOL_Obool)),U_889),U_890))) )
| ( ! [U_886] :
( ~ hBOOL(hAPP(U_891,U_886))
| ~ hBOOL(hAPP(hAPP(c_member(U_888),U_886),U_890)) )
& ! [U_885] :
( ~ hBOOL(hAPP(U_891,U_885))
| ~ hBOOL(hAPP(hAPP(c_member(U_888),U_885),U_889)) ) ) )
& ( ? [U_884] :
( hBOOL(hAPP(U_891,U_884))
& hBOOL(hAPP(hAPP(c_member(U_888),U_884),U_890)) )
| ? [U_883] :
( hBOOL(hAPP(U_891,U_883))
& hBOOL(hAPP(hAPP(c_member(U_888),U_883),U_889)) )
| ! [U_882] :
( ~ hBOOL(hAPP(U_891,U_882))
| ~ hBOOL(hAPP(hAPP(c_member(U_888),U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_888,tc_HOL_Obool)),U_889),U_890))) ) ) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
( ! [U_899,U_897,U_895,U_893] :
( ? [U_887] :
( hBOOL(hAPP(U_899,U_887))
& hBOOL(hAPP(hAPP(c_member(U_893),U_887),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_893,tc_HOL_Obool)),U_895),U_897))) )
| ( ! [U_886] :
( ~ hBOOL(hAPP(U_899,U_886))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_886),U_897)) )
& ! [U_885] :
( ~ hBOOL(hAPP(U_899,U_885))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_885),U_895)) ) ) )
& ! [U_898,U_896,U_894,U_892] :
( ? [U_884] :
( hBOOL(hAPP(U_898,U_884))
& hBOOL(hAPP(hAPP(c_member(U_892),U_884),U_896)) )
| ? [U_883] :
( hBOOL(hAPP(U_898,U_883))
& hBOOL(hAPP(hAPP(c_member(U_892),U_883),U_894)) )
| ! [U_882] :
( ~ hBOOL(hAPP(U_898,U_882))
| ~ hBOOL(hAPP(hAPP(c_member(U_892),U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_892,tc_HOL_Obool)),U_894),U_896))) ) ) ),
inference(miniscope,[status(thm)],[f_204_2]) ).
fof(f_204_4,plain,
( ! [U_899,U_897,U_895,U_893] :
( ? [U_887] :
( hBOOL(hAPP(U_899,U_887))
& hBOOL(hAPP(hAPP(c_member(U_893),U_887),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_893,tc_HOL_Obool)),U_895),U_897))) )
| ( ! [U_886] :
( ~ hBOOL(hAPP(U_899,U_886))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_886),U_897)) )
& ! [U_885] :
( ~ hBOOL(hAPP(U_899,U_885))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_885),U_895)) ) ) )
& ! [U_898,U_896,U_894,U_892] :
( ? [U_884] :
( hBOOL(hAPP(U_898,U_884))
& hBOOL(hAPP(hAPP(c_member(U_892),U_884),U_896)) )
| ( hBOOL(hAPP(U_898,sK36(U_898,U_896,U_894,U_892)))
& hBOOL(hAPP(hAPP(c_member(U_892),sK36(U_898,U_896,U_894,U_892)),U_894)) )
| ! [U_882] :
( ~ hBOOL(hAPP(U_898,U_882))
| ~ hBOOL(hAPP(hAPP(c_member(U_892),U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_892,tc_HOL_Obool)),U_894),U_896))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_883,sK36(U_898,U_896,U_894,U_892))],[f_204_3]) ).
fof(f_204_5,plain,
( ! [U_899,U_897,U_895,U_893] :
( ? [U_887] :
( hBOOL(hAPP(U_899,U_887))
& hBOOL(hAPP(hAPP(c_member(U_893),U_887),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_893,tc_HOL_Obool)),U_895),U_897))) )
| ( ! [U_886] :
( ~ hBOOL(hAPP(U_899,U_886))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_886),U_897)) )
& ! [U_885] :
( ~ hBOOL(hAPP(U_899,U_885))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_885),U_895)) ) ) )
& ! [U_898,U_896,U_894,U_892] :
( ( hBOOL(hAPP(U_898,sK37(U_898,U_896,U_894,U_892)))
& hBOOL(hAPP(hAPP(c_member(U_892),sK37(U_898,U_896,U_894,U_892)),U_896)) )
| ( hBOOL(hAPP(U_898,sK36(U_898,U_896,U_894,U_892)))
& hBOOL(hAPP(hAPP(c_member(U_892),sK36(U_898,U_896,U_894,U_892)),U_894)) )
| ! [U_882] :
( ~ hBOOL(hAPP(U_898,U_882))
| ~ hBOOL(hAPP(hAPP(c_member(U_892),U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_892,tc_HOL_Obool)),U_894),U_896))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_884,sK37(U_898,U_896,U_894,U_892))],[f_204_4]) ).
fof(f_204_6,plain,
( ! [U_899,U_897,U_895,U_893] :
( ( hBOOL(hAPP(U_899,sK38(U_899,U_897,U_895,U_893)))
& hBOOL(hAPP(hAPP(c_member(U_893),sK38(U_899,U_897,U_895,U_893)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_893,tc_HOL_Obool)),U_895),U_897))) )
| ( ! [U_886] :
( ~ hBOOL(hAPP(U_899,U_886))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_886),U_897)) )
& ! [U_885] :
( ~ hBOOL(hAPP(U_899,U_885))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_885),U_895)) ) ) )
& ! [U_898,U_896,U_894,U_892] :
( ( hBOOL(hAPP(U_898,sK37(U_898,U_896,U_894,U_892)))
& hBOOL(hAPP(hAPP(c_member(U_892),sK37(U_898,U_896,U_894,U_892)),U_896)) )
| ( hBOOL(hAPP(U_898,sK36(U_898,U_896,U_894,U_892)))
& hBOOL(hAPP(hAPP(c_member(U_892),sK36(U_898,U_896,U_894,U_892)),U_894)) )
| ! [U_882] :
( ~ hBOOL(hAPP(U_898,U_882))
| ~ hBOOL(hAPP(hAPP(c_member(U_892),U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_892,tc_HOL_Obool)),U_894),U_896))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_887,sK38(U_899,U_897,U_895,U_893))],[f_204_5]) ).
fof(f_204_7,plain,
( ! [U_899,U_897,U_895,U_893] :
( hBOOL(hAPP(U_899,sK38(U_899,U_897,U_895,U_893)))
| ~ sP71(U_899,U_897,U_895,U_893) )
& ! [U_899,U_897,U_895,U_893] :
( hBOOL(hAPP(hAPP(c_member(U_893),sK38(U_899,U_897,U_895,U_893)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_893,tc_HOL_Obool)),U_895),U_897)))
| ~ sP71(U_899,U_897,U_895,U_893) )
& ! [U_899,U_886,U_897,U_895,U_893,U_885] :
( ~ hBOOL(hAPP(U_899,U_886))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_886),U_897))
| ~ sP70(U_899,U_886,U_897,U_895,U_893,U_885) )
& ! [U_899,U_886,U_897,U_895,U_893,U_885] :
( ~ hBOOL(hAPP(U_899,U_885))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_885),U_895))
| ~ sP70(U_899,U_886,U_897,U_895,U_893,U_885) )
& ! [U_894,U_896,U_892,U_898] :
( hBOOL(hAPP(U_898,sK37(U_898,U_896,U_894,U_892)))
| ~ sP69(U_894,U_896,U_892,U_898) )
& ! [U_894,U_896,U_892,U_898] :
( hBOOL(hAPP(hAPP(c_member(U_892),sK37(U_898,U_896,U_894,U_892)),U_896))
| ~ sP69(U_894,U_896,U_892,U_898) )
& ! [U_894,U_896,U_892,U_898] :
( hBOOL(hAPP(U_898,sK36(U_898,U_896,U_894,U_892)))
| ~ sP68(U_894,U_896,U_892,U_898) )
& ! [U_894,U_896,U_892,U_898] :
( hBOOL(hAPP(hAPP(c_member(U_892),sK36(U_898,U_896,U_894,U_892)),U_894))
| ~ sP68(U_894,U_896,U_892,U_898) )
& ! [U_899,U_886,U_897,U_895,U_893,U_885] :
( sP71(U_899,U_897,U_895,U_893)
| sP70(U_899,U_886,U_897,U_895,U_893,U_885) )
& ! [U_894,U_882,U_896,U_892,U_898] :
( sP69(U_894,U_896,U_892,U_898)
| sP68(U_894,U_896,U_892,U_898)
| ~ hBOOL(hAPP(U_898,U_882))
| ~ hBOOL(hAPP(hAPP(c_member(U_892),U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_892,tc_HOL_Obool)),U_894),U_896))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68,sP69,sP70,sP71])],[f_204_6]) ).
cnf(f_204_8,plain,
( sP69(U_894,U_896,U_892,U_898)
| sP68(U_894,U_896,U_892,U_898)
| ~ hBOOL(hAPP(U_898,U_882))
| ~ hBOOL(hAPP(hAPP(c_member(U_892),U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_892,tc_HOL_Obool)),U_894),U_896))) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_9,plain,
( sP71(U_899,U_897,U_895,U_893)
| sP70(U_899,U_886,U_897,U_895,U_893,U_885) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_892),sK36(U_898,U_896,U_894,U_892)),U_894))
| ~ sP68(U_894,U_896,U_892,U_898) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_11,plain,
( hBOOL(hAPP(U_898,sK36(U_898,U_896,U_894,U_892)))
| ~ sP68(U_894,U_896,U_892,U_898) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_892),sK37(U_898,U_896,U_894,U_892)),U_896))
| ~ sP69(U_894,U_896,U_892,U_898) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_13,plain,
( hBOOL(hAPP(U_898,sK37(U_898,U_896,U_894,U_892)))
| ~ sP69(U_894,U_896,U_892,U_898) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_14,plain,
( ~ hBOOL(hAPP(U_899,U_885))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_885),U_895))
| ~ sP70(U_899,U_886,U_897,U_895,U_893,U_885) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_15,plain,
( ~ hBOOL(hAPP(U_899,U_886))
| ~ hBOOL(hAPP(hAPP(c_member(U_893),U_886),U_897))
| ~ sP70(U_899,U_886,U_897,U_895,U_893,U_885) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_16,plain,
( hBOOL(hAPP(hAPP(c_member(U_893),sK38(U_899,U_897,U_895,U_893)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_893,tc_HOL_Obool)),U_895),U_897)))
| ~ sP71(U_899,U_897,U_895,U_893) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_17,plain,
( hBOOL(hAPP(U_899,sK38(U_899,U_897,U_895,U_893)))
| ~ sP71(U_899,U_897,U_895,U_893) ),
inference(clausify,[status(thm)],[f_204_7]) ).
fof(f_205_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib2]) ).
fof(f_205_2,plain,
! [U_903,U_902,U_901,U_900] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool)),U_901),U_902)),U_903) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),U_901),U_903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),U_902),U_903)),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_903,U_900,U_901,U_902] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool)),U_901),U_902)),U_903) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),U_901),U_903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),U_902),U_903)),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool)),U_901),U_902)),U_903) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),U_901),U_903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_900,tc_HOL_Obool)),U_902),U_903)),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib2]) ).
fof(f_206_2,plain,
! [U_907,U_906,U_905,U_904] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_904,tc_HOL_Obool)),U_905),U_906)),U_907) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_904,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),U_905),U_907)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),U_906),U_907)),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_905,U_904,U_906,U_907] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_904,tc_HOL_Obool)),U_905),U_906)),U_907) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_904,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),U_905),U_907)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),U_906),U_907)),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_904,tc_HOL_Obool)),U_905),U_906)),U_907) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_904,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),U_905),U_907)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_904,tc_HOL_Obool)),U_906),U_907)),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib2]) ).
fof(f_207_2,plain,
! [U_911,U_910,U_909,U_908] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_908,tc_HOL_Obool)),U_909),U_910)),U_911) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_908,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),U_909),U_911)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),U_910),U_911)),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_908,U_909,U_910,U_911] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_908,tc_HOL_Obool)),U_909),U_910)),U_911) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_908,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),U_909),U_911)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),U_910),U_911)),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_908,tc_HOL_Obool)),U_909),U_910)),U_911) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_908,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),U_909),U_911)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_908,tc_HOL_Obool)),U_910),U_911)),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__Diff]) ).
fof(f_208_2,plain,
! [U_915,U_914,U_913,U_912] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_912,tc_HOL_Obool)),U_913),U_914)),U_915) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_912,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),U_913),U_915)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),U_914),U_915)),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
! [U_912,U_913,U_914,U_915] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_912,tc_HOL_Obool)),U_913),U_914)),U_915) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_912,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),U_913),U_915)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),U_914),U_915)),
inference(definitional_conversion,[status(esa)],[f_208_2]) ).
cnf(f_208_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_912,tc_HOL_Obool)),U_913),U_914)),U_915) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_912,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),U_913),U_915)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_912,tc_HOL_Obool)),U_914),U_915)),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__assoc]) ).
fof(f_209_2,plain,
! [U_919,U_918,U_917,U_916] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_917),U_918)),U_919) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_917),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_918),U_919)),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_916,U_917,U_918,U_919] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_917),U_918)),U_919) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_917),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_918),U_919)),
inference(definitional_conversion,[status(esa)],[f_209_2]) ).
cnf(f_209_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_917),U_918)),U_919) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_917),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_916,tc_HOL_Obool)),U_918),U_919)),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__assoc]) ).
fof(f_210_2,plain,
! [U_923,U_922,U_921,U_920] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_921),U_922)),U_923) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_921),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_922),U_923)),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_920,U_921,U_922,U_923] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_921),U_922)),U_923) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_921),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_922),U_923)),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_921),U_922)),U_923) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_921),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_920,tc_HOL_Obool)),U_922),U_923)),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__Diff]) ).
fof(f_211_2,plain,
! [U_927,U_926,U_925,U_924] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_924,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool)),U_925),U_926)),U_927) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool)),U_925),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_924,tc_HOL_Obool)),U_926),U_927)),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_924,U_925,U_926,U_927] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_924,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool)),U_925),U_926)),U_927) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool)),U_925),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_924,tc_HOL_Obool)),U_926),U_927)),
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_924,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool)),U_925),U_926)),U_927) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_924,tc_HOL_Obool)),U_925),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_924,tc_HOL_Obool)),U_926),U_927)),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel2]) ).
fof(f_212_2,plain,
! [U_930,U_929,U_928] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_928,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_928,tc_HOL_Obool)),U_929),U_930)),U_930) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_928,tc_HOL_Obool)),U_929),U_930),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_928,U_929,U_930] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_928,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_928,tc_HOL_Obool)),U_929),U_930)),U_930) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_928,tc_HOL_Obool)),U_929),U_930),
inference(definitional_conversion,[status(esa)],[f_212_2]) ).
cnf(f_212_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_928,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_928,tc_HOL_Obool)),U_929),U_930)),U_930) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_928,tc_HOL_Obool)),U_929),U_930),
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Diff__idemp]) ).
fof(f_213_2,plain,
! [U_933,U_932,U_931] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933)),U_933) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_931,U_932,U_933] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933)),U_933) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933)),U_933) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib]) ).
fof(f_214_2,plain,
! [U_937,U_936,U_935,U_934] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool)),U_936),U_937)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),U_936)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),U_937)),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
! [U_934,U_935,U_936,U_937] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool)),U_936),U_937)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),U_936)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),U_937)),
inference(definitional_conversion,[status(esa)],[f_214_2]) ).
cnf(f_214_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool)),U_936),U_937)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),U_936)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_934,tc_HOL_Obool)),U_935),U_937)),
inference(clausify,[status(thm)],[f_214_3]) ).
fof(f_215_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib]) ).
fof(f_215_2,plain,
! [U_941,U_940,U_939,U_938] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_938,tc_HOL_Obool)),U_940),U_941)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_938,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),U_940)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),U_941)),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_938,U_939,U_940,U_941] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_938,tc_HOL_Obool)),U_940),U_941)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_938,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),U_940)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),U_941)),
inference(definitional_conversion,[status(esa)],[f_215_2]) ).
cnf(f_215_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_938,tc_HOL_Obool)),U_940),U_941)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_938,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),U_940)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_938,tc_HOL_Obool)),U_939),U_941)),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib]) ).
fof(f_216_2,plain,
! [U_945,U_944,U_943,U_942] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_942,tc_HOL_Obool)),U_944),U_945)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_942,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),U_944)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),U_945)),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_942,U_943,U_944,U_945] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_942,tc_HOL_Obool)),U_944),U_945)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_942,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),U_944)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),U_945)),
inference(definitional_conversion,[status(esa)],[f_216_2]) ).
cnf(f_216_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_942,tc_HOL_Obool)),U_944),U_945)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_942,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),U_944)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_942,tc_HOL_Obool)),U_943),U_945)),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__Un]) ).
fof(f_217_2,plain,
! [U_949,U_948,U_947,U_946] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_946,tc_HOL_Obool)),U_948),U_949)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_946,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),U_948)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),U_949)),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_946,U_947,U_948,U_949] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_946,tc_HOL_Obool)),U_948),U_949)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_946,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),U_948)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),U_949)),
inference(definitional_conversion,[status(esa)],[f_217_2]) ).
cnf(f_217_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_946,tc_HOL_Obool)),U_948),U_949)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_946,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),U_948)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_946,tc_HOL_Obool)),U_947),U_949)),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int]) ).
fof(f_218_2,plain,
! [U_953,U_952,U_951,U_950] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_950,tc_HOL_Obool)),U_952),U_953)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_950,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),U_952)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),U_953)),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_950,U_951,U_952,U_953] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_950,tc_HOL_Obool)),U_952),U_953)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_950,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),U_952)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),U_953)),
inference(definitional_conversion,[status(esa)],[f_218_2]) ).
cnf(f_218_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_950,tc_HOL_Obool)),U_952),U_953)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_950,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),U_952)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_950,tc_HOL_Obool)),U_951),U_953)),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__left__commute]) ).
fof(f_219_2,plain,
! [U_957,U_956,U_955,U_954] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_956),U_957)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_956),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_955),U_957)),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_954,U_955,U_956,U_957] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_956),U_957)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_956),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_955),U_957)),
inference(definitional_conversion,[status(esa)],[f_219_2]) ).
cnf(f_219_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_956),U_957)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_956),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_954,tc_HOL_Obool)),U_955),U_957)),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__left__commute]) ).
fof(f_220_2,plain,
! [U_961,U_960,U_959,U_958] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_960),U_961)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_960),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_959),U_961)),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_958,U_959,U_960,U_961] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_960),U_961)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_960),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_959),U_961)),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_960),U_961)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_960),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_958,tc_HOL_Obool)),U_959),U_961)),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Un__left__absorb]) ).
fof(f_221_2,plain,
! [U_964,U_963,U_962] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),U_964)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),U_964),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_962,U_963,U_964] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),U_964)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),U_964),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),U_964)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_962,tc_HOL_Obool)),U_963),U_964),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel]) ).
fof(f_222_2,plain,
! [U_967,U_966,U_965] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_965,tc_HOL_Obool)),U_966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_965,tc_HOL_Obool)),U_967),U_966)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_965,tc_HOL_Obool)),U_966),U_967),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_965,U_966,U_967] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_965,tc_HOL_Obool)),U_966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_965,tc_HOL_Obool)),U_967),U_966)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_965,tc_HOL_Obool)),U_966),U_967),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_965,tc_HOL_Obool)),U_966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_965,tc_HOL_Obool)),U_967),U_966)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_965,tc_HOL_Obool)),U_966),U_967),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Int__left__absorb]) ).
fof(f_223_2,plain,
! [U_970,U_969,U_968] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),U_970)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),U_970),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_968,U_969,U_970] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),U_970)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),U_970),
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),U_970)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_968,tc_HOL_Obool)),U_969),U_970),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Un__commute]) ).
fof(f_224_2,plain,
! [U_973,U_972,U_971] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_971,tc_HOL_Obool)),U_972),U_973) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_971,tc_HOL_Obool)),U_973),U_972),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_971,U_972,U_973] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_971,tc_HOL_Obool)),U_972),U_973) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_971,tc_HOL_Obool)),U_973),U_972),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_971,tc_HOL_Obool)),U_972),U_973) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_971,tc_HOL_Obool)),U_973),U_972),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Int__commute]) ).
fof(f_225_2,plain,
! [U_976,U_975,U_974] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_974,tc_HOL_Obool)),U_975),U_976) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_974,tc_HOL_Obool)),U_976),U_975),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_974,U_975,U_976] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_974,tc_HOL_Obool)),U_975),U_976) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_974,tc_HOL_Obool)),U_976),U_975),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_974,tc_HOL_Obool)),U_975),U_976) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_974,tc_HOL_Obool)),U_976),U_975),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Un__absorb]) ).
fof(f_226_2,plain,
! [U_978,U_977] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_977,tc_HOL_Obool)),U_978),U_978) = U_978,
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_977,U_978] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_977,tc_HOL_Obool)),U_978),U_978) = U_978,
inference(definitional_conversion,[status(esa)],[f_226_2]) ).
cnf(f_226_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_977,tc_HOL_Obool)),U_978),U_978) = U_978,
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Int__absorb]) ).
fof(f_227_2,plain,
! [U_980,U_979] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_979,tc_HOL_Obool)),U_980),U_980) = U_980,
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_979,U_980] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_979,tc_HOL_Obool)),U_980),U_980) = U_980,
inference(definitional_conversion,[status(esa)],[f_227_2]) ).
cnf(f_227_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_979,tc_HOL_Obool)),U_980),U_980) = U_980,
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_1,plain,
! [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) = V_A_2
| 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)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__triv]) ).
fof(f_228_2,plain,
! [U_983,U_982,U_981] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_981,tc_HOL_Obool)),U_982),U_983) = U_982
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool)),U_982),U_983) != c_Orderings_Obot__class_Obot(tc_fun(U_981,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_981,U_982,U_983] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_981,tc_HOL_Obool)),U_982),U_983) = U_982
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool)),U_982),U_983) != c_Orderings_Obot__class_Obot(tc_fun(U_981,tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_228_2]) ).
cnf(f_228_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_981,tc_HOL_Obool)),U_982),U_983) = U_982
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool)),U_982),U_983) != c_Orderings_Obot__class_Obot(tc_fun(U_981,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__disjoint]) ).
fof(f_229_2,plain,
! [U_986,U_985,U_984] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_984,tc_HOL_Obool)),U_985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_984,tc_HOL_Obool)),U_986),U_985)) = c_Orderings_Obot__class_Obot(tc_fun(U_984,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_984,U_985,U_986] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_984,tc_HOL_Obool)),U_985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_984,tc_HOL_Obool)),U_986),U_985)) = c_Orderings_Obot__class_Obot(tc_fun(U_984,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_984,tc_HOL_Obool)),U_985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_984,tc_HOL_Obool)),U_986),U_985)) = c_Orderings_Obot__class_Obot(tc_fun(U_984,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [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)) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__partition]) ).
fof(f_230_2,plain,
! [U_989,U_988,U_987] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_987,tc_HOL_Obool)),U_988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_987,tc_HOL_Obool)),U_989),U_988)) = U_989
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_987,tc_HOL_Obool)),U_988),U_989)) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_988,U_987,U_989] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_987,tc_HOL_Obool)),U_988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_987,tc_HOL_Obool)),U_989),U_988)) = U_989
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_987,tc_HOL_Obool)),U_988),U_989)) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_987,tc_HOL_Obool)),U_988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_987,tc_HOL_Obool)),U_989),U_988)) = U_989
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_987,tc_HOL_Obool)),U_988),U_989)) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [V_C_2,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_C_2))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv]) ).
fof(f_231_2,plain,
! [U_993,U_992,U_991,U_990] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_990,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_990,tc_HOL_Obool)),U_991),U_992)),U_993))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_990,tc_HOL_Obool)),U_991),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_990,tc_HOL_Obool)),U_992),U_993))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_990,tc_HOL_Obool)),U_991),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_990,tc_HOL_Obool)),U_992),U_993)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_990,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_990,tc_HOL_Obool)),U_991),U_992)),U_993)) ) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
( ! [U_1001,U_999,U_997,U_995] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_995,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_995,tc_HOL_Obool)),U_997),U_999)),U_1001))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_995,tc_HOL_Obool)),U_997),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_995,tc_HOL_Obool)),U_999),U_1001))) )
& ! [U_1000,U_998,U_996,U_994] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),U_996),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_994,tc_HOL_Obool)),U_998),U_1000)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_994,tc_HOL_Obool)),U_996),U_998)),U_1000)) ) ),
inference(miniscope,[status(thm)],[f_231_2]) ).
fof(f_231_4,plain,
( ! [U_995,U_997,U_999,U_1001] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_995,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_995,tc_HOL_Obool)),U_997),U_999)),U_1001))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_995,tc_HOL_Obool)),U_997),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_995,tc_HOL_Obool)),U_999),U_1001))) )
& ! [U_1000,U_996,U_994,U_998] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),U_996),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_994,tc_HOL_Obool)),U_998),U_1000)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_994,tc_HOL_Obool)),U_996),U_998)),U_1000)) ) ),
inference(definitional_conversion,[status(esa)],[f_231_3]) ).
cnf(f_231_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),U_996),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_994,tc_HOL_Obool)),U_998),U_1000)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_994,tc_HOL_Obool)),U_996),U_998)),U_1000)) ),
inference(clausify,[status(thm)],[f_231_4]) ).
cnf(f_231_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_995,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_995,tc_HOL_Obool)),U_997),U_999)),U_1001))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_995,tc_HOL_Obool)),U_997),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_995,tc_HOL_Obool)),U_999),U_1001))) ),
inference(clausify,[status(thm)],[f_231_4]) ).
fof(f_232_1,plain,
! [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__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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_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)) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq]) ).
fof(f_232_2,plain,
! [U_1005,U_1004,U_1003,U_1002] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1002,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1002,tc_HOL_Obool)),U_1003),U_1004)),U_1005) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1002,tc_HOL_Obool)),U_1003),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1002,tc_HOL_Obool)),U_1004),U_1005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1002,tc_HOL_Obool)),U_1005),U_1003)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1002,tc_HOL_Obool)),U_1005),U_1003))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1002,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1002,tc_HOL_Obool)),U_1003),U_1004)),U_1005) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1002,tc_HOL_Obool)),U_1003),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1002,tc_HOL_Obool)),U_1004),U_1005)) ) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
( ! [U_1013,U_1011,U_1009,U_1007] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1007,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1007,tc_HOL_Obool)),U_1009),U_1011)),U_1013) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1007,tc_HOL_Obool)),U_1009),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1007,tc_HOL_Obool)),U_1011),U_1013))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1007,tc_HOL_Obool)),U_1013),U_1009)) )
& ! [U_1012,U_1010,U_1008,U_1006] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1006,tc_HOL_Obool)),U_1012),U_1008))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1006,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1006,tc_HOL_Obool)),U_1008),U_1010)),U_1012) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1006,tc_HOL_Obool)),U_1008),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1006,tc_HOL_Obool)),U_1010),U_1012)) ) ),
inference(miniscope,[status(thm)],[f_232_2]) ).
fof(f_232_4,plain,
( ! [U_1007,U_1009,U_1011,U_1013] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1007,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1007,tc_HOL_Obool)),U_1009),U_1011)),U_1013) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1007,tc_HOL_Obool)),U_1009),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1007,tc_HOL_Obool)),U_1011),U_1013))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1007,tc_HOL_Obool)),U_1013),U_1009)) )
& ! [U_1012,U_1008,U_1006,U_1010] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1006,tc_HOL_Obool)),U_1012),U_1008))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1006,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1006,tc_HOL_Obool)),U_1008),U_1010)),U_1012) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1006,tc_HOL_Obool)),U_1008),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1006,tc_HOL_Obool)),U_1010),U_1012)) ) ),
inference(definitional_conversion,[status(esa)],[f_232_3]) ).
cnf(f_232_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1006,tc_HOL_Obool)),U_1012),U_1008))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1006,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1006,tc_HOL_Obool)),U_1008),U_1010)),U_1012) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1006,tc_HOL_Obool)),U_1008),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1006,tc_HOL_Obool)),U_1010),U_1012)) ),
inference(clausify,[status(thm)],[f_232_4]) ).
cnf(f_232_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1007,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1007,tc_HOL_Obool)),U_1009),U_1011)),U_1013) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1007,tc_HOL_Obool)),U_1009),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1007,tc_HOL_Obool)),U_1011),U_1013))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1007,tc_HOL_Obool)),U_1013),U_1009)) ),
inference(clausify,[status(thm)],[f_232_4]) ).
fof(f_233_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Union__Un__distrib]) ).
fof(f_233_2,plain,
! [U_1016,U_1015,U_1014] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1014,tc_HOL_Obool),tc_HOL_Obool)),U_1015),U_1016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1014,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),U_1015)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),U_1016)),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_1014,U_1016,U_1015] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1014,tc_HOL_Obool),tc_HOL_Obool)),U_1015),U_1016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1014,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),U_1015)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),U_1016)),
inference(definitional_conversion,[status(esa)],[f_233_2]) ).
cnf(f_233_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1014,tc_HOL_Obool),tc_HOL_Obool)),U_1015),U_1016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1014,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),U_1015)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1014,tc_HOL_Obool),U_1016)),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Pow__Int__eq]) ).
fof(f_234_2,plain,
! [U_1019,U_1018,U_1017] : hAPP(c_Set_OPow(U_1017),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1017,tc_HOL_Obool)),U_1018),U_1019)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1017,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_1017),U_1018)),hAPP(c_Set_OPow(U_1017),U_1019)),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_1017,U_1018,U_1019] : hAPP(c_Set_OPow(U_1017),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1017,tc_HOL_Obool)),U_1018),U_1019)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1017,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_1017),U_1018)),hAPP(c_Set_OPow(U_1017),U_1019)),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
hAPP(c_Set_OPow(U_1017),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1017,tc_HOL_Obool)),U_1018),U_1019)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1017,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_1017),U_1018)),hAPP(c_Set_OPow(U_1017),U_1019)),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Inter__Un__distrib]) ).
fof(f_235_2,plain,
! [U_1022,U_1021,U_1020] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1020,tc_HOL_Obool),tc_HOL_Obool)),U_1021),U_1022)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1020,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),U_1021)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),U_1022)),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_1020,U_1021,U_1022] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1020,tc_HOL_Obool),tc_HOL_Obool)),U_1021),U_1022)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1020,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),U_1021)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),U_1022)),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1020,tc_HOL_Obool),tc_HOL_Obool)),U_1021),U_1022)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1020,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),U_1021)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1020,tc_HOL_Obool),U_1022)),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Union__Int__subset]) ).
fof(f_236_2,plain,
! [U_1025,U_1024,U_1023] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1023,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1023,tc_HOL_Obool),tc_HOL_Obool)),U_1024),U_1025))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1023,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),U_1024)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),U_1025)))),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_1023,U_1024,U_1025] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1023,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1023,tc_HOL_Obool),tc_HOL_Obool)),U_1024),U_1025))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1023,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),U_1024)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),U_1025)))),
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1023,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1023,tc_HOL_Obool),tc_HOL_Obool)),U_1024),U_1025))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1023,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),U_1024)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1023,tc_HOL_Obool),U_1025)))),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Inter__Un__subset]) ).
fof(f_237_2,plain,
! [U_1028,U_1027,U_1026] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1026,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1026,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),U_1027)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),U_1028))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1026,tc_HOL_Obool),tc_HOL_Obool)),U_1027),U_1028)))),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_1026,U_1027,U_1028] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1026,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1026,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),U_1027)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),U_1028))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1026,tc_HOL_Obool),tc_HOL_Obool)),U_1027),U_1028)))),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1026,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1026,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),U_1027)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),U_1028))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1026,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1026,tc_HOL_Obool),tc_HOL_Obool)),U_1027),U_1028)))),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Diff__iff]) ).
fof(f_238_2,plain,
! [U_1032,U_1031,U_1030,U_1029] :
( ( hBOOL(hAPP(hAPP(c_member(U_1029),U_1030),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1029,tc_HOL_Obool)),U_1031),U_1032)))
| hBOOL(hAPP(hAPP(c_member(U_1029),U_1030),U_1032))
| ~ hBOOL(hAPP(hAPP(c_member(U_1029),U_1030),U_1031)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(U_1029),U_1030),U_1032))
& hBOOL(hAPP(hAPP(c_member(U_1029),U_1030),U_1031)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1029),U_1030),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1029,tc_HOL_Obool)),U_1031),U_1032))) ) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
( ! [U_1040,U_1038,U_1036,U_1034] :
( hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1034,tc_HOL_Obool)),U_1038),U_1040)))
| hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),U_1040))
| ~ hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),U_1038)) )
& ! [U_1039,U_1037,U_1035,U_1033] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),U_1039))
& hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),U_1037)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1033,tc_HOL_Obool)),U_1037),U_1039))) ) ),
inference(miniscope,[status(thm)],[f_238_2]) ).
fof(f_238_4,plain,
( ! [U_1039,U_1035,U_1033,U_1037] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),U_1039))
| ~ sP72(U_1039,U_1035,U_1033,U_1037) )
& ! [U_1039,U_1035,U_1033,U_1037] :
( hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),U_1037))
| ~ sP72(U_1039,U_1035,U_1033,U_1037) )
& ! [U_1038,U_1036,U_1034,U_1040] :
( hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1034,tc_HOL_Obool)),U_1038),U_1040)))
| hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),U_1040))
| ~ hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),U_1038)) )
& ! [U_1039,U_1035,U_1033,U_1037] :
( sP72(U_1039,U_1035,U_1033,U_1037)
| ~ hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1033,tc_HOL_Obool)),U_1037),U_1039))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_238_3]) ).
cnf(f_238_5,plain,
( sP72(U_1039,U_1035,U_1033,U_1037)
| ~ hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1033,tc_HOL_Obool)),U_1037),U_1039))) ),
inference(clausify,[status(thm)],[f_238_4]) ).
cnf(f_238_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1034,tc_HOL_Obool)),U_1038),U_1040)))
| hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),U_1040))
| ~ hBOOL(hAPP(hAPP(c_member(U_1034),U_1036),U_1038)) ),
inference(clausify,[status(thm)],[f_238_4]) ).
cnf(f_238_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),U_1037))
| ~ sP72(U_1039,U_1035,U_1033,U_1037) ),
inference(clausify,[status(thm)],[f_238_4]) ).
cnf(f_238_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1033),U_1035),U_1039))
| ~ sP72(U_1039,U_1035,U_1033,U_1037) ),
inference(clausify,[status(thm)],[f_238_4]) ).
fof(f_239_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffD1]) ).
fof(f_239_2,plain,
! [U_1044,U_1043,U_1042,U_1041] :
( hBOOL(hAPP(hAPP(c_member(U_1041),U_1042),U_1043))
| ~ hBOOL(hAPP(hAPP(c_member(U_1041),U_1042),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1041,tc_HOL_Obool)),U_1043),U_1044))) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
! [U_1041,U_1042,U_1043,U_1044] :
( hBOOL(hAPP(hAPP(c_member(U_1041),U_1042),U_1043))
| ~ hBOOL(hAPP(hAPP(c_member(U_1041),U_1042),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1041,tc_HOL_Obool)),U_1043),U_1044))) ),
inference(definitional_conversion,[status(esa)],[f_239_2]) ).
cnf(f_239_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1041),U_1042),U_1043))
| ~ hBOOL(hAPP(hAPP(c_member(U_1041),U_1042),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1041,tc_HOL_Obool)),U_1043),U_1044))) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffD2]) ).
fof(f_240_2,plain,
! [U_1048,U_1047,U_1046,U_1045] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1045),U_1046),U_1048))
| ~ hBOOL(hAPP(hAPP(c_member(U_1045),U_1046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1045,tc_HOL_Obool)),U_1047),U_1048))) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_1045,U_1046,U_1047,U_1048] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1045),U_1046),U_1048))
| ~ hBOOL(hAPP(hAPP(c_member(U_1045),U_1046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1045,tc_HOL_Obool)),U_1047),U_1048))) ),
inference(definitional_conversion,[status(esa)],[f_240_2]) ).
cnf(f_240_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1045),U_1046),U_1048))
| ~ hBOOL(hAPP(hAPP(c_member(U_1045),U_1046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1045,tc_HOL_Obool)),U_1047),U_1048))) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__iff]) ).
fof(f_241_2,plain,
! [U_1052,U_1051,U_1050,U_1049] :
( ( hBOOL(hAPP(hAPP(c_member(U_1049),U_1050),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1049,tc_HOL_Obool)),U_1051),U_1052)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_1049),U_1050),U_1052))
& ~ hBOOL(hAPP(hAPP(c_member(U_1049),U_1050),U_1051)) ) )
& ( hBOOL(hAPP(hAPP(c_member(U_1049),U_1050),U_1052))
| hBOOL(hAPP(hAPP(c_member(U_1049),U_1050),U_1051))
| ~ hBOOL(hAPP(hAPP(c_member(U_1049),U_1050),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1049,tc_HOL_Obool)),U_1051),U_1052))) ) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
( ! [U_1060,U_1058,U_1056,U_1054] :
( hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1054,tc_HOL_Obool)),U_1058),U_1060)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),U_1060))
& ~ hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),U_1058)) ) )
& ! [U_1059,U_1057,U_1055,U_1053] :
( hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),U_1059))
| hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),U_1057))
| ~ hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1053,tc_HOL_Obool)),U_1057),U_1059))) ) ),
inference(miniscope,[status(thm)],[f_241_2]) ).
fof(f_241_4,plain,
( ! [U_1056,U_1054,U_1060,U_1058] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),U_1060))
| ~ sP73(U_1056,U_1054,U_1060,U_1058) )
& ! [U_1056,U_1054,U_1060,U_1058] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),U_1058))
| ~ sP73(U_1056,U_1054,U_1060,U_1058) )
& ! [U_1056,U_1054,U_1060,U_1058] :
( hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1054,tc_HOL_Obool)),U_1058),U_1060)))
| sP73(U_1056,U_1054,U_1060,U_1058) )
& ! [U_1059,U_1055,U_1053,U_1057] :
( hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),U_1059))
| hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),U_1057))
| ~ hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1053,tc_HOL_Obool)),U_1057),U_1059))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_241_3]) ).
cnf(f_241_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),U_1059))
| hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),U_1057))
| ~ hBOOL(hAPP(hAPP(c_member(U_1053),U_1055),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1053,tc_HOL_Obool)),U_1057),U_1059))) ),
inference(clausify,[status(thm)],[f_241_4]) ).
cnf(f_241_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1054,tc_HOL_Obool)),U_1058),U_1060)))
| sP73(U_1056,U_1054,U_1060,U_1058) ),
inference(clausify,[status(thm)],[f_241_4]) ).
cnf(f_241_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),U_1058))
| ~ sP73(U_1056,U_1054,U_1060,U_1058) ),
inference(clausify,[status(thm)],[f_241_4]) ).
cnf(f_241_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1054),U_1056),U_1060))
| ~ sP73(U_1056,U_1054,U_1060,U_1058) ),
inference(clausify,[status(thm)],[f_241_4]) ).
fof(f_242_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnI1]) ).
fof(f_242_2,plain,
! [U_1064,U_1063,U_1062,U_1061] :
( hBOOL(hAPP(hAPP(c_member(U_1061),U_1062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1061,tc_HOL_Obool)),U_1063),U_1064)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1061),U_1062),U_1063)) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_1061,U_1062,U_1063,U_1064] :
( hBOOL(hAPP(hAPP(c_member(U_1061),U_1062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1061,tc_HOL_Obool)),U_1063),U_1064)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1061),U_1062),U_1063)) ),
inference(definitional_conversion,[status(esa)],[f_242_2]) ).
cnf(f_242_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1061),U_1062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1061,tc_HOL_Obool)),U_1063),U_1064)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1061),U_1062),U_1063)) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_1,plain,
! [V_A_2,V_B_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnI2]) ).
fof(f_243_2,plain,
! [U_1068,U_1067,U_1066,U_1065] :
( hBOOL(hAPP(hAPP(c_member(U_1065),U_1066),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1065,tc_HOL_Obool)),U_1068),U_1067)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1065),U_1066),U_1067)) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_1065,U_1066,U_1067,U_1068] :
( hBOOL(hAPP(hAPP(c_member(U_1065),U_1066),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1065,tc_HOL_Obool)),U_1068),U_1067)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1065),U_1066),U_1067)) ),
inference(definitional_conversion,[status(esa)],[f_243_2]) ).
cnf(f_243_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1065),U_1066),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1065,tc_HOL_Obool)),U_1068),U_1067)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1065),U_1066),U_1067)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
& ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__iff]) ).
fof(f_244_2,plain,
! [U_1072,U_1071,U_1070,U_1069] :
( ( hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1072)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1072))
| ~ hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1071)) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1072))
& hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1071)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1072))) ) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
( ! [U_1080,U_1078,U_1076,U_1074] :
( hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1074,tc_HOL_Obool)),U_1078),U_1080)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),U_1080))
| ~ hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),U_1078)) )
& ! [U_1079,U_1077,U_1075,U_1073] :
( ( hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),U_1079))
& hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),U_1077)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1073,tc_HOL_Obool)),U_1077),U_1079))) ) ),
inference(miniscope,[status(thm)],[f_244_2]) ).
fof(f_244_4,plain,
( ! [U_1075,U_1079,U_1073,U_1077] :
( hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),U_1079))
| ~ sP74(U_1075,U_1079,U_1073,U_1077) )
& ! [U_1075,U_1079,U_1073,U_1077] :
( hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),U_1077))
| ~ sP74(U_1075,U_1079,U_1073,U_1077) )
& ! [U_1076,U_1074,U_1080,U_1078] :
( hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1074,tc_HOL_Obool)),U_1078),U_1080)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),U_1080))
| ~ hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),U_1078)) )
& ! [U_1075,U_1079,U_1073,U_1077] :
( sP74(U_1075,U_1079,U_1073,U_1077)
| ~ hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1073,tc_HOL_Obool)),U_1077),U_1079))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_244_3]) ).
cnf(f_244_5,plain,
( sP74(U_1075,U_1079,U_1073,U_1077)
| ~ hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1073,tc_HOL_Obool)),U_1077),U_1079))) ),
inference(clausify,[status(thm)],[f_244_4]) ).
cnf(f_244_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1074,tc_HOL_Obool)),U_1078),U_1080)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),U_1080))
| ~ hBOOL(hAPP(hAPP(c_member(U_1074),U_1076),U_1078)) ),
inference(clausify,[status(thm)],[f_244_4]) ).
cnf(f_244_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),U_1077))
| ~ sP74(U_1075,U_1079,U_1073,U_1077) ),
inference(clausify,[status(thm)],[f_244_4]) ).
cnf(f_244_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_1073),U_1075),U_1079))
| ~ sP74(U_1075,U_1079,U_1073,U_1077) ),
inference(clausify,[status(thm)],[f_244_4]) ).
fof(f_245_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD1]) ).
fof(f_245_2,plain,
! [U_1084,U_1083,U_1082,U_1081] :
( hBOOL(hAPP(hAPP(c_member(U_1081),U_1082),U_1083))
| ~ hBOOL(hAPP(hAPP(c_member(U_1081),U_1082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1081,tc_HOL_Obool)),U_1083),U_1084))) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_1082,U_1081,U_1083,U_1084] :
( hBOOL(hAPP(hAPP(c_member(U_1081),U_1082),U_1083))
| ~ hBOOL(hAPP(hAPP(c_member(U_1081),U_1082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1081,tc_HOL_Obool)),U_1083),U_1084))) ),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1081),U_1082),U_1083))
| ~ hBOOL(hAPP(hAPP(c_member(U_1081),U_1082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1081,tc_HOL_Obool)),U_1083),U_1084))) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_1,plain,
! [V_B_2,V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD2]) ).
fof(f_246_2,plain,
! [U_1088,U_1087,U_1086,U_1085] :
( hBOOL(hAPP(hAPP(c_member(U_1085),U_1086),U_1088))
| ~ hBOOL(hAPP(hAPP(c_member(U_1085),U_1086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1085,tc_HOL_Obool)),U_1087),U_1088))) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_1085,U_1086,U_1087,U_1088] :
( hBOOL(hAPP(hAPP(c_member(U_1085),U_1086),U_1088))
| ~ hBOOL(hAPP(hAPP(c_member(U_1085),U_1086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1085,tc_HOL_Obool)),U_1087),U_1088))) ),
inference(definitional_conversion,[status(esa)],[f_246_2]) ).
cnf(f_246_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1085),U_1086),U_1088))
| ~ hBOOL(hAPP(hAPP(c_member(U_1085),U_1086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1085,tc_HOL_Obool)),U_1087),U_1088))) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__cancel]) ).
fof(f_247_2,plain,
! [U_1090,U_1089] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1089,tc_HOL_Obool)),U_1090),U_1090) = c_Orderings_Obot__class_Obot(tc_fun(U_1089,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_1089,U_1090] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1089,tc_HOL_Obool)),U_1090),U_1090) = c_Orderings_Obot__class_Obot(tc_fun(U_1089,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1089,tc_HOL_Obool)),U_1090),U_1090) = c_Orderings_Obot__class_Obot(tc_fun(U_1089,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Diff__empty]) ).
fof(f_248_2,plain,
! [U_1092,U_1091] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1091,tc_HOL_Obool)),U_1092),c_Orderings_Obot__class_Obot(tc_fun(U_1091,tc_HOL_Obool))) = U_1092,
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_1091,U_1092] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1091,tc_HOL_Obool)),U_1092),c_Orderings_Obot__class_Obot(tc_fun(U_1091,tc_HOL_Obool))) = U_1092,
inference(definitional_conversion,[status(esa)],[f_248_2]) ).
cnf(f_248_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1091,tc_HOL_Obool)),U_1092),c_Orderings_Obot__class_Obot(tc_fun(U_1091,tc_HOL_Obool))) = U_1092,
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_empty__Diff]) ).
fof(f_249_2,plain,
! [U_1094,U_1093] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1093,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1093,tc_HOL_Obool))),U_1094) = c_Orderings_Obot__class_Obot(tc_fun(U_1093,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_1093,U_1094] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1093,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1093,tc_HOL_Obool))),U_1094) = c_Orderings_Obot__class_Obot(tc_fun(U_1093,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_249_2]) ).
cnf(f_249_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1093,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1093,tc_HOL_Obool))),U_1094) = c_Orderings_Obot__class_Obot(tc_fun(U_1093,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_1,plain,
! [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_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))
| V_A_2 != 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))
& V_A_2 = c_Orderings_Obot__class_Obot(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) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__empty]) ).
fof(f_250_2,plain,
! [U_1097,U_1096,U_1095] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1095,tc_HOL_Obool)),U_1096),U_1097) = c_Orderings_Obot__class_Obot(tc_fun(U_1095,tc_HOL_Obool))
| U_1097 != c_Orderings_Obot__class_Obot(tc_fun(U_1095,tc_HOL_Obool))
| U_1096 != c_Orderings_Obot__class_Obot(tc_fun(U_1095,tc_HOL_Obool)) )
& ( ( U_1097 = c_Orderings_Obot__class_Obot(tc_fun(U_1095,tc_HOL_Obool))
& U_1096 = c_Orderings_Obot__class_Obot(tc_fun(U_1095,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1095,tc_HOL_Obool)),U_1096),U_1097) != c_Orderings_Obot__class_Obot(tc_fun(U_1095,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
( ! [U_1103,U_1101,U_1099] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1099,tc_HOL_Obool)),U_1101),U_1103) = c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool))
| U_1103 != c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool))
| U_1101 != c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool)) )
& ! [U_1102,U_1100,U_1098] :
( ( U_1102 = c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool))
& U_1100 = c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1098,tc_HOL_Obool)),U_1100),U_1102) != c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_250_2]) ).
fof(f_250_4,plain,
( ! [U_1100,U_1098,U_1102] :
( U_1102 = c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool))
| ~ sP75(U_1100,U_1098,U_1102) )
& ! [U_1100,U_1098,U_1102] :
( U_1100 = c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool))
| ~ sP75(U_1100,U_1098,U_1102) )
& ! [U_1103,U_1099,U_1101] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1099,tc_HOL_Obool)),U_1101),U_1103) = c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool))
| U_1103 != c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool))
| U_1101 != c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool)) )
& ! [U_1100,U_1098,U_1102] :
( sP75(U_1100,U_1098,U_1102)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1098,tc_HOL_Obool)),U_1100),U_1102) != c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_250_3]) ).
cnf(f_250_5,plain,
( sP75(U_1100,U_1098,U_1102)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1098,tc_HOL_Obool)),U_1100),U_1102) != c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_250_4]) ).
cnf(f_250_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1099,tc_HOL_Obool)),U_1101),U_1103) = c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool))
| U_1103 != c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool))
| U_1101 != c_Orderings_Obot__class_Obot(tc_fun(U_1099,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_250_4]) ).
cnf(f_250_7,plain,
( U_1100 = c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool))
| ~ sP75(U_1100,U_1098,U_1102) ),
inference(clausify,[status(thm)],[f_250_4]) ).
cnf(f_250_8,plain,
( U_1102 = c_Orderings_Obot__class_Obot(tc_fun(U_1098,tc_HOL_Obool))
| ~ sP75(U_1100,U_1098,U_1102) ),
inference(clausify,[status(thm)],[f_250_4]) ).
fof(f_251_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Un__empty__right]) ).
fof(f_251_2,plain,
! [U_1105,U_1104] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1104,tc_HOL_Obool)),U_1105),c_Orderings_Obot__class_Obot(tc_fun(U_1104,tc_HOL_Obool))) = U_1105,
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_1104,U_1105] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1104,tc_HOL_Obool)),U_1105),c_Orderings_Obot__class_Obot(tc_fun(U_1104,tc_HOL_Obool))) = U_1105,
inference(definitional_conversion,[status(esa)],[f_251_2]) ).
cnf(f_251_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1104,tc_HOL_Obool)),U_1105),c_Orderings_Obot__class_Obot(tc_fun(U_1104,tc_HOL_Obool))) = U_1105,
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Un__empty__left]) ).
fof(f_252_2,plain,
! [U_1107,U_1106] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1106,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1106,tc_HOL_Obool))),U_1107) = U_1107,
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_1106,U_1107] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1106,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1106,tc_HOL_Obool))),U_1107) = U_1107,
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1106,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1106,tc_HOL_Obool))),U_1107) = U_1107,
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_1,plain,
! [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_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( ? [B_xa] :
( B_x = B_xa
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( B_x != B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_disjoint__iff__not__equal]) ).
fof(f_253_2,plain,
! [U_1114,U_1113,U_1112] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1112,tc_HOL_Obool)),U_1113),U_1114) = c_Orderings_Obot__class_Obot(tc_fun(U_1112,tc_HOL_Obool))
| ? [U_1111] :
( ? [U_1110] :
( U_1111 = U_1110
& hBOOL(hAPP(hAPP(c_member(U_1112),U_1110),U_1114)) )
& hBOOL(hAPP(hAPP(c_member(U_1112),U_1111),U_1113)) ) )
& ( ! [U_1109] :
( ! [U_1108] :
( U_1109 != U_1108
| ~ hBOOL(hAPP(hAPP(c_member(U_1112),U_1108),U_1114)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1112),U_1109),U_1113)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1112,tc_HOL_Obool)),U_1113),U_1114) != c_Orderings_Obot__class_Obot(tc_fun(U_1112,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ! [U_1120,U_1118,U_1116] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1116,tc_HOL_Obool)),U_1118),U_1120) = c_Orderings_Obot__class_Obot(tc_fun(U_1116,tc_HOL_Obool))
| ? [U_1111] :
( ? [U_1110] :
( U_1111 = U_1110
& hBOOL(hAPP(hAPP(c_member(U_1116),U_1110),U_1120)) )
& hBOOL(hAPP(hAPP(c_member(U_1116),U_1111),U_1118)) ) )
& ! [U_1119,U_1117,U_1115] :
( ! [U_1109] :
( ! [U_1108] :
( U_1109 != U_1108
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1108),U_1119)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1109),U_1117)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1115,tc_HOL_Obool)),U_1117),U_1119) != c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_253_2]) ).
fof(f_253_4,plain,
( ! [U_1120,U_1118,U_1116] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1116,tc_HOL_Obool)),U_1118),U_1120) = c_Orderings_Obot__class_Obot(tc_fun(U_1116,tc_HOL_Obool))
| ( ? [U_1110] :
( sK39(U_1120,U_1118,U_1116) = U_1110
& hBOOL(hAPP(hAPP(c_member(U_1116),U_1110),U_1120)) )
& hBOOL(hAPP(hAPP(c_member(U_1116),sK39(U_1120,U_1118,U_1116)),U_1118)) ) )
& ! [U_1119,U_1117,U_1115] :
( ! [U_1109] :
( ! [U_1108] :
( U_1109 != U_1108
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1108),U_1119)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1109),U_1117)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1115,tc_HOL_Obool)),U_1117),U_1119) != c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1111,sK39(U_1120,U_1118,U_1116))],[f_253_3]) ).
fof(f_253_5,plain,
( ! [U_1120,U_1118,U_1116] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1116,tc_HOL_Obool)),U_1118),U_1120) = c_Orderings_Obot__class_Obot(tc_fun(U_1116,tc_HOL_Obool))
| ( sK39(U_1120,U_1118,U_1116) = sK40(U_1120,U_1118,U_1116)
& hBOOL(hAPP(hAPP(c_member(U_1116),sK40(U_1120,U_1118,U_1116)),U_1120))
& hBOOL(hAPP(hAPP(c_member(U_1116),sK39(U_1120,U_1118,U_1116)),U_1118)) ) )
& ! [U_1119,U_1117,U_1115] :
( ! [U_1109] :
( ! [U_1108] :
( U_1109 != U_1108
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1108),U_1119)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1109),U_1117)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1115,tc_HOL_Obool)),U_1117),U_1119) != c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_1110,sK40(U_1120,U_1118,U_1116))],[f_253_4]) ).
fof(f_253_6,plain,
( ! [U_1118,U_1120,U_1116] :
( sK39(U_1120,U_1118,U_1116) = sK40(U_1120,U_1118,U_1116)
| ~ sP76(U_1118,U_1120,U_1116) )
& ! [U_1118,U_1120,U_1116] :
( hBOOL(hAPP(hAPP(c_member(U_1116),sK40(U_1120,U_1118,U_1116)),U_1120))
| ~ sP76(U_1118,U_1120,U_1116) )
& ! [U_1118,U_1120,U_1116] :
( hBOOL(hAPP(hAPP(c_member(U_1116),sK39(U_1120,U_1118,U_1116)),U_1118))
| ~ sP76(U_1118,U_1120,U_1116) )
& ! [U_1118,U_1120,U_1116] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1116,tc_HOL_Obool)),U_1118),U_1120) = c_Orderings_Obot__class_Obot(tc_fun(U_1116,tc_HOL_Obool))
| sP76(U_1118,U_1120,U_1116) )
& ! [U_1108,U_1119,U_1109,U_1115,U_1117] :
( U_1109 != U_1108
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1108),U_1119))
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1109),U_1117))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1115,tc_HOL_Obool)),U_1117),U_1119) != c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_253_5]) ).
cnf(f_253_7,plain,
( U_1109 != U_1108
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1108),U_1119))
| ~ hBOOL(hAPP(hAPP(c_member(U_1115),U_1109),U_1117))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1115,tc_HOL_Obool)),U_1117),U_1119) != c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_253_6]) ).
cnf(f_253_8,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1116,tc_HOL_Obool)),U_1118),U_1120) = c_Orderings_Obot__class_Obot(tc_fun(U_1116,tc_HOL_Obool))
| sP76(U_1118,U_1120,U_1116) ),
inference(clausify,[status(thm)],[f_253_6]) ).
cnf(f_253_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_1116),sK39(U_1120,U_1118,U_1116)),U_1118))
| ~ sP76(U_1118,U_1120,U_1116) ),
inference(clausify,[status(thm)],[f_253_6]) ).
cnf(f_253_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_1116),sK40(U_1120,U_1118,U_1116)),U_1120))
| ~ sP76(U_1118,U_1120,U_1116) ),
inference(clausify,[status(thm)],[f_253_6]) ).
cnf(f_253_11,plain,
( sK39(U_1120,U_1118,U_1116) = sK40(U_1120,U_1118,U_1116)
| ~ sP76(U_1118,U_1120,U_1116) ),
inference(clausify,[status(thm)],[f_253_6]) ).
fof(f_254_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__empty__right]) ).
fof(f_254_2,plain,
! [U_1122,U_1121] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1121,tc_HOL_Obool)),U_1122),c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_1122,U_1121] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1121,tc_HOL_Obool)),U_1122),c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_254_2]) ).
cnf(f_254_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1121,tc_HOL_Obool)),U_1122),c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__empty__left]) ).
fof(f_255_2,plain,
! [U_1124,U_1123] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1123,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1123,tc_HOL_Obool))),U_1124) = c_Orderings_Obot__class_Obot(tc_fun(U_1123,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_1123,U_1124] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1123,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1123,tc_HOL_Obool))),U_1124) = c_Orderings_Obot__class_Obot(tc_fun(U_1123,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_255_2]) ).
cnf(f_255_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1123,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1123,tc_HOL_Obool))),U_1124) = c_Orderings_Obot__class_Obot(tc_fun(U_1123,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [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_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
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_double__diff]) ).
fof(f_256_2,plain,
! [U_1128,U_1127,U_1126,U_1125] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1125,tc_HOL_Obool)),U_1127),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1125,tc_HOL_Obool)),U_1128),U_1126)) = U_1126
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1125,tc_HOL_Obool)),U_1127),U_1128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1125,tc_HOL_Obool)),U_1126),U_1127)) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_1126,U_1125,U_1127,U_1128] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1125,tc_HOL_Obool)),U_1127),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1125,tc_HOL_Obool)),U_1128),U_1126)) = U_1126
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1125,tc_HOL_Obool)),U_1127),U_1128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1125,tc_HOL_Obool)),U_1126),U_1127)) ),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1125,tc_HOL_Obool)),U_1127),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1125,tc_HOL_Obool)),U_1128),U_1126)) = U_1126
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1125,tc_HOL_Obool)),U_1127),U_1128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1125,tc_HOL_Obool)),U_1126),U_1127)) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_1,plain,
! [V_B_2,V_D_2,V_C_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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__mono]) ).
fof(f_257_2,plain,
! [U_1133,U_1132,U_1131,U_1130,U_1129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1130),U_1133)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1131),U_1132)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),U_1132),U_1133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),U_1130),U_1131)) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_1129,U_1130,U_1131,U_1132,U_1133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1130),U_1133)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1131),U_1132)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),U_1132),U_1133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),U_1130),U_1131)) ),
inference(definitional_conversion,[status(esa)],[f_257_2]) ).
cnf(f_257_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1130),U_1133)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1131),U_1132)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),U_1132),U_1133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1129,tc_HOL_Obool)),U_1130),U_1131)) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__subset]) ).
fof(f_258_2,plain,
! [U_1136,U_1135,U_1134] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1134,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1134,tc_HOL_Obool)),U_1135),U_1136)),U_1135)),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_1135,U_1134,U_1136] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1134,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1134,tc_HOL_Obool)),U_1135),U_1136)),U_1135)),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1134,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1134,tc_HOL_Obool)),U_1135),U_1136)),U_1135)),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__insert__left]) ).
fof(f_259_2,plain,
! [U_1140,U_1139,U_1138,U_1137] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1137,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1137),U_1138),U_1139)),U_1140) = hAPP(hAPP(c_Set_Oinsert(U_1137),U_1138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1137,tc_HOL_Obool)),U_1139),U_1140)),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_1137,U_1138,U_1139,U_1140] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1137,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1137),U_1138),U_1139)),U_1140) = hAPP(hAPP(c_Set_Oinsert(U_1137),U_1138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1137,tc_HOL_Obool)),U_1139),U_1140)),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1137,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1137),U_1138),U_1139)),U_1140) = hAPP(hAPP(c_Set_Oinsert(U_1137),U_1138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1137,tc_HOL_Obool)),U_1139),U_1140)),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__insert__right]) ).
fof(f_260_2,plain,
! [U_1144,U_1143,U_1142,U_1141] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1141,tc_HOL_Obool)),U_1142),hAPP(hAPP(c_Set_Oinsert(U_1141),U_1143),U_1144)) = hAPP(hAPP(c_Set_Oinsert(U_1141),U_1143),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1141,tc_HOL_Obool)),U_1142),U_1144)),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
! [U_1141,U_1142,U_1143,U_1144] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1141,tc_HOL_Obool)),U_1142),hAPP(hAPP(c_Set_Oinsert(U_1141),U_1143),U_1144)) = hAPP(hAPP(c_Set_Oinsert(U_1141),U_1143),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1141,tc_HOL_Obool)),U_1142),U_1144)),
inference(definitional_conversion,[status(esa)],[f_260_2]) ).
cnf(f_260_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1141,tc_HOL_Obool)),U_1142),hAPP(hAPP(c_Set_Oinsert(U_1141),U_1143),U_1144)) = hAPP(hAPP(c_Set_Oinsert(U_1141),U_1143),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1141,tc_HOL_Obool)),U_1142),U_1144)),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_insert__inter__insert]) ).
fof(f_261_2,plain,
! [U_1148,U_1147,U_1146,U_1145] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),U_1147)),hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),U_1148)) = hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_HOL_Obool)),U_1147),U_1148)),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
! [U_1145,U_1146,U_1147,U_1148] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),U_1147)),hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),U_1148)) = hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_HOL_Obool)),U_1147),U_1148)),
inference(definitional_conversion,[status(esa)],[f_261_2]) ).
cnf(f_261_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),U_1147)),hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),U_1148)) = hAPP(hAPP(c_Set_Oinsert(U_1145),U_1146),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1145,tc_HOL_Obool)),U_1147),U_1148)),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_1,plain,
! [V_D_2,V_B_2,V_C_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)),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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__mono]) ).
fof(f_262_2,plain,
! [U_1153,U_1152,U_1151,U_1150,U_1149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1149,tc_HOL_Obool)),U_1150),U_1152)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1149,tc_HOL_Obool)),U_1151),U_1153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),U_1152),U_1153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),U_1150),U_1151)) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_1149,U_1150,U_1151,U_1152,U_1153] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1149,tc_HOL_Obool)),U_1150),U_1152)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1149,tc_HOL_Obool)),U_1151),U_1153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),U_1152),U_1153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),U_1150),U_1151)) ),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1149,tc_HOL_Obool)),U_1150),U_1152)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1149,tc_HOL_Obool)),U_1151),U_1153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),U_1152),U_1153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1149,tc_HOL_Obool)),U_1150),U_1151)) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [V_B_2,V_C_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)),V_A_2),V_B_2)),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__least]) ).
fof(f_263_2,plain,
! [U_1157,U_1156,U_1155,U_1154] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1154,tc_HOL_Obool)),U_1155),U_1157)),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),U_1157),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),U_1155),U_1156)) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_1154,U_1155,U_1156,U_1157] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1154,tc_HOL_Obool)),U_1155),U_1157)),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),U_1157),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),U_1155),U_1156)) ),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1154,tc_HOL_Obool)),U_1155),U_1157)),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),U_1157),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1154,tc_HOL_Obool)),U_1155),U_1156)) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
! [V_A_2,V_B_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__absorb2]) ).
fof(f_264_2,plain,
! [U_1160,U_1159,U_1158] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1158,tc_HOL_Obool)),U_1160),U_1159) = U_1160
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1158,tc_HOL_Obool)),U_1159),U_1160)) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_1158,U_1159,U_1160] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1158,tc_HOL_Obool)),U_1160),U_1159) = U_1160
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1158,tc_HOL_Obool)),U_1159),U_1160)) ),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1158,tc_HOL_Obool)),U_1160),U_1159) = U_1160
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1158,tc_HOL_Obool)),U_1159),U_1160)) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [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) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__absorb1]) ).
fof(f_265_2,plain,
! [U_1163,U_1162,U_1161] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1161,tc_HOL_Obool)),U_1162),U_1163) = U_1163
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1161,tc_HOL_Obool)),U_1162),U_1163)) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_1161,U_1162,U_1163] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1161,tc_HOL_Obool)),U_1162),U_1163) = U_1163
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1161,tc_HOL_Obool)),U_1162),U_1163)) ),
inference(definitional_conversion,[status(esa)],[f_265_2]) ).
cnf(f_265_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1161,tc_HOL_Obool)),U_1162),U_1163) = U_1163
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1161,tc_HOL_Obool)),U_1162),U_1163)) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [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),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_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) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__Un__eq]) ).
fof(f_266_2,plain,
! [U_1166,U_1165,U_1164] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1164,tc_HOL_Obool)),U_1165),U_1166))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1164,tc_HOL_Obool)),U_1165),U_1166) != U_1166 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1164,tc_HOL_Obool)),U_1165),U_1166) = U_1166
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1164,tc_HOL_Obool)),U_1165),U_1166)) ) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
( ! [U_1172,U_1170,U_1168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1168,tc_HOL_Obool)),U_1170),U_1172))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1168,tc_HOL_Obool)),U_1170),U_1172) != U_1172 )
& ! [U_1171,U_1169,U_1167] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1167,tc_HOL_Obool)),U_1169),U_1171) = U_1171
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1167,tc_HOL_Obool)),U_1169),U_1171)) ) ),
inference(miniscope,[status(thm)],[f_266_2]) ).
fof(f_266_4,plain,
( ! [U_1168,U_1170,U_1172] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1168,tc_HOL_Obool)),U_1170),U_1172))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1168,tc_HOL_Obool)),U_1170),U_1172) != U_1172 )
& ! [U_1169,U_1171,U_1167] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1167,tc_HOL_Obool)),U_1169),U_1171) = U_1171
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1167,tc_HOL_Obool)),U_1169),U_1171)) ) ),
inference(definitional_conversion,[status(esa)],[f_266_3]) ).
cnf(f_266_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1167,tc_HOL_Obool)),U_1169),U_1171) = U_1171
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1167,tc_HOL_Obool)),U_1169),U_1171)) ),
inference(clausify,[status(thm)],[f_266_4]) ).
cnf(f_266_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1168,tc_HOL_Obool)),U_1170),U_1172))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1168,tc_HOL_Obool)),U_1170),U_1172) != U_1172 ),
inference(clausify,[status(thm)],[f_266_4]) ).
fof(f_267_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Un__upper2]) ).
fof(f_267_2,plain,
! [U_1175,U_1174,U_1173] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1173,tc_HOL_Obool)),U_1174),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1173,tc_HOL_Obool)),U_1175),U_1174))),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_1173,U_1174,U_1175] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1173,tc_HOL_Obool)),U_1174),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1173,tc_HOL_Obool)),U_1175),U_1174))),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1173,tc_HOL_Obool)),U_1174),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1173,tc_HOL_Obool)),U_1175),U_1174))),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Un__upper1]) ).
fof(f_268_2,plain,
! [U_1178,U_1177,U_1176] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1176,tc_HOL_Obool)),U_1177),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1176,tc_HOL_Obool)),U_1177),U_1178))),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_1176,U_1177,U_1178] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1176,tc_HOL_Obool)),U_1177),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1176,tc_HOL_Obool)),U_1177),U_1178))),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1176,tc_HOL_Obool)),U_1177),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1176,tc_HOL_Obool)),U_1177),U_1178))),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__UNIV__right]) ).
fof(f_269_2,plain,
! [U_1180,U_1179] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1179,tc_HOL_Obool)),U_1180),c_Orderings_Otop__class_Otop(tc_fun(U_1179,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1179,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
! [U_1179,U_1180] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1179,tc_HOL_Obool)),U_1180),c_Orderings_Otop__class_Otop(tc_fun(U_1179,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1179,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_269_2]) ).
cnf(f_269_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1179,tc_HOL_Obool)),U_1180),c_Orderings_Otop__class_Otop(tc_fun(U_1179,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1179,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__UNIV__left]) ).
fof(f_270_2,plain,
! [U_1182,U_1181] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1181,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1181,tc_HOL_Obool))),U_1182) = c_Orderings_Otop__class_Otop(tc_fun(U_1181,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_1181,U_1182] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1181,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1181,tc_HOL_Obool))),U_1182) = c_Orderings_Otop__class_Otop(tc_fun(U_1181,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1181,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1181,tc_HOL_Obool))),U_1182) = c_Orderings_Otop__class_Otop(tc_fun(U_1181,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [V_D_2,V_B_2,V_C_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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__mono]) ).
fof(f_271_2,plain,
! [U_1187,U_1186,U_1185,U_1184,U_1183] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1184),U_1186)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),U_1186),U_1187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),U_1184),U_1185)) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_1183,U_1184,U_1185,U_1186,U_1187] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1184),U_1186)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),U_1186),U_1187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),U_1184),U_1185)) ),
inference(definitional_conversion,[status(esa)],[f_271_2]) ).
cnf(f_271_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1184),U_1186)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),U_1186),U_1187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),U_1184),U_1185)) ),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__greatest]) ).
fof(f_272_2,plain,
! [U_1191,U_1190,U_1189,U_1188] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1188,tc_HOL_Obool)),U_1190),U_1191)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),U_1191))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),U_1190)) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_1189,U_1190,U_1188,U_1191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1188,tc_HOL_Obool)),U_1190),U_1191)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),U_1191))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),U_1190)) ),
inference(definitional_conversion,[status(esa)],[f_272_2]) ).
cnf(f_272_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1188,tc_HOL_Obool)),U_1190),U_1191)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),U_1191))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1189),U_1190)) ),
inference(clausify,[status(thm)],[f_272_3]) ).
fof(f_273_1,plain,
! [V_A_2,V_B_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__absorb1]) ).
fof(f_273_2,plain,
! [U_1194,U_1193,U_1192] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1192,tc_HOL_Obool)),U_1194),U_1193) = U_1193
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1192,tc_HOL_Obool)),U_1193),U_1194)) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_1192,U_1193,U_1194] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1192,tc_HOL_Obool)),U_1194),U_1193) = U_1193
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1192,tc_HOL_Obool)),U_1193),U_1194)) ),
inference(definitional_conversion,[status(esa)],[f_273_2]) ).
cnf(f_273_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1192,tc_HOL_Obool)),U_1194),U_1193) = U_1193
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1192,tc_HOL_Obool)),U_1193),U_1194)) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_1,plain,
! [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) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__absorb2]) ).
fof(f_274_2,plain,
! [U_1197,U_1196,U_1195] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1195,tc_HOL_Obool)),U_1196),U_1197) = U_1196
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1195,tc_HOL_Obool)),U_1196),U_1197)) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_1195,U_1196,U_1197] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1195,tc_HOL_Obool)),U_1196),U_1197) = U_1196
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1195,tc_HOL_Obool)),U_1196),U_1197)) ),
inference(definitional_conversion,[status(esa)],[f_274_2]) ).
cnf(f_274_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1195,tc_HOL_Obool)),U_1196),U_1197) = U_1196
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1195,tc_HOL_Obool)),U_1196),U_1197)) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__lower2]) ).
fof(f_275_2,plain,
! [U_1200,U_1199,U_1198] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1198,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1198,tc_HOL_Obool)),U_1199),U_1200)),U_1200)),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_1198,U_1199,U_1200] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1198,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1198,tc_HOL_Obool)),U_1199),U_1200)),U_1200)),
inference(definitional_conversion,[status(esa)],[f_275_2]) ).
cnf(f_275_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1198,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1198,tc_HOL_Obool)),U_1199),U_1200)),U_1200)),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__lower1]) ).
fof(f_276_2,plain,
! [U_1203,U_1202,U_1201] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1201,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1201,tc_HOL_Obool)),U_1202),U_1203)),U_1202)),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_1201,U_1202,U_1203] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1201,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1201,tc_HOL_Obool)),U_1202),U_1203)),U_1202)),
inference(definitional_conversion,[status(esa)],[f_276_2]) ).
cnf(f_276_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1201,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1201,tc_HOL_Obool)),U_1202),U_1203)),U_1202)),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Int__UNIV__right]) ).
fof(f_277_2,plain,
! [U_1205,U_1204] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1204,tc_HOL_Obool)),U_1205),c_Orderings_Otop__class_Otop(tc_fun(U_1204,tc_HOL_Obool))) = U_1205,
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
! [U_1204,U_1205] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1204,tc_HOL_Obool)),U_1205),c_Orderings_Otop__class_Otop(tc_fun(U_1204,tc_HOL_Obool))) = U_1205,
inference(definitional_conversion,[status(esa)],[f_277_2]) ).
cnf(f_277_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1204,tc_HOL_Obool)),U_1205),c_Orderings_Otop__class_Otop(tc_fun(U_1204,tc_HOL_Obool))) = U_1205,
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Int__UNIV__left]) ).
fof(f_278_2,plain,
! [U_1207,U_1206] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1206,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1206,tc_HOL_Obool))),U_1207) = U_1207,
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
! [U_1206,U_1207] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1206,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1206,tc_HOL_Obool))),U_1207) = U_1207,
inference(definitional_conversion,[status(esa)],[f_278_2]) ).
cnf(f_278_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1206,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1206,tc_HOL_Obool))),U_1207) = U_1207,
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Un__Pow__subset]) ).
fof(f_279_2,plain,
! [U_1210,U_1209,U_1208] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1208,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1208,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_1208),U_1209)),hAPP(c_Set_OPow(U_1208),U_1210))),hAPP(c_Set_OPow(U_1208),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1208,tc_HOL_Obool)),U_1209),U_1210)))),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1210,U_1208,U_1209] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1208,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1208,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_1208),U_1209)),hAPP(c_Set_OPow(U_1208),U_1210))),hAPP(c_Set_OPow(U_1208),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1208,tc_HOL_Obool)),U_1209),U_1210)))),
inference(definitional_conversion,[status(esa)],[f_279_2]) ).
cnf(f_279_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1208,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1208,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_1208),U_1209)),hAPP(c_Set_OPow(U_1208),U_1210))),hAPP(c_Set_OPow(U_1208),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1208,tc_HOL_Obool)),U_1209),U_1210)))),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_1,plain,
! [V_A_2,V_B_2,V_x_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff1]) ).
fof(f_280_2,plain,
! [U_1214,U_1213,U_1212,U_1211] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1211,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1211),U_1212),U_1214)),U_1213) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1211,tc_HOL_Obool)),U_1214),U_1213)
| ~ hBOOL(hAPP(hAPP(c_member(U_1211),U_1212),U_1213)) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_1211,U_1212,U_1213,U_1214] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1211,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1211),U_1212),U_1214)),U_1213) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1211,tc_HOL_Obool)),U_1214),U_1213)
| ~ hBOOL(hAPP(hAPP(c_member(U_1211),U_1212),U_1213)) ),
inference(definitional_conversion,[status(esa)],[f_280_2]) ).
cnf(f_280_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1211,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1211),U_1212),U_1214)),U_1213) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1211,tc_HOL_Obool)),U_1214),U_1213)
| ~ hBOOL(hAPP(hAPP(c_member(U_1211),U_1212),U_1213)) ),
inference(clausify,[status(thm)],[f_280_3]) ).
fof(f_281_1,plain,
! [V_A_2,V_B_2,V_x_2,T_b] :
( ( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff__if]) ).
fof(f_281_2,plain,
! [U_1218,U_1217,U_1216,U_1215] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1215,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1215),U_1216),U_1218)),U_1217) = hAPP(hAPP(c_Set_Oinsert(U_1215),U_1216),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1215,tc_HOL_Obool)),U_1218),U_1217))
| hBOOL(hAPP(hAPP(c_member(U_1215),U_1216),U_1217)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1215,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1215),U_1216),U_1218)),U_1217) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1215,tc_HOL_Obool)),U_1218),U_1217)
| ~ hBOOL(hAPP(hAPP(c_member(U_1215),U_1216),U_1217)) ) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
( ! [U_1226,U_1224,U_1222,U_1220] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),U_1226)),U_1224) = hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),U_1226),U_1224))
| hBOOL(hAPP(hAPP(c_member(U_1220),U_1222),U_1224)) )
& ! [U_1225,U_1223,U_1221,U_1219] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1219),U_1221),U_1225)),U_1223) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),U_1225),U_1223)
| ~ hBOOL(hAPP(hAPP(c_member(U_1219),U_1221),U_1223)) ) ),
inference(miniscope,[status(thm)],[f_281_2]) ).
fof(f_281_4,plain,
( ! [U_1220,U_1222,U_1224,U_1226] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),U_1226)),U_1224) = hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),U_1226),U_1224))
| hBOOL(hAPP(hAPP(c_member(U_1220),U_1222),U_1224)) )
& ! [U_1225,U_1221,U_1219,U_1223] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1219),U_1221),U_1225)),U_1223) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),U_1225),U_1223)
| ~ hBOOL(hAPP(hAPP(c_member(U_1219),U_1221),U_1223)) ) ),
inference(definitional_conversion,[status(esa)],[f_281_3]) ).
cnf(f_281_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1219),U_1221),U_1225)),U_1223) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),U_1225),U_1223)
| ~ hBOOL(hAPP(hAPP(c_member(U_1219),U_1221),U_1223)) ),
inference(clausify,[status(thm)],[f_281_4]) ).
cnf(f_281_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),U_1226)),U_1224) = hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),U_1226),U_1224))
| hBOOL(hAPP(hAPP(c_member(U_1220),U_1222),U_1224)) ),
inference(clausify,[status(thm)],[f_281_4]) ).
fof(f_282_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_insert__Diff__single]) ).
fof(f_282_2,plain,
! [U_1229,U_1228,U_1227] : hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1227,tc_HOL_Obool)),U_1229),hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),c_Orderings_Obot__class_Obot(tc_fun(U_1227,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),U_1229),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_1227,U_1228,U_1229] : hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1227,tc_HOL_Obool)),U_1229),hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),c_Orderings_Obot__class_Obot(tc_fun(U_1227,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),U_1229),
inference(definitional_conversion,[status(esa)],[f_282_2]) ).
cnf(f_282_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1227,tc_HOL_Obool)),U_1229),hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),c_Orderings_Obot__class_Obot(tc_fun(U_1227,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_1227),U_1228),U_1229),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Diff__insert2]) ).
fof(f_283_2,plain,
! [U_1233,U_1232,U_1231,U_1230] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),U_1231),hAPP(hAPP(c_Set_Oinsert(U_1230),U_1232),U_1233)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),U_1231),hAPP(hAPP(c_Set_Oinsert(U_1230),U_1232),c_Orderings_Obot__class_Obot(tc_fun(U_1230,tc_HOL_Obool))))),U_1233),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1230,U_1231,U_1232,U_1233] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),U_1231),hAPP(hAPP(c_Set_Oinsert(U_1230),U_1232),U_1233)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),U_1231),hAPP(hAPP(c_Set_Oinsert(U_1230),U_1232),c_Orderings_Obot__class_Obot(tc_fun(U_1230,tc_HOL_Obool))))),U_1233),
inference(definitional_conversion,[status(esa)],[f_283_2]) ).
cnf(f_283_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),U_1231),hAPP(hAPP(c_Set_Oinsert(U_1230),U_1232),U_1233)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1230,tc_HOL_Obool)),U_1231),hAPP(hAPP(c_Set_Oinsert(U_1230),U_1232),c_Orderings_Obot__class_Obot(tc_fun(U_1230,tc_HOL_Obool))))),U_1233),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Diff__insert]) ).
fof(f_284_2,plain,
! [U_1237,U_1236,U_1235,U_1234] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),U_1235),hAPP(hAPP(c_Set_Oinsert(U_1234),U_1236),U_1237)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),U_1235),U_1237)),hAPP(hAPP(c_Set_Oinsert(U_1234),U_1236),c_Orderings_Obot__class_Obot(tc_fun(U_1234,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_1234,U_1235,U_1236,U_1237] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),U_1235),hAPP(hAPP(c_Set_Oinsert(U_1234),U_1236),U_1237)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),U_1235),U_1237)),hAPP(hAPP(c_Set_Oinsert(U_1234),U_1236),c_Orderings_Obot__class_Obot(tc_fun(U_1234,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_284_2]) ).
cnf(f_284_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),U_1235),hAPP(hAPP(c_Set_Oinsert(U_1234),U_1236),U_1237)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1234,tc_HOL_Obool)),U_1235),U_1237)),hAPP(hAPP(c_Set_Oinsert(U_1234),U_1236),c_Orderings_Obot__class_Obot(tc_fun(U_1234,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_1,plain,
! [V_B_2,V_C_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_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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1]) ).
fof(f_285_2,plain,
! [U_1241,U_1240,U_1239,U_1238] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1238,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1238),U_1239),U_1241)),U_1240) = hAPP(hAPP(c_Set_Oinsert(U_1238),U_1239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1238,tc_HOL_Obool)),U_1241),U_1240))
| ~ hBOOL(hAPP(hAPP(c_member(U_1238),U_1239),U_1240)) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_1238,U_1239,U_1240,U_1241] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1238,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1238),U_1239),U_1241)),U_1240) = hAPP(hAPP(c_Set_Oinsert(U_1238),U_1239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1238,tc_HOL_Obool)),U_1241),U_1240))
| ~ hBOOL(hAPP(hAPP(c_member(U_1238),U_1239),U_1240)) ),
inference(definitional_conversion,[status(esa)],[f_285_2]) ).
cnf(f_285_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1238,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1238),U_1239),U_1241)),U_1240) = hAPP(hAPP(c_Set_Oinsert(U_1238),U_1239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1238,tc_HOL_Obool)),U_1241),U_1240))
| ~ hBOOL(hAPP(hAPP(c_member(U_1238),U_1239),U_1240)) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [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)),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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1]) ).
fof(f_286_2,plain,
! [U_1245,U_1244,U_1243,U_1242] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1242,tc_HOL_Obool)),U_1244),hAPP(hAPP(c_Set_Oinsert(U_1242),U_1243),U_1245)) = hAPP(hAPP(c_Set_Oinsert(U_1242),U_1243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1242,tc_HOL_Obool)),U_1244),U_1245))
| ~ hBOOL(hAPP(hAPP(c_member(U_1242),U_1243),U_1244)) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1242,U_1243,U_1244,U_1245] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1242,tc_HOL_Obool)),U_1244),hAPP(hAPP(c_Set_Oinsert(U_1242),U_1243),U_1245)) = hAPP(hAPP(c_Set_Oinsert(U_1242),U_1243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1242,tc_HOL_Obool)),U_1244),U_1245))
| ~ hBOOL(hAPP(hAPP(c_member(U_1242),U_1243),U_1244)) ),
inference(definitional_conversion,[status(esa)],[f_286_2]) ).
cnf(f_286_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1242,tc_HOL_Obool)),U_1244),hAPP(hAPP(c_Set_Oinsert(U_1242),U_1243),U_1245)) = hAPP(hAPP(c_Set_Oinsert(U_1242),U_1243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1242,tc_HOL_Obool)),U_1244),U_1245))
| ~ hBOOL(hAPP(hAPP(c_member(U_1242),U_1243),U_1244)) ),
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_1,plain,
! [V_B_2,V_C_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_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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if0]) ).
fof(f_287_2,plain,
! [U_1249,U_1248,U_1247,U_1246] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1246,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1246),U_1247),U_1249)),U_1248) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1246,tc_HOL_Obool)),U_1249),U_1248)
| hBOOL(hAPP(hAPP(c_member(U_1246),U_1247),U_1248)) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_1246,U_1247,U_1248,U_1249] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1246,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1246),U_1247),U_1249)),U_1248) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1246,tc_HOL_Obool)),U_1249),U_1248)
| hBOOL(hAPP(hAPP(c_member(U_1246),U_1247),U_1248)) ),
inference(definitional_conversion,[status(esa)],[f_287_2]) ).
cnf(f_287_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1246,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1246),U_1247),U_1249)),U_1248) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1246,tc_HOL_Obool)),U_1249),U_1248)
| hBOOL(hAPP(hAPP(c_member(U_1246),U_1247),U_1248)) ),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_1,plain,
! [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)),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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if0]) ).
fof(f_288_2,plain,
! [U_1253,U_1252,U_1251,U_1250] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1250,tc_HOL_Obool)),U_1252),hAPP(hAPP(c_Set_Oinsert(U_1250),U_1251),U_1253)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1250,tc_HOL_Obool)),U_1252),U_1253)
| hBOOL(hAPP(hAPP(c_member(U_1250),U_1251),U_1252)) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1250,U_1251,U_1252,U_1253] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1250,tc_HOL_Obool)),U_1252),hAPP(hAPP(c_Set_Oinsert(U_1250),U_1251),U_1253)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1250,tc_HOL_Obool)),U_1252),U_1253)
| hBOOL(hAPP(hAPP(c_member(U_1250),U_1251),U_1252)) ),
inference(definitional_conversion,[status(esa)],[f_288_2]) ).
cnf(f_288_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1250,tc_HOL_Obool)),U_1252),hAPP(hAPP(c_Set_Oinsert(U_1250),U_1251),U_1253)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1250,tc_HOL_Obool)),U_1252),U_1253)
| hBOOL(hAPP(hAPP(c_member(U_1250),U_1251),U_1252)) ),
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_1,plain,
! [V_B_2,V_C_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_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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left]) ).
fof(f_289_2,plain,
! [U_1257,U_1256,U_1255,U_1254] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1254,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1254),U_1255),U_1257)),U_1256) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1254,tc_HOL_Obool)),U_1257),U_1256)
| hBOOL(hAPP(hAPP(c_member(U_1254),U_1255),U_1256)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1254,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1254),U_1255),U_1257)),U_1256) = hAPP(hAPP(c_Set_Oinsert(U_1254),U_1255),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1254,tc_HOL_Obool)),U_1257),U_1256))
| ~ hBOOL(hAPP(hAPP(c_member(U_1254),U_1255),U_1256)) ) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
( ! [U_1265,U_1263,U_1261,U_1259] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1259,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1259),U_1261),U_1265)),U_1263) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1259,tc_HOL_Obool)),U_1265),U_1263)
| hBOOL(hAPP(hAPP(c_member(U_1259),U_1261),U_1263)) )
& ! [U_1264,U_1262,U_1260,U_1258] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1258,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1258),U_1260),U_1264)),U_1262) = hAPP(hAPP(c_Set_Oinsert(U_1258),U_1260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1258,tc_HOL_Obool)),U_1264),U_1262))
| ~ hBOOL(hAPP(hAPP(c_member(U_1258),U_1260),U_1262)) ) ),
inference(miniscope,[status(thm)],[f_289_2]) ).
fof(f_289_4,plain,
( ! [U_1259,U_1261,U_1263,U_1265] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1259,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1259),U_1261),U_1265)),U_1263) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1259,tc_HOL_Obool)),U_1265),U_1263)
| hBOOL(hAPP(hAPP(c_member(U_1259),U_1261),U_1263)) )
& ! [U_1260,U_1264,U_1258,U_1262] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1258,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1258),U_1260),U_1264)),U_1262) = hAPP(hAPP(c_Set_Oinsert(U_1258),U_1260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1258,tc_HOL_Obool)),U_1264),U_1262))
| ~ hBOOL(hAPP(hAPP(c_member(U_1258),U_1260),U_1262)) ) ),
inference(definitional_conversion,[status(esa)],[f_289_3]) ).
cnf(f_289_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1258,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1258),U_1260),U_1264)),U_1262) = hAPP(hAPP(c_Set_Oinsert(U_1258),U_1260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1258,tc_HOL_Obool)),U_1264),U_1262))
| ~ hBOOL(hAPP(hAPP(c_member(U_1258),U_1260),U_1262)) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1259,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1259),U_1261),U_1265)),U_1263) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1259,tc_HOL_Obool)),U_1265),U_1263)
| hBOOL(hAPP(hAPP(c_member(U_1259),U_1261),U_1263)) ),
inference(clausify,[status(thm)],[f_289_4]) ).
fof(f_290_1,plain,
! [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)),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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right]) ).
fof(f_290_2,plain,
! [U_1269,U_1268,U_1267,U_1266] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1266,tc_HOL_Obool)),U_1268),hAPP(hAPP(c_Set_Oinsert(U_1266),U_1267),U_1269)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1266,tc_HOL_Obool)),U_1268),U_1269)
| hBOOL(hAPP(hAPP(c_member(U_1266),U_1267),U_1268)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1266,tc_HOL_Obool)),U_1268),hAPP(hAPP(c_Set_Oinsert(U_1266),U_1267),U_1269)) = hAPP(hAPP(c_Set_Oinsert(U_1266),U_1267),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1266,tc_HOL_Obool)),U_1268),U_1269))
| ~ hBOOL(hAPP(hAPP(c_member(U_1266),U_1267),U_1268)) ) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
( ! [U_1277,U_1275,U_1273,U_1271] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1271,tc_HOL_Obool)),U_1275),hAPP(hAPP(c_Set_Oinsert(U_1271),U_1273),U_1277)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1271,tc_HOL_Obool)),U_1275),U_1277)
| hBOOL(hAPP(hAPP(c_member(U_1271),U_1273),U_1275)) )
& ! [U_1276,U_1274,U_1272,U_1270] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1270,tc_HOL_Obool)),U_1274),hAPP(hAPP(c_Set_Oinsert(U_1270),U_1272),U_1276)) = hAPP(hAPP(c_Set_Oinsert(U_1270),U_1272),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1270,tc_HOL_Obool)),U_1274),U_1276))
| ~ hBOOL(hAPP(hAPP(c_member(U_1270),U_1272),U_1274)) ) ),
inference(miniscope,[status(thm)],[f_290_2]) ).
fof(f_290_4,plain,
( ! [U_1271,U_1273,U_1275,U_1277] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1271,tc_HOL_Obool)),U_1275),hAPP(hAPP(c_Set_Oinsert(U_1271),U_1273),U_1277)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1271,tc_HOL_Obool)),U_1275),U_1277)
| hBOOL(hAPP(hAPP(c_member(U_1271),U_1273),U_1275)) )
& ! [U_1274,U_1276,U_1272,U_1270] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1270,tc_HOL_Obool)),U_1274),hAPP(hAPP(c_Set_Oinsert(U_1270),U_1272),U_1276)) = hAPP(hAPP(c_Set_Oinsert(U_1270),U_1272),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1270,tc_HOL_Obool)),U_1274),U_1276))
| ~ hBOOL(hAPP(hAPP(c_member(U_1270),U_1272),U_1274)) ) ),
inference(definitional_conversion,[status(esa)],[f_290_3]) ).
cnf(f_290_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1270,tc_HOL_Obool)),U_1274),hAPP(hAPP(c_Set_Oinsert(U_1270),U_1272),U_1276)) = hAPP(hAPP(c_Set_Oinsert(U_1270),U_1272),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1270,tc_HOL_Obool)),U_1274),U_1276))
| ~ hBOOL(hAPP(hAPP(c_member(U_1270),U_1272),U_1274)) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1271,tc_HOL_Obool)),U_1275),hAPP(hAPP(c_Set_Oinsert(U_1271),U_1273),U_1277)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1271,tc_HOL_Obool)),U_1275),U_1277)
| hBOOL(hAPP(hAPP(c_member(U_1271),U_1273),U_1275)) ),
inference(clausify,[status(thm)],[f_290_4]) ).
fof(f_291_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__UNIV]) ).
fof(f_291_2,plain,
! [U_1279,U_1278] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1278,tc_HOL_Obool)),U_1279),c_Orderings_Otop__class_Otop(tc_fun(U_1278,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1278,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_1278,U_1279] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1278,tc_HOL_Obool)),U_1279),c_Orderings_Otop__class_Otop(tc_fun(U_1278,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1278,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_291_2]) ).
cnf(f_291_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1278,tc_HOL_Obool)),U_1279),c_Orderings_Otop__class_Otop(tc_fun(U_1278,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1278,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_1,plain,
! [V_A_2,V_a_2,T_b] :
( 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))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__insert]) ).
fof(f_292_2,plain,
! [U_1282,U_1281,U_1280] :
( c_Complete__Lattice_OSup__class_OSup(U_1280,hAPP(hAPP(c_Set_Oinsert(U_1280),U_1281),U_1282)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1280),U_1281),c_Complete__Lattice_OSup__class_OSup(U_1280,U_1282))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1280) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1280,U_1281,U_1282] :
( c_Complete__Lattice_OSup__class_OSup(U_1280,hAPP(hAPP(c_Set_Oinsert(U_1280),U_1281),U_1282)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1280),U_1281),c_Complete__Lattice_OSup__class_OSup(U_1280,U_1282))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1280) ),
inference(definitional_conversion,[status(esa)],[f_292_2]) ).
cnf(f_292_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_1280,hAPP(hAPP(c_Set_Oinsert(U_1280),U_1281),U_1282)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1280),U_1281),c_Complete__Lattice_OSup__class_OSup(U_1280,U_1282))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1280) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_insert__is__Un]) ).
fof(f_293_2,plain,
! [U_1285,U_1284,U_1283] : hAPP(hAPP(c_Set_Oinsert(U_1283),U_1284),U_1285) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1283,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1283),U_1284),c_Orderings_Obot__class_Obot(tc_fun(U_1283,tc_HOL_Obool)))),U_1285),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_1283,U_1284,U_1285] : hAPP(hAPP(c_Set_Oinsert(U_1283),U_1284),U_1285) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1283,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1283),U_1284),c_Orderings_Obot__class_Obot(tc_fun(U_1283,tc_HOL_Obool)))),U_1285),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_1283),U_1284),U_1285) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1283,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1283),U_1284),c_Orderings_Obot__class_Obot(tc_fun(U_1283,tc_HOL_Obool)))),U_1285),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_1,plain,
! [V_A_2,V_a_2,T_b] :
( 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))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__insert]) ).
fof(f_294_2,plain,
! [U_1288,U_1287,U_1286] :
( c_Complete__Lattice_OInf__class_OInf(U_1286,hAPP(hAPP(c_Set_Oinsert(U_1286),U_1287),U_1288)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1286),U_1287),c_Complete__Lattice_OInf__class_OInf(U_1286,U_1288))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1286) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_1286,U_1287,U_1288] :
( c_Complete__Lattice_OInf__class_OInf(U_1286,hAPP(hAPP(c_Set_Oinsert(U_1286),U_1287),U_1288)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1286),U_1287),c_Complete__Lattice_OInf__class_OInf(U_1286,U_1288))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1286) ),
inference(definitional_conversion,[status(esa)],[f_294_2]) ).
cnf(f_294_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_1286,hAPP(hAPP(c_Set_Oinsert(U_1286),U_1287),U_1288)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1286),U_1287),c_Complete__Lattice_OInf__class_OInf(U_1286,U_1288))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1286) ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_1,plain,
! [V_A_2,V_C_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_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( 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))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) ) )
& ( ! [B_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_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_C_2)),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Union__disjoint]) ).
fof(f_295_2,plain,
! [U_1293,U_1292,U_1291] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1291,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1291,tc_HOL_Obool),U_1292)),U_1293) = c_Orderings_Obot__class_Obot(tc_fun(U_1291,tc_HOL_Obool))
| ? [U_1290] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1291,tc_HOL_Obool)),U_1290),U_1293) != c_Orderings_Obot__class_Obot(tc_fun(U_1291,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1291,tc_HOL_Obool)),U_1290),U_1292)) ) )
& ( ! [U_1289] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1291,tc_HOL_Obool)),U_1289),U_1293) = c_Orderings_Obot__class_Obot(tc_fun(U_1291,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1291,tc_HOL_Obool)),U_1289),U_1292)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1291,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1291,tc_HOL_Obool),U_1292)),U_1293) != c_Orderings_Obot__class_Obot(tc_fun(U_1291,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
( ! [U_1299,U_1297,U_1295] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1295,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1295,tc_HOL_Obool),U_1297)),U_1299) = c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
| ? [U_1290] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1295,tc_HOL_Obool)),U_1290),U_1299) != c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1295,tc_HOL_Obool)),U_1290),U_1297)) ) )
& ! [U_1298,U_1296,U_1294] :
( ! [U_1289] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1294,tc_HOL_Obool)),U_1289),U_1298) = c_Orderings_Obot__class_Obot(tc_fun(U_1294,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1294,tc_HOL_Obool)),U_1289),U_1296)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1294,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1294,tc_HOL_Obool),U_1296)),U_1298) != c_Orderings_Obot__class_Obot(tc_fun(U_1294,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_295_2]) ).
fof(f_295_4,plain,
( ! [U_1299,U_1297,U_1295] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1295,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1295,tc_HOL_Obool),U_1297)),U_1299) = c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1295,tc_HOL_Obool)),sK41(U_1299,U_1297,U_1295)),U_1299) != c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1295,tc_HOL_Obool)),sK41(U_1299,U_1297,U_1295)),U_1297)) ) )
& ! [U_1298,U_1296,U_1294] :
( ! [U_1289] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1294,tc_HOL_Obool)),U_1289),U_1298) = c_Orderings_Obot__class_Obot(tc_fun(U_1294,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1294,tc_HOL_Obool)),U_1289),U_1296)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1294,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1294,tc_HOL_Obool),U_1296)),U_1298) != c_Orderings_Obot__class_Obot(tc_fun(U_1294,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_1290,sK41(U_1299,U_1297,U_1295))],[f_295_3]) ).
fof(f_295_5,plain,
( ! [U_1299,U_1295,U_1297] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1295,tc_HOL_Obool)),sK41(U_1299,U_1297,U_1295)),U_1299) != c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
| ~ sP77(U_1299,U_1295,U_1297) )
& ! [U_1299,U_1295,U_1297] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1295,tc_HOL_Obool)),sK41(U_1299,U_1297,U_1295)),U_1297))
| ~ sP77(U_1299,U_1295,U_1297) )
& ! [U_1299,U_1295,U_1297] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1295,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1295,tc_HOL_Obool),U_1297)),U_1299) = c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
| sP77(U_1299,U_1295,U_1297) )
& ! [U_1296,U_1289,U_1294,U_1298] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1294,tc_HOL_Obool)),U_1289),U_1298) = c_Orderings_Obot__class_Obot(tc_fun(U_1294,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1294,tc_HOL_Obool)),U_1289),U_1296))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1294,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1294,tc_HOL_Obool),U_1296)),U_1298) != c_Orderings_Obot__class_Obot(tc_fun(U_1294,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_295_4]) ).
cnf(f_295_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1294,tc_HOL_Obool)),U_1289),U_1298) = c_Orderings_Obot__class_Obot(tc_fun(U_1294,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1294,tc_HOL_Obool)),U_1289),U_1296))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1294,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1294,tc_HOL_Obool),U_1296)),U_1298) != c_Orderings_Obot__class_Obot(tc_fun(U_1294,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_295_5]) ).
cnf(f_295_7,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1295,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1295,tc_HOL_Obool),U_1297)),U_1299) = c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
| sP77(U_1299,U_1295,U_1297) ),
inference(clausify,[status(thm)],[f_295_5]) ).
cnf(f_295_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1295,tc_HOL_Obool)),sK41(U_1299,U_1297,U_1295)),U_1297))
| ~ sP77(U_1299,U_1295,U_1297) ),
inference(clausify,[status(thm)],[f_295_5]) ).
cnf(f_295_9,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1295,tc_HOL_Obool)),sK41(U_1299,U_1297,U_1295)),U_1299) != c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
| ~ sP77(U_1299,U_1295,U_1297) ),
inference(clausify,[status(thm)],[f_295_5]) ).
fof(f_296_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J]) ).
fof(f_296_2,plain,
! [U_1303,U_1302,U_1301,U_1300] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1300,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1301,U_1302)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1302,U_1303)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1301,U_1303)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1300),U_1302),U_1303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1300),U_1301),U_1302))
| ~ class_Orderings_Olinorder(U_1300) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_1300,U_1302,U_1303,U_1301] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1300,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1301,U_1302)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1302,U_1303)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1301,U_1303)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1300),U_1302),U_1303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1300),U_1301),U_1302))
| ~ class_Orderings_Olinorder(U_1300) ),
inference(definitional_conversion,[status(esa)],[f_296_2]) ).
cnf(f_296_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1300,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1301,U_1302)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1302,U_1303)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1300,U_1301,U_1303)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1300),U_1302),U_1303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1300),U_1301),U_1302))
| ~ class_Orderings_Olinorder(U_1300) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J]) ).
fof(f_297_2,plain,
! [U_1307,U_1306,U_1305,U_1304] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1304,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1304,U_1305,U_1306)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1304,U_1306,U_1307)) = c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1304) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_1305,U_1306,U_1304,U_1307] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1304,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1304,U_1305,U_1306)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1304,U_1306,U_1307)) = c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1304) ),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1304,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1304,U_1305,U_1306)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1304,U_1306,U_1307)) = c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1304) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Union__insert]) ).
fof(f_298_2,plain,
! [U_1310,U_1309,U_1308] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1308,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1308,tc_HOL_Obool)),U_1309),U_1310)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1308,tc_HOL_Obool)),U_1309),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1308,tc_HOL_Obool),U_1310)),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_1308,U_1309,U_1310] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1308,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1308,tc_HOL_Obool)),U_1309),U_1310)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1308,tc_HOL_Obool)),U_1309),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1308,tc_HOL_Obool),U_1310)),
inference(definitional_conversion,[status(esa)],[f_298_2]) ).
cnf(f_298_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1308,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1308,tc_HOL_Obool)),U_1309),U_1310)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1308,tc_HOL_Obool)),U_1309),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1308,tc_HOL_Obool),U_1310)),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Inter__insert]) ).
fof(f_299_2,plain,
! [U_1313,U_1312,U_1311] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1311,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1311,tc_HOL_Obool)),U_1312),U_1313)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1311,tc_HOL_Obool)),U_1312),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1311,tc_HOL_Obool),U_1313)),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_1311,U_1312,U_1313] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1311,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1311,tc_HOL_Obool)),U_1312),U_1313)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1311,tc_HOL_Obool)),U_1312),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1311,tc_HOL_Obool),U_1313)),
inference(definitional_conversion,[status(esa)],[f_299_2]) ).
cnf(f_299_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1311,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1311,tc_HOL_Obool)),U_1312),U_1313)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1311,tc_HOL_Obool)),U_1312),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1311,tc_HOL_Obool),U_1313)),
inference(clausify,[status(thm)],[f_299_3]) ).
fof(f_300_1,plain,
! [V_A_2,V_x_2,T_b] :
( 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
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__insert__absorb]) ).
fof(f_300_2,plain,
! [U_1316,U_1315,U_1314] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1314,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1314),U_1315),U_1316)),hAPP(hAPP(c_Set_Oinsert(U_1314),U_1315),c_Orderings_Obot__class_Obot(tc_fun(U_1314,tc_HOL_Obool)))) = U_1316
| hBOOL(hAPP(hAPP(c_member(U_1314),U_1315),U_1316)) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_1314,U_1315,U_1316] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1314,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1314),U_1315),U_1316)),hAPP(hAPP(c_Set_Oinsert(U_1314),U_1315),c_Orderings_Obot__class_Obot(tc_fun(U_1314,tc_HOL_Obool)))) = U_1316
| hBOOL(hAPP(hAPP(c_member(U_1314),U_1315),U_1316)) ),
inference(definitional_conversion,[status(esa)],[f_300_2]) ).
cnf(f_300_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1314,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1314),U_1315),U_1316)),hAPP(hAPP(c_Set_Oinsert(U_1314),U_1315),c_Orderings_Obot__class_Obot(tc_fun(U_1314,tc_HOL_Obool)))) = U_1316
| hBOOL(hAPP(hAPP(c_member(U_1314),U_1315),U_1316)) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_1,plain,
! [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))))) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff]) ).
fof(f_301_2,plain,
! [U_1319,U_1318,U_1317] :
( hAPP(hAPP(c_Set_Oinsert(U_1317),U_1318),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1317,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1317),U_1318),c_Orderings_Obot__class_Obot(tc_fun(U_1317,tc_HOL_Obool))))) = U_1319
| ~ hBOOL(hAPP(hAPP(c_member(U_1317),U_1318),U_1319)) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_1317,U_1318,U_1319] :
( hAPP(hAPP(c_Set_Oinsert(U_1317),U_1318),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1317,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1317),U_1318),c_Orderings_Obot__class_Obot(tc_fun(U_1317,tc_HOL_Obool))))) = U_1319
| ~ hBOOL(hAPP(hAPP(c_member(U_1317),U_1318),U_1319)) ),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_1317),U_1318),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1317,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1317),U_1318),c_Orderings_Obot__class_Obot(tc_fun(U_1317,tc_HOL_Obool))))) = U_1319
| ~ hBOOL(hAPP(hAPP(c_member(U_1317),U_1318),U_1319)) ),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_1,plain,
! [V_b_2,V_a_2,T_b] :
( 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)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__binary]) ).
fof(f_302_2,plain,
! [U_1322,U_1321,U_1320] :
( c_Complete__Lattice_OSup__class_OSup(U_1320,hAPP(hAPP(c_Set_Oinsert(U_1320),U_1321),hAPP(hAPP(c_Set_Oinsert(U_1320),U_1322),c_Orderings_Obot__class_Obot(tc_fun(U_1320,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1320),U_1321),U_1322)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1320) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_1320,U_1321,U_1322] :
( c_Complete__Lattice_OSup__class_OSup(U_1320,hAPP(hAPP(c_Set_Oinsert(U_1320),U_1321),hAPP(hAPP(c_Set_Oinsert(U_1320),U_1322),c_Orderings_Obot__class_Obot(tc_fun(U_1320,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1320),U_1321),U_1322)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1320) ),
inference(definitional_conversion,[status(esa)],[f_302_2]) ).
cnf(f_302_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_1320,hAPP(hAPP(c_Set_Oinsert(U_1320),U_1321),hAPP(hAPP(c_Set_Oinsert(U_1320),U_1322),c_Orderings_Obot__class_Obot(tc_fun(U_1320,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1320),U_1321),U_1322)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1320) ),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_1,plain,
! [V_b_2,V_a_2,T_b] :
( 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)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__binary]) ).
fof(f_303_2,plain,
! [U_1325,U_1324,U_1323] :
( c_Complete__Lattice_OInf__class_OInf(U_1323,hAPP(hAPP(c_Set_Oinsert(U_1323),U_1324),hAPP(hAPP(c_Set_Oinsert(U_1323),U_1325),c_Orderings_Obot__class_Obot(tc_fun(U_1323,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1323),U_1324),U_1325)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1323) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
! [U_1323,U_1324,U_1325] :
( c_Complete__Lattice_OInf__class_OInf(U_1323,hAPP(hAPP(c_Set_Oinsert(U_1323),U_1324),hAPP(hAPP(c_Set_Oinsert(U_1323),U_1325),c_Orderings_Obot__class_Obot(tc_fun(U_1323,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1323),U_1324),U_1325)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1323) ),
inference(definitional_conversion,[status(esa)],[f_303_2]) ).
cnf(f_303_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_1323,hAPP(hAPP(c_Set_Oinsert(U_1323),U_1324),hAPP(hAPP(c_Set_Oinsert(U_1323),U_1325),c_Orderings_Obot__class_Obot(tc_fun(U_1323,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1323),U_1324),U_1325)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1323) ),
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_1,plain,
! [V_k_2,T_b] :
( 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)))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan]) ).
fof(f_304_2,plain,
! [U_1327,U_1326] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1326,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1326),U_1327),c_Orderings_Obot__class_Obot(tc_fun(U_1326,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_1326),U_1327)) = hAPP(hAPP(c_Set_Oinsert(U_1326),U_1327),c_Orderings_Obot__class_Obot(tc_fun(U_1326,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1326) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_1326,U_1327] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1326,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1326),U_1327),c_Orderings_Obot__class_Obot(tc_fun(U_1326,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_1326),U_1327)) = hAPP(hAPP(c_Set_Oinsert(U_1326),U_1327),c_Orderings_Obot__class_Obot(tc_fun(U_1326,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1326) ),
inference(definitional_conversion,[status(esa)],[f_304_2]) ).
cnf(f_304_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1326,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1326),U_1327),c_Orderings_Obot__class_Obot(tc_fun(U_1326,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_1326),U_1327)) = hAPP(hAPP(c_Set_Oinsert(U_1326),U_1327),c_Orderings_Obot__class_Obot(tc_fun(U_1326,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1326) ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J]) ).
fof(f_305_2,plain,
! [U_1330,U_1329,U_1328] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1328),U_1329)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1328,U_1329,U_1330)) = hAPP(c_SetInterval_Oord__class_OatMost(U_1328),U_1330)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1328),U_1329),U_1330))
| ~ class_Orderings_Olinorder(U_1328) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
! [U_1328,U_1329,U_1330] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1328),U_1329)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1328,U_1329,U_1330)) = hAPP(c_SetInterval_Oord__class_OatMost(U_1328),U_1330)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1328),U_1329),U_1330))
| ~ class_Orderings_Olinorder(U_1328) ),
inference(definitional_conversion,[status(esa)],[f_305_2]) ).
cnf(f_305_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1328),U_1329)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1328,U_1329,U_1330)) = hAPP(c_SetInterval_Oord__class_OatMost(U_1328),U_1330)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1328),U_1329),U_1330))
| ~ class_Orderings_Olinorder(U_1328) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J]) ).
fof(f_306_2,plain,
! [U_1333,U_1332,U_1331] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1331,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1331),U_1332)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1331,U_1332,U_1333)) = c_Orderings_Obot__class_Obot(tc_fun(U_1331,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1331) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_1331,U_1332,U_1333] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1331,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1331),U_1332)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1331,U_1332,U_1333)) = c_Orderings_Obot__class_Obot(tc_fun(U_1331,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1331) ),
inference(definitional_conversion,[status(esa)],[f_306_2]) ).
cnf(f_306_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1331,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1331),U_1332)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1331,U_1332,U_1333)) = c_Orderings_Obot__class_Obot(tc_fun(U_1331,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1331) ),
inference(clausify,[status(thm)],[f_306_3]) ).
fof(f_307_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J]) ).
fof(f_307_2,plain,
! [U_1336,U_1335,U_1334] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1334,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1334),U_1335)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1334,U_1335,U_1336)) = c_Orderings_Obot__class_Obot(tc_fun(U_1334,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1334) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_1334,U_1335,U_1336] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1334,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1334),U_1335)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1334,U_1335,U_1336)) = c_Orderings_Obot__class_Obot(tc_fun(U_1334,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1334) ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1334,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1334),U_1335)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1334,U_1335,U_1336)) = c_Orderings_Obot__class_Obot(tc_fun(U_1334,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1334) ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J]) ).
fof(f_308_2,plain,
! [U_1340,U_1339,U_1338,U_1337] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1337,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1337,U_1338,U_1339)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1337,U_1339,U_1340)) = c_Orderings_Obot__class_Obot(tc_fun(U_1337,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1337) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
! [U_1337,U_1338,U_1339,U_1340] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1337,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1337,U_1338,U_1339)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1337,U_1339,U_1340)) = c_Orderings_Obot__class_Obot(tc_fun(U_1337,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1337) ),
inference(definitional_conversion,[status(esa)],[f_308_2]) ).
cnf(f_308_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1337,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1337,U_1338,U_1339)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1337,U_1339,U_1340)) = c_Orderings_Obot__class_Obot(tc_fun(U_1337,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1337) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_distrib__sup__le]) ).
fof(f_309_2,plain,
! [U_1344,U_1343,U_1342,U_1341] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1341),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1341),U_1343),U_1344))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1341),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),U_1343)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),U_1344))))
| ~ class_Lattices_Olattice(U_1341) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_1341,U_1342,U_1343,U_1344] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1341),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1341),U_1343),U_1344))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1341),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),U_1343)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),U_1344))))
| ~ class_Lattices_Olattice(U_1341) ),
inference(definitional_conversion,[status(esa)],[f_309_2]) ).
cnf(f_309_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1341),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1341),U_1343),U_1344))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1341),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),U_1343)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1341),U_1342),U_1344))))
| ~ class_Lattices_Olattice(U_1341) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_distrib__inf__le]) ).
fof(f_310_2,plain,
! [U_1348,U_1347,U_1346,U_1345] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1345),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1345),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),U_1347)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),U_1348))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1345),U_1347),U_1348))))
| ~ class_Lattices_Olattice(U_1345) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_1345,U_1346,U_1347,U_1348] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1345),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1345),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),U_1347)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),U_1348))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1345),U_1347),U_1348))))
| ~ class_Lattices_Olattice(U_1345) ),
inference(definitional_conversion,[status(esa)],[f_310_2]) ).
cnf(f_310_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1345),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1345),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),U_1347)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),U_1348))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1345),U_1346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1345),U_1347),U_1348))))
| ~ class_Lattices_Olattice(U_1345) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
| ~ class_Groups_Ominus(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).
fof(f_311_2,plain,
! [U_1353,U_1352,U_1351,U_1350,U_1349] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1350,U_1349)),U_1351),U_1352),U_1353) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1349),hAPP(U_1351,U_1353)),hAPP(U_1352,U_1353))
| ~ class_Groups_Ominus(U_1349) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
! [U_1349,U_1350,U_1351,U_1352,U_1353] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1350,U_1349)),U_1351),U_1352),U_1353) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1349),hAPP(U_1351,U_1353)),hAPP(U_1352,U_1353))
| ~ class_Groups_Ominus(U_1349) ),
inference(definitional_conversion,[status(esa)],[f_311_2]) ).
cnf(f_311_4,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1350,U_1349)),U_1351),U_1352),U_1353) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1349),hAPP(U_1351,U_1353)),hAPP(U_1352,U_1353))
| ~ class_Groups_Ominus(U_1349) ),
inference(clausify,[status(thm)],[f_311_3]) ).
fof(f_312_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( 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))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__apply]) ).
fof(f_312_2,plain,
! [U_1358,U_1357,U_1356,U_1355,U_1354] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1355,U_1354)),U_1356),U_1357),U_1358) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1354),hAPP(U_1356,U_1358)),hAPP(U_1357,U_1358))
| ~ class_Lattices_Olattice(U_1354) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
! [U_1354,U_1355,U_1356,U_1357,U_1358] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1355,U_1354)),U_1356),U_1357),U_1358) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1354),hAPP(U_1356,U_1358)),hAPP(U_1357,U_1358))
| ~ class_Lattices_Olattice(U_1354) ),
inference(definitional_conversion,[status(esa)],[f_312_2]) ).
cnf(f_312_4,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1355,U_1354)),U_1356),U_1357),U_1358) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1354),hAPP(U_1356,U_1358)),hAPP(U_1357,U_1358))
| ~ class_Lattices_Olattice(U_1354) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( 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))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__apply]) ).
fof(f_313_2,plain,
! [U_1363,U_1362,U_1361,U_1360,U_1359] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1360,U_1359)),U_1361),U_1362),U_1363) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1359),hAPP(U_1361,U_1363)),hAPP(U_1362,U_1363))
| ~ class_Lattices_Olattice(U_1359) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
! [U_1359,U_1360,U_1361,U_1362,U_1363] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1360,U_1359)),U_1361),U_1362),U_1363) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1359),hAPP(U_1361,U_1363)),hAPP(U_1362,U_1363))
| ~ class_Lattices_Olattice(U_1359) ),
inference(definitional_conversion,[status(esa)],[f_313_2]) ).
cnf(f_313_4,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1360,U_1359)),U_1361),U_1362),U_1363) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1359),hAPP(U_1361,U_1363)),hAPP(U_1362,U_1363))
| ~ class_Lattices_Olattice(U_1359) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x
| ~ class_Lattices_Obounded__lattice__top(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__top__left]) ).
fof(f_314_2,plain,
! [U_1365,U_1364] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1364),c_Orderings_Otop__class_Otop(U_1364)),U_1365) = U_1365
| ~ class_Lattices_Obounded__lattice__top(U_1364) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
! [U_1365,U_1364] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1364),c_Orderings_Otop__class_Otop(U_1364)),U_1365) = U_1365
| ~ class_Lattices_Obounded__lattice__top(U_1364) ),
inference(definitional_conversion,[status(esa)],[f_314_2]) ).
cnf(f_314_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1364),c_Orderings_Otop__class_Otop(U_1364)),U_1365) = U_1365
| ~ class_Lattices_Obounded__lattice__top(U_1364) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x
| ~ class_Lattices_Obounded__lattice__top(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__top__right]) ).
fof(f_315_2,plain,
! [U_1367,U_1366] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1366),U_1367),c_Orderings_Otop__class_Otop(U_1366)) = U_1367
| ~ class_Lattices_Obounded__lattice__top(U_1366) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
! [U_1366,U_1367] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1366),U_1367),c_Orderings_Otop__class_Otop(U_1366)) = U_1367
| ~ class_Lattices_Obounded__lattice__top(U_1366) ),
inference(definitional_conversion,[status(esa)],[f_315_2]) ).
cnf(f_315_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1366),U_1367),c_Orderings_Otop__class_Otop(U_1366)) = U_1367
| ~ class_Lattices_Obounded__lattice__top(U_1366) ),
inference(clausify,[status(thm)],[f_315_3]) ).
fof(f_316_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
| V_y_2 != c_Orderings_Otop__class_Otop(T_b)
| V_x_2 != c_Orderings_Otop__class_Otop(T_b) )
& ( ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
& V_x_2 = c_Orderings_Otop__class_Otop(T_b) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) != c_Orderings_Otop__class_Otop(T_b) ) )
| ~ class_Lattices_Obounded__lattice__top(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff]) ).
fof(f_316_2,plain,
! [U_1370,U_1369,U_1368] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1368),U_1369),U_1370) = c_Orderings_Otop__class_Otop(U_1368)
| U_1370 != c_Orderings_Otop__class_Otop(U_1368)
| U_1369 != c_Orderings_Otop__class_Otop(U_1368) )
& ( ( U_1370 = c_Orderings_Otop__class_Otop(U_1368)
& U_1369 = c_Orderings_Otop__class_Otop(U_1368) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1368),U_1369),U_1370) != c_Orderings_Otop__class_Otop(U_1368) ) )
| ~ class_Lattices_Obounded__lattice__top(U_1368) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
( ! [U_1368,U_1369,U_1370] :
( U_1370 = c_Orderings_Otop__class_Otop(U_1368)
| ~ sP78(U_1368,U_1369,U_1370) )
& ! [U_1368,U_1369,U_1370] :
( U_1369 = c_Orderings_Otop__class_Otop(U_1368)
| ~ sP78(U_1368,U_1369,U_1370) )
& ! [U_1368,U_1369,U_1370] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1368),U_1369),U_1370) = c_Orderings_Otop__class_Otop(U_1368)
| U_1370 != c_Orderings_Otop__class_Otop(U_1368)
| U_1369 != c_Orderings_Otop__class_Otop(U_1368)
| ~ sP79(U_1368,U_1369,U_1370) )
& ! [U_1368,U_1369,U_1370] :
( sP78(U_1368,U_1369,U_1370)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1368),U_1369),U_1370) != c_Orderings_Otop__class_Otop(U_1368)
| ~ sP79(U_1368,U_1369,U_1370) )
& ! [U_1368,U_1369,U_1370] :
( sP79(U_1368,U_1369,U_1370)
| ~ class_Lattices_Obounded__lattice__top(U_1368) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78,sP79])],[f_316_2]) ).
cnf(f_316_4,plain,
( sP79(U_1368,U_1369,U_1370)
| ~ class_Lattices_Obounded__lattice__top(U_1368) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_5,plain,
( sP78(U_1368,U_1369,U_1370)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1368),U_1369),U_1370) != c_Orderings_Otop__class_Otop(U_1368)
| ~ sP79(U_1368,U_1369,U_1370) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1368),U_1369),U_1370) = c_Orderings_Otop__class_Otop(U_1368)
| U_1370 != c_Orderings_Otop__class_Otop(U_1368)
| U_1369 != c_Orderings_Otop__class_Otop(U_1368)
| ~ sP79(U_1368,U_1369,U_1370) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_7,plain,
( U_1369 = c_Orderings_Otop__class_Otop(U_1368)
| ~ sP78(U_1368,U_1369,U_1370) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_8,plain,
( U_1370 = c_Orderings_Otop__class_Otop(U_1368)
| ~ sP78(U_1368,U_1369,U_1370) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Lattices_Obounded__lattice__top(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__top__left]) ).
fof(f_317_2,plain,
! [U_1372,U_1371] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1371),c_Orderings_Otop__class_Otop(U_1371)),U_1372) = c_Orderings_Otop__class_Otop(U_1371)
| ~ class_Lattices_Obounded__lattice__top(U_1371) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
! [U_1372,U_1371] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1371),c_Orderings_Otop__class_Otop(U_1371)),U_1372) = c_Orderings_Otop__class_Otop(U_1371)
| ~ class_Lattices_Obounded__lattice__top(U_1371) ),
inference(definitional_conversion,[status(esa)],[f_317_2]) ).
cnf(f_317_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1371),c_Orderings_Otop__class_Otop(U_1371)),U_1372) = c_Orderings_Otop__class_Otop(U_1371)
| ~ class_Lattices_Obounded__lattice__top(U_1371) ),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Lattices_Obounded__lattice__top(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__top__right]) ).
fof(f_318_2,plain,
! [U_1374,U_1373] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1373),U_1374),c_Orderings_Otop__class_Otop(U_1373)) = c_Orderings_Otop__class_Otop(U_1373)
| ~ class_Lattices_Obounded__lattice__top(U_1373) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
! [U_1373,U_1374] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1373),U_1374),c_Orderings_Otop__class_Otop(U_1373)) = c_Orderings_Otop__class_Otop(U_1373)
| ~ class_Lattices_Obounded__lattice__top(U_1373) ),
inference(definitional_conversion,[status(esa)],[f_318_2]) ).
cnf(f_318_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1373),U_1374),c_Orderings_Otop__class_Otop(U_1373)) = c_Orderings_Otop__class_Otop(U_1373)
| ~ class_Lattices_Obounded__lattice__top(U_1373) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_1,plain,
! [V_y,V_x,T_a] :
( 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
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb]) ).
fof(f_319_2,plain,
! [U_1377,U_1376,U_1375] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1375),U_1376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1375),U_1376),U_1377)) = U_1376
| ~ class_Lattices_Olattice(U_1375) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_1375,U_1376,U_1377] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1375),U_1376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1375),U_1376),U_1377)) = U_1376
| ~ class_Lattices_Olattice(U_1375) ),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1375),U_1376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1375),U_1376),U_1377)) = U_1376
| ~ class_Lattices_Olattice(U_1375) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__assoc]) ).
fof(f_320_2,plain,
! [U_1381,U_1380,U_1379,U_1378] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1379),U_1380)),U_1381) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1379),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1380),U_1381))
| ~ class_Lattices_Osemilattice__sup(U_1378) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_1378,U_1379,U_1380,U_1381] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1379),U_1380)),U_1381) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1379),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1380),U_1381))
| ~ class_Lattices_Osemilattice__sup(U_1378) ),
inference(definitional_conversion,[status(esa)],[f_320_2]) ).
cnf(f_320_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1379),U_1380)),U_1381) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1379),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1378),U_1380),U_1381))
| ~ class_Lattices_Osemilattice__sup(U_1378) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J]) ).
fof(f_321_2,plain,
! [U_1385,U_1384,U_1383,U_1382] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1383),U_1384)),U_1385) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1383),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1384),U_1385))
| ~ class_Lattices_Olattice(U_1382) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
! [U_1382,U_1383,U_1384,U_1385] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1383),U_1384)),U_1385) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1383),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1384),U_1385))
| ~ class_Lattices_Olattice(U_1382) ),
inference(definitional_conversion,[status(esa)],[f_321_2]) ).
cnf(f_321_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1383),U_1384)),U_1385) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1383),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1382),U_1384),U_1385))
| ~ class_Lattices_Olattice(U_1382) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup_Oassoc]) ).
fof(f_322_2,plain,
! [U_1389,U_1388,U_1387,U_1386] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1387),U_1388)),U_1389) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1387),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1388),U_1389))
| ~ class_Lattices_Osemilattice__sup(U_1386) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
! [U_1386,U_1387,U_1388,U_1389] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1387),U_1388)),U_1389) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1387),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1388),U_1389))
| ~ class_Lattices_Osemilattice__sup(U_1386) ),
inference(definitional_conversion,[status(esa)],[f_322_2]) ).
cnf(f_322_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1387),U_1388)),U_1389) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1387),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1386),U_1388),U_1389))
| ~ class_Lattices_Osemilattice__sup(U_1386) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__left__commute]) ).
fof(f_323_2,plain,
! [U_1393,U_1392,U_1391,U_1390] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1391),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1392),U_1393)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1392),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1391),U_1393))
| ~ class_Lattices_Osemilattice__sup(U_1390) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
! [U_1390,U_1391,U_1392,U_1393] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1391),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1392),U_1393)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1392),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1391),U_1393))
| ~ class_Lattices_Osemilattice__sup(U_1390) ),
inference(definitional_conversion,[status(esa)],[f_323_2]) ).
cnf(f_323_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1391),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1392),U_1393)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1392),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1390),U_1391),U_1393))
| ~ class_Lattices_Osemilattice__sup(U_1390) ),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J]) ).
fof(f_324_2,plain,
! [U_1397,U_1396,U_1395,U_1394] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1396),U_1397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1395),U_1397))
| ~ class_Lattices_Olattice(U_1394) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
! [U_1394,U_1395,U_1396,U_1397] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1396),U_1397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1395),U_1397))
| ~ class_Lattices_Olattice(U_1394) ),
inference(definitional_conversion,[status(esa)],[f_324_2]) ).
cnf(f_324_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1396),U_1397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1394),U_1395),U_1397))
| ~ class_Lattices_Olattice(U_1394) ),
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute]) ).
fof(f_325_2,plain,
! [U_1401,U_1400,U_1399,U_1398] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1399),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1400),U_1401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1399),U_1401))
| ~ class_Lattices_Osemilattice__sup(U_1398) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1398,U_1399,U_1400,U_1401] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1399),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1400),U_1401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1399),U_1401))
| ~ class_Lattices_Osemilattice__sup(U_1398) ),
inference(definitional_conversion,[status(esa)],[f_325_2]) ).
cnf(f_325_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1399),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1400),U_1401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1398),U_1399),U_1401))
| ~ class_Lattices_Osemilattice__sup(U_1398) ),
inference(clausify,[status(thm)],[f_325_3]) ).
fof(f_326_1,plain,
! [V_y,V_x,T_a] :
( 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)
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__left__idem]) ).
fof(f_326_2,plain,
! [U_1404,U_1403,U_1402] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),U_1404)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),U_1404)
| ~ class_Lattices_Osemilattice__sup(U_1402) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1403,U_1402,U_1404] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),U_1404)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),U_1404)
| ~ class_Lattices_Osemilattice__sup(U_1402) ),
inference(definitional_conversion,[status(esa)],[f_326_2]) ).
cnf(f_326_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),U_1404)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1402),U_1403),U_1404)
| ~ class_Lattices_Osemilattice__sup(U_1402) ),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_1,plain,
! [V_y,V_x,T_a] :
( 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)
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J]) ).
fof(f_327_2,plain,
! [U_1407,U_1406,U_1405] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),U_1407)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),U_1407)
| ~ class_Lattices_Olattice(U_1405) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_1405,U_1406,U_1407] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),U_1407)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),U_1407)
| ~ class_Lattices_Olattice(U_1405) ),
inference(definitional_conversion,[status(esa)],[f_327_2]) ).
cnf(f_327_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),U_1407)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1405),U_1406),U_1407)
| ~ class_Lattices_Olattice(U_1405) ),
inference(clausify,[status(thm)],[f_327_3]) ).
fof(f_328_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem]) ).
fof(f_328_2,plain,
! [U_1410,U_1409,U_1408] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),U_1410)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),U_1410)
| ~ class_Lattices_Osemilattice__sup(U_1408) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
! [U_1408,U_1409,U_1410] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),U_1410)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),U_1410)
| ~ class_Lattices_Osemilattice__sup(U_1408) ),
inference(definitional_conversion,[status(esa)],[f_328_2]) ).
cnf(f_328_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),U_1410)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1408),U_1409),U_1410)
| ~ class_Lattices_Osemilattice__sup(U_1408) ),
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_1,plain,
! [V_y,V_x,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_y),V_x)
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__commute]) ).
fof(f_329_2,plain,
! [U_1413,U_1412,U_1411] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1411),U_1412),U_1413) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1411),U_1413),U_1412)
| ~ class_Lattices_Osemilattice__sup(U_1411) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
! [U_1411,U_1412,U_1413] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1411),U_1412),U_1413) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1411),U_1413),U_1412)
| ~ class_Lattices_Osemilattice__sup(U_1411) ),
inference(definitional_conversion,[status(esa)],[f_329_2]) ).
cnf(f_329_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1411),U_1412),U_1413) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1411),U_1413),U_1412)
| ~ class_Lattices_Osemilattice__sup(U_1411) ),
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_1,plain,
! [V_y,V_x,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_y),V_x)
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J]) ).
fof(f_330_2,plain,
! [U_1416,U_1415,U_1414] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1414),U_1415),U_1416) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1414),U_1416),U_1415)
| ~ class_Lattices_Olattice(U_1414) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
! [U_1414,U_1415,U_1416] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1414),U_1415),U_1416) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1414),U_1416),U_1415)
| ~ class_Lattices_Olattice(U_1414) ),
inference(definitional_conversion,[status(esa)],[f_330_2]) ).
cnf(f_330_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1414),U_1415),U_1416) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1414),U_1416),U_1415)
| ~ class_Lattices_Olattice(U_1414) ),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_1,plain,
! [V_b,V_a,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_b),V_a)
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup_Ocommute]) ).
fof(f_331_2,plain,
! [U_1419,U_1418,U_1417] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1417),U_1418),U_1419) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1417),U_1419),U_1418)
| ~ class_Lattices_Osemilattice__sup(U_1417) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_1417,U_1418,U_1419] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1417),U_1418),U_1419) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1417),U_1419),U_1418)
| ~ class_Lattices_Osemilattice__sup(U_1417) ),
inference(definitional_conversion,[status(esa)],[f_331_2]) ).
cnf(f_331_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1417),U_1418),U_1419) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1417),U_1419),U_1418)
| ~ class_Lattices_Osemilattice__sup(U_1417) ),
inference(clausify,[status(thm)],[f_331_3]) ).
fof(f_332_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__idem]) ).
fof(f_332_2,plain,
! [U_1421,U_1420] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1420),U_1421),U_1421) = U_1421
| ~ class_Lattices_Osemilattice__sup(U_1420) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_1420,U_1421] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1420),U_1421),U_1421) = U_1421
| ~ class_Lattices_Osemilattice__sup(U_1420) ),
inference(definitional_conversion,[status(esa)],[f_332_2]) ).
cnf(f_332_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1420),U_1421),U_1421) = U_1421
| ~ class_Lattices_Osemilattice__sup(U_1420) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup_Oidem]) ).
fof(f_333_2,plain,
! [U_1423,U_1422] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1422),U_1423),U_1423) = U_1423
| ~ class_Lattices_Osemilattice__sup(U_1422) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_1422,U_1423] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1422),U_1423),U_1423) = U_1423
| ~ class_Lattices_Osemilattice__sup(U_1422) ),
inference(definitional_conversion,[status(esa)],[f_333_2]) ).
cnf(f_333_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1422),U_1423),U_1423) = U_1423
| ~ class_Lattices_Osemilattice__sup(U_1422) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__assoc]) ).
fof(f_334_2,plain,
! [U_1427,U_1426,U_1425,U_1424] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1425),U_1426)),U_1427) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1425),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1426),U_1427))
| ~ class_Lattices_Osemilattice__inf(U_1424) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1424,U_1425,U_1426,U_1427] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1425),U_1426)),U_1427) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1425),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1426),U_1427))
| ~ class_Lattices_Osemilattice__inf(U_1424) ),
inference(definitional_conversion,[status(esa)],[f_334_2]) ).
cnf(f_334_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1425),U_1426)),U_1427) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1425),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1424),U_1426),U_1427))
| ~ class_Lattices_Osemilattice__inf(U_1424) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J]) ).
fof(f_335_2,plain,
! [U_1431,U_1430,U_1429,U_1428] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1429),U_1430)),U_1431) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1429),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1430),U_1431))
| ~ class_Lattices_Olattice(U_1428) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_1428,U_1429,U_1430,U_1431] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1429),U_1430)),U_1431) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1429),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1430),U_1431))
| ~ class_Lattices_Olattice(U_1428) ),
inference(definitional_conversion,[status(esa)],[f_335_2]) ).
cnf(f_335_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1429),U_1430)),U_1431) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1429),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1428),U_1430),U_1431))
| ~ class_Lattices_Olattice(U_1428) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf_Oassoc]) ).
fof(f_336_2,plain,
! [U_1435,U_1434,U_1433,U_1432] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1433),U_1434)),U_1435) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1433),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1434),U_1435))
| ~ class_Lattices_Osemilattice__inf(U_1432) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_1432,U_1433,U_1434,U_1435] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1433),U_1434)),U_1435) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1433),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1434),U_1435))
| ~ class_Lattices_Osemilattice__inf(U_1432) ),
inference(definitional_conversion,[status(esa)],[f_336_2]) ).
cnf(f_336_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1433),U_1434)),U_1435) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1433),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1432),U_1434),U_1435))
| ~ class_Lattices_Osemilattice__inf(U_1432) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__left__commute]) ).
fof(f_337_2,plain,
! [U_1439,U_1438,U_1437,U_1436] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1437),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1438),U_1439)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1438),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1437),U_1439))
| ~ class_Lattices_Osemilattice__inf(U_1436) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_1436,U_1437,U_1438,U_1439] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1437),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1438),U_1439)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1438),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1437),U_1439))
| ~ class_Lattices_Osemilattice__inf(U_1436) ),
inference(definitional_conversion,[status(esa)],[f_337_2]) ).
cnf(f_337_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1437),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1438),U_1439)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1438),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1436),U_1437),U_1439))
| ~ class_Lattices_Osemilattice__inf(U_1436) ),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J]) ).
fof(f_338_2,plain,
! [U_1443,U_1442,U_1441,U_1440] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1441),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1442),U_1443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1442),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1441),U_1443))
| ~ class_Lattices_Olattice(U_1440) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1440,U_1441,U_1442,U_1443] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1441),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1442),U_1443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1442),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1441),U_1443))
| ~ class_Lattices_Olattice(U_1440) ),
inference(definitional_conversion,[status(esa)],[f_338_2]) ).
cnf(f_338_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1441),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1442),U_1443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1442),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1440),U_1441),U_1443))
| ~ class_Lattices_Olattice(U_1440) ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute]) ).
fof(f_339_2,plain,
! [U_1447,U_1446,U_1445,U_1444] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1445),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1446),U_1447)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1446),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1445),U_1447))
| ~ class_Lattices_Osemilattice__inf(U_1444) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
! [U_1444,U_1445,U_1446,U_1447] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1445),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1446),U_1447)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1446),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1445),U_1447))
| ~ class_Lattices_Osemilattice__inf(U_1444) ),
inference(definitional_conversion,[status(esa)],[f_339_2]) ).
cnf(f_339_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1445),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1446),U_1447)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1446),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1444),U_1445),U_1447))
| ~ class_Lattices_Osemilattice__inf(U_1444) ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_1,plain,
! [V_y,V_x,T_a] :
( 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)
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__left__idem]) ).
fof(f_340_2,plain,
! [U_1450,U_1449,U_1448] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),U_1450)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),U_1450)
| ~ class_Lattices_Osemilattice__inf(U_1448) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
! [U_1449,U_1448,U_1450] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),U_1450)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),U_1450)
| ~ class_Lattices_Osemilattice__inf(U_1448) ),
inference(definitional_conversion,[status(esa)],[f_340_2]) ).
cnf(f_340_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),U_1450)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1448),U_1449),U_1450)
| ~ class_Lattices_Osemilattice__inf(U_1448) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_1,plain,
! [V_y,V_x,T_a] :
( 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)
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J]) ).
fof(f_341_2,plain,
! [U_1453,U_1452,U_1451] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),U_1453)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),U_1453)
| ~ class_Lattices_Olattice(U_1451) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_1451,U_1452,U_1453] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),U_1453)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),U_1453)
| ~ class_Lattices_Olattice(U_1451) ),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),U_1453)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1452),U_1453)
| ~ class_Lattices_Olattice(U_1451) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem]) ).
fof(f_342_2,plain,
! [U_1456,U_1455,U_1454] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),U_1456)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),U_1456)
| ~ class_Lattices_Osemilattice__inf(U_1454) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_1454,U_1455,U_1456] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),U_1456)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),U_1456)
| ~ class_Lattices_Osemilattice__inf(U_1454) ),
inference(definitional_conversion,[status(esa)],[f_342_2]) ).
cnf(f_342_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),U_1456)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1454),U_1455),U_1456)
| ~ class_Lattices_Osemilattice__inf(U_1454) ),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_1,plain,
! [V_y,V_x,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_y),V_x)
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__commute]) ).
fof(f_343_2,plain,
! [U_1459,U_1458,U_1457] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1457),U_1458),U_1459) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1457),U_1459),U_1458)
| ~ class_Lattices_Osemilattice__inf(U_1457) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
! [U_1457,U_1458,U_1459] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1457),U_1458),U_1459) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1457),U_1459),U_1458)
| ~ class_Lattices_Osemilattice__inf(U_1457) ),
inference(definitional_conversion,[status(esa)],[f_343_2]) ).
cnf(f_343_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1457),U_1458),U_1459) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1457),U_1459),U_1458)
| ~ class_Lattices_Osemilattice__inf(U_1457) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_1,plain,
! [V_y,V_x,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_y),V_x)
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J]) ).
fof(f_344_2,plain,
! [U_1462,U_1461,U_1460] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1460),U_1461),U_1462) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1460),U_1462),U_1461)
| ~ class_Lattices_Olattice(U_1460) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_1460,U_1461,U_1462] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1460),U_1461),U_1462) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1460),U_1462),U_1461)
| ~ class_Lattices_Olattice(U_1460) ),
inference(definitional_conversion,[status(esa)],[f_344_2]) ).
cnf(f_344_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1460),U_1461),U_1462) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1460),U_1462),U_1461)
| ~ class_Lattices_Olattice(U_1460) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_1,plain,
! [V_b,V_a,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_b),V_a)
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf_Ocommute]) ).
fof(f_345_2,plain,
! [U_1465,U_1464,U_1463] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1463),U_1464),U_1465) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1463),U_1465),U_1464)
| ~ class_Lattices_Osemilattice__inf(U_1463) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
! [U_1463,U_1464,U_1465] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1463),U_1464),U_1465) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1463),U_1465),U_1464)
| ~ class_Lattices_Osemilattice__inf(U_1463) ),
inference(definitional_conversion,[status(esa)],[f_345_2]) ).
cnf(f_345_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1463),U_1464),U_1465) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1463),U_1465),U_1464)
| ~ class_Lattices_Osemilattice__inf(U_1463) ),
inference(clausify,[status(thm)],[f_345_3]) ).
fof(f_346_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__idem]) ).
fof(f_346_2,plain,
! [U_1467,U_1466] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1466),U_1467),U_1467) = U_1467
| ~ class_Lattices_Osemilattice__inf(U_1466) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
! [U_1466,U_1467] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1466),U_1467),U_1467) = U_1467
| ~ class_Lattices_Osemilattice__inf(U_1466) ),
inference(definitional_conversion,[status(esa)],[f_346_2]) ).
cnf(f_346_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1466),U_1467),U_1467) = U_1467
| ~ class_Lattices_Osemilattice__inf(U_1466) ),
inference(clausify,[status(thm)],[f_346_3]) ).
fof(f_347_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf_Oidem]) ).
fof(f_347_2,plain,
! [U_1469,U_1468] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1468),U_1469),U_1469) = U_1469
| ~ class_Lattices_Osemilattice__inf(U_1468) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
! [U_1468,U_1469] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1468),U_1469),U_1469) = U_1469
| ~ class_Lattices_Osemilattice__inf(U_1468) ),
inference(definitional_conversion,[status(esa)],[f_347_2]) ).
cnf(f_347_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1468),U_1469),U_1469) = U_1469
| ~ class_Lattices_Osemilattice__inf(U_1468) ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_1,plain,
! [V_x,V_b,V_a,T_a] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) )
| ~ 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))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__supE]) ).
fof(f_348_2,plain,
! [U_1473,U_1472,U_1471,U_1470] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),U_1472),U_1473))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),U_1471),U_1473)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1470),U_1471),U_1472)),U_1473))
| ~ class_Lattices_Osemilattice__sup(U_1470) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
( ! [U_1470,U_1471,U_1472,U_1473] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),U_1472),U_1473))
| ~ sP80(U_1470,U_1471,U_1472,U_1473) )
& ! [U_1470,U_1471,U_1472,U_1473] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),U_1471),U_1473))
| ~ sP80(U_1470,U_1471,U_1472,U_1473) )
& ! [U_1470,U_1471,U_1472,U_1473] :
( sP80(U_1470,U_1471,U_1472,U_1473)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1470),U_1471),U_1472)),U_1473))
| ~ class_Lattices_Osemilattice__sup(U_1470) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_348_2]) ).
cnf(f_348_4,plain,
( sP80(U_1470,U_1471,U_1472,U_1473)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1470),U_1471),U_1472)),U_1473))
| ~ class_Lattices_Osemilattice__sup(U_1470) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),U_1471),U_1473))
| ~ sP80(U_1470,U_1471,U_1472,U_1473) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1470),U_1472),U_1473))
| ~ sP80(U_1470,U_1471,U_1472,U_1473) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__mono]) ).
fof(f_349_2,plain,
! [U_1478,U_1477,U_1476,U_1475,U_1474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1474),U_1475),U_1477)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1474),U_1476),U_1478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),U_1477),U_1478))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),U_1475),U_1476))
| ~ class_Lattices_Osemilattice__sup(U_1474) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
! [U_1474,U_1475,U_1476,U_1477,U_1478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1474),U_1475),U_1477)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1474),U_1476),U_1478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),U_1477),U_1478))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),U_1475),U_1476))
| ~ class_Lattices_Osemilattice__sup(U_1474) ),
inference(definitional_conversion,[status(esa)],[f_349_2]) ).
cnf(f_349_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1474),U_1475),U_1477)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1474),U_1476),U_1478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),U_1477),U_1478))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1474),U_1475),U_1476))
| ~ class_Lattices_Osemilattice__sup(U_1474) ),
inference(clausify,[status(thm)],[f_349_3]) ).
fof(f_350_1,plain,
! [V_z,V_x,V_y,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__least]) ).
fof(f_350_2,plain,
! [U_1482,U_1481,U_1480,U_1479] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1479),U_1480),U_1482)),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),U_1482),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),U_1480),U_1481))
| ~ class_Lattices_Osemilattice__sup(U_1479) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_1480,U_1479,U_1481,U_1482] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1479),U_1480),U_1482)),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),U_1482),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),U_1480),U_1481))
| ~ class_Lattices_Osemilattice__sup(U_1479) ),
inference(definitional_conversion,[status(esa)],[f_350_2]) ).
cnf(f_350_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1479),U_1480),U_1482)),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),U_1482),U_1481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1479),U_1480),U_1481))
| ~ class_Lattices_Osemilattice__sup(U_1479) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_1,plain,
! [V_b,V_x,V_a,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__supI]) ).
fof(f_351_2,plain,
! [U_1486,U_1485,U_1484,U_1483] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1483),U_1484),U_1486)),U_1485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),U_1486),U_1485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),U_1484),U_1485))
| ~ class_Lattices_Osemilattice__sup(U_1483) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
! [U_1484,U_1483,U_1485,U_1486] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1483),U_1484),U_1486)),U_1485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),U_1486),U_1485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),U_1484),U_1485))
| ~ class_Lattices_Osemilattice__sup(U_1483) ),
inference(definitional_conversion,[status(esa)],[f_351_2]) ).
cnf(f_351_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1483),U_1484),U_1486)),U_1485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),U_1486),U_1485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1483),U_1484),U_1485))
| ~ class_Lattices_Osemilattice__sup(U_1483) ),
inference(clausify,[status(thm)],[f_351_3]) ).
fof(f_352_1,plain,
! [V_x,V_y,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__absorb1]) ).
fof(f_352_2,plain,
! [U_1489,U_1488,U_1487] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1487),U_1489),U_1488) = U_1489
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1487),U_1488),U_1489))
| ~ class_Lattices_Osemilattice__sup(U_1487) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
! [U_1489,U_1488,U_1487] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1487),U_1489),U_1488) = U_1489
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1487),U_1488),U_1489))
| ~ class_Lattices_Osemilattice__sup(U_1487) ),
inference(definitional_conversion,[status(esa)],[f_352_2]) ).
cnf(f_352_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1487),U_1489),U_1488) = U_1489
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1487),U_1488),U_1489))
| ~ class_Lattices_Osemilattice__sup(U_1487) ),
inference(clausify,[status(thm)],[f_352_3]) ).
fof(f_353_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__absorb2]) ).
fof(f_353_2,plain,
! [U_1492,U_1491,U_1490] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1490),U_1491),U_1492) = U_1492
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492))
| ~ class_Lattices_Osemilattice__sup(U_1490) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
! [U_1490,U_1491,U_1492] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1490),U_1491),U_1492) = U_1492
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492))
| ~ class_Lattices_Osemilattice__sup(U_1490) ),
inference(definitional_conversion,[status(esa)],[f_353_2]) ).
cnf(f_353_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1490),U_1491),U_1492) = U_1492
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492))
| ~ class_Lattices_Osemilattice__sup(U_1490) ),
inference(clausify,[status(thm)],[f_353_3]) ).
fof(f_354_1,plain,
! [V_a,V_b,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__supI2]) ).
fof(f_354_2,plain,
! [U_1496,U_1495,U_1494,U_1493] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),U_1494),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1493),U_1496),U_1495)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),U_1494),U_1495))
| ~ class_Lattices_Osemilattice__sup(U_1493) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_1493,U_1494,U_1495,U_1496] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),U_1494),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1493),U_1496),U_1495)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),U_1494),U_1495))
| ~ class_Lattices_Osemilattice__sup(U_1493) ),
inference(definitional_conversion,[status(esa)],[f_354_2]) ).
cnf(f_354_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),U_1494),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1493),U_1496),U_1495)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),U_1494),U_1495))
| ~ class_Lattices_Osemilattice__sup(U_1493) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [V_b,V_a,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__supI1]) ).
fof(f_355_2,plain,
! [U_1500,U_1499,U_1498,U_1497] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1497),U_1498),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1497),U_1499),U_1500)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1497),U_1498),U_1499))
| ~ class_Lattices_Osemilattice__sup(U_1497) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
! [U_1497,U_1498,U_1499,U_1500] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1497),U_1498),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1497),U_1499),U_1500)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1497),U_1498),U_1499))
| ~ class_Lattices_Osemilattice__sup(U_1497) ),
inference(definitional_conversion,[status(esa)],[f_355_2]) ).
cnf(f_355_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1497),U_1498),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1497),U_1499),U_1500)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1497),U_1498),U_1499))
| ~ class_Lattices_Osemilattice__sup(U_1497) ),
inference(clausify,[status(thm)],[f_355_3]) ).
fof(f_356_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
| ~ 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)) ) )
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__sup__iff]) ).
fof(f_356_2,plain,
! [U_1504,U_1503,U_1502,U_1501] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1501),U_1502),U_1503)),U_1504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1503),U_1504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1502),U_1504)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1503),U_1504))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1502),U_1504)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1501),U_1502),U_1503)),U_1504)) ) )
| ~ class_Lattices_Osemilattice__sup(U_1501) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
( ! [U_1501,U_1502,U_1503,U_1504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1503),U_1504))
| ~ sP81(U_1501,U_1502,U_1503,U_1504) )
& ! [U_1501,U_1502,U_1503,U_1504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1502),U_1504))
| ~ sP81(U_1501,U_1502,U_1503,U_1504) )
& ! [U_1501,U_1502,U_1503,U_1504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1501),U_1502),U_1503)),U_1504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1503),U_1504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1502),U_1504))
| ~ sP82(U_1501,U_1502,U_1503,U_1504) )
& ! [U_1501,U_1502,U_1503,U_1504] :
( sP81(U_1501,U_1502,U_1503,U_1504)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1501),U_1502),U_1503)),U_1504))
| ~ sP82(U_1501,U_1502,U_1503,U_1504) )
& ! [U_1501,U_1502,U_1503,U_1504] :
( sP82(U_1501,U_1502,U_1503,U_1504)
| ~ class_Lattices_Osemilattice__sup(U_1501) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81,sP82])],[f_356_2]) ).
cnf(f_356_4,plain,
( sP82(U_1501,U_1502,U_1503,U_1504)
| ~ class_Lattices_Osemilattice__sup(U_1501) ),
inference(clausify,[status(thm)],[f_356_3]) ).
cnf(f_356_5,plain,
( sP81(U_1501,U_1502,U_1503,U_1504)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1501),U_1502),U_1503)),U_1504))
| ~ sP82(U_1501,U_1502,U_1503,U_1504) ),
inference(clausify,[status(thm)],[f_356_3]) ).
cnf(f_356_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1501),U_1502),U_1503)),U_1504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1503),U_1504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1502),U_1504))
| ~ sP82(U_1501,U_1502,U_1503,U_1504) ),
inference(clausify,[status(thm)],[f_356_3]) ).
cnf(f_356_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1502),U_1504))
| ~ sP81(U_1501,U_1502,U_1503,U_1504) ),
inference(clausify,[status(thm)],[f_356_3]) ).
cnf(f_356_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1501),U_1503),U_1504))
| ~ sP81(U_1501,U_1502,U_1503,U_1504) ),
inference(clausify,[status(thm)],[f_356_3]) ).
fof(f_357_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) != V_y_2 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__sup]) ).
fof(f_357_2,plain,
! [U_1507,U_1506,U_1505] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1505),U_1506),U_1507))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1505),U_1506),U_1507) != U_1507 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1505),U_1506),U_1507) = U_1507
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1505),U_1506),U_1507)) ) )
| ~ class_Lattices_Osemilattice__sup(U_1505) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
( ! [U_1507,U_1506,U_1505] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1505),U_1506),U_1507))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1505),U_1506),U_1507) != U_1507
| ~ sP83(U_1507,U_1506,U_1505) )
& ! [U_1507,U_1506,U_1505] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1505),U_1506),U_1507) = U_1507
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1505),U_1506),U_1507))
| ~ sP83(U_1507,U_1506,U_1505) )
& ! [U_1507,U_1506,U_1505] :
( sP83(U_1507,U_1506,U_1505)
| ~ class_Lattices_Osemilattice__sup(U_1505) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_357_2]) ).
cnf(f_357_4,plain,
( sP83(U_1507,U_1506,U_1505)
| ~ class_Lattices_Osemilattice__sup(U_1505) ),
inference(clausify,[status(thm)],[f_357_3]) ).
cnf(f_357_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1505),U_1506),U_1507) = U_1507
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1505),U_1506),U_1507))
| ~ sP83(U_1507,U_1506,U_1505) ),
inference(clausify,[status(thm)],[f_357_3]) ).
cnf(f_357_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1505),U_1506),U_1507))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1505),U_1506),U_1507) != U_1507
| ~ sP83(U_1507,U_1506,U_1505) ),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_1,plain,
! [V_x,V_y,T_a] :
( 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)))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__ge2]) ).
fof(f_358_2,plain,
! [U_1510,U_1509,U_1508] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1508),U_1509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1508),U_1510),U_1509)))
| ~ class_Lattices_Osemilattice__sup(U_1508) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
! [U_1509,U_1508,U_1510] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1508),U_1509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1508),U_1510),U_1509)))
| ~ class_Lattices_Osemilattice__sup(U_1508) ),
inference(definitional_conversion,[status(esa)],[f_358_2]) ).
cnf(f_358_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1508),U_1509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1508),U_1510),U_1509)))
| ~ class_Lattices_Osemilattice__sup(U_1508) ),
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_1,plain,
! [V_x,V_y,T_a] :
( 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)))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J]) ).
fof(f_359_2,plain,
! [U_1513,U_1512,U_1511] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1511),U_1512),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1511),U_1513),U_1512)))
| ~ class_Lattices_Olattice(U_1511) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_1511,U_1512,U_1513] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1511),U_1512),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1511),U_1513),U_1512)))
| ~ class_Lattices_Olattice(U_1511) ),
inference(definitional_conversion,[status(esa)],[f_359_2]) ).
cnf(f_359_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1511),U_1512),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1511),U_1513),U_1512)))
| ~ class_Lattices_Olattice(U_1511) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__ge1]) ).
fof(f_360_2,plain,
! [U_1516,U_1515,U_1514] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1514),U_1515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1514),U_1515),U_1516)))
| ~ class_Lattices_Osemilattice__sup(U_1514) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_1514,U_1515,U_1516] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1514),U_1515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1514),U_1515),U_1516)))
| ~ class_Lattices_Osemilattice__sup(U_1514) ),
inference(definitional_conversion,[status(esa)],[f_360_2]) ).
cnf(f_360_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1514),U_1515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1514),U_1515),U_1516)))
| ~ class_Lattices_Osemilattice__sup(U_1514) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J]) ).
fof(f_361_2,plain,
! [U_1519,U_1518,U_1517] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1517),U_1518),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),U_1518),U_1519)))
| ~ class_Lattices_Olattice(U_1517) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_1517,U_1518,U_1519] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1517),U_1518),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),U_1518),U_1519)))
| ~ class_Lattices_Olattice(U_1517) ),
inference(definitional_conversion,[status(esa)],[f_361_2]) ).
cnf(f_361_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1517),U_1518),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),U_1518),U_1519)))
| ~ class_Lattices_Olattice(U_1517) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [V_b,V_a,V_x,T_a] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) )
| ~ 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)))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__infE]) ).
fof(f_362_2,plain,
! [U_1523,U_1522,U_1521,U_1520] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),U_1523))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),U_1522)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1520),U_1522),U_1523)))
| ~ class_Lattices_Osemilattice__inf(U_1520) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
( ! [U_1520,U_1521,U_1522,U_1523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),U_1523))
| ~ sP84(U_1520,U_1521,U_1522,U_1523) )
& ! [U_1520,U_1521,U_1522,U_1523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),U_1522))
| ~ sP84(U_1520,U_1521,U_1522,U_1523) )
& ! [U_1520,U_1521,U_1522,U_1523] :
( sP84(U_1520,U_1521,U_1522,U_1523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1520),U_1522),U_1523)))
| ~ class_Lattices_Osemilattice__inf(U_1520) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_362_2]) ).
cnf(f_362_4,plain,
( sP84(U_1520,U_1521,U_1522,U_1523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1520),U_1522),U_1523)))
| ~ class_Lattices_Osemilattice__inf(U_1520) ),
inference(clausify,[status(thm)],[f_362_3]) ).
cnf(f_362_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),U_1522))
| ~ sP84(U_1520,U_1521,U_1522,U_1523) ),
inference(clausify,[status(thm)],[f_362_3]) ).
cnf(f_362_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1520),U_1521),U_1523))
| ~ sP84(U_1520,U_1521,U_1522,U_1523) ),
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__mono]) ).
fof(f_363_2,plain,
! [U_1528,U_1527,U_1526,U_1525,U_1524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1524),U_1525),U_1527)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1524),U_1526),U_1528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),U_1527),U_1528))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),U_1525),U_1526))
| ~ class_Lattices_Osemilattice__inf(U_1524) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
! [U_1524,U_1525,U_1526,U_1527,U_1528] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1524),U_1525),U_1527)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1524),U_1526),U_1528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),U_1527),U_1528))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),U_1525),U_1526))
| ~ class_Lattices_Osemilattice__inf(U_1524) ),
inference(definitional_conversion,[status(esa)],[f_363_2]) ).
cnf(f_363_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1524),U_1525),U_1527)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1524),U_1526),U_1528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),U_1527),U_1528))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1524),U_1525),U_1526))
| ~ class_Lattices_Osemilattice__inf(U_1524) ),
inference(clausify,[status(thm)],[f_363_3]) ).
fof(f_364_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__greatest]) ).
fof(f_364_2,plain,
! [U_1532,U_1531,U_1530,U_1529] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1531),U_1532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),U_1532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),U_1531))
| ~ class_Lattices_Osemilattice__inf(U_1529) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
! [U_1529,U_1530,U_1531,U_1532] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1531),U_1532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),U_1532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),U_1531))
| ~ class_Lattices_Osemilattice__inf(U_1529) ),
inference(definitional_conversion,[status(esa)],[f_364_2]) ).
cnf(f_364_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1531),U_1532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),U_1532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529),U_1530),U_1531))
| ~ class_Lattices_Osemilattice__inf(U_1529) ),
inference(clausify,[status(thm)],[f_364_3]) ).
fof(f_365_1,plain,
! [V_b,V_a,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__infI]) ).
fof(f_365_2,plain,
! [U_1536,U_1535,U_1534,U_1533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1533),U_1535),U_1536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),U_1536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),U_1535))
| ~ class_Lattices_Osemilattice__inf(U_1533) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
! [U_1533,U_1534,U_1535,U_1536] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1533),U_1535),U_1536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),U_1536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),U_1535))
| ~ class_Lattices_Osemilattice__inf(U_1533) ),
inference(definitional_conversion,[status(esa)],[f_365_2]) ).
cnf(f_365_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1533),U_1535),U_1536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),U_1536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),U_1535))
| ~ class_Lattices_Osemilattice__inf(U_1533) ),
inference(clausify,[status(thm)],[f_365_3]) ).
fof(f_366_1,plain,
! [V_x,V_y,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__absorb2]) ).
fof(f_366_2,plain,
! [U_1539,U_1538,U_1537] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1537),U_1539),U_1538) = U_1538
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1537),U_1538),U_1539))
| ~ class_Lattices_Osemilattice__inf(U_1537) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
! [U_1539,U_1538,U_1537] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1537),U_1539),U_1538) = U_1538
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1537),U_1538),U_1539))
| ~ class_Lattices_Osemilattice__inf(U_1537) ),
inference(definitional_conversion,[status(esa)],[f_366_2]) ).
cnf(f_366_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1537),U_1539),U_1538) = U_1538
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1537),U_1538),U_1539))
| ~ class_Lattices_Osemilattice__inf(U_1537) ),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__absorb1]) ).
fof(f_367_2,plain,
! [U_1542,U_1541,U_1540] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1540),U_1541),U_1542) = U_1541
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1540),U_1541),U_1542))
| ~ class_Lattices_Osemilattice__inf(U_1540) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
! [U_1540,U_1541,U_1542] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1540),U_1541),U_1542) = U_1541
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1540),U_1541),U_1542))
| ~ class_Lattices_Osemilattice__inf(U_1540) ),
inference(definitional_conversion,[status(esa)],[f_367_2]) ).
cnf(f_367_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1540),U_1541),U_1542) = U_1541
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1540),U_1541),U_1542))
| ~ class_Lattices_Osemilattice__inf(U_1540) ),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_1,plain,
! [V_a,V_x,V_b,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__infI2]) ).
fof(f_368_2,plain,
! [U_1546,U_1545,U_1544,U_1543] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1543),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1543),U_1546),U_1544)),U_1545))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1543),U_1544),U_1545))
| ~ class_Lattices_Osemilattice__inf(U_1543) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
! [U_1543,U_1544,U_1545,U_1546] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1543),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1543),U_1546),U_1544)),U_1545))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1543),U_1544),U_1545))
| ~ class_Lattices_Osemilattice__inf(U_1543) ),
inference(definitional_conversion,[status(esa)],[f_368_2]) ).
cnf(f_368_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1543),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1543),U_1546),U_1544)),U_1545))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1543),U_1544),U_1545))
| ~ class_Lattices_Osemilattice__inf(U_1543) ),
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_1,plain,
! [V_b,V_x,V_a,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__infI1]) ).
fof(f_369_2,plain,
! [U_1550,U_1549,U_1548,U_1547] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1547),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1547),U_1548),U_1550)),U_1549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1547),U_1548),U_1549))
| ~ class_Lattices_Osemilattice__inf(U_1547) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
! [U_1547,U_1548,U_1549,U_1550] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1547),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1547),U_1548),U_1550)),U_1549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1547),U_1548),U_1549))
| ~ class_Lattices_Osemilattice__inf(U_1547) ),
inference(definitional_conversion,[status(esa)],[f_369_2]) ).
cnf(f_369_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1547),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1547),U_1548),U_1550)),U_1549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1547),U_1548),U_1549))
| ~ class_Lattices_Osemilattice__inf(U_1547) ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| ~ 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))) ) )
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__inf__iff]) ).
fof(f_370_2,plain,
! [U_1554,U_1553,U_1552,U_1551] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1551),U_1553),U_1554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1553)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1554))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1553)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1551),U_1553),U_1554))) ) )
| ~ class_Lattices_Osemilattice__inf(U_1551) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
( ! [U_1551,U_1552,U_1553,U_1554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1554))
| ~ sP85(U_1551,U_1552,U_1553,U_1554) )
& ! [U_1551,U_1552,U_1553,U_1554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1553))
| ~ sP85(U_1551,U_1552,U_1553,U_1554) )
& ! [U_1551,U_1552,U_1553,U_1554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1551),U_1553),U_1554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1553))
| ~ sP86(U_1551,U_1552,U_1553,U_1554) )
& ! [U_1551,U_1552,U_1553,U_1554] :
( sP85(U_1551,U_1552,U_1553,U_1554)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1551),U_1553),U_1554)))
| ~ sP86(U_1551,U_1552,U_1553,U_1554) )
& ! [U_1551,U_1552,U_1553,U_1554] :
( sP86(U_1551,U_1552,U_1553,U_1554)
| ~ class_Lattices_Osemilattice__inf(U_1551) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85,sP86])],[f_370_2]) ).
cnf(f_370_4,plain,
( sP86(U_1551,U_1552,U_1553,U_1554)
| ~ class_Lattices_Osemilattice__inf(U_1551) ),
inference(clausify,[status(thm)],[f_370_3]) ).
cnf(f_370_5,plain,
( sP85(U_1551,U_1552,U_1553,U_1554)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1551),U_1553),U_1554)))
| ~ sP86(U_1551,U_1552,U_1553,U_1554) ),
inference(clausify,[status(thm)],[f_370_3]) ).
cnf(f_370_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1551),U_1553),U_1554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1553))
| ~ sP86(U_1551,U_1552,U_1553,U_1554) ),
inference(clausify,[status(thm)],[f_370_3]) ).
cnf(f_370_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1553))
| ~ sP85(U_1551,U_1552,U_1553,U_1554) ),
inference(clausify,[status(thm)],[f_370_3]) ).
cnf(f_370_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1551),U_1552),U_1554))
| ~ sP85(U_1551,U_1552,U_1553,U_1554) ),
inference(clausify,[status(thm)],[f_370_3]) ).
fof(f_371_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) != V_x_2 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__inf]) ).
fof(f_371_2,plain,
! [U_1557,U_1556,U_1555] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1555),U_1556),U_1557))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1555),U_1556),U_1557) != U_1556 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1555),U_1556),U_1557) = U_1556
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1555),U_1556),U_1557)) ) )
| ~ class_Lattices_Osemilattice__inf(U_1555) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
( ! [U_1555,U_1556,U_1557] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1555),U_1556),U_1557))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1555),U_1556),U_1557) != U_1556
| ~ sP87(U_1555,U_1556,U_1557) )
& ! [U_1555,U_1556,U_1557] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1555),U_1556),U_1557) = U_1556
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1555),U_1556),U_1557))
| ~ sP87(U_1555,U_1556,U_1557) )
& ! [U_1555,U_1556,U_1557] :
( sP87(U_1555,U_1556,U_1557)
| ~ class_Lattices_Osemilattice__inf(U_1555) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_371_2]) ).
cnf(f_371_4,plain,
( sP87(U_1555,U_1556,U_1557)
| ~ class_Lattices_Osemilattice__inf(U_1555) ),
inference(clausify,[status(thm)],[f_371_3]) ).
cnf(f_371_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1555),U_1556),U_1557) = U_1556
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1555),U_1556),U_1557))
| ~ sP87(U_1555,U_1556,U_1557) ),
inference(clausify,[status(thm)],[f_371_3]) ).
cnf(f_371_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1555),U_1556),U_1557))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1555),U_1556),U_1557) != U_1556
| ~ sP87(U_1555,U_1556,U_1557) ),
inference(clausify,[status(thm)],[f_371_3]) ).
fof(f_372_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__le2]) ).
fof(f_372_2,plain,
! [U_1560,U_1559,U_1558] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1558),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1558),U_1559),U_1560)),U_1560))
| ~ class_Lattices_Osemilattice__inf(U_1558) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
! [U_1558,U_1560,U_1559] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1558),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1558),U_1559),U_1560)),U_1560))
| ~ class_Lattices_Osemilattice__inf(U_1558) ),
inference(definitional_conversion,[status(esa)],[f_372_2]) ).
cnf(f_372_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1558),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1558),U_1559),U_1560)),U_1560))
| ~ class_Lattices_Osemilattice__inf(U_1558) ),
inference(clausify,[status(thm)],[f_372_3]) ).
fof(f_373_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J]) ).
fof(f_373_2,plain,
! [U_1563,U_1562,U_1561] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1561),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1561),U_1562),U_1563)),U_1563))
| ~ class_Lattices_Olattice(U_1561) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
! [U_1561,U_1562,U_1563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1561),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1561),U_1562),U_1563)),U_1563))
| ~ class_Lattices_Olattice(U_1561) ),
inference(definitional_conversion,[status(esa)],[f_373_2]) ).
cnf(f_373_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1561),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1561),U_1562),U_1563)),U_1563))
| ~ class_Lattices_Olattice(U_1561) ),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__le1]) ).
fof(f_374_2,plain,
! [U_1566,U_1565,U_1564] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1564),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1564),U_1565),U_1566)),U_1565))
| ~ class_Lattices_Osemilattice__inf(U_1564) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
! [U_1564,U_1565,U_1566] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1564),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1564),U_1565),U_1566)),U_1565))
| ~ class_Lattices_Osemilattice__inf(U_1564) ),
inference(definitional_conversion,[status(esa)],[f_374_2]) ).
cnf(f_374_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1564),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1564),U_1565),U_1566)),U_1565))
| ~ class_Lattices_Osemilattice__inf(U_1564) ),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J]) ).
fof(f_375_2,plain,
! [U_1569,U_1568,U_1567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1567),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1567),U_1568),U_1569)),U_1568))
| ~ class_Lattices_Olattice(U_1567) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
! [U_1568,U_1569,U_1567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1567),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1567),U_1568),U_1569)),U_1568))
| ~ class_Lattices_Olattice(U_1567) ),
inference(definitional_conversion,[status(esa)],[f_375_2]) ).
cnf(f_375_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1567),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1567),U_1568),U_1569)),U_1568))
| ~ class_Lattices_Olattice(U_1567) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
| V_y_2 != c_Orderings_Obot__class_Obot(T_b)
| V_x_2 != c_Orderings_Obot__class_Obot(T_b) )
& ( ( V_y_2 = c_Orderings_Obot__class_Obot(T_b)
& V_x_2 = c_Orderings_Obot__class_Obot(T_b) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) != c_Orderings_Obot__class_Obot(T_b) ) )
| ~ class_Lattices_Obounded__lattice__bot(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff]) ).
fof(f_376_2,plain,
! [U_1572,U_1571,U_1570] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1570),U_1571),U_1572) = c_Orderings_Obot__class_Obot(U_1570)
| U_1572 != c_Orderings_Obot__class_Obot(U_1570)
| U_1571 != c_Orderings_Obot__class_Obot(U_1570) )
& ( ( U_1572 = c_Orderings_Obot__class_Obot(U_1570)
& U_1571 = c_Orderings_Obot__class_Obot(U_1570) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1570),U_1571),U_1572) != c_Orderings_Obot__class_Obot(U_1570) ) )
| ~ class_Lattices_Obounded__lattice__bot(U_1570) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
( ! [U_1570,U_1571,U_1572] :
( U_1572 = c_Orderings_Obot__class_Obot(U_1570)
| ~ sP88(U_1570,U_1571,U_1572) )
& ! [U_1570,U_1571,U_1572] :
( U_1571 = c_Orderings_Obot__class_Obot(U_1570)
| ~ sP88(U_1570,U_1571,U_1572) )
& ! [U_1570,U_1571,U_1572] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1570),U_1571),U_1572) = c_Orderings_Obot__class_Obot(U_1570)
| U_1572 != c_Orderings_Obot__class_Obot(U_1570)
| U_1571 != c_Orderings_Obot__class_Obot(U_1570)
| ~ sP89(U_1570,U_1571,U_1572) )
& ! [U_1570,U_1571,U_1572] :
( sP88(U_1570,U_1571,U_1572)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1570),U_1571),U_1572) != c_Orderings_Obot__class_Obot(U_1570)
| ~ sP89(U_1570,U_1571,U_1572) )
& ! [U_1570,U_1571,U_1572] :
( sP89(U_1570,U_1571,U_1572)
| ~ class_Lattices_Obounded__lattice__bot(U_1570) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88,sP89])],[f_376_2]) ).
cnf(f_376_4,plain,
( sP89(U_1570,U_1571,U_1572)
| ~ class_Lattices_Obounded__lattice__bot(U_1570) ),
inference(clausify,[status(thm)],[f_376_3]) ).
cnf(f_376_5,plain,
( sP88(U_1570,U_1571,U_1572)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1570),U_1571),U_1572) != c_Orderings_Obot__class_Obot(U_1570)
| ~ sP89(U_1570,U_1571,U_1572) ),
inference(clausify,[status(thm)],[f_376_3]) ).
cnf(f_376_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1570),U_1571),U_1572) = c_Orderings_Obot__class_Obot(U_1570)
| U_1572 != c_Orderings_Obot__class_Obot(U_1570)
| U_1571 != c_Orderings_Obot__class_Obot(U_1570)
| ~ sP89(U_1570,U_1571,U_1572) ),
inference(clausify,[status(thm)],[f_376_3]) ).
cnf(f_376_7,plain,
( U_1571 = c_Orderings_Obot__class_Obot(U_1570)
| ~ sP88(U_1570,U_1571,U_1572) ),
inference(clausify,[status(thm)],[f_376_3]) ).
cnf(f_376_8,plain,
( U_1572 = c_Orderings_Obot__class_Obot(U_1570)
| ~ sP88(U_1570,U_1571,U_1572) ),
inference(clausify,[status(thm)],[f_376_3]) ).
fof(f_377_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x
| ~ class_Lattices_Obounded__lattice__bot(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__bot__right]) ).
fof(f_377_2,plain,
! [U_1574,U_1573] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1573),U_1574),c_Orderings_Obot__class_Obot(U_1573)) = U_1574
| ~ class_Lattices_Obounded__lattice__bot(U_1573) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
! [U_1574,U_1573] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1573),U_1574),c_Orderings_Obot__class_Obot(U_1573)) = U_1574
| ~ class_Lattices_Obounded__lattice__bot(U_1573) ),
inference(definitional_conversion,[status(esa)],[f_377_2]) ).
cnf(f_377_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1573),U_1574),c_Orderings_Obot__class_Obot(U_1573)) = U_1574
| ~ class_Lattices_Obounded__lattice__bot(U_1573) ),
inference(clausify,[status(thm)],[f_377_3]) ).
fof(f_378_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x
| ~ class_Lattices_Obounded__lattice__bot(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__bot__left]) ).
fof(f_378_2,plain,
! [U_1576,U_1575] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1575),c_Orderings_Obot__class_Obot(U_1575)),U_1576) = U_1576
| ~ class_Lattices_Obounded__lattice__bot(U_1575) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
! [U_1576,U_1575] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1575),c_Orderings_Obot__class_Obot(U_1575)),U_1576) = U_1576
| ~ class_Lattices_Obounded__lattice__bot(U_1575) ),
inference(definitional_conversion,[status(esa)],[f_378_2]) ).
cnf(f_378_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1575),c_Orderings_Obot__class_Obot(U_1575)),U_1576) = U_1576
| ~ class_Lattices_Obounded__lattice__bot(U_1575) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Lattices_Obounded__lattice__bot(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__bot__right]) ).
fof(f_379_2,plain,
! [U_1578,U_1577] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1578),c_Orderings_Obot__class_Obot(U_1577)) = c_Orderings_Obot__class_Obot(U_1577)
| ~ class_Lattices_Obounded__lattice__bot(U_1577) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_1578,U_1577] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1578),c_Orderings_Obot__class_Obot(U_1577)) = c_Orderings_Obot__class_Obot(U_1577)
| ~ class_Lattices_Obounded__lattice__bot(U_1577) ),
inference(definitional_conversion,[status(esa)],[f_379_2]) ).
cnf(f_379_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1578),c_Orderings_Obot__class_Obot(U_1577)) = c_Orderings_Obot__class_Obot(U_1577)
| ~ class_Lattices_Obounded__lattice__bot(U_1577) ),
inference(clausify,[status(thm)],[f_379_3]) ).
fof(f_380_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Lattices_Obounded__lattice__bot(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__bot__left]) ).
fof(f_380_2,plain,
! [U_1580,U_1579] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1579),c_Orderings_Obot__class_Obot(U_1579)),U_1580) = c_Orderings_Obot__class_Obot(U_1579)
| ~ class_Lattices_Obounded__lattice__bot(U_1579) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
! [U_1579,U_1580] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1579),c_Orderings_Obot__class_Obot(U_1579)),U_1580) = c_Orderings_Obot__class_Obot(U_1579)
| ~ class_Lattices_Obounded__lattice__bot(U_1579) ),
inference(definitional_conversion,[status(esa)],[f_380_2]) ).
cnf(f_380_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1579),c_Orderings_Obot__class_Obot(U_1579)),U_1580) = c_Orderings_Obot__class_Obot(U_1579)
| ~ class_Lattices_Obounded__lattice__bot(U_1579) ),
inference(clausify,[status(thm)],[f_380_3]) ).
fof(f_381_1,plain,
! [V_x,V_z,V_y,T_a] :
( 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))
| ~ class_Lattices_Odistrib__lattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2]) ).
fof(f_381_2,plain,
! [U_1584,U_1583,U_1582,U_1581] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1581),U_1582),U_1583)),U_1584) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1581),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),U_1582),U_1584)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),U_1583),U_1584))
| ~ class_Lattices_Odistrib__lattice(U_1581) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
! [U_1581,U_1582,U_1583,U_1584] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1581),U_1582),U_1583)),U_1584) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1581),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),U_1582),U_1584)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),U_1583),U_1584))
| ~ class_Lattices_Odistrib__lattice(U_1581) ),
inference(definitional_conversion,[status(esa)],[f_381_2]) ).
cnf(f_381_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1581),U_1582),U_1583)),U_1584) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1581),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),U_1582),U_1584)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1581),U_1583),U_1584))
| ~ class_Lattices_Odistrib__lattice(U_1581) ),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_1,plain,
! [V_x,V_z,V_y,T_a] :
( 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))
| ~ class_Lattices_Odistrib__lattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2]) ).
fof(f_382_2,plain,
! [U_1588,U_1587,U_1586,U_1585] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1585),U_1586),U_1587)),U_1588) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1585),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1586),U_1588)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1587),U_1588))
| ~ class_Lattices_Odistrib__lattice(U_1585) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
! [U_1585,U_1586,U_1587,U_1588] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1585),U_1586),U_1587)),U_1588) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1585),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1586),U_1588)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1587),U_1588))
| ~ class_Lattices_Odistrib__lattice(U_1585) ),
inference(definitional_conversion,[status(esa)],[f_382_2]) ).
cnf(f_382_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1585),U_1586),U_1587)),U_1588) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1585),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1586),U_1588)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1587),U_1588))
| ~ class_Lattices_Odistrib__lattice(U_1585) ),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_1,plain,
! [V_z,V_y,V_x,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))
| ~ class_Lattices_Odistrib__lattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1]) ).
fof(f_383_2,plain,
! [U_1592,U_1591,U_1590,U_1589] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1591),U_1592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),U_1591)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),U_1592))
| ~ class_Lattices_Odistrib__lattice(U_1589) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
! [U_1589,U_1590,U_1591,U_1592] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1591),U_1592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),U_1591)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),U_1592))
| ~ class_Lattices_Odistrib__lattice(U_1589) ),
inference(definitional_conversion,[status(esa)],[f_383_2]) ).
cnf(f_383_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1591),U_1592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),U_1591)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1589),U_1590),U_1592))
| ~ class_Lattices_Odistrib__lattice(U_1589) ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Odistrib__lattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1]) ).
fof(f_384_2,plain,
! [U_1596,U_1595,U_1594,U_1593] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1593),U_1595),U_1596)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1593),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),U_1595)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),U_1596))
| ~ class_Lattices_Odistrib__lattice(U_1593) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
! [U_1593,U_1594,U_1595,U_1596] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1593),U_1595),U_1596)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1593),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),U_1595)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),U_1596))
| ~ class_Lattices_Odistrib__lattice(U_1593) ),
inference(definitional_conversion,[status(esa)],[f_384_2]) ).
cnf(f_384_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1593),U_1595),U_1596)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1593),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),U_1595)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),U_1596))
| ~ class_Lattices_Odistrib__lattice(U_1593) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_1,plain,
! [V_y,V_x,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_x),V_y)) = V_x
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb]) ).
fof(f_385_2,plain,
! [U_1599,U_1598,U_1597] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1597),U_1598),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1597),U_1598),U_1599)) = U_1598
| ~ class_Lattices_Olattice(U_1597) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
! [U_1597,U_1598,U_1599] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1597),U_1598),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1597),U_1598),U_1599)) = U_1598
| ~ class_Lattices_Olattice(U_1597) ),
inference(definitional_conversion,[status(esa)],[f_385_2]) ).
cnf(f_385_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1597),U_1598),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1597),U_1598),U_1599)) = U_1598
| ~ class_Lattices_Olattice(U_1597) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
| 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_ca_2),V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).
fof(f_386_2,plain,
! [U_1604,U_1603,U_1602,U_1601,U_1600] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1601),U_1602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1603),U_1604)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1603),U_1604))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1601),U_1602)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1600),U_1601),U_1602) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1600),U_1603),U_1604)
| ~ class_Groups_Oordered__ab__group__add(U_1600) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
( ! [U_1600,U_1601,U_1602,U_1603,U_1604] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1601),U_1602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1603),U_1604))
| ~ sP90(U_1600,U_1601,U_1602,U_1603,U_1604) )
& ! [U_1600,U_1601,U_1602,U_1603,U_1604] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1603),U_1604))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1601),U_1602))
| ~ sP90(U_1600,U_1601,U_1602,U_1603,U_1604) )
& ! [U_1600,U_1601,U_1602,U_1603,U_1604] :
( sP90(U_1600,U_1601,U_1602,U_1603,U_1604)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1600),U_1601),U_1602) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1600),U_1603),U_1604)
| ~ class_Groups_Oordered__ab__group__add(U_1600) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_386_2]) ).
cnf(f_386_4,plain,
( sP90(U_1600,U_1601,U_1602,U_1603,U_1604)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1600),U_1601),U_1602) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1600),U_1603),U_1604)
| ~ class_Groups_Oordered__ab__group__add(U_1600) ),
inference(clausify,[status(thm)],[f_386_3]) ).
cnf(f_386_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1603),U_1604))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1601),U_1602))
| ~ sP90(U_1600,U_1601,U_1602,U_1603,U_1604) ),
inference(clausify,[status(thm)],[f_386_3]) ).
cnf(f_386_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1601),U_1602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1600),U_1603),U_1604))
| ~ sP90(U_1600,U_1601,U_1602,U_1603,U_1604) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_1,plain,
! [V_u_2,V_l_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_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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J]) ).
fof(f_387_2,plain,
! [U_1607,U_1606,U_1605] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1605,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1605),U_1606),c_Orderings_Obot__class_Obot(tc_fun(U_1605,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1605,U_1606,U_1607)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1605,U_1606,U_1607)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1605),U_1606),U_1607))
| ~ class_Orderings_Olinorder(U_1605) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
! [U_1605,U_1606,U_1607] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1605,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1605),U_1606),c_Orderings_Obot__class_Obot(tc_fun(U_1605,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1605,U_1606,U_1607)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1605,U_1606,U_1607)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1605),U_1606),U_1607))
| ~ class_Orderings_Olinorder(U_1605) ),
inference(definitional_conversion,[status(esa)],[f_387_2]) ).
cnf(f_387_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1605,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1605),U_1606),c_Orderings_Obot__class_Obot(tc_fun(U_1605,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1605,U_1606,U_1607)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1605,U_1606,U_1607)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1605),U_1606),U_1607))
| ~ class_Orderings_Olinorder(U_1605) ),
inference(clausify,[status(thm)],[f_387_3]) ).
fof(f_388_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J]) ).
fof(f_388_2,plain,
! [U_1610,U_1609,U_1608] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1608,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,U_1609,U_1610)),hAPP(hAPP(c_Set_Oinsert(U_1608),U_1610),c_Orderings_Obot__class_Obot(tc_fun(U_1608,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1608,U_1609,U_1610)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1608),U_1609),U_1610))
| ~ class_Orderings_Olinorder(U_1608) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
! [U_1608,U_1609,U_1610] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1608,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,U_1609,U_1610)),hAPP(hAPP(c_Set_Oinsert(U_1608),U_1610),c_Orderings_Obot__class_Obot(tc_fun(U_1608,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1608,U_1609,U_1610)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1608),U_1609),U_1610))
| ~ class_Orderings_Olinorder(U_1608) ),
inference(definitional_conversion,[status(esa)],[f_388_2]) ).
cnf(f_388_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1608,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,U_1609,U_1610)),hAPP(hAPP(c_Set_Oinsert(U_1608),U_1610),c_Orderings_Obot__class_Obot(tc_fun(U_1608,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1608,U_1609,U_1610)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1608),U_1609),U_1610))
| ~ class_Orderings_Olinorder(U_1608) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J]) ).
fof(f_389_2,plain,
! [U_1613,U_1612,U_1611] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1611,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1611,U_1612,U_1613)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1611),U_1613)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_1611),U_1612)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1611),U_1612),U_1613))
| ~ class_Orderings_Olinorder(U_1611) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
! [U_1611,U_1612,U_1613] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1611,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1611,U_1612,U_1613)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1611),U_1613)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_1611),U_1612)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1611),U_1612),U_1613))
| ~ class_Orderings_Olinorder(U_1611) ),
inference(definitional_conversion,[status(esa)],[f_389_2]) ).
cnf(f_389_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1611,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1611,U_1612,U_1613)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1611),U_1613)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_1611),U_1612)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1611),U_1612),U_1613))
| ~ class_Orderings_Olinorder(U_1611) ),
inference(clausify,[status(thm)],[f_389_3]) ).
fof(f_390_1,plain,
! [V_B_2,V_x_2,V_A_2,T_b] :
( ( 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)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
| ( ~ 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))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_psubset__insert__iff]) ).
fof(f_390_2,plain,
! [U_1617,U_1616,U_1615,U_1614] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1614,tc_HOL_Obool)),U_1615),hAPP(hAPP(c_Set_Oinsert(U_1614),U_1616),U_1617)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1614,tc_HOL_Obool)),U_1615),U_1617))
& ~ hBOOL(hAPP(hAPP(c_member(U_1614),U_1616),U_1615)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1614,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1614,tc_HOL_Obool)),U_1615),hAPP(hAPP(c_Set_Oinsert(U_1614),U_1616),c_Orderings_Obot__class_Obot(tc_fun(U_1614,tc_HOL_Obool))))),U_1617))
& hBOOL(hAPP(hAPP(c_member(U_1614),U_1616),U_1615)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(U_1614),U_1616),U_1617)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1614,tc_HOL_Obool)),U_1615),U_1617))
& hBOOL(hAPP(hAPP(c_member(U_1614),U_1616),U_1617)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1614,tc_HOL_Obool)),U_1615),U_1617))
| hBOOL(hAPP(hAPP(c_member(U_1614),U_1616),U_1615)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1614,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1614,tc_HOL_Obool)),U_1615),hAPP(hAPP(c_Set_Oinsert(U_1614),U_1616),c_Orderings_Obot__class_Obot(tc_fun(U_1614,tc_HOL_Obool))))),U_1617))
| ~ hBOOL(hAPP(hAPP(c_member(U_1614),U_1616),U_1615)) ) )
| hBOOL(hAPP(hAPP(c_member(U_1614),U_1616),U_1617)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1614,tc_HOL_Obool)),U_1615),U_1617))
| ~ hBOOL(hAPP(hAPP(c_member(U_1614),U_1616),U_1617)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1614,tc_HOL_Obool)),U_1615),hAPP(hAPP(c_Set_Oinsert(U_1614),U_1616),U_1617))) ) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
( ! [U_1625,U_1623,U_1621,U_1619] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),U_1621),hAPP(hAPP(c_Set_Oinsert(U_1619),U_1623),U_1625)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1619,tc_HOL_Obool)),U_1621),U_1625))
& ~ hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1621)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1619,tc_HOL_Obool)),U_1621),hAPP(hAPP(c_Set_Oinsert(U_1619),U_1623),c_Orderings_Obot__class_Obot(tc_fun(U_1619,tc_HOL_Obool))))),U_1625))
& hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1621)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1625)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),U_1621),U_1625))
& hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1625)) ) )
& ! [U_1624,U_1622,U_1620,U_1618] :
( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1618,tc_HOL_Obool)),U_1620),U_1624))
| hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1620)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1618,tc_HOL_Obool)),U_1620),hAPP(hAPP(c_Set_Oinsert(U_1618),U_1622),c_Orderings_Obot__class_Obot(tc_fun(U_1618,tc_HOL_Obool))))),U_1624))
| ~ hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1620)) ) )
| hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1624)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),U_1620),U_1624))
| ~ hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1624)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),U_1620),hAPP(hAPP(c_Set_Oinsert(U_1618),U_1622),U_1624))) ) ),
inference(miniscope,[status(thm)],[f_390_2]) ).
fof(f_390_4,plain,
( ! [U_1625,U_1619,U_1621,U_1623] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1619,tc_HOL_Obool)),U_1621),U_1625))
| ~ sP95(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1625,U_1619,U_1621,U_1623] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1621))
| ~ sP95(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1625,U_1619,U_1621,U_1623] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1619,tc_HOL_Obool)),U_1621),hAPP(hAPP(c_Set_Oinsert(U_1619),U_1623),c_Orderings_Obot__class_Obot(tc_fun(U_1619,tc_HOL_Obool))))),U_1625))
| ~ sP94(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1625,U_1619,U_1621,U_1623] :
( hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1621))
| ~ sP94(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1625,U_1619,U_1621,U_1623] :
( sP95(U_1625,U_1619,U_1621,U_1623)
| sP94(U_1625,U_1619,U_1621,U_1623)
| ~ sP96(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1625,U_1619,U_1621,U_1623] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1625))
| ~ sP96(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1625,U_1619,U_1621,U_1623] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),U_1621),U_1625))
| ~ sP93(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1625,U_1619,U_1621,U_1623] :
( hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1625))
| ~ sP93(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1618,U_1620,U_1622,U_1624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1618,tc_HOL_Obool)),U_1620),U_1624))
| hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1620))
| ~ sP91(U_1618,U_1620,U_1622,U_1624) )
& ! [U_1618,U_1620,U_1622,U_1624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1618,tc_HOL_Obool)),U_1620),hAPP(hAPP(c_Set_Oinsert(U_1618),U_1622),c_Orderings_Obot__class_Obot(tc_fun(U_1618,tc_HOL_Obool))))),U_1624))
| ~ hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1620))
| ~ sP91(U_1618,U_1620,U_1622,U_1624) )
& ! [U_1618,U_1620,U_1622,U_1624] :
( sP91(U_1618,U_1620,U_1622,U_1624)
| hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1624))
| ~ sP92(U_1618,U_1620,U_1622,U_1624) )
& ! [U_1618,U_1620,U_1622,U_1624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),U_1620),U_1624))
| ~ hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1624))
| ~ sP92(U_1618,U_1620,U_1622,U_1624) )
& ! [U_1625,U_1619,U_1621,U_1623] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),U_1621),hAPP(hAPP(c_Set_Oinsert(U_1619),U_1623),U_1625)))
| sP96(U_1625,U_1619,U_1621,U_1623)
| sP93(U_1625,U_1619,U_1621,U_1623) )
& ! [U_1618,U_1620,U_1622,U_1624] :
( sP92(U_1618,U_1620,U_1622,U_1624)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),U_1620),hAPP(hAPP(c_Set_Oinsert(U_1618),U_1622),U_1624))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91,sP92,sP93,sP94,sP95,sP96])],[f_390_3]) ).
cnf(f_390_5,plain,
( sP92(U_1618,U_1620,U_1622,U_1624)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),U_1620),hAPP(hAPP(c_Set_Oinsert(U_1618),U_1622),U_1624))) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),U_1621),hAPP(hAPP(c_Set_Oinsert(U_1619),U_1623),U_1625)))
| sP96(U_1625,U_1619,U_1621,U_1623)
| sP93(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),U_1620),U_1624))
| ~ hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1624))
| ~ sP92(U_1618,U_1620,U_1622,U_1624) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_8,plain,
( sP91(U_1618,U_1620,U_1622,U_1624)
| hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1624))
| ~ sP92(U_1618,U_1620,U_1622,U_1624) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1618,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1618,tc_HOL_Obool)),U_1620),hAPP(hAPP(c_Set_Oinsert(U_1618),U_1622),c_Orderings_Obot__class_Obot(tc_fun(U_1618,tc_HOL_Obool))))),U_1624))
| ~ hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1620))
| ~ sP91(U_1618,U_1620,U_1622,U_1624) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1618,tc_HOL_Obool)),U_1620),U_1624))
| hBOOL(hAPP(hAPP(c_member(U_1618),U_1622),U_1620))
| ~ sP91(U_1618,U_1620,U_1622,U_1624) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1625))
| ~ sP93(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),U_1621),U_1625))
| ~ sP93(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1625))
| ~ sP96(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_14,plain,
( sP95(U_1625,U_1619,U_1621,U_1623)
| sP94(U_1625,U_1619,U_1621,U_1623)
| ~ sP96(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_15,plain,
( hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1621))
| ~ sP94(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1619,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1619,tc_HOL_Obool)),U_1621),hAPP(hAPP(c_Set_Oinsert(U_1619),U_1623),c_Orderings_Obot__class_Obot(tc_fun(U_1619,tc_HOL_Obool))))),U_1625))
| ~ sP94(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_17,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1619),U_1623),U_1621))
| ~ sP95(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1619,tc_HOL_Obool)),U_1621),U_1625))
| ~ sP95(U_1625,U_1619,U_1621,U_1623) ),
inference(clausify,[status(thm)],[f_390_4]) ).
fof(f_391_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J]) ).
fof(f_391_2,plain,
! [U_1628,U_1627,U_1626] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1626,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1626),U_1627)),c_SetInterval_Oord__class_OatLeastAtMost(U_1626,U_1627,U_1628)) = hAPP(c_SetInterval_Oord__class_OatMost(U_1626),U_1628)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1626),U_1627),U_1628))
| ~ class_Orderings_Olinorder(U_1626) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
! [U_1626,U_1627,U_1628] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1626,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1626),U_1627)),c_SetInterval_Oord__class_OatLeastAtMost(U_1626,U_1627,U_1628)) = hAPP(c_SetInterval_Oord__class_OatMost(U_1626),U_1628)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1626),U_1627),U_1628))
| ~ class_Orderings_Olinorder(U_1626) ),
inference(definitional_conversion,[status(esa)],[f_391_2]) ).
cnf(f_391_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1626,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1626),U_1627)),c_SetInterval_Oord__class_OatLeastAtMost(U_1626,U_1627,U_1628)) = hAPP(c_SetInterval_Oord__class_OatMost(U_1626),U_1628)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1626),U_1627),U_1628))
| ~ class_Orderings_Olinorder(U_1626) ),
inference(clausify,[status(thm)],[f_391_3]) ).
fof(f_392_1,plain,
! [V_Qa_2,V_Pa_2,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),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))))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Qa_2,B_x))
& hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__Collect__mono]) ).
fof(f_392_2,plain,
! [U_1634,U_1633,U_1632,U_1631,U_1630] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1630,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1630,tc_HOL_Obool)),U_1631),hAPP(c_Set_OCollect(U_1630),U_1633))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1630,tc_HOL_Obool)),U_1632),hAPP(c_Set_OCollect(U_1630),U_1634))))
| ? [U_1629] :
( ~ hBOOL(hAPP(U_1634,U_1629))
& hBOOL(hAPP(U_1633,U_1629))
& hBOOL(hAPP(hAPP(c_member(U_1630),U_1629),U_1631)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1630,tc_HOL_Obool)),U_1631),U_1632)) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
! [U_1634,U_1633,U_1632,U_1631,U_1630] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1630,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1630,tc_HOL_Obool)),U_1631),hAPP(c_Set_OCollect(U_1630),U_1633))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1630,tc_HOL_Obool)),U_1632),hAPP(c_Set_OCollect(U_1630),U_1634))))
| ( ~ hBOOL(hAPP(U_1634,sK42(U_1634,U_1633,U_1632,U_1631,U_1630)))
& hBOOL(hAPP(U_1633,sK42(U_1634,U_1633,U_1632,U_1631,U_1630)))
& hBOOL(hAPP(hAPP(c_member(U_1630),sK42(U_1634,U_1633,U_1632,U_1631,U_1630)),U_1631)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1630,tc_HOL_Obool)),U_1631),U_1632)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_1629,sK42(U_1634,U_1633,U_1632,U_1631,U_1630))],[f_392_2]) ).
fof(f_392_4,plain,
( ! [U_1633,U_1630,U_1631,U_1634,U_1632] :
( ~ hBOOL(hAPP(U_1634,sK42(U_1634,U_1633,U_1632,U_1631,U_1630)))
| ~ sP97(U_1633,U_1630,U_1631,U_1634,U_1632) )
& ! [U_1633,U_1630,U_1631,U_1634,U_1632] :
( hBOOL(hAPP(U_1633,sK42(U_1634,U_1633,U_1632,U_1631,U_1630)))
| ~ sP97(U_1633,U_1630,U_1631,U_1634,U_1632) )
& ! [U_1633,U_1630,U_1631,U_1634,U_1632] :
( hBOOL(hAPP(hAPP(c_member(U_1630),sK42(U_1634,U_1633,U_1632,U_1631,U_1630)),U_1631))
| ~ sP97(U_1633,U_1630,U_1631,U_1634,U_1632) )
& ! [U_1633,U_1630,U_1631,U_1634,U_1632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1630,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1630,tc_HOL_Obool)),U_1631),hAPP(c_Set_OCollect(U_1630),U_1633))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1630,tc_HOL_Obool)),U_1632),hAPP(c_Set_OCollect(U_1630),U_1634))))
| sP97(U_1633,U_1630,U_1631,U_1634,U_1632)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1630,tc_HOL_Obool)),U_1631),U_1632)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97])],[f_392_3]) ).
cnf(f_392_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1630,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1630,tc_HOL_Obool)),U_1631),hAPP(c_Set_OCollect(U_1630),U_1633))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1630,tc_HOL_Obool)),U_1632),hAPP(c_Set_OCollect(U_1630),U_1634))))
| sP97(U_1633,U_1630,U_1631,U_1634,U_1632)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1630,tc_HOL_Obool)),U_1631),U_1632)) ),
inference(clausify,[status(thm)],[f_392_4]) ).
cnf(f_392_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1630),sK42(U_1634,U_1633,U_1632,U_1631,U_1630)),U_1631))
| ~ sP97(U_1633,U_1630,U_1631,U_1634,U_1632) ),
inference(clausify,[status(thm)],[f_392_4]) ).
cnf(f_392_7,plain,
( hBOOL(hAPP(U_1633,sK42(U_1634,U_1633,U_1632,U_1631,U_1630)))
| ~ sP97(U_1633,U_1630,U_1631,U_1634,U_1632) ),
inference(clausify,[status(thm)],[f_392_4]) ).
cnf(f_392_8,plain,
( ~ hBOOL(hAPP(U_1634,sK42(U_1634,U_1633,U_1632,U_1631,U_1630)))
| ~ sP97(U_1633,U_1630,U_1631,U_1634,U_1632) ),
inference(clausify,[status(thm)],[f_392_4]) ).
fof(f_393_1,plain,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( 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))
| ~ 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J]) ).
fof(f_393_2,plain,
! [U_1641,U_1640,U_1639,U_1638,U_1637,U_1636,U_1635] :
( c_Nitpick_Ofold__graph_H(U_1635,U_1638,U_1639,U_1640,U_1637,hAPP(hAPP(U_1639,U_1636),U_1641))
| ~ c_Nitpick_Ofold__graph_H(U_1635,U_1638,U_1639,U_1640,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1635,tc_HOL_Obool)),U_1637),hAPP(hAPP(c_Set_Oinsert(U_1635),U_1636),c_Orderings_Obot__class_Obot(tc_fun(U_1635,tc_HOL_Obool)))),U_1641)
| ~ hBOOL(hAPP(hAPP(c_member(U_1635),U_1636),U_1637)) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
! [U_1638,U_1637,U_1636,U_1639,U_1635,U_1640,U_1641] :
( c_Nitpick_Ofold__graph_H(U_1635,U_1638,U_1639,U_1640,U_1637,hAPP(hAPP(U_1639,U_1636),U_1641))
| ~ c_Nitpick_Ofold__graph_H(U_1635,U_1638,U_1639,U_1640,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1635,tc_HOL_Obool)),U_1637),hAPP(hAPP(c_Set_Oinsert(U_1635),U_1636),c_Orderings_Obot__class_Obot(tc_fun(U_1635,tc_HOL_Obool)))),U_1641)
| ~ hBOOL(hAPP(hAPP(c_member(U_1635),U_1636),U_1637)) ),
inference(definitional_conversion,[status(esa)],[f_393_2]) ).
cnf(f_393_4,plain,
( c_Nitpick_Ofold__graph_H(U_1635,U_1638,U_1639,U_1640,U_1637,hAPP(hAPP(U_1639,U_1636),U_1641))
| ~ c_Nitpick_Ofold__graph_H(U_1635,U_1638,U_1639,U_1640,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1635,tc_HOL_Obool)),U_1637),hAPP(hAPP(c_Set_Oinsert(U_1635),U_1636),c_Orderings_Obot__class_Obot(tc_fun(U_1635,tc_HOL_Obool)))),U_1641)
| ~ hBOOL(hAPP(hAPP(c_member(U_1635),U_1636),U_1637)) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J]) ).
fof(f_394_2,plain,
! [U_1644,U_1643,U_1642] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1642,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1642,U_1643,U_1644)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1642),U_1644)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1642),U_1643)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1642),U_1643),U_1644))
| ~ class_Orderings_Olinorder(U_1642) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_1642,U_1643,U_1644] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1642,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1642,U_1643,U_1644)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1642),U_1644)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1642),U_1643)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1642),U_1643),U_1644))
| ~ class_Orderings_Olinorder(U_1642) ),
inference(definitional_conversion,[status(esa)],[f_394_2]) ).
cnf(f_394_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1642,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1642,U_1643,U_1644)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1642),U_1644)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1642),U_1643)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1642),U_1643),U_1644))
| ~ class_Orderings_Olinorder(U_1642) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_1,plain,
! [V_F_2,V_x_2,T_b] :
( 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))
| ? [B_x] :
( ? [B_xa] :
( 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))
& B_x != B_xa
& 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))) )
& 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))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__partition]) ).
fof(f_395_2,plain,
! [U_1649,U_1648,U_1647] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),U_1648),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1647,tc_HOL_Obool),U_1649)) = c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
| ? [U_1646] :
( ? [U_1645] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),U_1646),U_1645) != c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
& U_1646 != U_1645
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),U_1645),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),U_1646),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
! [U_1649,U_1648,U_1647] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),U_1648),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1647,tc_HOL_Obool),U_1649)) = c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
| ( ? [U_1645] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),sK43(U_1649,U_1648,U_1647)),U_1645) != c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
& sK43(U_1649,U_1648,U_1647) != U_1645
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),U_1645),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),sK43(U_1649,U_1648,U_1647)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_1646,sK43(U_1649,U_1648,U_1647))],[f_395_2]) ).
fof(f_395_4,plain,
! [U_1649,U_1648,U_1647] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),U_1648),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1647,tc_HOL_Obool),U_1649)) = c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),sK43(U_1649,U_1648,U_1647)),sK44(U_1649,U_1648,U_1647)) != c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
& sK43(U_1649,U_1648,U_1647) != sK44(U_1649,U_1648,U_1647)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),sK44(U_1649,U_1648,U_1647)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),sK43(U_1649,U_1648,U_1647)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_1645,sK44(U_1649,U_1648,U_1647))],[f_395_3]) ).
fof(f_395_5,plain,
( ! [U_1647,U_1648,U_1649] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),sK43(U_1649,U_1648,U_1647)),sK44(U_1649,U_1648,U_1647)) != c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
| ~ sP98(U_1647,U_1648,U_1649) )
& ! [U_1647,U_1648,U_1649] :
( sK43(U_1649,U_1648,U_1647) != sK44(U_1649,U_1648,U_1647)
| ~ sP98(U_1647,U_1648,U_1649) )
& ! [U_1647,U_1648,U_1649] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),sK44(U_1649,U_1648,U_1647)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)))
| ~ sP98(U_1647,U_1648,U_1649) )
& ! [U_1647,U_1648,U_1649] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),sK43(U_1649,U_1648,U_1647)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)))
| ~ sP98(U_1647,U_1648,U_1649) )
& ! [U_1647,U_1648,U_1649] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),U_1648),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1647,tc_HOL_Obool),U_1649)) = c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
| sP98(U_1647,U_1648,U_1649)
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_395_4]) ).
cnf(f_395_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),U_1648),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1647,tc_HOL_Obool),U_1649)) = c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
| sP98(U_1647,U_1648,U_1649)
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)) ),
inference(clausify,[status(thm)],[f_395_5]) ).
cnf(f_395_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),sK43(U_1649,U_1648,U_1647)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)))
| ~ sP98(U_1647,U_1648,U_1649) ),
inference(clausify,[status(thm)],[f_395_5]) ).
cnf(f_395_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1647,tc_HOL_Obool)),sK44(U_1649,U_1648,U_1647)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1647,tc_HOL_Obool)),U_1648),U_1649)))
| ~ sP98(U_1647,U_1648,U_1649) ),
inference(clausify,[status(thm)],[f_395_5]) ).
cnf(f_395_9,plain,
( sK43(U_1649,U_1648,U_1647) != sK44(U_1649,U_1648,U_1647)
| ~ sP98(U_1647,U_1648,U_1649) ),
inference(clausify,[status(thm)],[f_395_5]) ).
cnf(f_395_10,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1647,tc_HOL_Obool)),sK43(U_1649,U_1648,U_1647)),sK44(U_1649,U_1648,U_1647)) != c_Orderings_Obot__class_Obot(tc_fun(U_1647,tc_HOL_Obool))
| ~ sP98(U_1647,U_1648,U_1649) ),
inference(clausify,[status(thm)],[f_395_5]) ).
fof(f_396_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( 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_ca_2,V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
| ~ 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_ca_2,V_d_2))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).
fof(f_396_2,plain,
! [U_1654,U_1653,U_1652,U_1651,U_1650] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1650,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1651,U_1652)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1653,U_1654)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1654))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1652),U_1654))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1653),U_1651)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1652),U_1654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1651)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1651),U_1652)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1654))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1652),U_1654))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1653),U_1651)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1652),U_1654))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1651)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1651),U_1652)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1650,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1651,U_1652)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1653,U_1654))) ) )
| ~ class_Orderings_Oorder(U_1650) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
( ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1652),U_1654))
| ~ sP101(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1653),U_1651))
| ~ sP101(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( sP101(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1652),U_1654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1651))
| ~ sP102(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1651),U_1652))
| ~ sP102(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1652),U_1654))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1653),U_1651))
| ~ sP99(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1652),U_1654))
| ~ sP99(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1651))
| ~ sP99(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1654))
| ~ sP100(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( sP99(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1651),U_1652))
| ~ sP100(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1650,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1651,U_1652)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1653,U_1654)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1654))
| sP102(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ sP103(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( sP100(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1650,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1651,U_1652)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1653,U_1654)))
| ~ sP103(U_1650,U_1652,U_1653,U_1651,U_1654) )
& ! [U_1650,U_1652,U_1653,U_1651,U_1654] :
( sP103(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ class_Orderings_Oorder(U_1650) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99,sP100,sP101,sP102,sP103])],[f_396_2]) ).
cnf(f_396_4,plain,
( sP103(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ class_Orderings_Oorder(U_1650) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_5,plain,
( sP100(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1650,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1651,U_1652)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1653,U_1654)))
| ~ sP103(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1650,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1651,U_1652)),c_SetInterval_Oord__class_OatLeastAtMost(U_1650,U_1653,U_1654)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1654))
| sP102(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ sP103(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_7,plain,
( sP99(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1651),U_1652))
| ~ sP100(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1654))
| ~ sP100(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1651))
| ~ sP99(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1652),U_1654))
| ~ sP99(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1652),U_1654))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1653),U_1651))
| ~ sP99(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1651),U_1652))
| ~ sP102(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_13,plain,
( sP101(U_1650,U_1652,U_1653,U_1651,U_1654)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1652),U_1654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1650),U_1653),U_1651))
| ~ sP102(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1653),U_1651))
| ~ sP101(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1650),U_1652),U_1654))
| ~ sP101(U_1650,U_1652,U_1653,U_1651,U_1654) ),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__cases]) ).
fof(f_397_2,plain,
! [U_1657,U_1656,U_1655] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1657),U_1656))
| U_1656 = U_1657
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1656),U_1657))
| ~ class_Orderings_Olinorder(U_1655) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
fof(f_397_3,plain,
! [U_1656,U_1657,U_1655] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1657),U_1656))
| U_1656 = U_1657
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1656),U_1657))
| ~ class_Orderings_Olinorder(U_1655) ),
inference(definitional_conversion,[status(esa)],[f_397_2]) ).
cnf(f_397_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1657),U_1656))
| U_1656 = U_1657
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1656),U_1657))
| ~ class_Orderings_Olinorder(U_1655) ),
inference(clausify,[status(thm)],[f_397_3]) ).
fof(f_398_1,plain,
! [V_y,V_x,T_a] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__asym]) ).
fof(f_398_2,plain,
! [U_1660,U_1659,U_1658] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1660),U_1659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1659),U_1660))
| ~ class_Orderings_Opreorder(U_1658) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
! [U_1660,U_1659,U_1658] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1660),U_1659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1659),U_1660))
| ~ class_Orderings_Opreorder(U_1658) ),
inference(definitional_conversion,[status(esa)],[f_398_2]) ).
cnf(f_398_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1660),U_1659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1659),U_1660))
| ~ class_Orderings_Opreorder(U_1658) ),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I10_J]) ).
fof(f_399_2,plain,
! [U_1664,U_1663,U_1662,U_1661] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1664),U_1663))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1664),U_1662))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1662),U_1663))
| ~ class_Orderings_Oorder(U_1661) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
! [U_1661,U_1662,U_1663,U_1664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1664),U_1663))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1664),U_1662))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1662),U_1663))
| ~ class_Orderings_Oorder(U_1661) ),
inference(definitional_conversion,[status(esa)],[f_399_2]) ).
cnf(f_399_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1664),U_1663))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1664),U_1662))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1662),U_1663))
| ~ class_Orderings_Oorder(U_1661) ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__trans]) ).
fof(f_400_2,plain,
! [U_1668,U_1667,U_1666,U_1665] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1666),U_1668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1667),U_1668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1666),U_1667))
| ~ class_Orderings_Opreorder(U_1665) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
fof(f_400_3,plain,
! [U_1668,U_1665,U_1667,U_1666] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1666),U_1668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1667),U_1668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1666),U_1667))
| ~ class_Orderings_Opreorder(U_1665) ),
inference(definitional_conversion,[status(esa)],[f_400_2]) ).
cnf(f_400_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1666),U_1668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1667),U_1668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1665),U_1666),U_1667))
| ~ class_Orderings_Opreorder(U_1665) ),
inference(clausify,[status(thm)],[f_400_3]) ).
fof(f_401_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a))
| V_b != V_c
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I2_J]) ).
fof(f_401_2,plain,
! [U_1672,U_1671,U_1670,U_1669] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1669),U_1672),U_1671))
| U_1670 != U_1672
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1669),U_1670),U_1671))
| ~ class_Orderings_Oorder(U_1669) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
! [U_1669,U_1670,U_1671,U_1672] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1669),U_1672),U_1671))
| U_1670 != U_1672
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1669),U_1670),U_1671))
| ~ class_Orderings_Oorder(U_1669) ),
inference(definitional_conversion,[status(esa)],[f_401_2]) ).
cnf(f_401_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1669),U_1672),U_1671))
| U_1670 != U_1672
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1669),U_1670),U_1671))
| ~ class_Orderings_Oorder(U_1669) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c))
| V_b != V_c
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__less__eq__trans]) ).
fof(f_402_2,plain,
! [U_1676,U_1675,U_1674,U_1673] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1676))
| U_1675 != U_1676
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675))
| ~ class_Orderings_Oord(U_1673) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
! [U_1673,U_1674,U_1675,U_1676] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1676))
| U_1675 != U_1676
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675))
| ~ class_Orderings_Oord(U_1673) ),
inference(definitional_conversion,[status(esa)],[f_402_2]) ).
cnf(f_402_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1676))
| U_1675 != U_1676
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675))
| ~ class_Orderings_Oord(U_1673) ),
inference(clausify,[status(thm)],[f_402_3]) ).
fof(f_403_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
| V_a != V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I1_J]) ).
fof(f_403_2,plain,
! [U_1680,U_1679,U_1678,U_1677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1677),U_1680),U_1678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1677),U_1680),U_1679))
| U_1678 != U_1679
| ~ class_Orderings_Oorder(U_1677) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
fof(f_403_3,plain,
! [U_1677,U_1679,U_1678,U_1680] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1677),U_1680),U_1678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1677),U_1680),U_1679))
| U_1678 != U_1679
| ~ class_Orderings_Oorder(U_1677) ),
inference(definitional_conversion,[status(esa)],[f_403_2]) ).
cnf(f_403_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1677),U_1680),U_1678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1677),U_1680),U_1679))
| U_1678 != U_1679
| ~ class_Orderings_Oorder(U_1677) ),
inference(clausify,[status(thm)],[f_403_3]) ).
fof(f_404_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
| V_a != V_b
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__eq__less__trans]) ).
fof(f_404_2,plain,
! [U_1684,U_1683,U_1682,U_1681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1682),U_1684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),U_1684))
| U_1682 != U_1683
| ~ class_Orderings_Oord(U_1681) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
! [U_1684,U_1681,U_1682,U_1683] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1682),U_1684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),U_1684))
| U_1682 != U_1683
| ~ class_Orderings_Oord(U_1681) ),
inference(definitional_conversion,[status(esa)],[f_404_2]) ).
cnf(f_404_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1682),U_1684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),U_1684))
| U_1682 != U_1683
| ~ class_Orderings_Oord(U_1681) ),
inference(clausify,[status(thm)],[f_404_3]) ).
fof(f_405_1,plain,
! [V_a,V_b,T_a] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I9_J]) ).
fof(f_405_2,plain,
! [U_1687,U_1686,U_1685] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1685),U_1687),U_1686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1685),U_1686),U_1687))
| ~ class_Orderings_Oorder(U_1685) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
! [U_1686,U_1685,U_1687] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1685),U_1687),U_1686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1685),U_1686),U_1687))
| ~ class_Orderings_Oorder(U_1685) ),
inference(definitional_conversion,[status(esa)],[f_405_2]) ).
cnf(f_405_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1685),U_1687),U_1686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1685),U_1686),U_1687))
| ~ class_Orderings_Oorder(U_1685) ),
inference(clausify,[status(thm)],[f_405_3]) ).
fof(f_406_1,plain,
! [V_b,V_a,T_a] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__asym_H]) ).
fof(f_406_2,plain,
! [U_1690,U_1689,U_1688] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1688),U_1690),U_1689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1688),U_1689),U_1690))
| ~ class_Orderings_Opreorder(U_1688) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
fof(f_406_3,plain,
! [U_1688,U_1689,U_1690] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1688),U_1690),U_1689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1688),U_1689),U_1690))
| ~ class_Orderings_Opreorder(U_1688) ),
inference(definitional_conversion,[status(esa)],[f_406_2]) ).
cnf(f_406_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1688),U_1690),U_1689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1688),U_1689),U_1690))
| ~ class_Orderings_Opreorder(U_1688) ),
inference(clausify,[status(thm)],[f_406_3]) ).
fof(f_407_1,plain,
! [V_y,V_x,T_a] :
( V_y != V_x
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2]) ).
fof(f_407_2,plain,
! [U_1693,U_1692,U_1691] :
( U_1693 != U_1692
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1691),U_1692),U_1693))
| ~ class_Orderings_Oorder(U_1691) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_1691,U_1692,U_1693] :
( U_1693 != U_1692
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1691),U_1692),U_1693))
| ~ class_Orderings_Oorder(U_1691) ),
inference(definitional_conversion,[status(esa)],[f_407_2]) ).
cnf(f_407_4,plain,
( U_1693 != U_1692
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1691),U_1692),U_1693))
| ~ class_Orderings_Oorder(U_1691) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq]) ).
fof(f_408_2,plain,
! [U_1696,U_1695,U_1694] :
( U_1695 != U_1696
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1694),U_1695),U_1696))
| ~ class_Orderings_Oorder(U_1694) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
! [U_1694,U_1695,U_1696] :
( U_1695 != U_1696
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1694),U_1695),U_1696))
| ~ class_Orderings_Oorder(U_1694) ),
inference(definitional_conversion,[status(esa)],[f_408_2]) ).
cnf(f_408_4,plain,
( U_1695 != U_1696
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1694),U_1695),U_1696))
| ~ class_Orderings_Oorder(U_1694) ),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_1,plain,
! [V_y,V_x,T_a] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(f_409_2,plain,
! [U_1699,U_1698,U_1697] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1697),U_1699),U_1698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1697),U_1698),U_1699))
| ~ class_Orderings_Opreorder(U_1697) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
fof(f_409_3,plain,
! [U_1697,U_1698,U_1699] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1697),U_1699),U_1698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1697),U_1698),U_1699))
| ~ class_Orderings_Opreorder(U_1697) ),
inference(definitional_conversion,[status(esa)],[f_409_2]) ).
cnf(f_409_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1697),U_1699),U_1698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1697),U_1698),U_1699))
| ~ class_Orderings_Opreorder(U_1697) ),
inference(clausify,[status(thm)],[f_409_3]) ).
fof(f_410_1,plain,
! [V_y,V_x,T_a] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__not__sym]) ).
fof(f_410_2,plain,
! [U_1702,U_1701,U_1700] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1700),U_1702),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1700),U_1701),U_1702))
| ~ class_Orderings_Opreorder(U_1700) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
! [U_1700,U_1701,U_1702] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1700),U_1702),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1700),U_1701),U_1702))
| ~ class_Orderings_Opreorder(U_1700) ),
inference(definitional_conversion,[status(esa)],[f_410_2]) ).
cnf(f_410_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1700),U_1702),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1700),U_1701),U_1702))
| ~ class_Orderings_Opreorder(U_1700) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__neq]) ).
fof(f_411_2,plain,
! [U_1705,U_1704,U_1703] :
( U_1704 != U_1705
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1704),U_1705))
| ~ class_Orderings_Oorder(U_1703) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
fof(f_411_3,plain,
! [U_1703,U_1704,U_1705] :
( U_1704 != U_1705
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1704),U_1705))
| ~ class_Orderings_Oorder(U_1703) ),
inference(definitional_conversion,[status(esa)],[f_411_2]) ).
cnf(f_411_4,plain,
( U_1704 != U_1705
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1704),U_1705))
| ~ class_Orderings_Oorder(U_1703) ),
inference(clausify,[status(thm)],[f_411_3]) ).
fof(f_412_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE]) ).
fof(f_412_2,plain,
! [U_1708,U_1707,U_1706] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1706),U_1708),U_1707))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1706),U_1707),U_1708))
| U_1707 = U_1708
| ~ class_Orderings_Olinorder(U_1706) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
fof(f_412_3,plain,
! [U_1706,U_1707,U_1708] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1706),U_1708),U_1707))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1706),U_1707),U_1708))
| U_1707 = U_1708
| ~ class_Orderings_Olinorder(U_1706) ),
inference(definitional_conversion,[status(esa)],[f_412_2]) ).
cnf(f_412_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1706),U_1708),U_1707))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1706),U_1707),U_1708))
| U_1707 = U_1708
| ~ class_Orderings_Olinorder(U_1706) ),
inference(clausify,[status(thm)],[f_412_3]) ).
fof(f_413_1,plain,
! [V_x_2,V_y_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_413_2,plain,
! [U_1711,U_1710,U_1709] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1711),U_1710))
| U_1711 != U_1710 )
& ( U_1711 = U_1710
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1711),U_1710)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1710),U_1711))
| ~ class_Orderings_Olinorder(U_1709) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
( ! [U_1710,U_1711,U_1709] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1711),U_1710))
| U_1711 != U_1710
| ~ sP104(U_1710,U_1711,U_1709) )
& ! [U_1710,U_1711,U_1709] :
( U_1711 = U_1710
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1711),U_1710))
| ~ sP104(U_1710,U_1711,U_1709) )
& ! [U_1710,U_1711,U_1709] :
( sP104(U_1710,U_1711,U_1709)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1710),U_1711))
| ~ class_Orderings_Olinorder(U_1709) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_413_2]) ).
cnf(f_413_4,plain,
( sP104(U_1710,U_1711,U_1709)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1710),U_1711))
| ~ class_Orderings_Olinorder(U_1709) ),
inference(clausify,[status(thm)],[f_413_3]) ).
cnf(f_413_5,plain,
( U_1711 = U_1710
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1711),U_1710))
| ~ sP104(U_1710,U_1711,U_1709) ),
inference(clausify,[status(thm)],[f_413_3]) ).
cnf(f_413_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1709),U_1711),U_1710))
| U_1711 != U_1710
| ~ sP104(U_1710,U_1711,U_1709) ),
inference(clausify,[status(thm)],[f_413_3]) ).
fof(f_414_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__less__linear]) ).
fof(f_414_2,plain,
! [U_1714,U_1713,U_1712] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),U_1714),U_1713))
| U_1713 = U_1714
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),U_1713),U_1714))
| ~ class_Orderings_Olinorder(U_1712) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
fof(f_414_3,plain,
! [U_1714,U_1713,U_1712] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),U_1714),U_1713))
| U_1713 = U_1714
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),U_1713),U_1714))
| ~ class_Orderings_Olinorder(U_1712) ),
inference(definitional_conversion,[status(esa)],[f_414_2]) ).
cnf(f_414_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),U_1714),U_1713))
| U_1713 = U_1714
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),U_1713),U_1714))
| ~ class_Orderings_Olinorder(U_1712) ),
inference(clausify,[status(thm)],[f_414_3]) ).
fof(f_415_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_415_2,plain,
! [U_1717,U_1716,U_1715] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1716),U_1717))
| ( U_1716 != U_1717
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1717),U_1716)) ) )
& ( U_1716 = U_1717
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1717),U_1716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1716),U_1717)) ) )
| ~ class_Orderings_Olinorder(U_1715) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
( ! [U_1715,U_1716,U_1717] :
( U_1716 != U_1717
| ~ sP105(U_1715,U_1716,U_1717) )
& ! [U_1715,U_1716,U_1717] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1717),U_1716))
| ~ sP105(U_1715,U_1716,U_1717) )
& ! [U_1715,U_1716,U_1717] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1716),U_1717))
| sP105(U_1715,U_1716,U_1717)
| ~ sP106(U_1715,U_1716,U_1717) )
& ! [U_1715,U_1716,U_1717] :
( U_1716 = U_1717
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1717),U_1716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1716),U_1717))
| ~ sP106(U_1715,U_1716,U_1717) )
& ! [U_1715,U_1716,U_1717] :
( sP106(U_1715,U_1716,U_1717)
| ~ class_Orderings_Olinorder(U_1715) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105,sP106])],[f_415_2]) ).
cnf(f_415_4,plain,
( sP106(U_1715,U_1716,U_1717)
| ~ class_Orderings_Olinorder(U_1715) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_5,plain,
( U_1716 = U_1717
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1717),U_1716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1716),U_1717))
| ~ sP106(U_1715,U_1716,U_1717) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1716),U_1717))
| sP105(U_1715,U_1716,U_1717)
| ~ sP106(U_1715,U_1716,U_1717) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1715),U_1717),U_1716))
| ~ sP105(U_1715,U_1716,U_1717) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_8,plain,
( U_1716 != U_1717
| ~ sP105(U_1715,U_1716,U_1717) ),
inference(clausify,[status(thm)],[f_415_3]) ).
fof(f_416_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( V_x_2 != V_y_2
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| V_x_2 = V_y_2 ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_416_2,plain,
! [U_1720,U_1719,U_1718] :
( ( ( U_1719 != U_1720
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1720),U_1719))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1719),U_1720)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1720),U_1719))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1719),U_1720))
| U_1719 = U_1720 ) )
| ~ class_Orderings_Olinorder(U_1718) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
fof(f_416_3,plain,
( ! [U_1718,U_1720,U_1719] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1720),U_1719))
| ~ sP107(U_1718,U_1720,U_1719) )
& ! [U_1718,U_1720,U_1719] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1719),U_1720))
| ~ sP107(U_1718,U_1720,U_1719) )
& ! [U_1718,U_1720,U_1719] :
( U_1719 != U_1720
| sP107(U_1718,U_1720,U_1719)
| ~ sP108(U_1718,U_1720,U_1719) )
& ! [U_1718,U_1720,U_1719] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1720),U_1719))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1719),U_1720))
| U_1719 = U_1720
| ~ sP108(U_1718,U_1720,U_1719) )
& ! [U_1718,U_1720,U_1719] :
( sP108(U_1718,U_1720,U_1719)
| ~ class_Orderings_Olinorder(U_1718) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107,sP108])],[f_416_2]) ).
cnf(f_416_4,plain,
( sP108(U_1718,U_1720,U_1719)
| ~ class_Orderings_Olinorder(U_1718) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1720),U_1719))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1719),U_1720))
| U_1719 = U_1720
| ~ sP108(U_1718,U_1720,U_1719) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_6,plain,
( U_1719 != U_1720
| sP107(U_1718,U_1720,U_1719)
| ~ sP108(U_1718,U_1720,U_1719) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1719),U_1720))
| ~ sP107(U_1718,U_1720,U_1719) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1718),U_1720),U_1719))
| ~ sP107(U_1718,U_1720,U_1719) ),
inference(clausify,[status(thm)],[f_416_3]) ).
fof(f_417_1,plain,
! [V_x,T_a] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__irrefl]) ).
fof(f_417_2,plain,
! [U_1722,U_1721] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1721),U_1722),U_1722))
| ~ class_Orderings_Opreorder(U_1721) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
! [U_1722,U_1721] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1721),U_1722),U_1722))
| ~ class_Orderings_Opreorder(U_1721) ),
inference(definitional_conversion,[status(esa)],[f_417_2]) ).
cnf(f_417_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1721),U_1722),U_1722))
| ~ class_Orderings_Opreorder(U_1721) ),
inference(clausify,[status(thm)],[f_417_3]) ).
fof(f_418_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__trans]) ).
fof(f_418_2,plain,
! [U_1726,U_1725,U_1724,U_1723] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1724),U_1726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1725),U_1726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1724),U_1725)) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
! [U_1723,U_1724,U_1725,U_1726] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1724),U_1726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1725),U_1726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1724),U_1725)) ),
inference(definitional_conversion,[status(esa)],[f_418_2]) ).
cnf(f_418_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1724),U_1726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1725),U_1726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1723,tc_HOL_Obool)),U_1724),U_1725)) ),
inference(clausify,[status(thm)],[f_418_3]) ).
fof(f_419_1,plain,
! [V_a_2,V_b_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty]) ).
fof(f_419_2,plain,
! [U_1729,U_1728,U_1727] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1727,U_1729,U_1728) = c_Orderings_Obot__class_Obot(tc_fun(U_1727,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1727),U_1728),U_1729))
| ~ class_Orderings_Oorder(U_1727) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
fof(f_419_3,plain,
! [U_1727,U_1728,U_1729] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1727,U_1729,U_1728) = c_Orderings_Obot__class_Obot(tc_fun(U_1727,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1727),U_1728),U_1729))
| ~ class_Orderings_Oorder(U_1727) ),
inference(definitional_conversion,[status(esa)],[f_419_2]) ).
cnf(f_419_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1727,U_1729,U_1728) = c_Orderings_Obot__class_Obot(tc_fun(U_1727,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1727),U_1728),U_1729))
| ~ class_Orderings_Oorder(U_1727) ),
inference(clausify,[status(thm)],[f_419_3]) ).
fof(f_420_1,plain,
! [V_n_2,V_m_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2))
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff]) ).
fof(f_420_2,plain,
! [U_1732,U_1731,U_1730] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1730,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1731)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1730),U_1731),U_1732)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1730),U_1731),U_1732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1730,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1731)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1732))) ) )
| ~ class_Orderings_Olinorder(U_1730) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
( ! [U_1732,U_1731,U_1730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1730,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1731)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1730),U_1731),U_1732))
| ~ sP109(U_1732,U_1731,U_1730) )
& ! [U_1732,U_1731,U_1730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1730),U_1731),U_1732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1730,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1731)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1732)))
| ~ sP109(U_1732,U_1731,U_1730) )
& ! [U_1732,U_1731,U_1730] :
( sP109(U_1732,U_1731,U_1730)
| ~ class_Orderings_Olinorder(U_1730) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_420_2]) ).
cnf(f_420_4,plain,
( sP109(U_1732,U_1731,U_1730)
| ~ class_Orderings_Olinorder(U_1730) ),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1730),U_1731),U_1732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1730,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1731)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1732)))
| ~ sP109(U_1732,U_1731,U_1730) ),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1730,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1731)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1730),U_1732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1730),U_1731),U_1732))
| ~ sP109(U_1732,U_1731,U_1730) ),
inference(clausify,[status(thm)],[f_420_3]) ).
fof(f_421_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
| 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_ca_2),V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).
fof(f_421_2,plain,
! [U_1737,U_1736,U_1735,U_1734,U_1733] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1734),U_1735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1736),U_1737)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1736),U_1737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1734),U_1735)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1733),U_1734),U_1735) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1733),U_1736),U_1737)
| ~ class_Groups_Oordered__ab__group__add(U_1733) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
( ! [U_1734,U_1733,U_1735,U_1736,U_1737] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1734),U_1735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1736),U_1737))
| ~ sP110(U_1734,U_1733,U_1735,U_1736,U_1737) )
& ! [U_1734,U_1733,U_1735,U_1736,U_1737] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1736),U_1737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1734),U_1735))
| ~ sP110(U_1734,U_1733,U_1735,U_1736,U_1737) )
& ! [U_1734,U_1733,U_1735,U_1736,U_1737] :
( sP110(U_1734,U_1733,U_1735,U_1736,U_1737)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1733),U_1734),U_1735) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1733),U_1736),U_1737)
| ~ class_Groups_Oordered__ab__group__add(U_1733) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_421_2]) ).
cnf(f_421_4,plain,
( sP110(U_1734,U_1733,U_1735,U_1736,U_1737)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1733),U_1734),U_1735) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1733),U_1736),U_1737)
| ~ class_Groups_Oordered__ab__group__add(U_1733) ),
inference(clausify,[status(thm)],[f_421_3]) ).
cnf(f_421_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1736),U_1737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1734),U_1735))
| ~ sP110(U_1734,U_1733,U_1735,U_1736,U_1737) ),
inference(clausify,[status(thm)],[f_421_3]) ).
cnf(f_421_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1734),U_1735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1733),U_1736),U_1737))
| ~ sP110(U_1734,U_1733,U_1735,U_1736,U_1737) ),
inference(clausify,[status(thm)],[f_421_3]) ).
fof(f_422_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).
fof(f_422_2,plain,
! [U_1741,U_1740,U_1739,U_1738] : c_Nitpick_Ofold__graph_H(U_1738,U_1739,U_1740,U_1741,c_Orderings_Obot__class_Obot(tc_fun(U_1738,tc_HOL_Obool)),U_1741),
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
! [U_1738,U_1740,U_1741,U_1739] : c_Nitpick_Ofold__graph_H(U_1738,U_1739,U_1740,U_1741,c_Orderings_Obot__class_Obot(tc_fun(U_1738,tc_HOL_Obool)),U_1741),
inference(definitional_conversion,[status(esa)],[f_422_2]) ).
cnf(f_422_4,plain,
c_Nitpick_Ofold__graph_H(U_1738,U_1739,U_1740,U_1741,c_Orderings_Obot__class_Obot(tc_fun(U_1738,tc_HOL_Obool)),U_1741),
inference(clausify,[status(thm)],[f_422_3]) ).
fof(f_423_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).
fof(f_423_2,plain,
! [U_1745,U_1744,U_1743,U_1742] : c_Nitpick_Ofold__graph_H(U_1742,U_1743,U_1744,U_1745,c_Orderings_Obot__class_Obot(tc_fun(U_1742,tc_HOL_Obool)),U_1745),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
! [U_1742,U_1743,U_1745,U_1744] : c_Nitpick_Ofold__graph_H(U_1742,U_1743,U_1744,U_1745,c_Orderings_Obot__class_Obot(tc_fun(U_1742,tc_HOL_Obool)),U_1745),
inference(definitional_conversion,[status(esa)],[f_423_2]) ).
cnf(f_423_4,plain,
c_Nitpick_Ofold__graph_H(U_1742,U_1743,U_1744,U_1745,c_Orderings_Obot__class_Obot(tc_fun(U_1742,tc_HOL_Obool)),U_1745),
inference(clausify,[status(thm)],[f_423_3]) ).
fof(f_424_1,plain,
! [V_g_2,V_f_2,T_b,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_424_2,plain,
! [U_1749,U_1748,U_1747,U_1746] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1749),U_1748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1748),U_1749)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1749),U_1748))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1748),U_1749)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1747,U_1746)),U_1748),U_1749)) ) )
| ~ class_Orderings_Oord(U_1746) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
( ! [U_1747,U_1746,U_1748,U_1749] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1749),U_1748))
| ~ sP111(U_1747,U_1746,U_1748,U_1749) )
& ! [U_1747,U_1746,U_1748,U_1749] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| ~ sP111(U_1747,U_1746,U_1748,U_1749) )
& ! [U_1747,U_1746,U_1748,U_1749] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1749),U_1748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| ~ sP112(U_1747,U_1746,U_1748,U_1749) )
& ! [U_1747,U_1746,U_1748,U_1749] :
( sP111(U_1747,U_1746,U_1748,U_1749)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| ~ sP112(U_1747,U_1746,U_1748,U_1749) )
& ! [U_1747,U_1746,U_1748,U_1749] :
( sP112(U_1747,U_1746,U_1748,U_1749)
| ~ class_Orderings_Oord(U_1746) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111,sP112])],[f_424_2]) ).
cnf(f_424_4,plain,
( sP112(U_1747,U_1746,U_1748,U_1749)
| ~ class_Orderings_Oord(U_1746) ),
inference(clausify,[status(thm)],[f_424_3]) ).
cnf(f_424_5,plain,
( sP111(U_1747,U_1746,U_1748,U_1749)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| ~ sP112(U_1747,U_1746,U_1748,U_1749) ),
inference(clausify,[status(thm)],[f_424_3]) ).
cnf(f_424_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1749),U_1748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| ~ sP112(U_1747,U_1746,U_1748,U_1749) ),
inference(clausify,[status(thm)],[f_424_3]) ).
cnf(f_424_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1748),U_1749))
| ~ sP111(U_1747,U_1746,U_1748,U_1749) ),
inference(clausify,[status(thm)],[f_424_3]) ).
cnf(f_424_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1747,U_1746)),U_1749),U_1748))
| ~ sP111(U_1747,U_1746,U_1748,U_1749) ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_425_2,plain,
! [U_1752,U_1751,U_1750] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1750),U_1751),U_1752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1750),U_1752),U_1751)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1750),U_1752),U_1751))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1750),U_1751),U_1752)) ) )
| ~ class_Orderings_Olinorder(U_1750) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
( ! [U_1752,U_1751,U_1750] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1750),U_1751),U_1752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1750),U_1752),U_1751))
| ~ sP113(U_1752,U_1751,U_1750) )
& ! [U_1752,U_1751,U_1750] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1750),U_1752),U_1751))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1750),U_1751),U_1752))
| ~ sP113(U_1752,U_1751,U_1750) )
& ! [U_1752,U_1751,U_1750] :
( sP113(U_1752,U_1751,U_1750)
| ~ class_Orderings_Olinorder(U_1750) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_425_2]) ).
cnf(f_425_4,plain,
( sP113(U_1752,U_1751,U_1750)
| ~ class_Orderings_Olinorder(U_1750) ),
inference(clausify,[status(thm)],[f_425_3]) ).
cnf(f_425_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1750),U_1752),U_1751))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1750),U_1751),U_1752))
| ~ sP113(U_1752,U_1751,U_1750) ),
inference(clausify,[status(thm)],[f_425_3]) ).
cnf(f_425_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1750),U_1751),U_1752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1750),U_1752),U_1751))
| ~ sP113(U_1752,U_1751,U_1750) ),
inference(clausify,[status(thm)],[f_425_3]) ).
fof(f_426_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_426_2,plain,
! [U_1755,U_1754,U_1753] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1753),U_1754),U_1755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1753),U_1755),U_1754)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1753),U_1755),U_1754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1753),U_1754),U_1755)) ) )
| ~ class_Orderings_Olinorder(U_1753) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
( ! [U_1754,U_1755,U_1753] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1753),U_1754),U_1755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1753),U_1755),U_1754))
| ~ sP114(U_1754,U_1755,U_1753) )
& ! [U_1754,U_1755,U_1753] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1753),U_1755),U_1754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1753),U_1754),U_1755))
| ~ sP114(U_1754,U_1755,U_1753) )
& ! [U_1754,U_1755,U_1753] :
( sP114(U_1754,U_1755,U_1753)
| ~ class_Orderings_Olinorder(U_1753) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_426_2]) ).
cnf(f_426_4,plain,
( sP114(U_1754,U_1755,U_1753)
| ~ class_Orderings_Olinorder(U_1753) ),
inference(clausify,[status(thm)],[f_426_3]) ).
cnf(f_426_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1753),U_1755),U_1754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1753),U_1754),U_1755))
| ~ sP114(U_1754,U_1755,U_1753) ),
inference(clausify,[status(thm)],[f_426_3]) ).
cnf(f_426_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1753),U_1754),U_1755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1753),U_1755),U_1754))
| ~ sP114(U_1754,U_1755,U_1753) ),
inference(clausify,[status(thm)],[f_426_3]) ).
fof(f_427_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear]) ).
fof(f_427_2,plain,
! [U_1758,U_1757,U_1756] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1756),U_1758),U_1757))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1756),U_1757),U_1758))
| ~ class_Orderings_Olinorder(U_1756) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
! [U_1758,U_1756,U_1757] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1756),U_1758),U_1757))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1756),U_1757),U_1758))
| ~ class_Orderings_Olinorder(U_1756) ),
inference(definitional_conversion,[status(esa)],[f_427_2]) ).
cnf(f_427_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1756),U_1758),U_1757))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1756),U_1757),U_1758))
| ~ class_Orderings_Olinorder(U_1756) ),
inference(clausify,[status(thm)],[f_427_3]) ).
fof(f_428_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_428_2,plain,
! [U_1761,U_1760,U_1759] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1759),U_1760),U_1761))
| U_1760 = U_1761
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1759),U_1760),U_1761)) )
& ( ( U_1760 != U_1761
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1759),U_1760),U_1761)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1759),U_1760),U_1761)) ) )
| ~ class_Orderings_Oorder(U_1759) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
( ! [U_1759,U_1760,U_1761] :
( U_1760 != U_1761
| ~ sP115(U_1759,U_1760,U_1761) )
& ! [U_1759,U_1760,U_1761] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1759),U_1760),U_1761))
| ~ sP115(U_1759,U_1760,U_1761) )
& ! [U_1759,U_1760,U_1761] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1759),U_1760),U_1761))
| U_1760 = U_1761
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1759),U_1760),U_1761))
| ~ sP116(U_1759,U_1760,U_1761) )
& ! [U_1759,U_1760,U_1761] :
( sP115(U_1759,U_1760,U_1761)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1759),U_1760),U_1761))
| ~ sP116(U_1759,U_1760,U_1761) )
& ! [U_1759,U_1760,U_1761] :
( sP116(U_1759,U_1760,U_1761)
| ~ class_Orderings_Oorder(U_1759) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115,sP116])],[f_428_2]) ).
cnf(f_428_4,plain,
( sP116(U_1759,U_1760,U_1761)
| ~ class_Orderings_Oorder(U_1759) ),
inference(clausify,[status(thm)],[f_428_3]) ).
cnf(f_428_5,plain,
( sP115(U_1759,U_1760,U_1761)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1759),U_1760),U_1761))
| ~ sP116(U_1759,U_1760,U_1761) ),
inference(clausify,[status(thm)],[f_428_3]) ).
cnf(f_428_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1759),U_1760),U_1761))
| U_1760 = U_1761
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1759),U_1760),U_1761))
| ~ sP116(U_1759,U_1760,U_1761) ),
inference(clausify,[status(thm)],[f_428_3]) ).
cnf(f_428_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1759),U_1760),U_1761))
| ~ sP115(U_1759,U_1760,U_1761) ),
inference(clausify,[status(thm)],[f_428_3]) ).
cnf(f_428_8,plain,
( U_1760 != U_1761
| ~ sP115(U_1759,U_1760,U_1761) ),
inference(clausify,[status(thm)],[f_428_3]) ).
fof(f_429_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Opreorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_429_2,plain,
! [U_1764,U_1763,U_1762] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1762),U_1763),U_1764))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1764),U_1763))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1763),U_1764)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1764),U_1763))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1763),U_1764)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1762),U_1763),U_1764)) ) )
| ~ class_Orderings_Opreorder(U_1762) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
( ! [U_1764,U_1763,U_1762] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1764),U_1763))
| ~ sP117(U_1764,U_1763,U_1762) )
& ! [U_1764,U_1763,U_1762] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1763),U_1764))
| ~ sP117(U_1764,U_1763,U_1762) )
& ! [U_1764,U_1763,U_1762] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1762),U_1763),U_1764))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1764),U_1763))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1763),U_1764))
| ~ sP118(U_1764,U_1763,U_1762) )
& ! [U_1764,U_1763,U_1762] :
( sP117(U_1764,U_1763,U_1762)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1762),U_1763),U_1764))
| ~ sP118(U_1764,U_1763,U_1762) )
& ! [U_1764,U_1763,U_1762] :
( sP118(U_1764,U_1763,U_1762)
| ~ class_Orderings_Opreorder(U_1762) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117,sP118])],[f_429_2]) ).
cnf(f_429_4,plain,
( sP118(U_1764,U_1763,U_1762)
| ~ class_Orderings_Opreorder(U_1762) ),
inference(clausify,[status(thm)],[f_429_3]) ).
cnf(f_429_5,plain,
( sP117(U_1764,U_1763,U_1762)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1762),U_1763),U_1764))
| ~ sP118(U_1764,U_1763,U_1762) ),
inference(clausify,[status(thm)],[f_429_3]) ).
cnf(f_429_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1762),U_1763),U_1764))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1764),U_1763))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1763),U_1764))
| ~ sP118(U_1764,U_1763,U_1762) ),
inference(clausify,[status(thm)],[f_429_3]) ).
cnf(f_429_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1763),U_1764))
| ~ sP117(U_1764,U_1763,U_1762) ),
inference(clausify,[status(thm)],[f_429_3]) ).
cnf(f_429_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),U_1764),U_1763))
| ~ sP117(U_1764,U_1763,U_1762) ),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_430_2,plain,
! [U_1767,U_1766,U_1765] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1765),U_1766),U_1767))
| ( U_1766 != U_1767
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767)) ) )
& ( U_1766 = U_1767
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1765),U_1766),U_1767)) ) )
| ~ class_Orderings_Oorder(U_1765) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
( ! [U_1767,U_1766,U_1765] :
( U_1766 != U_1767
| ~ sP119(U_1767,U_1766,U_1765) )
& ! [U_1767,U_1766,U_1765] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767))
| ~ sP119(U_1767,U_1766,U_1765) )
& ! [U_1767,U_1766,U_1765] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1765),U_1766),U_1767))
| sP119(U_1767,U_1766,U_1765)
| ~ sP120(U_1767,U_1766,U_1765) )
& ! [U_1767,U_1766,U_1765] :
( U_1766 = U_1767
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1765),U_1766),U_1767))
| ~ sP120(U_1767,U_1766,U_1765) )
& ! [U_1767,U_1766,U_1765] :
( sP120(U_1767,U_1766,U_1765)
| ~ class_Orderings_Oorder(U_1765) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119,sP120])],[f_430_2]) ).
cnf(f_430_4,plain,
( sP120(U_1767,U_1766,U_1765)
| ~ class_Orderings_Oorder(U_1765) ),
inference(clausify,[status(thm)],[f_430_3]) ).
cnf(f_430_5,plain,
( U_1766 = U_1767
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1765),U_1766),U_1767))
| ~ sP120(U_1767,U_1766,U_1765) ),
inference(clausify,[status(thm)],[f_430_3]) ).
cnf(f_430_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1765),U_1766),U_1767))
| sP119(U_1767,U_1766,U_1765)
| ~ sP120(U_1767,U_1766,U_1765) ),
inference(clausify,[status(thm)],[f_430_3]) ).
cnf(f_430_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767))
| ~ sP119(U_1767,U_1766,U_1765) ),
inference(clausify,[status(thm)],[f_430_3]) ).
cnf(f_430_8,plain,
( U_1766 != U_1767
| ~ sP119(U_1767,U_1766,U_1765) ),
inference(clausify,[status(thm)],[f_430_3]) ).
fof(f_431_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leI]) ).
fof(f_431_2,plain,
! [U_1770,U_1769,U_1768] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1768),U_1770),U_1769))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1768),U_1769),U_1770))
| ~ class_Orderings_Olinorder(U_1768) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
! [U_1768,U_1769,U_1770] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1768),U_1770),U_1769))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1768),U_1769),U_1770))
| ~ class_Orderings_Olinorder(U_1768) ),
inference(definitional_conversion,[status(esa)],[f_431_2]) ).
cnf(f_431_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1768),U_1770),U_1769))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1768),U_1769),U_1770))
| ~ class_Orderings_Olinorder(U_1768) ),
inference(clausify,[status(thm)],[f_431_3]) ).
fof(f_432_1,plain,
! [V_x,V_y,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__leE]) ).
fof(f_432_2,plain,
! [U_1773,U_1772,U_1771] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1771),U_1773),U_1772))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1771),U_1772),U_1773))
| ~ class_Orderings_Olinorder(U_1771) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_1772,U_1771,U_1773] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1771),U_1773),U_1772))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1771),U_1772),U_1773))
| ~ class_Orderings_Olinorder(U_1771) ),
inference(definitional_conversion,[status(esa)],[f_432_2]) ).
cnf(f_432_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1771),U_1773),U_1772))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1771),U_1772),U_1773))
| ~ class_Orderings_Olinorder(U_1771) ),
inference(clausify,[status(thm)],[f_432_3]) ).
fof(f_433_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_433_2,plain,
! [U_1776,U_1775,U_1774] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1774),U_1775),U_1776))
| U_1775 != U_1776 )
& ( U_1775 = U_1776
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1774),U_1775),U_1776)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1774),U_1775),U_1776))
| ~ class_Orderings_Olinorder(U_1774) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
( ! [U_1774,U_1775,U_1776] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1774),U_1775),U_1776))
| U_1775 != U_1776
| ~ sP121(U_1774,U_1775,U_1776) )
& ! [U_1774,U_1775,U_1776] :
( U_1775 = U_1776
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1774),U_1775),U_1776))
| ~ sP121(U_1774,U_1775,U_1776) )
& ! [U_1774,U_1775,U_1776] :
( sP121(U_1774,U_1775,U_1776)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1774),U_1775),U_1776))
| ~ class_Orderings_Olinorder(U_1774) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_433_2]) ).
cnf(f_433_4,plain,
( sP121(U_1774,U_1775,U_1776)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1774),U_1775),U_1776))
| ~ class_Orderings_Olinorder(U_1774) ),
inference(clausify,[status(thm)],[f_433_3]) ).
cnf(f_433_5,plain,
( U_1775 = U_1776
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1774),U_1775),U_1776))
| ~ sP121(U_1774,U_1775,U_1776) ),
inference(clausify,[status(thm)],[f_433_3]) ).
cnf(f_433_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1774),U_1775),U_1776))
| U_1775 != U_1776
| ~ sP121(U_1774,U_1775,U_1776) ),
inference(clausify,[status(thm)],[f_433_3]) ).
fof(f_434_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| V_a = V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans]) ).
fof(f_434_2,plain,
! [U_1779,U_1778,U_1777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1777),U_1778),U_1779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1777),U_1778),U_1779))
| U_1778 = U_1779
| ~ class_Orderings_Oorder(U_1777) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_1779,U_1778,U_1777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1777),U_1778),U_1779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1777),U_1778),U_1779))
| U_1778 = U_1779
| ~ class_Orderings_Oorder(U_1777) ),
inference(definitional_conversion,[status(esa)],[f_434_2]) ).
cnf(f_434_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1777),U_1778),U_1779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1777),U_1778),U_1779))
| U_1778 = U_1779
| ~ class_Orderings_Oorder(U_1777) ),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
| V_a = V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I12_J]) ).
fof(f_435_2,plain,
! [U_1782,U_1781,U_1780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1780),U_1782),U_1781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1780),U_1782),U_1781))
| U_1781 = U_1782
| ~ class_Orderings_Oorder(U_1780) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
! [U_1780,U_1782,U_1781] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1780),U_1782),U_1781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1780),U_1782),U_1781))
| U_1781 = U_1782
| ~ class_Orderings_Oorder(U_1780) ),
inference(definitional_conversion,[status(esa)],[f_435_2]) ).
cnf(f_435_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1780),U_1782),U_1781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1780),U_1782),U_1781))
| U_1781 = U_1782
| ~ class_Orderings_Oorder(U_1780) ),
inference(clausify,[status(thm)],[f_435_3]) ).
fof(f_436_1,plain,
! [V_x,V_y,T_a] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leD]) ).
fof(f_436_2,plain,
! [U_1785,U_1784,U_1783] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1783),U_1785),U_1784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1783),U_1784),U_1785))
| ~ class_Orderings_Olinorder(U_1783) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
! [U_1784,U_1783,U_1785] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1783),U_1785),U_1784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1783),U_1784),U_1785))
| ~ class_Orderings_Olinorder(U_1783) ),
inference(definitional_conversion,[status(esa)],[f_436_2]) ).
cnf(f_436_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1783),U_1785),U_1784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1783),U_1784),U_1785))
| ~ class_Orderings_Olinorder(U_1783) ),
inference(clausify,[status(thm)],[f_436_3]) ).
fof(f_437_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__le]) ).
fof(f_437_2,plain,
! [U_1788,U_1787,U_1786] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1786),U_1787),U_1788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1786),U_1787),U_1788))
| ~ class_Orderings_Opreorder(U_1786) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
! [U_1786,U_1787,U_1788] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1786),U_1787),U_1788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1786),U_1787),U_1788))
| ~ class_Orderings_Opreorder(U_1786) ),
inference(definitional_conversion,[status(esa)],[f_437_2]) ).
cnf(f_437_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1786),U_1787),U_1788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1786),U_1787),U_1788))
| ~ class_Orderings_Opreorder(U_1786) ),
inference(clausify,[status(thm)],[f_437_3]) ).
fof(f_438_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_438_2,plain,
! [U_1791,U_1790,U_1789] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1791))
| U_1790 != U_1791 )
& ( U_1790 = U_1791
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1791)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1789),U_1790),U_1791))
| ~ class_Orderings_Olinorder(U_1789) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
( ! [U_1789,U_1790,U_1791] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1791))
| U_1790 != U_1791
| ~ sP122(U_1789,U_1790,U_1791) )
& ! [U_1789,U_1790,U_1791] :
( U_1790 = U_1791
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1791))
| ~ sP122(U_1789,U_1790,U_1791) )
& ! [U_1789,U_1790,U_1791] :
( sP122(U_1789,U_1790,U_1791)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1789),U_1790),U_1791))
| ~ class_Orderings_Olinorder(U_1789) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_438_2]) ).
cnf(f_438_4,plain,
( sP122(U_1789,U_1790,U_1791)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1789),U_1790),U_1791))
| ~ class_Orderings_Olinorder(U_1789) ),
inference(clausify,[status(thm)],[f_438_3]) ).
cnf(f_438_5,plain,
( U_1790 = U_1791
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1791))
| ~ sP122(U_1789,U_1790,U_1791) ),
inference(clausify,[status(thm)],[f_438_3]) ).
cnf(f_438_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1791))
| U_1790 != U_1791
| ~ sP122(U_1789,U_1790,U_1791) ),
inference(clausify,[status(thm)],[f_438_3]) ).
fof(f_439_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq]) ).
fof(f_439_2,plain,
! [U_1794,U_1793,U_1792] :
( U_1793 = U_1794
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1792),U_1793),U_1794))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1792),U_1793),U_1794))
| ~ class_Orderings_Oorder(U_1792) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
fof(f_439_3,plain,
! [U_1794,U_1792,U_1793] :
( U_1793 = U_1794
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1792),U_1793),U_1794))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1792),U_1793),U_1794))
| ~ class_Orderings_Oorder(U_1792) ),
inference(definitional_conversion,[status(esa)],[f_439_2]) ).
cnf(f_439_4,plain,
( U_1793 = U_1794
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1792),U_1793),U_1794))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1792),U_1793),U_1794))
| ~ class_Orderings_Oorder(U_1792) ),
inference(clausify,[status(thm)],[f_439_3]) ).
fof(f_440_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans]) ).
fof(f_440_2,plain,
! [U_1797,U_1796,U_1795] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1795),U_1796),U_1797))
| U_1796 = U_1797
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1795),U_1796),U_1797))
| ~ class_Orderings_Oorder(U_1795) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
! [U_1795,U_1796,U_1797] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1795),U_1796),U_1797))
| U_1796 = U_1797
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1795),U_1796),U_1797))
| ~ class_Orderings_Oorder(U_1795) ),
inference(definitional_conversion,[status(esa)],[f_440_2]) ).
cnf(f_440_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1795),U_1796),U_1797))
| U_1796 = U_1797
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1795),U_1796),U_1797))
| ~ class_Orderings_Oorder(U_1795) ),
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_1,plain,
! [V_a,V_b,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I11_J]) ).
fof(f_441_2,plain,
! [U_1800,U_1799,U_1798] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1798),U_1799),U_1800))
| U_1800 = U_1799
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1798),U_1799),U_1800))
| ~ class_Orderings_Oorder(U_1798) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
! [U_1799,U_1798,U_1800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1798),U_1799),U_1800))
| U_1800 = U_1799
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1798),U_1799),U_1800))
| ~ class_Orderings_Oorder(U_1798) ),
inference(definitional_conversion,[status(esa)],[f_441_2]) ).
cnf(f_441_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1798),U_1799),U_1800))
| U_1800 = U_1799
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1798),U_1799),U_1800))
| ~ class_Orderings_Oorder(U_1798) ),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le__trans]) ).
fof(f_442_2,plain,
! [U_1804,U_1803,U_1802,U_1801] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1801),U_1802),U_1804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1801),U_1803),U_1804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1801),U_1802),U_1803))
| ~ class_Orderings_Opreorder(U_1801) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
! [U_1802,U_1801,U_1803,U_1804] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1801),U_1802),U_1804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1801),U_1803),U_1804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1801),U_1802),U_1803))
| ~ class_Orderings_Opreorder(U_1801) ),
inference(definitional_conversion,[status(esa)],[f_442_2]) ).
cnf(f_442_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1801),U_1802),U_1804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1801),U_1803),U_1804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1801),U_1802),U_1803))
| ~ class_Orderings_Opreorder(U_1801) ),
inference(clausify,[status(thm)],[f_442_3]) ).
fof(f_443_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I7_J]) ).
fof(f_443_2,plain,
! [U_1808,U_1807,U_1806,U_1805] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1805),U_1808),U_1807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1805),U_1808),U_1806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1805),U_1806),U_1807))
| ~ class_Orderings_Oorder(U_1805) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
! [U_1805,U_1806,U_1807,U_1808] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1805),U_1808),U_1807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1805),U_1808),U_1806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1805),U_1806),U_1807))
| ~ class_Orderings_Oorder(U_1805) ),
inference(definitional_conversion,[status(esa)],[f_443_2]) ).
cnf(f_443_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1805),U_1808),U_1807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1805),U_1808),U_1806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1805),U_1806),U_1807))
| ~ class_Orderings_Oorder(U_1805) ),
inference(clausify,[status(thm)],[f_443_3]) ).
fof(f_444_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less__trans]) ).
fof(f_444_2,plain,
! [U_1812,U_1811,U_1810,U_1809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),U_1810),U_1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),U_1811),U_1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1809),U_1810),U_1811))
| ~ class_Orderings_Opreorder(U_1809) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
! [U_1810,U_1809,U_1811,U_1812] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),U_1810),U_1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),U_1811),U_1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1809),U_1810),U_1811))
| ~ class_Orderings_Opreorder(U_1809) ),
inference(definitional_conversion,[status(esa)],[f_444_2]) ).
cnf(f_444_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),U_1810),U_1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),U_1811),U_1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1809),U_1810),U_1811))
| ~ class_Orderings_Opreorder(U_1809) ),
inference(clausify,[status(thm)],[f_444_3]) ).
fof(f_445_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I8_J]) ).
fof(f_445_2,plain,
! [U_1816,U_1815,U_1814,U_1813] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1816),U_1815))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1816),U_1814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1813),U_1814),U_1815))
| ~ class_Orderings_Oorder(U_1813) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
! [U_1814,U_1813,U_1815,U_1816] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1816),U_1815))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1816),U_1814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1813),U_1814),U_1815))
| ~ class_Orderings_Oorder(U_1813) ),
inference(definitional_conversion,[status(esa)],[f_445_2]) ).
cnf(f_445_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1816),U_1815))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1816),U_1814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1813),U_1814),U_1815))
| ~ class_Orderings_Oorder(U_1813) ),
inference(clausify,[status(thm)],[f_445_3]) ).
fof(f_446_1,plain,
! [V_ca_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubsetD]) ).
fof(f_446_2,plain,
! [U_1820,U_1819,U_1818,U_1817] :
( hBOOL(hAPP(hAPP(c_member(U_1817),U_1820),U_1819))
| ~ hBOOL(hAPP(hAPP(c_member(U_1817),U_1820),U_1818))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1817,tc_HOL_Obool)),U_1818),U_1819)) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
! [U_1818,U_1817,U_1819,U_1820] :
( hBOOL(hAPP(hAPP(c_member(U_1817),U_1820),U_1819))
| ~ hBOOL(hAPP(hAPP(c_member(U_1817),U_1820),U_1818))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1817,tc_HOL_Obool)),U_1818),U_1819)) ),
inference(definitional_conversion,[status(esa)],[f_446_2]) ).
cnf(f_446_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1817),U_1820),U_1819))
| ~ hBOOL(hAPP(hAPP(c_member(U_1817),U_1820),U_1818))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1817,tc_HOL_Obool)),U_1818),U_1819)) ),
inference(clausify,[status(thm)],[f_446_3]) ).
fof(f_447_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_not__psubset__empty]) ).
fof(f_447_2,plain,
! [U_1822,U_1821] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1821,tc_HOL_Obool)),U_1822),c_Orderings_Obot__class_Obot(tc_fun(U_1821,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_447_1]) ).
fof(f_447_3,plain,
! [U_1821,U_1822] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1821,tc_HOL_Obool)),U_1822),c_Orderings_Obot__class_Obot(tc_fun(U_1821,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_447_2]) ).
cnf(f_447_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1821,tc_HOL_Obool)),U_1822),c_Orderings_Obot__class_Obot(tc_fun(U_1821,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_447_3]) ).
fof(f_448_1,plain,
! [V_b,V_a,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__supI1]) ).
fof(f_448_2,plain,
! [U_1826,U_1825,U_1824,U_1823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1823),U_1824),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1823),U_1825),U_1826)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1823),U_1824),U_1825))
| ~ class_Lattices_Osemilattice__sup(U_1823) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
! [U_1826,U_1823,U_1824,U_1825] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1823),U_1824),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1823),U_1825),U_1826)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1823),U_1824),U_1825))
| ~ class_Lattices_Osemilattice__sup(U_1823) ),
inference(definitional_conversion,[status(esa)],[f_448_2]) ).
cnf(f_448_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1823),U_1824),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1823),U_1825),U_1826)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1823),U_1824),U_1825))
| ~ class_Lattices_Osemilattice__sup(U_1823) ),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_1,plain,
! [V_a,V_b,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
| ~ class_Lattices_Osemilattice__sup(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__supI2]) ).
fof(f_449_2,plain,
! [U_1830,U_1829,U_1828,U_1827] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1827),U_1828),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1827),U_1830),U_1829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1827),U_1828),U_1829))
| ~ class_Lattices_Osemilattice__sup(U_1827) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
! [U_1827,U_1828,U_1829,U_1830] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1827),U_1828),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1827),U_1830),U_1829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1827),U_1828),U_1829))
| ~ class_Lattices_Osemilattice__sup(U_1827) ),
inference(definitional_conversion,[status(esa)],[f_449_2]) ).
cnf(f_449_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1827),U_1828),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1827),U_1830),U_1829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1827),U_1828),U_1829))
| ~ class_Lattices_Osemilattice__sup(U_1827) ),
inference(clausify,[status(thm)],[f_449_3]) ).
fof(f_450_1,plain,
! [V_b,V_x,V_a,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__infI1]) ).
fof(f_450_2,plain,
! [U_1834,U_1833,U_1832,U_1831] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1831),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1831),U_1832),U_1834)),U_1833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1831),U_1832),U_1833))
| ~ class_Lattices_Osemilattice__inf(U_1831) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
! [U_1831,U_1832,U_1833,U_1834] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1831),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1831),U_1832),U_1834)),U_1833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1831),U_1832),U_1833))
| ~ class_Lattices_Osemilattice__inf(U_1831) ),
inference(definitional_conversion,[status(esa)],[f_450_2]) ).
cnf(f_450_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1831),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1831),U_1832),U_1834)),U_1833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1831),U_1832),U_1833))
| ~ class_Lattices_Osemilattice__inf(U_1831) ),
inference(clausify,[status(thm)],[f_450_3]) ).
fof(f_451_1,plain,
! [V_a,V_x,V_b,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
| ~ class_Lattices_Osemilattice__inf(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__infI2]) ).
fof(f_451_2,plain,
! [U_1838,U_1837,U_1836,U_1835] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1835),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1835),U_1838),U_1836)),U_1837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1835),U_1836),U_1837))
| ~ class_Lattices_Osemilattice__inf(U_1835) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
! [U_1835,U_1836,U_1837,U_1838] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1835),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1835),U_1838),U_1836)),U_1837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1835),U_1836),U_1837))
| ~ class_Lattices_Osemilattice__inf(U_1835) ),
inference(definitional_conversion,[status(esa)],[f_451_2]) ).
cnf(f_451_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1835),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1835),U_1838),U_1836)),U_1837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1835),U_1836),U_1837))
| ~ class_Lattices_Osemilattice__inf(U_1835) ),
inference(clausify,[status(thm)],[f_451_3]) ).
fof(f_452_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans]) ).
fof(f_452_2,plain,
! [U_1842,U_1841,U_1840,U_1839] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1839,tc_HOL_Obool)),U_1840),U_1842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1839,tc_HOL_Obool)),U_1841),U_1842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1839,tc_HOL_Obool)),U_1840),U_1841)) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
! [U_1839,U_1840,U_1841,U_1842] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1839,tc_HOL_Obool)),U_1840),U_1842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1839,tc_HOL_Obool)),U_1841),U_1842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1839,tc_HOL_Obool)),U_1840),U_1841)) ),
inference(definitional_conversion,[status(esa)],[f_452_2]) ).
cnf(f_452_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1839,tc_HOL_Obool)),U_1840),U_1842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1839,tc_HOL_Obool)),U_1841),U_1842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1839,tc_HOL_Obool)),U_1840),U_1841)) ),
inference(clausify,[status(thm)],[f_452_3]) ).
fof(f_453_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans]) ).
fof(f_453_2,plain,
! [U_1846,U_1845,U_1844,U_1843] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1843,tc_HOL_Obool)),U_1844),U_1846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1843,tc_HOL_Obool)),U_1845),U_1846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1843,tc_HOL_Obool)),U_1844),U_1845)) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
! [U_1843,U_1844,U_1845,U_1846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1843,tc_HOL_Obool)),U_1844),U_1846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1843,tc_HOL_Obool)),U_1845),U_1846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1843,tc_HOL_Obool)),U_1844),U_1845)) ),
inference(definitional_conversion,[status(esa)],[f_453_2]) ).
cnf(f_453_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1843,tc_HOL_Obool)),U_1844),U_1846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1843,tc_HOL_Obool)),U_1845),U_1846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1843,tc_HOL_Obool)),U_1844),U_1845)) ),
inference(clausify,[status(thm)],[f_453_3]) ).
fof(f_454_1,plain,
! [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),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset]) ).
fof(f_454_2,plain,
! [U_1849,U_1848,U_1847] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1847,tc_HOL_Obool)),U_1848),U_1849))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1847,tc_HOL_Obool)),U_1848),U_1849)) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
! [U_1847,U_1848,U_1849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1847,tc_HOL_Obool)),U_1848),U_1849))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1847,tc_HOL_Obool)),U_1848),U_1849)) ),
inference(definitional_conversion,[status(esa)],[f_454_2]) ).
cnf(f_454_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1847,tc_HOL_Obool)),U_1848),U_1849))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1847,tc_HOL_Obool)),U_1848),U_1849)) ),
inference(clausify,[status(thm)],[f_454_3]) ).
fof(f_455_1,plain,
! [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),V_B_2))
| ( V_A_2 != V_B_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
& ( V_A_2 = V_B_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq]) ).
fof(f_455_2,plain,
! [U_1852,U_1851,U_1850] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1850,tc_HOL_Obool)),U_1851),U_1852))
| ( U_1851 != U_1852
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1850,tc_HOL_Obool)),U_1851),U_1852)) ) )
& ( U_1851 = U_1852
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1850,tc_HOL_Obool)),U_1851),U_1852))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1850,tc_HOL_Obool)),U_1851),U_1852)) ) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
( ! [U_1858,U_1856,U_1854] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1854,tc_HOL_Obool)),U_1856),U_1858))
| ( U_1856 != U_1858
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1854,tc_HOL_Obool)),U_1856),U_1858)) ) )
& ! [U_1857,U_1855,U_1853] :
( U_1855 = U_1857
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1853,tc_HOL_Obool)),U_1855),U_1857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1853,tc_HOL_Obool)),U_1855),U_1857)) ) ),
inference(miniscope,[status(thm)],[f_455_2]) ).
fof(f_455_4,plain,
( ! [U_1856,U_1854,U_1858] :
( U_1856 != U_1858
| ~ sP123(U_1856,U_1854,U_1858) )
& ! [U_1856,U_1854,U_1858] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1854,tc_HOL_Obool)),U_1856),U_1858))
| ~ sP123(U_1856,U_1854,U_1858) )
& ! [U_1856,U_1854,U_1858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1854,tc_HOL_Obool)),U_1856),U_1858))
| sP123(U_1856,U_1854,U_1858) )
& ! [U_1855,U_1853,U_1857] :
( U_1855 = U_1857
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1853,tc_HOL_Obool)),U_1855),U_1857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1853,tc_HOL_Obool)),U_1855),U_1857)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_455_3]) ).
cnf(f_455_5,plain,
( U_1855 = U_1857
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1853,tc_HOL_Obool)),U_1855),U_1857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1853,tc_HOL_Obool)),U_1855),U_1857)) ),
inference(clausify,[status(thm)],[f_455_4]) ).
cnf(f_455_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1854,tc_HOL_Obool)),U_1856),U_1858))
| sP123(U_1856,U_1854,U_1858) ),
inference(clausify,[status(thm)],[f_455_4]) ).
cnf(f_455_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1854,tc_HOL_Obool)),U_1856),U_1858))
| ~ sP123(U_1856,U_1854,U_1858) ),
inference(clausify,[status(thm)],[f_455_4]) ).
cnf(f_455_8,plain,
( U_1856 != U_1858
| ~ sP123(U_1856,U_1854,U_1858) ),
inference(clausify,[status(thm)],[f_455_4]) ).
fof(f_456_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( ( V_A_2 != V_B_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_psubset__eq]) ).
fof(f_456_2,plain,
! [U_1861,U_1860,U_1859] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1859,tc_HOL_Obool)),U_1860),U_1861))
| U_1860 = U_1861
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1859,tc_HOL_Obool)),U_1860),U_1861)) )
& ( ( U_1860 != U_1861
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1859,tc_HOL_Obool)),U_1860),U_1861)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1859,tc_HOL_Obool)),U_1860),U_1861)) ) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
( ! [U_1867,U_1865,U_1863] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1863,tc_HOL_Obool)),U_1865),U_1867))
| U_1865 = U_1867
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1863,tc_HOL_Obool)),U_1865),U_1867)) )
& ! [U_1866,U_1864,U_1862] :
( ( U_1864 != U_1866
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1862,tc_HOL_Obool)),U_1864),U_1866)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1862,tc_HOL_Obool)),U_1864),U_1866)) ) ),
inference(miniscope,[status(thm)],[f_456_2]) ).
fof(f_456_4,plain,
( ! [U_1864,U_1862,U_1866] :
( U_1864 != U_1866
| ~ sP124(U_1864,U_1862,U_1866) )
& ! [U_1864,U_1862,U_1866] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1862,tc_HOL_Obool)),U_1864),U_1866))
| ~ sP124(U_1864,U_1862,U_1866) )
& ! [U_1865,U_1863,U_1867] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1863,tc_HOL_Obool)),U_1865),U_1867))
| U_1865 = U_1867
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1863,tc_HOL_Obool)),U_1865),U_1867)) )
& ! [U_1864,U_1862,U_1866] :
( sP124(U_1864,U_1862,U_1866)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1862,tc_HOL_Obool)),U_1864),U_1866)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_456_3]) ).
cnf(f_456_5,plain,
( sP124(U_1864,U_1862,U_1866)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1862,tc_HOL_Obool)),U_1864),U_1866)) ),
inference(clausify,[status(thm)],[f_456_4]) ).
cnf(f_456_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1863,tc_HOL_Obool)),U_1865),U_1867))
| U_1865 = U_1867
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1863,tc_HOL_Obool)),U_1865),U_1867)) ),
inference(clausify,[status(thm)],[f_456_4]) ).
cnf(f_456_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1862,tc_HOL_Obool)),U_1864),U_1866))
| ~ sP124(U_1864,U_1862,U_1866) ),
inference(clausify,[status(thm)],[f_456_4]) ).
cnf(f_456_8,plain,
( U_1864 != U_1866
| ~ sP124(U_1864,U_1862,U_1866) ),
inference(clausify,[status(thm)],[f_456_4]) ).
fof(f_457_1,plain,
! [V_S_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__Sup__iff]) ).
fof(f_457_2,plain,
! [U_1872,U_1871,U_1870] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),c_Complete__Lattice_OSup__class_OSup(U_1870,U_1872)))
| ! [U_1869] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1869))
| ~ hBOOL(hAPP(hAPP(c_member(U_1870),U_1869),U_1872)) ) )
& ( ? [U_1868] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1868))
& hBOOL(hAPP(hAPP(c_member(U_1870),U_1868),U_1872)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),c_Complete__Lattice_OSup__class_OSup(U_1870,U_1872))) ) )
| ~ class_Orderings_Olinorder(U_1870)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1870) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
! [U_1872,U_1871,U_1870] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),c_Complete__Lattice_OSup__class_OSup(U_1870,U_1872)))
| ! [U_1869] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1869))
| ~ hBOOL(hAPP(hAPP(c_member(U_1870),U_1869),U_1872)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),sK45(U_1872,U_1871,U_1870)))
& hBOOL(hAPP(hAPP(c_member(U_1870),sK45(U_1872,U_1871,U_1870)),U_1872)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),c_Complete__Lattice_OSup__class_OSup(U_1870,U_1872))) ) )
| ~ class_Orderings_Olinorder(U_1870)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1870) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_1868,sK45(U_1872,U_1871,U_1870))],[f_457_2]) ).
fof(f_457_4,plain,
( ! [U_1870,U_1871,U_1872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),sK45(U_1872,U_1871,U_1870)))
| ~ sP125(U_1870,U_1871,U_1872) )
& ! [U_1870,U_1871,U_1872] :
( hBOOL(hAPP(hAPP(c_member(U_1870),sK45(U_1872,U_1871,U_1870)),U_1872))
| ~ sP125(U_1870,U_1871,U_1872) )
& ! [U_1870,U_1869,U_1871,U_1872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),c_Complete__Lattice_OSup__class_OSup(U_1870,U_1872)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1869))
| ~ hBOOL(hAPP(hAPP(c_member(U_1870),U_1869),U_1872))
| ~ sP126(U_1870,U_1869,U_1871,U_1872) )
& ! [U_1870,U_1869,U_1871,U_1872] :
( sP125(U_1870,U_1871,U_1872)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),c_Complete__Lattice_OSup__class_OSup(U_1870,U_1872)))
| ~ sP126(U_1870,U_1869,U_1871,U_1872) )
& ! [U_1870,U_1869,U_1871,U_1872] :
( sP126(U_1870,U_1869,U_1871,U_1872)
| ~ class_Orderings_Olinorder(U_1870)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1870) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125,sP126])],[f_457_3]) ).
cnf(f_457_5,plain,
( sP126(U_1870,U_1869,U_1871,U_1872)
| ~ class_Orderings_Olinorder(U_1870)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1870) ),
inference(clausify,[status(thm)],[f_457_4]) ).
cnf(f_457_6,plain,
( sP125(U_1870,U_1871,U_1872)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),c_Complete__Lattice_OSup__class_OSup(U_1870,U_1872)))
| ~ sP126(U_1870,U_1869,U_1871,U_1872) ),
inference(clausify,[status(thm)],[f_457_4]) ).
cnf(f_457_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),c_Complete__Lattice_OSup__class_OSup(U_1870,U_1872)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1869))
| ~ hBOOL(hAPP(hAPP(c_member(U_1870),U_1869),U_1872))
| ~ sP126(U_1870,U_1869,U_1871,U_1872) ),
inference(clausify,[status(thm)],[f_457_4]) ).
cnf(f_457_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_1870),sK45(U_1872,U_1871,U_1870)),U_1872))
| ~ sP125(U_1870,U_1871,U_1872) ),
inference(clausify,[status(thm)],[f_457_4]) ).
cnf(f_457_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),sK45(U_1872,U_1871,U_1870)))
| ~ sP125(U_1870,U_1871,U_1872) ),
inference(clausify,[status(thm)],[f_457_4]) ).
fof(f_458_1,plain,
! [V_a_2,V_S_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__less__iff]) ).
fof(f_458_2,plain,
! [U_1877,U_1876,U_1875] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),c_Complete__Lattice_OInf__class_OInf(U_1875,U_1876)),U_1877))
| ! [U_1874] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1874),U_1877))
| ~ hBOOL(hAPP(hAPP(c_member(U_1875),U_1874),U_1876)) ) )
& ( ? [U_1873] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1873),U_1877))
& hBOOL(hAPP(hAPP(c_member(U_1875),U_1873),U_1876)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),c_Complete__Lattice_OInf__class_OInf(U_1875,U_1876)),U_1877)) ) )
| ~ class_Orderings_Olinorder(U_1875)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1875) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
! [U_1877,U_1876,U_1875] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),c_Complete__Lattice_OInf__class_OInf(U_1875,U_1876)),U_1877))
| ! [U_1874] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1874),U_1877))
| ~ hBOOL(hAPP(hAPP(c_member(U_1875),U_1874),U_1876)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),sK46(U_1877,U_1876,U_1875)),U_1877))
& hBOOL(hAPP(hAPP(c_member(U_1875),sK46(U_1877,U_1876,U_1875)),U_1876)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),c_Complete__Lattice_OInf__class_OInf(U_1875,U_1876)),U_1877)) ) )
| ~ class_Orderings_Olinorder(U_1875)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1875) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_1873,sK46(U_1877,U_1876,U_1875))],[f_458_2]) ).
fof(f_458_4,plain,
( ! [U_1875,U_1877,U_1876] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),sK46(U_1877,U_1876,U_1875)),U_1877))
| ~ sP127(U_1875,U_1877,U_1876) )
& ! [U_1875,U_1877,U_1876] :
( hBOOL(hAPP(hAPP(c_member(U_1875),sK46(U_1877,U_1876,U_1875)),U_1876))
| ~ sP127(U_1875,U_1877,U_1876) )
& ! [U_1875,U_1877,U_1876,U_1874] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),c_Complete__Lattice_OInf__class_OInf(U_1875,U_1876)),U_1877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1874),U_1877))
| ~ hBOOL(hAPP(hAPP(c_member(U_1875),U_1874),U_1876))
| ~ sP128(U_1875,U_1877,U_1876,U_1874) )
& ! [U_1875,U_1877,U_1876,U_1874] :
( sP127(U_1875,U_1877,U_1876)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),c_Complete__Lattice_OInf__class_OInf(U_1875,U_1876)),U_1877))
| ~ sP128(U_1875,U_1877,U_1876,U_1874) )
& ! [U_1875,U_1877,U_1876,U_1874] :
( sP128(U_1875,U_1877,U_1876,U_1874)
| ~ class_Orderings_Olinorder(U_1875)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1875) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127,sP128])],[f_458_3]) ).
cnf(f_458_5,plain,
( sP128(U_1875,U_1877,U_1876,U_1874)
| ~ class_Orderings_Olinorder(U_1875)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1875) ),
inference(clausify,[status(thm)],[f_458_4]) ).
cnf(f_458_6,plain,
( sP127(U_1875,U_1877,U_1876)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),c_Complete__Lattice_OInf__class_OInf(U_1875,U_1876)),U_1877))
| ~ sP128(U_1875,U_1877,U_1876,U_1874) ),
inference(clausify,[status(thm)],[f_458_4]) ).
cnf(f_458_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),c_Complete__Lattice_OInf__class_OInf(U_1875,U_1876)),U_1877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1874),U_1877))
| ~ hBOOL(hAPP(hAPP(c_member(U_1875),U_1874),U_1876))
| ~ sP128(U_1875,U_1877,U_1876,U_1874) ),
inference(clausify,[status(thm)],[f_458_4]) ).
cnf(f_458_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_1875),sK46(U_1877,U_1876,U_1875)),U_1876))
| ~ sP127(U_1875,U_1877,U_1876) ),
inference(clausify,[status(thm)],[f_458_4]) ).
cnf(f_458_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),sK46(U_1877,U_1876,U_1875)),U_1877))
| ~ sP127(U_1875,U_1877,U_1876) ),
inference(clausify,[status(thm)],[f_458_4]) ).
fof(f_459_1,plain,
! [V_k_2,V_i_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__iff]) ).
fof(f_459_2,plain,
! [U_1880,U_1879,U_1878] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_1878),U_1879),hAPP(c_SetInterval_Oord__class_OlessThan(U_1878),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),U_1880)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),U_1880))
| ~ hBOOL(hAPP(hAPP(c_member(U_1878),U_1879),hAPP(c_SetInterval_Oord__class_OlessThan(U_1878),U_1880))) ) )
| ~ class_Orderings_Oord(U_1878) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
( ! [U_1880,U_1878,U_1879] :
( hBOOL(hAPP(hAPP(c_member(U_1878),U_1879),hAPP(c_SetInterval_Oord__class_OlessThan(U_1878),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),U_1880))
| ~ sP129(U_1880,U_1878,U_1879) )
& ! [U_1880,U_1878,U_1879] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),U_1880))
| ~ hBOOL(hAPP(hAPP(c_member(U_1878),U_1879),hAPP(c_SetInterval_Oord__class_OlessThan(U_1878),U_1880)))
| ~ sP129(U_1880,U_1878,U_1879) )
& ! [U_1880,U_1878,U_1879] :
( sP129(U_1880,U_1878,U_1879)
| ~ class_Orderings_Oord(U_1878) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_459_2]) ).
cnf(f_459_4,plain,
( sP129(U_1880,U_1878,U_1879)
| ~ class_Orderings_Oord(U_1878) ),
inference(clausify,[status(thm)],[f_459_3]) ).
cnf(f_459_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),U_1880))
| ~ hBOOL(hAPP(hAPP(c_member(U_1878),U_1879),hAPP(c_SetInterval_Oord__class_OlessThan(U_1878),U_1880)))
| ~ sP129(U_1880,U_1878,U_1879) ),
inference(clausify,[status(thm)],[f_459_3]) ).
cnf(f_459_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1878),U_1879),hAPP(c_SetInterval_Oord__class_OlessThan(U_1878),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),U_1880))
| ~ sP129(U_1880,U_1878,U_1879) ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J]) ).
fof(f_460_2,plain,
! [U_1884,U_1883,U_1882,U_1881] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1881,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1881,U_1882,U_1883)),c_SetInterval_Oord__class_OatLeastAtMost(U_1881,U_1883,U_1884)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1881,U_1882,U_1884)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1881),U_1883),U_1884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),U_1882),U_1883))
| ~ class_Orderings_Olinorder(U_1881) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
! [U_1882,U_1881,U_1883,U_1884] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1881,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1881,U_1882,U_1883)),c_SetInterval_Oord__class_OatLeastAtMost(U_1881,U_1883,U_1884)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1881,U_1882,U_1884)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1881),U_1883),U_1884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),U_1882),U_1883))
| ~ class_Orderings_Olinorder(U_1881) ),
inference(definitional_conversion,[status(esa)],[f_460_2]) ).
cnf(f_460_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1881,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1881,U_1882,U_1883)),c_SetInterval_Oord__class_OatLeastAtMost(U_1881,U_1883,U_1884)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1881,U_1882,U_1884)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1881),U_1883),U_1884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),U_1882),U_1883))
| ~ class_Orderings_Olinorder(U_1881) ),
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [V_l_2,V_k_2,T_b] :
( ( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))
| 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)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).
fof(f_461_2,plain,
! [U_1887,U_1886,U_1885] :
( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_1885,U_1886,U_1887) = c_Orderings_Obot__class_Obot(tc_fun(U_1885,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1885),U_1886),U_1887)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1885),U_1886),U_1887))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_1885,U_1886,U_1887) != c_Orderings_Obot__class_Obot(tc_fun(U_1885,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_1885) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
( ! [U_1887,U_1885,U_1886] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_1885,U_1886,U_1887) = c_Orderings_Obot__class_Obot(tc_fun(U_1885,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1885),U_1886),U_1887))
| ~ sP130(U_1887,U_1885,U_1886) )
& ! [U_1887,U_1885,U_1886] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1885),U_1886),U_1887))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_1885,U_1886,U_1887) != c_Orderings_Obot__class_Obot(tc_fun(U_1885,tc_HOL_Obool))
| ~ sP130(U_1887,U_1885,U_1886) )
& ! [U_1887,U_1885,U_1886] :
( sP130(U_1887,U_1885,U_1886)
| ~ class_Orderings_Oorder(U_1885) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_461_2]) ).
cnf(f_461_4,plain,
( sP130(U_1887,U_1885,U_1886)
| ~ class_Orderings_Oorder(U_1885) ),
inference(clausify,[status(thm)],[f_461_3]) ).
cnf(f_461_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1885),U_1886),U_1887))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_1885,U_1886,U_1887) != c_Orderings_Obot__class_Obot(tc_fun(U_1885,tc_HOL_Obool))
| ~ sP130(U_1887,U_1885,U_1886) ),
inference(clausify,[status(thm)],[f_461_3]) ).
cnf(f_461_6,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_1885,U_1886,U_1887) = c_Orderings_Obot__class_Obot(tc_fun(U_1885,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1885),U_1886),U_1887))
| ~ sP130(U_1887,U_1885,U_1886) ),
inference(clausify,[status(thm)],[f_461_3]) ).
fof(f_462_1,plain,
! [V_l_2,V_k_2,T_b] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))
| 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) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).
fof(f_462_2,plain,
! [U_1890,U_1889,U_1888] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_1888,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1888,U_1889,U_1890)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),U_1889),U_1890)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),U_1889),U_1890))
| c_Orderings_Obot__class_Obot(tc_fun(U_1888,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_1888,U_1889,U_1890) ) )
| ~ class_Orderings_Oorder(U_1888) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
( ! [U_1889,U_1890,U_1888] :
( c_Orderings_Obot__class_Obot(tc_fun(U_1888,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1888,U_1889,U_1890)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),U_1889),U_1890))
| ~ sP131(U_1889,U_1890,U_1888) )
& ! [U_1889,U_1890,U_1888] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),U_1889),U_1890))
| c_Orderings_Obot__class_Obot(tc_fun(U_1888,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_1888,U_1889,U_1890)
| ~ sP131(U_1889,U_1890,U_1888) )
& ! [U_1889,U_1890,U_1888] :
( sP131(U_1889,U_1890,U_1888)
| ~ class_Orderings_Oorder(U_1888) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_462_2]) ).
cnf(f_462_4,plain,
( sP131(U_1889,U_1890,U_1888)
| ~ class_Orderings_Oorder(U_1888) ),
inference(clausify,[status(thm)],[f_462_3]) ).
cnf(f_462_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),U_1889),U_1890))
| c_Orderings_Obot__class_Obot(tc_fun(U_1888,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_1888,U_1889,U_1890)
| ~ sP131(U_1889,U_1890,U_1888) ),
inference(clausify,[status(thm)],[f_462_3]) ).
cnf(f_462_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_1888,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1888,U_1889,U_1890)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),U_1889),U_1890))
| ~ sP131(U_1889,U_1890,U_1888) ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_1,plain,
! [V_k_2,V_i_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__iff]) ).
fof(f_463_2,plain,
! [U_1893,U_1892,U_1891] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_1891),U_1892),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1891),U_1893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),U_1892)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),U_1892))
| ~ hBOOL(hAPP(hAPP(c_member(U_1891),U_1892),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1891),U_1893))) ) )
| ~ class_Orderings_Oord(U_1891) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
fof(f_463_3,plain,
( ! [U_1893,U_1892,U_1891] :
( hBOOL(hAPP(hAPP(c_member(U_1891),U_1892),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1891),U_1893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),U_1892))
| ~ sP132(U_1893,U_1892,U_1891) )
& ! [U_1893,U_1892,U_1891] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),U_1892))
| ~ hBOOL(hAPP(hAPP(c_member(U_1891),U_1892),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1891),U_1893)))
| ~ sP132(U_1893,U_1892,U_1891) )
& ! [U_1893,U_1892,U_1891] :
( sP132(U_1893,U_1892,U_1891)
| ~ class_Orderings_Oord(U_1891) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_463_2]) ).
cnf(f_463_4,plain,
( sP132(U_1893,U_1892,U_1891)
| ~ class_Orderings_Oord(U_1891) ),
inference(clausify,[status(thm)],[f_463_3]) ).
cnf(f_463_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),U_1892))
| ~ hBOOL(hAPP(hAPP(c_member(U_1891),U_1892),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1891),U_1893)))
| ~ sP132(U_1893,U_1892,U_1891) ),
inference(clausify,[status(thm)],[f_463_3]) ).
cnf(f_463_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1891),U_1892),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1891),U_1893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),U_1892))
| ~ sP132(U_1893,U_1892,U_1891) ),
inference(clausify,[status(thm)],[f_463_3]) ).
fof(f_464_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| 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)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff]) ).
fof(f_464_2,plain,
! [U_1896,U_1895,U_1894] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_1894,U_1895,U_1896) = c_Orderings_Obot__class_Obot(tc_fun(U_1894,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1894),U_1895),U_1896)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1894),U_1895),U_1896))
| c_SetInterval_Oord__class_OatLeastAtMost(U_1894,U_1895,U_1896) != c_Orderings_Obot__class_Obot(tc_fun(U_1894,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_1894) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
fof(f_464_3,plain,
( ! [U_1896,U_1895,U_1894] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1894,U_1895,U_1896) = c_Orderings_Obot__class_Obot(tc_fun(U_1894,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1894),U_1895),U_1896))
| ~ sP133(U_1896,U_1895,U_1894) )
& ! [U_1896,U_1895,U_1894] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1894),U_1895),U_1896))
| c_SetInterval_Oord__class_OatLeastAtMost(U_1894,U_1895,U_1896) != c_Orderings_Obot__class_Obot(tc_fun(U_1894,tc_HOL_Obool))
| ~ sP133(U_1896,U_1895,U_1894) )
& ! [U_1896,U_1895,U_1894] :
( sP133(U_1896,U_1895,U_1894)
| ~ class_Orderings_Oorder(U_1894) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_464_2]) ).
cnf(f_464_4,plain,
( sP133(U_1896,U_1895,U_1894)
| ~ class_Orderings_Oorder(U_1894) ),
inference(clausify,[status(thm)],[f_464_3]) ).
cnf(f_464_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1894),U_1895),U_1896))
| c_SetInterval_Oord__class_OatLeastAtMost(U_1894,U_1895,U_1896) != c_Orderings_Obot__class_Obot(tc_fun(U_1894,tc_HOL_Obool))
| ~ sP133(U_1896,U_1895,U_1894) ),
inference(clausify,[status(thm)],[f_464_3]) ).
cnf(f_464_6,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1894,U_1895,U_1896) = c_Orderings_Obot__class_Obot(tc_fun(U_1894,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1894),U_1895),U_1896))
| ~ sP133(U_1896,U_1895,U_1894) ),
inference(clausify,[status(thm)],[f_464_3]) ).
fof(f_465_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| 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) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).
fof(f_465_2,plain,
! [U_1899,U_1898,U_1897] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_1897,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1897,U_1898,U_1899)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1898),U_1899)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1898),U_1899))
| c_Orderings_Obot__class_Obot(tc_fun(U_1897,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_1897,U_1898,U_1899) ) )
| ~ class_Orderings_Oorder(U_1897) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
fof(f_465_3,plain,
( ! [U_1897,U_1899,U_1898] :
( c_Orderings_Obot__class_Obot(tc_fun(U_1897,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1897,U_1898,U_1899)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1898),U_1899))
| ~ sP134(U_1897,U_1899,U_1898) )
& ! [U_1897,U_1899,U_1898] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1898),U_1899))
| c_Orderings_Obot__class_Obot(tc_fun(U_1897,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_1897,U_1898,U_1899)
| ~ sP134(U_1897,U_1899,U_1898) )
& ! [U_1897,U_1899,U_1898] :
( sP134(U_1897,U_1899,U_1898)
| ~ class_Orderings_Oorder(U_1897) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134])],[f_465_2]) ).
cnf(f_465_4,plain,
( sP134(U_1897,U_1899,U_1898)
| ~ class_Orderings_Oorder(U_1897) ),
inference(clausify,[status(thm)],[f_465_3]) ).
cnf(f_465_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1898),U_1899))
| c_Orderings_Obot__class_Obot(tc_fun(U_1897,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_1897,U_1898,U_1899)
| ~ sP134(U_1897,U_1899,U_1898) ),
inference(clausify,[status(thm)],[f_465_3]) ).
cnf(f_465_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_1897,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1897,U_1898,U_1899)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1898),U_1899))
| ~ sP134(U_1897,U_1899,U_1898) ),
inference(clausify,[status(thm)],[f_465_3]) ).
fof(f_466_1,plain,
! [V_d_2,V_ca_2,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_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ 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_ca_2,V_d_2))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__subset__iff]) ).
fof(f_466_2,plain,
! [U_1904,U_1903,U_1902,U_1901,U_1900] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1901,U_1902)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1903,U_1904)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1903),U_1901)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1901),U_1902)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1904))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1903),U_1901)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1901),U_1902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1901,U_1902)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1903,U_1904))) ) )
| ~ class_Orderings_Oorder(U_1900) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
( ! [U_1901,U_1900,U_1902,U_1903,U_1904] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1903),U_1901))
| ~ sP136(U_1901,U_1900,U_1902,U_1903,U_1904) )
& ! [U_1901,U_1900,U_1902,U_1903,U_1904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1901),U_1902))
| ~ sP136(U_1901,U_1900,U_1902,U_1903,U_1904) )
& ! [U_1901,U_1900,U_1902,U_1903,U_1904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1904))
| ~ sP135(U_1901,U_1900,U_1902,U_1903,U_1904) )
& ! [U_1901,U_1900,U_1902,U_1903,U_1904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1903),U_1901))
| ~ sP135(U_1901,U_1900,U_1902,U_1903,U_1904) )
& ! [U_1901,U_1900,U_1902,U_1903,U_1904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1901,U_1902)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1903,U_1904)))
| sP136(U_1901,U_1900,U_1902,U_1903,U_1904)
| ~ sP137(U_1901,U_1900,U_1902,U_1903,U_1904) )
& ! [U_1901,U_1900,U_1902,U_1903,U_1904] :
( sP135(U_1901,U_1900,U_1902,U_1903,U_1904)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1901),U_1902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1901,U_1902)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1903,U_1904)))
| ~ sP137(U_1901,U_1900,U_1902,U_1903,U_1904) )
& ! [U_1901,U_1900,U_1902,U_1903,U_1904] :
( sP137(U_1901,U_1900,U_1902,U_1903,U_1904)
| ~ class_Orderings_Oorder(U_1900) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135,sP136,sP137])],[f_466_2]) ).
cnf(f_466_4,plain,
( sP137(U_1901,U_1900,U_1902,U_1903,U_1904)
| ~ class_Orderings_Oorder(U_1900) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_5,plain,
( sP135(U_1901,U_1900,U_1902,U_1903,U_1904)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1901),U_1902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1901,U_1902)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1903,U_1904)))
| ~ sP137(U_1901,U_1900,U_1902,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1901,U_1902)),c_SetInterval_Oord__class_OatLeastAtMost(U_1900,U_1903,U_1904)))
| sP136(U_1901,U_1900,U_1902,U_1903,U_1904)
| ~ sP137(U_1901,U_1900,U_1902,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1903),U_1901))
| ~ sP135(U_1901,U_1900,U_1902,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1904))
| ~ sP135(U_1901,U_1900,U_1902,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1901),U_1902))
| ~ sP136(U_1901,U_1900,U_1902,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1903),U_1901))
| ~ sP136(U_1901,U_1900,U_1902,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_1,plain,
! [V_b_2,V_a_2,T_b] :
( 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)))
| V_a_2 != V_b_2
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H]) ).
fof(f_467_2,plain,
! [U_1907,U_1906,U_1905] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1905,U_1906,U_1907) = hAPP(hAPP(c_Set_Oinsert(U_1905),U_1906),c_Orderings_Obot__class_Obot(tc_fun(U_1905,tc_HOL_Obool)))
| U_1906 != U_1907
| ~ class_Orderings_Oorder(U_1905) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
! [U_1907,U_1906,U_1905] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1905,U_1906,U_1907) = hAPP(hAPP(c_Set_Oinsert(U_1905),U_1906),c_Orderings_Obot__class_Obot(tc_fun(U_1905,tc_HOL_Obool)))
| U_1906 != U_1907
| ~ class_Orderings_Oorder(U_1905) ),
inference(definitional_conversion,[status(esa)],[f_467_2]) ).
cnf(f_467_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1905,U_1906,U_1907) = hAPP(hAPP(c_Set_Oinsert(U_1905),U_1906),c_Orderings_Obot__class_Obot(tc_fun(U_1905,tc_HOL_Obool)))
| U_1906 != U_1907
| ~ class_Orderings_Oorder(U_1905) ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| V_b_2 != V_ca_2
| V_a_2 != V_b_2 )
& ( ( V_b_2 = V_ca_2
& V_a_2 = V_b_2 )
| c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff]) ).
fof(f_468_2,plain,
! [U_1911,U_1910,U_1909,U_1908] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_1908,U_1909,U_1910) = hAPP(hAPP(c_Set_Oinsert(U_1908),U_1911),c_Orderings_Obot__class_Obot(tc_fun(U_1908,tc_HOL_Obool)))
| U_1910 != U_1911
| U_1909 != U_1910 )
& ( ( U_1910 = U_1911
& U_1909 = U_1910 )
| c_SetInterval_Oord__class_OatLeastAtMost(U_1908,U_1909,U_1910) != hAPP(hAPP(c_Set_Oinsert(U_1908),U_1911),c_Orderings_Obot__class_Obot(tc_fun(U_1908,tc_HOL_Obool))) ) )
| ~ class_Orderings_Oorder(U_1908) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
( ! [U_1909,U_1910,U_1911] :
( U_1910 = U_1911
| ~ sP138(U_1909,U_1910,U_1911) )
& ! [U_1909,U_1910,U_1911] :
( U_1909 = U_1910
| ~ sP138(U_1909,U_1910,U_1911) )
& ! [U_1909,U_1910,U_1911,U_1908] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1908,U_1909,U_1910) = hAPP(hAPP(c_Set_Oinsert(U_1908),U_1911),c_Orderings_Obot__class_Obot(tc_fun(U_1908,tc_HOL_Obool)))
| U_1910 != U_1911
| U_1909 != U_1910
| ~ sP139(U_1909,U_1910,U_1911,U_1908) )
& ! [U_1909,U_1910,U_1911,U_1908] :
( sP138(U_1909,U_1910,U_1911)
| c_SetInterval_Oord__class_OatLeastAtMost(U_1908,U_1909,U_1910) != hAPP(hAPP(c_Set_Oinsert(U_1908),U_1911),c_Orderings_Obot__class_Obot(tc_fun(U_1908,tc_HOL_Obool)))
| ~ sP139(U_1909,U_1910,U_1911,U_1908) )
& ! [U_1909,U_1910,U_1911,U_1908] :
( sP139(U_1909,U_1910,U_1911,U_1908)
| ~ class_Orderings_Oorder(U_1908) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138,sP139])],[f_468_2]) ).
cnf(f_468_4,plain,
( sP139(U_1909,U_1910,U_1911,U_1908)
| ~ class_Orderings_Oorder(U_1908) ),
inference(clausify,[status(thm)],[f_468_3]) ).
cnf(f_468_5,plain,
( sP138(U_1909,U_1910,U_1911)
| c_SetInterval_Oord__class_OatLeastAtMost(U_1908,U_1909,U_1910) != hAPP(hAPP(c_Set_Oinsert(U_1908),U_1911),c_Orderings_Obot__class_Obot(tc_fun(U_1908,tc_HOL_Obool)))
| ~ sP139(U_1909,U_1910,U_1911,U_1908) ),
inference(clausify,[status(thm)],[f_468_3]) ).
cnf(f_468_6,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1908,U_1909,U_1910) = hAPP(hAPP(c_Set_Oinsert(U_1908),U_1911),c_Orderings_Obot__class_Obot(tc_fun(U_1908,tc_HOL_Obool)))
| U_1910 != U_1911
| U_1909 != U_1910
| ~ sP139(U_1909,U_1910,U_1911,U_1908) ),
inference(clausify,[status(thm)],[f_468_3]) ).
cnf(f_468_7,plain,
( U_1909 = U_1910
| ~ sP138(U_1909,U_1910,U_1911) ),
inference(clausify,[status(thm)],[f_468_3]) ).
cnf(f_468_8,plain,
( U_1910 = U_1911
| ~ sP138(U_1909,U_1910,U_1911) ),
inference(clausify,[status(thm)],[f_468_3]) ).
fof(f_469_1,plain,
! [V_a_2,T_b] :
( 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)))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton]) ).
fof(f_469_2,plain,
! [U_1913,U_1912] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1912,U_1913,U_1913) = hAPP(hAPP(c_Set_Oinsert(U_1912),U_1913),c_Orderings_Obot__class_Obot(tc_fun(U_1912,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1912) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
fof(f_469_3,plain,
! [U_1912,U_1913] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1912,U_1913,U_1913) = hAPP(hAPP(c_Set_Oinsert(U_1912),U_1913),c_Orderings_Obot__class_Obot(tc_fun(U_1912,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1912) ),
inference(definitional_conversion,[status(esa)],[f_469_2]) ).
cnf(f_469_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1912,U_1913,U_1913) = hAPP(hAPP(c_Set_Oinsert(U_1912),U_1913),c_Orderings_Obot__class_Obot(tc_fun(U_1912,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1912) ),
inference(clausify,[status(thm)],[f_469_3]) ).
fof(f_470_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = V_b_2
| V_ca_2 != V_d_2 )
& ( V_ca_2 = V_d_2
| V_a_2 != V_b_2 ) )
| 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_ca_2),V_d_2)
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).
fof(f_470_2,plain,
! [U_1918,U_1917,U_1916,U_1915,U_1914] :
( ( ( U_1915 = U_1916
| U_1917 != U_1918 )
& ( U_1917 = U_1918
| U_1915 != U_1916 ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1914),U_1915),U_1916) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1914),U_1917),U_1918)
| ~ class_Groups_Oab__group__add(U_1914) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
( ! [U_1917,U_1915,U_1916,U_1918] :
( U_1915 = U_1916
| U_1917 != U_1918
| ~ sP140(U_1917,U_1915,U_1916,U_1918) )
& ! [U_1917,U_1915,U_1916,U_1918] :
( U_1917 = U_1918
| U_1915 != U_1916
| ~ sP140(U_1917,U_1915,U_1916,U_1918) )
& ! [U_1914,U_1917,U_1915,U_1916,U_1918] :
( sP140(U_1917,U_1915,U_1916,U_1918)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1914),U_1915),U_1916) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1914),U_1917),U_1918)
| ~ class_Groups_Oab__group__add(U_1914) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_470_2]) ).
cnf(f_470_4,plain,
( sP140(U_1917,U_1915,U_1916,U_1918)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1914),U_1915),U_1916) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1914),U_1917),U_1918)
| ~ class_Groups_Oab__group__add(U_1914) ),
inference(clausify,[status(thm)],[f_470_3]) ).
cnf(f_470_5,plain,
( U_1917 = U_1918
| U_1915 != U_1916
| ~ sP140(U_1917,U_1915,U_1916,U_1918) ),
inference(clausify,[status(thm)],[f_470_3]) ).
cnf(f_470_6,plain,
( U_1915 = U_1916
| U_1917 != U_1918
| ~ sP140(U_1917,U_1915,U_1916,U_1918) ),
inference(clausify,[status(thm)],[f_470_3]) ).
fof(f_471_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J]) ).
fof(f_471_2,plain,
! [U_1922,U_1921,U_1920,U_1919] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1919,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1919,U_1920,U_1921)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1919,U_1921,U_1922)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1919,U_1920,U_1922)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1919),U_1921),U_1922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1919),U_1920),U_1921))
| ~ class_Orderings_Olinorder(U_1919) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
! [U_1919,U_1922,U_1920,U_1921] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1919,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1919,U_1920,U_1921)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1919,U_1921,U_1922)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1919,U_1920,U_1922)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1919),U_1921),U_1922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1919),U_1920),U_1921))
| ~ class_Orderings_Olinorder(U_1919) ),
inference(definitional_conversion,[status(esa)],[f_471_2]) ).
cnf(f_471_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1919,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1919,U_1920,U_1921)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1919,U_1921,U_1922)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1919,U_1920,U_1922)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1919),U_1921),U_1922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1919),U_1920),U_1921))
| ~ class_Orderings_Olinorder(U_1919) ),
inference(clausify,[status(thm)],[f_471_3]) ).
fof(f_472_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J]) ).
fof(f_472_2,plain,
! [U_1925,U_1924,U_1923] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1923,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1923),U_1924)),c_SetInterval_Oord__class_OatLeastAtMost(U_1923,U_1924,U_1925)) = c_Orderings_Obot__class_Obot(tc_fun(U_1923,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1923) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
! [U_1925,U_1923,U_1924] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1923,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1923),U_1924)),c_SetInterval_Oord__class_OatLeastAtMost(U_1923,U_1924,U_1925)) = c_Orderings_Obot__class_Obot(tc_fun(U_1923,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1923) ),
inference(definitional_conversion,[status(esa)],[f_472_2]) ).
cnf(f_472_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1923,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1923),U_1924)),c_SetInterval_Oord__class_OatLeastAtMost(U_1923,U_1924,U_1925)) = c_Orderings_Obot__class_Obot(tc_fun(U_1923,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1923) ),
inference(clausify,[status(thm)],[f_472_3]) ).
fof(f_473_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J]) ).
fof(f_473_2,plain,
! [U_1929,U_1928,U_1927,U_1926] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1926,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1926,U_1927,U_1928)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1926,U_1928,U_1929)) = c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1926) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
! [U_1926,U_1927,U_1928,U_1929] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1926,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1926,U_1927,U_1928)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1926,U_1928,U_1929)) = c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1926) ),
inference(definitional_conversion,[status(esa)],[f_473_2]) ).
cnf(f_473_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1926,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1926,U_1927,U_1928)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1926,U_1928,U_1929)) = c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1926) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J]) ).
fof(f_474_2,plain,
! [U_1933,U_1932,U_1931,U_1930] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1930,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1930,U_1931,U_1932)),c_SetInterval_Oord__class_OatLeastAtMost(U_1930,U_1932,U_1933)) = c_Orderings_Obot__class_Obot(tc_fun(U_1930,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1930) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
fof(f_474_3,plain,
! [U_1930,U_1931,U_1932,U_1933] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1930,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1930,U_1931,U_1932)),c_SetInterval_Oord__class_OatLeastAtMost(U_1930,U_1932,U_1933)) = c_Orderings_Obot__class_Obot(tc_fun(U_1930,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1930) ),
inference(definitional_conversion,[status(esa)],[f_474_2]) ).
cnf(f_474_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1930,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1930,U_1931,U_1932)),c_SetInterval_Oord__class_OatLeastAtMost(U_1930,U_1932,U_1933)) = c_Orderings_Obot__class_Obot(tc_fun(U_1930,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1930) ),
inference(clausify,[status(thm)],[f_474_3]) ).
fof(f_475_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J]) ).
fof(f_475_2,plain,
! [U_1937,U_1936,U_1935,U_1934] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1934,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1934,U_1935,U_1936)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1934,U_1936,U_1937)) = c_Orderings_Obot__class_Obot(tc_fun(U_1934,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1934) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
fof(f_475_3,plain,
! [U_1934,U_1935,U_1936,U_1937] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1934,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1934,U_1935,U_1936)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1934,U_1936,U_1937)) = c_Orderings_Obot__class_Obot(tc_fun(U_1934,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1934) ),
inference(definitional_conversion,[status(esa)],[f_475_2]) ).
cnf(f_475_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1934,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1934,U_1935,U_1936)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1934,U_1936,U_1937)) = c_Orderings_Obot__class_Obot(tc_fun(U_1934,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1934) ),
inference(clausify,[status(thm)],[f_475_3]) ).
fof(f_476_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J]) ).
fof(f_476_2,plain,
! [U_1940,U_1939,U_1938] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1938,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1938,U_1939,U_1940)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1938),U_1940)) = c_Orderings_Obot__class_Obot(tc_fun(U_1938,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1938) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
! [U_1938,U_1939,U_1940] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1938,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1938,U_1939,U_1940)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1938),U_1940)) = c_Orderings_Obot__class_Obot(tc_fun(U_1938,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1938) ),
inference(definitional_conversion,[status(esa)],[f_476_2]) ).
cnf(f_476_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1938,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1938,U_1939,U_1940)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1938),U_1940)) = c_Orderings_Obot__class_Obot(tc_fun(U_1938,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1938) ),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J]) ).
fof(f_477_2,plain,
! [U_1944,U_1943,U_1942,U_1941] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1941,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1941,U_1942,U_1943)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1941,U_1943,U_1944)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1941,U_1942,U_1944)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1943),U_1944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1941),U_1942),U_1943))
| ~ class_Orderings_Olinorder(U_1941) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
! [U_1941,U_1942,U_1943,U_1944] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1941,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1941,U_1942,U_1943)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1941,U_1943,U_1944)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1941,U_1942,U_1944)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1943),U_1944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1941),U_1942),U_1943))
| ~ class_Orderings_Olinorder(U_1941) ),
inference(definitional_conversion,[status(esa)],[f_477_2]) ).
cnf(f_477_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1941,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1941,U_1942,U_1943)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1941,U_1943,U_1944)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1941,U_1942,U_1944)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1943),U_1944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1941),U_1942),U_1943))
| ~ class_Orderings_Olinorder(U_1941) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J]) ).
fof(f_478_2,plain,
! [U_1947,U_1946,U_1945] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1945,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1945),U_1946)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1945,U_1946,U_1947)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_1945),U_1947)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),U_1946),U_1947))
| ~ class_Orderings_Olinorder(U_1945) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
! [U_1946,U_1945,U_1947] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1945,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1945),U_1946)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1945,U_1946,U_1947)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_1945),U_1947)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),U_1946),U_1947))
| ~ class_Orderings_Olinorder(U_1945) ),
inference(definitional_conversion,[status(esa)],[f_478_2]) ).
cnf(f_478_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1945,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1945),U_1946)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1945,U_1946,U_1947)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_1945),U_1947)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),U_1946),U_1947))
| ~ class_Orderings_Olinorder(U_1945) ),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_1,plain,
! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
( ( 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))
| ( ! [B_x,B_y] :
( ~ 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
| hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) != hAPP(hAPP(V_a3_2,B_x),B_y) )
& ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) != V_a4_2
| V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
& ( ? [B_x,B_y] :
( 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)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
& hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) )
| ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2
& V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I2_J]) ).
fof(f_479_2,plain,
! [U_1958,U_1957,U_1956,U_1955,U_1954,U_1953,U_1952] :
( ( c_Nitpick_Ofold__graph_H(U_1952,U_1953,U_1954,U_1955,U_1956,hAPP(hAPP(U_1954,U_1957),U_1958))
| ( ! [U_1951,U_1950] :
( ~ c_Nitpick_Ofold__graph_H(U_1952,U_1953,U_1954,U_1955,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1952,tc_HOL_Obool)),U_1956),hAPP(hAPP(c_Set_Oinsert(U_1952),U_1951),c_Orderings_Obot__class_Obot(tc_fun(U_1952,tc_HOL_Obool)))),U_1950)
| ~ hBOOL(hAPP(hAPP(c_member(U_1952),U_1951),U_1956))
| hAPP(hAPP(U_1954,U_1957),U_1958) != hAPP(hAPP(U_1954,U_1951),U_1950) )
& ( hAPP(hAPP(U_1954,U_1957),U_1958) != U_1955
| U_1956 != c_Orderings_Obot__class_Obot(tc_fun(U_1952,tc_HOL_Obool)) ) ) )
& ( ? [U_1949,U_1948] :
( c_Nitpick_Ofold__graph_H(U_1952,U_1953,U_1954,U_1955,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1952,tc_HOL_Obool)),U_1956),hAPP(hAPP(c_Set_Oinsert(U_1952),U_1949),c_Orderings_Obot__class_Obot(tc_fun(U_1952,tc_HOL_Obool)))),U_1948)
& hBOOL(hAPP(hAPP(c_member(U_1952),U_1949),U_1956))
& hAPP(hAPP(U_1954,U_1957),U_1958) = hAPP(hAPP(U_1954,U_1949),U_1948) )
| ( hAPP(hAPP(U_1954,U_1957),U_1958) = U_1955
& U_1956 = c_Orderings_Obot__class_Obot(tc_fun(U_1952,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_1952,U_1953,U_1954,U_1955,U_1956,hAPP(hAPP(U_1954,U_1957),U_1958)) ) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
( ! [U_1972,U_1970,U_1968,U_1966,U_1964,U_1962,U_1960] :
( c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,U_1968,hAPP(hAPP(U_1964,U_1970),U_1972))
| ( ! [U_1951] :
( ! [U_1950] :
( ~ c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1960,tc_HOL_Obool)),U_1968),hAPP(hAPP(c_Set_Oinsert(U_1960),U_1951),c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool)))),U_1950)
| hAPP(hAPP(U_1964,U_1970),U_1972) != hAPP(hAPP(U_1964,U_1951),U_1950) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1960),U_1951),U_1968)) )
& ( hAPP(hAPP(U_1964,U_1970),U_1972) != U_1966
| U_1968 != c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool)) ) ) )
& ! [U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959] :
( ? [U_1949] :
( ? [U_1948] :
( c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),U_1967),hAPP(hAPP(c_Set_Oinsert(U_1959),U_1949),c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool)))),U_1948)
& hAPP(hAPP(U_1963,U_1969),U_1971) = hAPP(hAPP(U_1963,U_1949),U_1948) )
& hBOOL(hAPP(hAPP(c_member(U_1959),U_1949),U_1967)) )
| ( hAPP(hAPP(U_1963,U_1969),U_1971) = U_1965
& U_1967 = c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,U_1967,hAPP(hAPP(U_1963,U_1969),U_1971)) ) ),
inference(miniscope,[status(thm)],[f_479_2]) ).
fof(f_479_4,plain,
( ! [U_1972,U_1970,U_1968,U_1966,U_1964,U_1962,U_1960] :
( c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,U_1968,hAPP(hAPP(U_1964,U_1970),U_1972))
| ( ! [U_1951] :
( ! [U_1950] :
( ~ c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1960,tc_HOL_Obool)),U_1968),hAPP(hAPP(c_Set_Oinsert(U_1960),U_1951),c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool)))),U_1950)
| hAPP(hAPP(U_1964,U_1970),U_1972) != hAPP(hAPP(U_1964,U_1951),U_1950) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1960),U_1951),U_1968)) )
& ( hAPP(hAPP(U_1964,U_1970),U_1972) != U_1966
| U_1968 != c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool)) ) ) )
& ! [U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959] :
( ( ? [U_1948] :
( c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),U_1967),hAPP(hAPP(c_Set_Oinsert(U_1959),sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool)))),U_1948)
& hAPP(hAPP(U_1963,U_1969),U_1971) = hAPP(hAPP(U_1963,sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),U_1948) )
& hBOOL(hAPP(hAPP(c_member(U_1959),sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),U_1967)) )
| ( hAPP(hAPP(U_1963,U_1969),U_1971) = U_1965
& U_1967 = c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,U_1967,hAPP(hAPP(U_1963,U_1969),U_1971)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_1949,sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959))],[f_479_3]) ).
fof(f_479_5,plain,
( ! [U_1972,U_1970,U_1968,U_1966,U_1964,U_1962,U_1960] :
( c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,U_1968,hAPP(hAPP(U_1964,U_1970),U_1972))
| ( ! [U_1951] :
( ! [U_1950] :
( ~ c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1960,tc_HOL_Obool)),U_1968),hAPP(hAPP(c_Set_Oinsert(U_1960),U_1951),c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool)))),U_1950)
| hAPP(hAPP(U_1964,U_1970),U_1972) != hAPP(hAPP(U_1964,U_1951),U_1950) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1960),U_1951),U_1968)) )
& ( hAPP(hAPP(U_1964,U_1970),U_1972) != U_1966
| U_1968 != c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool)) ) ) )
& ! [U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959] :
( ( c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),U_1967),hAPP(hAPP(c_Set_Oinsert(U_1959),sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool)))),sK48(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959))
& hAPP(hAPP(U_1963,U_1969),U_1971) = hAPP(hAPP(U_1963,sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),sK48(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959))
& hBOOL(hAPP(hAPP(c_member(U_1959),sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),U_1967)) )
| ( hAPP(hAPP(U_1963,U_1969),U_1971) = U_1965
& U_1967 = c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,U_1967,hAPP(hAPP(U_1963,U_1969),U_1971)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_1948,sK48(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959))],[f_479_4]) ).
fof(f_479_6,plain,
( ! [U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970] :
( ~ c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1960,tc_HOL_Obool)),U_1968),hAPP(hAPP(c_Set_Oinsert(U_1960),U_1951),c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool)))),U_1950)
| hAPP(hAPP(U_1964,U_1970),U_1972) != hAPP(hAPP(U_1964,U_1951),U_1950)
| ~ hBOOL(hAPP(hAPP(c_member(U_1960),U_1951),U_1968))
| ~ sP143(U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970) )
& ! [U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970] :
( hAPP(hAPP(U_1964,U_1970),U_1972) != U_1966
| U_1968 != c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool))
| ~ sP143(U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970) )
& ! [U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971] :
( c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),U_1967),hAPP(hAPP(c_Set_Oinsert(U_1959),sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool)))),sK48(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959))
| ~ sP142(U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) )
& ! [U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971] :
( hAPP(hAPP(U_1963,U_1969),U_1971) = hAPP(hAPP(U_1963,sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),sK48(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959))
| ~ sP142(U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) )
& ! [U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971] :
( hBOOL(hAPP(hAPP(c_member(U_1959),sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),U_1967))
| ~ sP142(U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) )
& ! [U_1959,U_1965,U_1969,U_1963,U_1967,U_1971] :
( hAPP(hAPP(U_1963,U_1969),U_1971) = U_1965
| ~ sP141(U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) )
& ! [U_1959,U_1965,U_1969,U_1963,U_1967,U_1971] :
( U_1967 = c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool))
| ~ sP141(U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) )
& ! [U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970] :
( c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,U_1968,hAPP(hAPP(U_1964,U_1970),U_1972))
| sP143(U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970) )
& ! [U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971] :
( sP142(U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971)
| sP141(U_1959,U_1965,U_1969,U_1963,U_1967,U_1971)
| ~ c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,U_1967,hAPP(hAPP(U_1963,U_1969),U_1971)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141,sP142,sP143])],[f_479_5]) ).
cnf(f_479_7,plain,
( sP142(U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971)
| sP141(U_1959,U_1965,U_1969,U_1963,U_1967,U_1971)
| ~ c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,U_1967,hAPP(hAPP(U_1963,U_1969),U_1971)) ),
inference(clausify,[status(thm)],[f_479_6]) ).
cnf(f_479_8,plain,
( c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,U_1968,hAPP(hAPP(U_1964,U_1970),U_1972))
| sP143(U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970) ),
inference(clausify,[status(thm)],[f_479_6]) ).
cnf(f_479_9,plain,
( U_1967 = c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool))
| ~ sP141(U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) ),
inference(clausify,[status(thm)],[f_479_6]) ).
cnf(f_479_10,plain,
( hAPP(hAPP(U_1963,U_1969),U_1971) = U_1965
| ~ sP141(U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) ),
inference(clausify,[status(thm)],[f_479_6]) ).
cnf(f_479_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_1959),sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),U_1967))
| ~ sP142(U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) ),
inference(clausify,[status(thm)],[f_479_6]) ).
cnf(f_479_12,plain,
( hAPP(hAPP(U_1963,U_1969),U_1971) = hAPP(hAPP(U_1963,sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),sK48(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959))
| ~ sP142(U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) ),
inference(clausify,[status(thm)],[f_479_6]) ).
cnf(f_479_13,plain,
( c_Nitpick_Ofold__graph_H(U_1959,U_1961,U_1963,U_1965,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),U_1967),hAPP(hAPP(c_Set_Oinsert(U_1959),sK47(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959)),c_Orderings_Obot__class_Obot(tc_fun(U_1959,tc_HOL_Obool)))),sK48(U_1971,U_1969,U_1967,U_1965,U_1963,U_1961,U_1959))
| ~ sP142(U_1961,U_1959,U_1965,U_1969,U_1963,U_1967,U_1971) ),
inference(clausify,[status(thm)],[f_479_6]) ).
cnf(f_479_14,plain,
( hAPP(hAPP(U_1964,U_1970),U_1972) != U_1966
| U_1968 != c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool))
| ~ sP143(U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970) ),
inference(clausify,[status(thm)],[f_479_6]) ).
cnf(f_479_15,plain,
( ~ c_Nitpick_Ofold__graph_H(U_1960,U_1962,U_1964,U_1966,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1960,tc_HOL_Obool)),U_1968),hAPP(hAPP(c_Set_Oinsert(U_1960),U_1951),c_Orderings_Obot__class_Obot(tc_fun(U_1960,tc_HOL_Obool)))),U_1950)
| hAPP(hAPP(U_1964,U_1970),U_1972) != hAPP(hAPP(U_1964,U_1951),U_1950)
| ~ hBOOL(hAPP(hAPP(c_member(U_1960),U_1951),U_1968))
| ~ sP143(U_1968,U_1962,U_1950,U_1951,U_1966,U_1972,U_1964,U_1960,U_1970) ),
inference(clausify,[status(thm)],[f_479_6]) ).
fof(f_480_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J]) ).
fof(f_480_2,plain,
! [U_1976,U_1975,U_1974,U_1973] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1973,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1973,U_1974,U_1975)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1973,U_1975,U_1976)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1973,U_1974),U_1976)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1973),U_1975),U_1976))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1973),U_1974),U_1975))
| ~ class_Orderings_Olinorder(U_1973) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
! [U_1974,U_1973,U_1976,U_1975] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1973,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1973,U_1974,U_1975)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1973,U_1975,U_1976)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1973,U_1974),U_1976)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1973),U_1975),U_1976))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1973),U_1974),U_1975))
| ~ class_Orderings_Olinorder(U_1973) ),
inference(definitional_conversion,[status(esa)],[f_480_2]) ).
cnf(f_480_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1973,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1973,U_1974,U_1975)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1973,U_1975,U_1976)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1973,U_1974),U_1976)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1973),U_1975),U_1976))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1973),U_1974),U_1975))
| ~ class_Orderings_Olinorder(U_1973) ),
inference(clausify,[status(thm)],[f_480_3]) ).
fof(f_481_1,plain,
! [V_u_2,V_l_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_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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J]) ).
fof(f_481_2,plain,
! [U_1979,U_1978,U_1977] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1977,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1977),U_1978),c_Orderings_Obot__class_Obot(tc_fun(U_1977,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1977,U_1978,U_1979)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1977,U_1978),U_1979)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1977),U_1978),U_1979))
| ~ class_Orderings_Olinorder(U_1977) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
! [U_1977,U_1978,U_1979] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1977,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1977),U_1978),c_Orderings_Obot__class_Obot(tc_fun(U_1977,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1977,U_1978,U_1979)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1977,U_1978),U_1979)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1977),U_1978),U_1979))
| ~ class_Orderings_Olinorder(U_1977) ),
inference(definitional_conversion,[status(esa)],[f_481_2]) ).
cnf(f_481_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1977,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1977),U_1978),c_Orderings_Obot__class_Obot(tc_fun(U_1977,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1977,U_1978,U_1979)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1977,U_1978),U_1979)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1977),U_1978),U_1979))
| ~ class_Orderings_Olinorder(U_1977) ),
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J]) ).
fof(f_482_2,plain,
! [U_1982,U_1981,U_1980] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1980,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1980,U_1981),U_1982)),hAPP(hAPP(c_Set_Oinsert(U_1980),U_1982),c_Orderings_Obot__class_Obot(tc_fun(U_1980,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_1980,U_1981,U_1982)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1980),U_1981),U_1982))
| ~ class_Orderings_Olinorder(U_1980) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
fof(f_482_3,plain,
! [U_1980,U_1981,U_1982] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1980,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1980,U_1981),U_1982)),hAPP(hAPP(c_Set_Oinsert(U_1980),U_1982),c_Orderings_Obot__class_Obot(tc_fun(U_1980,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_1980,U_1981,U_1982)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1980),U_1981),U_1982))
| ~ class_Orderings_Olinorder(U_1980) ),
inference(definitional_conversion,[status(esa)],[f_482_2]) ).
cnf(f_482_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1980,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1980,U_1981),U_1982)),hAPP(hAPP(c_Set_Oinsert(U_1980),U_1982),c_Orderings_Obot__class_Obot(tc_fun(U_1980,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_1980,U_1981,U_1982)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1980),U_1981),U_1982))
| ~ class_Orderings_Olinorder(U_1980) ),
inference(clausify,[status(thm)],[f_482_3]) ).
fof(f_483_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J]) ).
fof(f_483_2,plain,
! [U_1986,U_1985,U_1984,U_1983] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1983,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1983,U_1984,U_1985)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1983,U_1985),U_1986)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1983,U_1984,U_1986)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1983),U_1985),U_1986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1984),U_1985))
| ~ class_Orderings_Olinorder(U_1983) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
fof(f_483_3,plain,
! [U_1983,U_1984,U_1985,U_1986] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1983,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1983,U_1984,U_1985)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1983,U_1985),U_1986)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1983,U_1984,U_1986)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1983),U_1985),U_1986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1984),U_1985))
| ~ class_Orderings_Olinorder(U_1983) ),
inference(definitional_conversion,[status(esa)],[f_483_2]) ).
cnf(f_483_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1983,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1983,U_1984,U_1985)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1983,U_1985),U_1986)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1983,U_1984,U_1986)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1983),U_1985),U_1986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1984),U_1985))
| ~ class_Orderings_Olinorder(U_1983) ),
inference(clausify,[status(thm)],[f_483_3]) ).
fof(f_484_1,plain,
! [V_y_2,V_x_2,V_A_2,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,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph]) ).
fof(f_484_2,plain,
! [U_1993,U_1992,U_1991,U_1990,U_1989,U_1988,U_1987] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1987,U_1988,U_1989,U_1990,U_1991),hAPP(hAPP(U_1989,U_1992),U_1993)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1987),U_1992),U_1991))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1987,U_1988,U_1989,U_1990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1987,tc_HOL_Obool)),U_1991),hAPP(hAPP(c_Set_Oinsert(U_1987),U_1992),c_Orderings_Obot__class_Obot(tc_fun(U_1987,tc_HOL_Obool))))),U_1993)) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
fof(f_484_3,plain,
! [U_1988,U_1987,U_1989,U_1990,U_1991,U_1992,U_1993] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1987,U_1988,U_1989,U_1990,U_1991),hAPP(hAPP(U_1989,U_1992),U_1993)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1987),U_1992),U_1991))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1987,U_1988,U_1989,U_1990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1987,tc_HOL_Obool)),U_1991),hAPP(hAPP(c_Set_Oinsert(U_1987),U_1992),c_Orderings_Obot__class_Obot(tc_fun(U_1987,tc_HOL_Obool))))),U_1993)) ),
inference(definitional_conversion,[status(esa)],[f_484_2]) ).
cnf(f_484_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1987,U_1988,U_1989,U_1990,U_1991),hAPP(hAPP(U_1989,U_1992),U_1993)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1987),U_1992),U_1991))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1987,U_1988,U_1989,U_1990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1987,tc_HOL_Obool)),U_1991),hAPP(hAPP(c_Set_Oinsert(U_1987),U_1992),c_Orderings_Obot__class_Obot(tc_fun(U_1987,tc_HOL_Obool))))),U_1993)) ),
inference(clausify,[status(thm)],[f_484_3]) ).
fof(f_485_1,plain,
! [V_B_2,V_A_2,T_b] :
( ? [B_b] : 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__imp__ex__mem]) ).
fof(f_485_2,plain,
! [U_1997,U_1996,U_1995] :
( ? [U_1994] : hBOOL(hAPP(hAPP(c_member(U_1995),U_1994),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1995,tc_HOL_Obool)),U_1997),U_1996)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1995,tc_HOL_Obool)),U_1996),U_1997)) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
fof(f_485_3,plain,
! [U_1997,U_1996,U_1995] :
( hBOOL(hAPP(hAPP(c_member(U_1995),sK49(U_1997,U_1996,U_1995)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1995,tc_HOL_Obool)),U_1997),U_1996)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1995,tc_HOL_Obool)),U_1996),U_1997)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_1994,sK49(U_1997,U_1996,U_1995))],[f_485_2]) ).
fof(f_485_4,plain,
! [U_1995,U_1996,U_1997] :
( hBOOL(hAPP(hAPP(c_member(U_1995),sK49(U_1997,U_1996,U_1995)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1995,tc_HOL_Obool)),U_1997),U_1996)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1995,tc_HOL_Obool)),U_1996),U_1997)) ),
inference(definitional_conversion,[status(esa)],[f_485_3]) ).
cnf(f_485_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_1995),sK49(U_1997,U_1996,U_1995)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1995,tc_HOL_Obool)),U_1997),U_1996)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1995,tc_HOL_Obool)),U_1996),U_1997)) ),
inference(clausify,[status(thm)],[f_485_4]) ).
fof(f_486_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J]) ).
fof(f_486_2,plain,
! [U_2000,U_1999,U_1998] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1998,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1998,U_1999),U_2000)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1998),U_2000)) = c_Orderings_Obot__class_Obot(tc_fun(U_1998,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1998) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
fof(f_486_3,plain,
! [U_1998,U_1999,U_2000] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1998,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1998,U_1999),U_2000)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1998),U_2000)) = c_Orderings_Obot__class_Obot(tc_fun(U_1998,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1998) ),
inference(definitional_conversion,[status(esa)],[f_486_2]) ).
cnf(f_486_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1998,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1998,U_1999),U_2000)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1998),U_2000)) = c_Orderings_Obot__class_Obot(tc_fun(U_1998,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1998) ),
inference(clausify,[status(thm)],[f_486_3]) ).
fof(f_487_1,plain,
! [V_y,V_x,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) != c_Orderings_Otop__class_Otop(T_a)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) != c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__unique]) ).
fof(f_487_2,plain,
! [U_2003,U_2002,U_2001] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2001),U_2002) = U_2003
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2001),U_2002),U_2003) != c_Orderings_Otop__class_Otop(U_2001)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2001),U_2002),U_2003) != c_Orderings_Obot__class_Obot(U_2001)
| ~ class_Lattices_Oboolean__algebra(U_2001) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
fof(f_487_3,plain,
! [U_2001,U_2002,U_2003] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2001),U_2002) = U_2003
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2001),U_2002),U_2003) != c_Orderings_Otop__class_Otop(U_2001)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2001),U_2002),U_2003) != c_Orderings_Obot__class_Obot(U_2001)
| ~ class_Lattices_Oboolean__algebra(U_2001) ),
inference(definitional_conversion,[status(esa)],[f_487_2]) ).
cnf(f_487_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2001),U_2002) = U_2003
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2001),U_2002),U_2003) != c_Orderings_Otop__class_Otop(U_2001)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2001),U_2002),U_2003) != c_Orderings_Obot__class_Obot(U_2001)
| ~ class_Lattices_Oboolean__algebra(U_2001) ),
inference(clausify,[status(thm)],[f_487_3]) ).
fof(f_488_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J]) ).
fof(f_488_2,plain,
! [U_2006,U_2005,U_2004] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2004,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2004,U_2005),U_2006)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2004),U_2006)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2004),U_2005)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2004),U_2005),U_2006))
| ~ class_Orderings_Olinorder(U_2004) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
fof(f_488_3,plain,
! [U_2004,U_2005,U_2006] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2004,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2004,U_2005),U_2006)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2004),U_2006)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2004),U_2005)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2004),U_2005),U_2006))
| ~ class_Orderings_Olinorder(U_2004) ),
inference(definitional_conversion,[status(esa)],[f_488_2]) ).
cnf(f_488_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2004,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2004,U_2005),U_2006)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2004),U_2006)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2004),U_2005)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2004),U_2005),U_2006))
| ~ class_Orderings_Olinorder(U_2004) ),
inference(clausify,[status(thm)],[f_488_3]) ).
fof(f_489_1,plain,
! [V_A_2,V_ca_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_ComplI]) ).
fof(f_489_2,plain,
! [U_2009,U_2008,U_2007] :
( hBOOL(hAPP(hAPP(c_member(U_2007),U_2008),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2007,tc_HOL_Obool)),U_2009)))
| hBOOL(hAPP(hAPP(c_member(U_2007),U_2008),U_2009)) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
! [U_2007,U_2008,U_2009] :
( hBOOL(hAPP(hAPP(c_member(U_2007),U_2008),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2007,tc_HOL_Obool)),U_2009)))
| hBOOL(hAPP(hAPP(c_member(U_2007),U_2008),U_2009)) ),
inference(definitional_conversion,[status(esa)],[f_489_2]) ).
cnf(f_489_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2007),U_2008),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2007,tc_HOL_Obool)),U_2009)))
| hBOOL(hAPP(hAPP(c_member(U_2007),U_2008),U_2009)) ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__minus]) ).
fof(f_490_2,plain,
! [U_2011,U_2010] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2011)) = U_2011
| ~ class_Groups_Ogroup__add(U_2010) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
fof(f_490_3,plain,
! [U_2010,U_2011] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2011)) = U_2011
| ~ class_Groups_Ogroup__add(U_2010) ),
inference(definitional_conversion,[status(esa)],[f_490_2]) ).
cnf(f_490_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2011)) = U_2011
| ~ class_Groups_Ogroup__add(U_2010) ),
inference(clausify,[status(thm)],[f_490_3]) ).
fof(f_491_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| V_b_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) )
& ( V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).
fof(f_491_2,plain,
! [U_2014,U_2013,U_2012] :
( ( ( U_2013 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2014)
| U_2014 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2013) )
& ( U_2014 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2013)
| U_2013 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2014) ) )
| ~ class_Groups_Ogroup__add(U_2012) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
fof(f_491_3,plain,
( ! [U_2012,U_2013,U_2014] :
( U_2013 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2014)
| U_2014 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2013)
| ~ sP144(U_2012,U_2013,U_2014) )
& ! [U_2012,U_2013,U_2014] :
( U_2014 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2013)
| U_2013 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2014)
| ~ sP144(U_2012,U_2013,U_2014) )
& ! [U_2012,U_2013,U_2014] :
( sP144(U_2012,U_2013,U_2014)
| ~ class_Groups_Ogroup__add(U_2012) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144])],[f_491_2]) ).
cnf(f_491_4,plain,
( sP144(U_2012,U_2013,U_2014)
| ~ class_Groups_Ogroup__add(U_2012) ),
inference(clausify,[status(thm)],[f_491_3]) ).
cnf(f_491_5,plain,
( U_2014 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2013)
| U_2013 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2014)
| ~ sP144(U_2012,U_2013,U_2014) ),
inference(clausify,[status(thm)],[f_491_3]) ).
cnf(f_491_6,plain,
( U_2013 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2014)
| U_2014 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2012),U_2013)
| ~ sP144(U_2012,U_2013,U_2014) ),
inference(clausify,[status(thm)],[f_491_3]) ).
fof(f_492_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) != V_a_2 )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != V_b_2 ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).
fof(f_492_2,plain,
! [U_2017,U_2016,U_2015] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2016) = U_2017
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2017) != U_2016 )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2017) = U_2016
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2016) != U_2017 ) )
| ~ class_Groups_Ogroup__add(U_2015) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
( ! [U_2016,U_2017,U_2015] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2016) = U_2017
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2017) != U_2016
| ~ sP145(U_2016,U_2017,U_2015) )
& ! [U_2016,U_2017,U_2015] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2017) = U_2016
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2016) != U_2017
| ~ sP145(U_2016,U_2017,U_2015) )
& ! [U_2016,U_2017,U_2015] :
( sP145(U_2016,U_2017,U_2015)
| ~ class_Groups_Ogroup__add(U_2015) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145])],[f_492_2]) ).
cnf(f_492_4,plain,
( sP145(U_2016,U_2017,U_2015)
| ~ class_Groups_Ogroup__add(U_2015) ),
inference(clausify,[status(thm)],[f_492_3]) ).
cnf(f_492_5,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2017) = U_2016
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2016) != U_2017
| ~ sP145(U_2016,U_2017,U_2015) ),
inference(clausify,[status(thm)],[f_492_3]) ).
cnf(f_492_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2016) = U_2017
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2015),U_2017) != U_2016
| ~ sP145(U_2016,U_2017,U_2015) ),
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).
fof(f_493_2,plain,
! [U_2020,U_2019,U_2018] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2019) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2020)
| U_2019 != U_2020 )
& ( U_2019 = U_2020
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2019) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2020) ) )
| ~ class_Groups_Ogroup__add(U_2018) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
( ! [U_2020,U_2019,U_2018] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2019) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2020)
| U_2019 != U_2020
| ~ sP146(U_2020,U_2019,U_2018) )
& ! [U_2020,U_2019,U_2018] :
( U_2019 = U_2020
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2019) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2020)
| ~ sP146(U_2020,U_2019,U_2018) )
& ! [U_2020,U_2019,U_2018] :
( sP146(U_2020,U_2019,U_2018)
| ~ class_Groups_Ogroup__add(U_2018) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146])],[f_493_2]) ).
cnf(f_493_4,plain,
( sP146(U_2020,U_2019,U_2018)
| ~ class_Groups_Ogroup__add(U_2018) ),
inference(clausify,[status(thm)],[f_493_3]) ).
cnf(f_493_5,plain,
( U_2019 = U_2020
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2019) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2020)
| ~ sP146(U_2020,U_2019,U_2018) ),
inference(clausify,[status(thm)],[f_493_3]) ).
cnf(f_493_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2019) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2018),U_2020)
| U_2019 != U_2020
| ~ sP146(U_2020,U_2019,U_2018) ),
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_1,plain,
! [V_x,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__compl]) ).
fof(f_494_2,plain,
! [U_2022,U_2021] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2021),hAPP(c_Groups_Ouminus__class_Ouminus(U_2021),U_2022)) = U_2022
| ~ class_Lattices_Oboolean__algebra(U_2021) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
! [U_2022,U_2021] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2021),hAPP(c_Groups_Ouminus__class_Ouminus(U_2021),U_2022)) = U_2022
| ~ class_Lattices_Oboolean__algebra(U_2021) ),
inference(definitional_conversion,[status(esa)],[f_494_2]) ).
cnf(f_494_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2021),hAPP(c_Groups_Ouminus__class_Ouminus(U_2021),U_2022)) = U_2022
| ~ class_Lattices_Oboolean__algebra(U_2021) ),
inference(clausify,[status(thm)],[f_494_3]) ).
fof(f_495_1,plain,
! [V_x_2,V_A_2,T_c,T_b] :
( 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))
| ~ class_Groups_Ouminus(T_b) ),
inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).
fof(f_495_2,plain,
! [U_2026,U_2025,U_2024,U_2023] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2024,U_2023)),U_2025),U_2026) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2023),hAPP(U_2025,U_2026))
| ~ class_Groups_Ouminus(U_2023) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
! [U_2023,U_2024,U_2025,U_2026] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2024,U_2023)),U_2025),U_2026) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2023),hAPP(U_2025,U_2026))
| ~ class_Groups_Ouminus(U_2023) ),
inference(definitional_conversion,[status(esa)],[f_495_2]) ).
cnf(f_495_4,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2024,U_2023)),U_2025),U_2026) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2023),hAPP(U_2025,U_2026))
| ~ class_Groups_Ouminus(U_2023) ),
inference(clausify,[status(thm)],[f_495_3]) ).
fof(f_496_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) ) )
| ~ class_Lattices_Oboolean__algebra(T_b) ),
inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).
fof(f_496_2,plain,
! [U_2029,U_2028,U_2027] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2028) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2029)
| U_2028 != U_2029 )
& ( U_2028 = U_2029
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2028) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2029) ) )
| ~ class_Lattices_Oboolean__algebra(U_2027) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
( ! [U_2027,U_2028,U_2029] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2028) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2029)
| U_2028 != U_2029
| ~ sP147(U_2027,U_2028,U_2029) )
& ! [U_2027,U_2028,U_2029] :
( U_2028 = U_2029
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2028) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2029)
| ~ sP147(U_2027,U_2028,U_2029) )
& ! [U_2027,U_2028,U_2029] :
( sP147(U_2027,U_2028,U_2029)
| ~ class_Lattices_Oboolean__algebra(U_2027) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147])],[f_496_2]) ).
cnf(f_496_4,plain,
( sP147(U_2027,U_2028,U_2029)
| ~ class_Lattices_Oboolean__algebra(U_2027) ),
inference(clausify,[status(thm)],[f_496_3]) ).
cnf(f_496_5,plain,
( U_2028 = U_2029
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2028) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2029)
| ~ sP147(U_2027,U_2028,U_2029) ),
inference(clausify,[status(thm)],[f_496_3]) ).
cnf(f_496_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2028) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),U_2029)
| U_2028 != U_2029
| ~ sP147(U_2027,U_2028,U_2029) ),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__mono]) ).
fof(f_497_2,plain,
! [U_2032,U_2031,U_2030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(c_Groups_Ouminus__class_Ouminus(U_2030),U_2032)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2030),U_2031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),U_2031),U_2032))
| ~ class_Lattices_Oboolean__algebra(U_2030) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
fof(f_497_3,plain,
! [U_2030,U_2031,U_2032] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(c_Groups_Ouminus__class_Ouminus(U_2030),U_2032)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2030),U_2031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),U_2031),U_2032))
| ~ class_Lattices_Oboolean__algebra(U_2030) ),
inference(definitional_conversion,[status(esa)],[f_497_2]) ).
cnf(f_497_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(c_Groups_Ouminus__class_Ouminus(U_2030),U_2032)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2030),U_2031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),U_2031),U_2032))
| ~ class_Lattices_Oboolean__algebra(U_2030) ),
inference(clausify,[status(thm)],[f_497_3]) ).
fof(f_498_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ 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))) ) )
| ~ class_Lattices_Oboolean__algebra(T_b) ),
inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).
fof(f_498_2,plain,
! [U_2035,U_2034,U_2033] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2034)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2035)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),U_2035),U_2034)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),U_2035),U_2034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2034)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2035))) ) )
| ~ class_Lattices_Oboolean__algebra(U_2033) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
fof(f_498_3,plain,
( ! [U_2034,U_2035,U_2033] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2034)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2035)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),U_2035),U_2034))
| ~ sP148(U_2034,U_2035,U_2033) )
& ! [U_2034,U_2035,U_2033] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),U_2035),U_2034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2034)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2035)))
| ~ sP148(U_2034,U_2035,U_2033) )
& ! [U_2034,U_2035,U_2033] :
( sP148(U_2034,U_2035,U_2033)
| ~ class_Lattices_Oboolean__algebra(U_2033) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148])],[f_498_2]) ).
cnf(f_498_4,plain,
( sP148(U_2034,U_2035,U_2033)
| ~ class_Lattices_Oboolean__algebra(U_2033) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),U_2035),U_2034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2034)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2035)))
| ~ sP148(U_2034,U_2035,U_2033) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2034)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2033),U_2035)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2033),U_2035),U_2034))
| ~ sP148(U_2034,U_2035,U_2033) ),
inference(clausify,[status(thm)],[f_498_3]) ).
fof(f_499_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le]) ).
fof(f_499_2,plain,
! [U_2038,U_2037,U_2036] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2036),hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),U_2038)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),U_2037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2036),U_2037),U_2038))
| ~ class_Groups_Oordered__ab__group__add(U_2036) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
! [U_2037,U_2036,U_2038] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2036),hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),U_2038)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),U_2037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2036),U_2037),U_2038))
| ~ class_Groups_Oordered__ab__group__add(U_2036) ),
inference(definitional_conversion,[status(esa)],[f_499_2]) ).
cnf(f_499_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2036),hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),U_2038)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),U_2037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2036),U_2037),U_2038))
| ~ class_Groups_Oordered__ab__group__add(U_2036) ),
inference(clausify,[status(thm)],[f_499_3]) ).
fof(f_500_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).
fof(f_500_2,plain,
! [U_2041,U_2040,U_2039] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2040)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2041)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),U_2041),U_2040)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),U_2041),U_2040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2040)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2041))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2039) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
fof(f_500_3,plain,
( ! [U_2040,U_2039,U_2041] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2040)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2041)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),U_2041),U_2040))
| ~ sP149(U_2040,U_2039,U_2041) )
& ! [U_2040,U_2039,U_2041] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),U_2041),U_2040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2040)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2041)))
| ~ sP149(U_2040,U_2039,U_2041) )
& ! [U_2040,U_2039,U_2041] :
( sP149(U_2040,U_2039,U_2041)
| ~ class_Groups_Oordered__ab__group__add(U_2039) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149])],[f_500_2]) ).
cnf(f_500_4,plain,
( sP149(U_2040,U_2039,U_2041)
| ~ class_Groups_Oordered__ab__group__add(U_2039) ),
inference(clausify,[status(thm)],[f_500_3]) ).
cnf(f_500_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),U_2041),U_2040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2040)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2041)))
| ~ sP149(U_2040,U_2039,U_2041) ),
inference(clausify,[status(thm)],[f_500_3]) ).
cnf(f_500_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2040)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2039),U_2041)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2039),U_2041),U_2040))
| ~ sP149(U_2040,U_2039,U_2041) ),
inference(clausify,[status(thm)],[f_500_3]) ).
fof(f_501_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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))
| ~ 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)) )
& ( 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))
| ~ 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)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).
fof(f_501_2,plain,
! [U_2044,U_2043,U_2042] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2043)),U_2044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2044)),U_2043)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2044)),U_2043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2043)),U_2044)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2042) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
( ! [U_2043,U_2044,U_2042] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2043)),U_2044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2044)),U_2043))
| ~ sP150(U_2043,U_2044,U_2042) )
& ! [U_2043,U_2044,U_2042] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2044)),U_2043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2043)),U_2044))
| ~ sP150(U_2043,U_2044,U_2042) )
& ! [U_2043,U_2044,U_2042] :
( sP150(U_2043,U_2044,U_2042)
| ~ class_Groups_Oordered__ab__group__add(U_2042) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150])],[f_501_2]) ).
cnf(f_501_4,plain,
( sP150(U_2043,U_2044,U_2042)
| ~ class_Groups_Oordered__ab__group__add(U_2042) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2044)),U_2043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2043)),U_2044))
| ~ sP150(U_2043,U_2044,U_2042) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2043)),U_2044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2042),hAPP(c_Groups_Ouminus__class_Ouminus(U_2042),U_2044)),U_2043))
| ~ sP150(U_2043,U_2044,U_2042) ),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)))
| ~ 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))) )
& ( 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)))
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).
fof(f_502_2,plain,
! [U_2047,U_2046,U_2045] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2046),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2047),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2046))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2047),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2046),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2047))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2045) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
( ! [U_2047,U_2046,U_2045] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2046),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2047),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2046)))
| ~ sP151(U_2047,U_2046,U_2045) )
& ! [U_2047,U_2046,U_2045] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2047),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2046),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2047)))
| ~ sP151(U_2047,U_2046,U_2045) )
& ! [U_2047,U_2046,U_2045] :
( sP151(U_2047,U_2046,U_2045)
| ~ class_Groups_Oordered__ab__group__add(U_2045) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_502_2]) ).
cnf(f_502_4,plain,
( sP151(U_2047,U_2046,U_2045)
| ~ class_Groups_Oordered__ab__group__add(U_2045) ),
inference(clausify,[status(thm)],[f_502_3]) ).
cnf(f_502_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2047),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2046),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2047)))
| ~ sP151(U_2047,U_2046,U_2045) ),
inference(clausify,[status(thm)],[f_502_3]) ).
cnf(f_502_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2046),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2045),U_2047),hAPP(c_Groups_Ouminus__class_Ouminus(U_2045),U_2046)))
| ~ sP151(U_2047,U_2046,U_2045) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).
fof(f_503_2,plain,
! [U_2050,U_2049,U_2048] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2049)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2050)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),U_2050),U_2049)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),U_2050),U_2049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2049)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2050))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2048) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
( ! [U_2050,U_2049,U_2048] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2049)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2050)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),U_2050),U_2049))
| ~ sP152(U_2050,U_2049,U_2048) )
& ! [U_2050,U_2049,U_2048] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),U_2050),U_2049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2049)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2050)))
| ~ sP152(U_2050,U_2049,U_2048) )
& ! [U_2050,U_2049,U_2048] :
( sP152(U_2050,U_2049,U_2048)
| ~ class_Groups_Oordered__ab__group__add(U_2048) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_503_2]) ).
cnf(f_503_4,plain,
( sP152(U_2050,U_2049,U_2048)
| ~ class_Groups_Oordered__ab__group__add(U_2048) ),
inference(clausify,[status(thm)],[f_503_3]) ).
cnf(f_503_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),U_2050),U_2049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2049)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2050)))
| ~ sP152(U_2050,U_2049,U_2048) ),
inference(clausify,[status(thm)],[f_503_3]) ).
cnf(f_503_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2049)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2048),U_2050)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2048),U_2050),U_2049))
| ~ sP152(U_2050,U_2049,U_2048) ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).
fof(f_504_2,plain,
! [U_2053,U_2052,U_2051] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2052)),U_2053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2053)),U_2052)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2053)),U_2052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2052)),U_2053)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2051) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
fof(f_504_3,plain,
( ! [U_2052,U_2051,U_2053] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2052)),U_2053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2053)),U_2052))
| ~ sP153(U_2052,U_2051,U_2053) )
& ! [U_2052,U_2051,U_2053] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2053)),U_2052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2052)),U_2053))
| ~ sP153(U_2052,U_2051,U_2053) )
& ! [U_2052,U_2051,U_2053] :
( sP153(U_2052,U_2051,U_2053)
| ~ class_Groups_Oordered__ab__group__add(U_2051) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153])],[f_504_2]) ).
cnf(f_504_4,plain,
( sP153(U_2052,U_2051,U_2053)
| ~ class_Groups_Oordered__ab__group__add(U_2051) ),
inference(clausify,[status(thm)],[f_504_3]) ).
cnf(f_504_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2053)),U_2052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2052)),U_2053))
| ~ sP153(U_2052,U_2051,U_2053) ),
inference(clausify,[status(thm)],[f_504_3]) ).
cnf(f_504_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2052)),U_2053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2051),hAPP(c_Groups_Ouminus__class_Ouminus(U_2051),U_2053)),U_2052))
| ~ sP153(U_2052,U_2051,U_2053) ),
inference(clausify,[status(thm)],[f_504_3]) ).
fof(f_505_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).
fof(f_505_2,plain,
! [U_2056,U_2055,U_2054] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2056),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2056),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2056))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2054) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
fof(f_505_3,plain,
( ! [U_2056,U_2055,U_2054] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2056),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)))
| ~ sP154(U_2056,U_2055,U_2054) )
& ! [U_2056,U_2055,U_2054] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2056),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2056)))
| ~ sP154(U_2056,U_2055,U_2054) )
& ! [U_2056,U_2055,U_2054] :
( sP154(U_2056,U_2055,U_2054)
| ~ class_Groups_Oordered__ab__group__add(U_2054) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP154])],[f_505_2]) ).
cnf(f_505_4,plain,
( sP154(U_2056,U_2055,U_2054)
| ~ class_Groups_Oordered__ab__group__add(U_2054) ),
inference(clausify,[status(thm)],[f_505_3]) ).
cnf(f_505_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2056),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2056)))
| ~ sP154(U_2056,U_2055,U_2054) ),
inference(clausify,[status(thm)],[f_505_3]) ).
cnf(f_505_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),U_2056),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)))
| ~ sP154(U_2056,U_2055,U_2054) ),
inference(clausify,[status(thm)],[f_505_3]) ).
fof(f_506_1,plain,
! [V_A_2,V_ca_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ComplE]) ).
fof(f_506_2,plain,
! [U_2059,U_2058,U_2057] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2057),U_2058),U_2059))
| ~ hBOOL(hAPP(hAPP(c_member(U_2057),U_2058),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2057,tc_HOL_Obool)),U_2059))) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
fof(f_506_3,plain,
! [U_2058,U_2057,U_2059] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2057),U_2058),U_2059))
| ~ hBOOL(hAPP(hAPP(c_member(U_2057),U_2058),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2057,tc_HOL_Obool)),U_2059))) ),
inference(definitional_conversion,[status(esa)],[f_506_2]) ).
cnf(f_506_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2057),U_2058),U_2059))
| ~ hBOOL(hAPP(hAPP(c_member(U_2057),U_2058),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2057,tc_HOL_Obool)),U_2059))) ),
inference(clausify,[status(thm)],[f_506_3]) ).
fof(f_507_1,plain,
! [V_A_2,V_ca_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ComplD]) ).
fof(f_507_2,plain,
! [U_2062,U_2061,U_2060] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2060),U_2061),U_2062))
| ~ hBOOL(hAPP(hAPP(c_member(U_2060),U_2061),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2060,tc_HOL_Obool)),U_2062))) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
fof(f_507_3,plain,
! [U_2060,U_2061,U_2062] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2060),U_2061),U_2062))
| ~ hBOOL(hAPP(hAPP(c_member(U_2060),U_2061),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2060,tc_HOL_Obool)),U_2062))) ),
inference(definitional_conversion,[status(esa)],[f_507_2]) ).
cnf(f_507_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2060),U_2061),U_2062))
| ~ hBOOL(hAPP(hAPP(c_member(U_2060),U_2061),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2060,tc_HOL_Obool)),U_2062))) ),
inference(clausify,[status(thm)],[f_507_3]) ).
fof(f_508_1,plain,
! [V_A_2,V_ca_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__iff]) ).
fof(f_508_2,plain,
! [U_2065,U_2064,U_2063] :
( ( hBOOL(hAPP(hAPP(c_member(U_2063),U_2064),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2063,tc_HOL_Obool)),U_2065)))
| hBOOL(hAPP(hAPP(c_member(U_2063),U_2064),U_2065)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(U_2063),U_2064),U_2065))
| ~ hBOOL(hAPP(hAPP(c_member(U_2063),U_2064),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2063,tc_HOL_Obool)),U_2065))) ) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
fof(f_508_3,plain,
( ! [U_2071,U_2069,U_2067] :
( hBOOL(hAPP(hAPP(c_member(U_2067),U_2069),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2067,tc_HOL_Obool)),U_2071)))
| hBOOL(hAPP(hAPP(c_member(U_2067),U_2069),U_2071)) )
& ! [U_2070,U_2068,U_2066] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2066),U_2068),U_2070))
| ~ hBOOL(hAPP(hAPP(c_member(U_2066),U_2068),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2066,tc_HOL_Obool)),U_2070))) ) ),
inference(miniscope,[status(thm)],[f_508_2]) ).
fof(f_508_4,plain,
( ! [U_2067,U_2069,U_2071] :
( hBOOL(hAPP(hAPP(c_member(U_2067),U_2069),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2067,tc_HOL_Obool)),U_2071)))
| hBOOL(hAPP(hAPP(c_member(U_2067),U_2069),U_2071)) )
& ! [U_2068,U_2070,U_2066] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2066),U_2068),U_2070))
| ~ hBOOL(hAPP(hAPP(c_member(U_2066),U_2068),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2066,tc_HOL_Obool)),U_2070))) ) ),
inference(definitional_conversion,[status(esa)],[f_508_3]) ).
cnf(f_508_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2066),U_2068),U_2070))
| ~ hBOOL(hAPP(hAPP(c_member(U_2066),U_2068),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2066,tc_HOL_Obool)),U_2070))) ),
inference(clausify,[status(thm)],[f_508_4]) ).
cnf(f_508_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2067),U_2069),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2067,tc_HOL_Obool)),U_2071)))
| hBOOL(hAPP(hAPP(c_member(U_2067),U_2069),U_2071)) ),
inference(clausify,[status(thm)],[f_508_4]) ).
fof(f_509_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__diff__eq]) ).
fof(f_509_2,plain,
! [U_2074,U_2073,U_2072] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2073),U_2074)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2074),U_2073)
| ~ class_Groups_Oab__group__add(U_2072) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
fof(f_509_3,plain,
! [U_2074,U_2072,U_2073] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2073),U_2074)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2074),U_2073)
| ~ class_Groups_Oab__group__add(U_2072) ),
inference(definitional_conversion,[status(esa)],[f_509_2]) ).
cnf(f_509_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2073),U_2074)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2074),U_2073)
| ~ class_Groups_Oab__group__add(U_2072) ),
inference(clausify,[status(thm)],[f_509_3]) ).
fof(f_510_1,plain,
! [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(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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff]) ).
fof(f_510_2,plain,
! [U_2077,U_2076,U_2075] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2075,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2075,tc_HOL_Obool)),U_2076)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2075,tc_HOL_Obool)),U_2077)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2075,tc_HOL_Obool)),U_2077),U_2076)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2075,tc_HOL_Obool)),U_2077),U_2076))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2075,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2075,tc_HOL_Obool)),U_2076)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2075,tc_HOL_Obool)),U_2077))) ) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
( ! [U_2083,U_2081,U_2079] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2079,tc_HOL_Obool)),U_2081)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2079,tc_HOL_Obool)),U_2083)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool)),U_2083),U_2081)) )
& ! [U_2082,U_2080,U_2078] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2078,tc_HOL_Obool)),U_2082),U_2080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2078,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2078,tc_HOL_Obool)),U_2080)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2078,tc_HOL_Obool)),U_2082))) ) ),
inference(miniscope,[status(thm)],[f_510_2]) ).
fof(f_510_4,plain,
( ! [U_2079,U_2081,U_2083] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2079,tc_HOL_Obool)),U_2081)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2079,tc_HOL_Obool)),U_2083)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool)),U_2083),U_2081)) )
& ! [U_2078,U_2082,U_2080] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2078,tc_HOL_Obool)),U_2082),U_2080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2078,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2078,tc_HOL_Obool)),U_2080)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2078,tc_HOL_Obool)),U_2082))) ) ),
inference(definitional_conversion,[status(esa)],[f_510_3]) ).
cnf(f_510_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2078,tc_HOL_Obool)),U_2082),U_2080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2078,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2078,tc_HOL_Obool)),U_2080)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2078,tc_HOL_Obool)),U_2082))) ),
inference(clausify,[status(thm)],[f_510_4]) ).
cnf(f_510_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2079,tc_HOL_Obool)),U_2081)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2079,tc_HOL_Obool)),U_2083)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2079,tc_HOL_Obool)),U_2083),U_2081)) ),
inference(clausify,[status(thm)],[f_510_4]) ).
fof(f_511_1,plain,
! [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(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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono]) ).
fof(f_511_2,plain,
! [U_2086,U_2085,U_2084] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2084,tc_HOL_Obool)),U_2086)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2084,tc_HOL_Obool)),U_2085)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool)),U_2085),U_2086)) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
! [U_2085,U_2084,U_2086] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2084,tc_HOL_Obool)),U_2086)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2084,tc_HOL_Obool)),U_2085)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool)),U_2085),U_2086)) ),
inference(definitional_conversion,[status(esa)],[f_511_2]) ).
cnf(f_511_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2084,tc_HOL_Obool)),U_2086)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2084,tc_HOL_Obool)),U_2085)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2084,tc_HOL_Obool)),U_2085),U_2086)) ),
inference(clausify,[status(thm)],[f_511_3]) ).
fof(f_512_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
| V_b_2 != V_d_2
| V_a_2 != V_ca_2 )
& ( ( V_b_2 = V_d_2
& V_a_2 = V_ca_2 )
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff]) ).
fof(f_512_2,plain,
! [U_2091,U_2090,U_2089,U_2088,U_2087] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2088),U_2089) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2090),U_2091)
| U_2089 != U_2091
| U_2088 != U_2090 )
& ( ( U_2089 = U_2091
& U_2088 = U_2090 )
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2088),U_2089) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2090),U_2091) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2087),U_2090),U_2091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2087),U_2088),U_2089))
| ~ class_Orderings_Olinorder(U_2087) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
( ! [U_2088,U_2089,U_2090,U_2091] :
( U_2089 = U_2091
| ~ sP155(U_2088,U_2089,U_2090,U_2091) )
& ! [U_2088,U_2089,U_2090,U_2091] :
( U_2088 = U_2090
| ~ sP155(U_2088,U_2089,U_2090,U_2091) )
& ! [U_2087,U_2088,U_2089,U_2090,U_2091] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2088),U_2089) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2090),U_2091)
| U_2089 != U_2091
| U_2088 != U_2090
| ~ sP156(U_2087,U_2088,U_2089,U_2090,U_2091) )
& ! [U_2087,U_2088,U_2089,U_2090,U_2091] :
( sP155(U_2088,U_2089,U_2090,U_2091)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2088),U_2089) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2090),U_2091)
| ~ sP156(U_2087,U_2088,U_2089,U_2090,U_2091) )
& ! [U_2087,U_2088,U_2089,U_2090,U_2091] :
( sP156(U_2087,U_2088,U_2089,U_2090,U_2091)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2087),U_2090),U_2091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2087),U_2088),U_2089))
| ~ class_Orderings_Olinorder(U_2087) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155,sP156])],[f_512_2]) ).
cnf(f_512_4,plain,
( sP156(U_2087,U_2088,U_2089,U_2090,U_2091)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2087),U_2090),U_2091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2087),U_2088),U_2089))
| ~ class_Orderings_Olinorder(U_2087) ),
inference(clausify,[status(thm)],[f_512_3]) ).
cnf(f_512_5,plain,
( sP155(U_2088,U_2089,U_2090,U_2091)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2088),U_2089) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2090),U_2091)
| ~ sP156(U_2087,U_2088,U_2089,U_2090,U_2091) ),
inference(clausify,[status(thm)],[f_512_3]) ).
cnf(f_512_6,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2088),U_2089) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2087,U_2090),U_2091)
| U_2089 != U_2091
| U_2088 != U_2090
| ~ sP156(U_2087,U_2088,U_2089,U_2090,U_2091) ),
inference(clausify,[status(thm)],[f_512_3]) ).
cnf(f_512_7,plain,
( U_2088 = U_2090
| ~ sP155(U_2088,U_2089,U_2090,U_2091) ),
inference(clausify,[status(thm)],[f_512_3]) ).
cnf(f_512_8,plain,
( U_2089 = U_2091
| ~ sP155(U_2088,U_2089,U_2090,U_2091) ),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( V_a_2 = V_ca_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J]) ).
fof(f_513_2,plain,
! [U_2096,U_2095,U_2094,U_2093,U_2092] :
( U_2093 = U_2095
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2092),U_2095),U_2096))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2092),U_2093),U_2094))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2092,U_2093),U_2094) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2092,U_2095),U_2096)
| ~ class_Orderings_Olinorder(U_2092) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
! [U_2092,U_2096,U_2093,U_2094,U_2095] :
( U_2093 = U_2095
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2092),U_2095),U_2096))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2092),U_2093),U_2094))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2092,U_2093),U_2094) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2092,U_2095),U_2096)
| ~ class_Orderings_Olinorder(U_2092) ),
inference(definitional_conversion,[status(esa)],[f_513_2]) ).
cnf(f_513_4,plain,
( U_2093 = U_2095
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2092),U_2095),U_2096))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2092),U_2093),U_2094))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2092,U_2093),U_2094) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2092,U_2095),U_2096)
| ~ class_Orderings_Olinorder(U_2092) ),
inference(clausify,[status(thm)],[f_513_3]) ).
fof(f_514_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( V_b_2 = V_d_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J]) ).
fof(f_514_2,plain,
! [U_2101,U_2100,U_2099,U_2098,U_2097] :
( U_2099 = U_2101
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2097),U_2100),U_2101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2097),U_2098),U_2099))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2097,U_2098),U_2099) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2097,U_2100),U_2101)
| ~ class_Orderings_Olinorder(U_2097) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
! [U_2097,U_2100,U_2099,U_2098,U_2101] :
( U_2099 = U_2101
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2097),U_2100),U_2101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2097),U_2098),U_2099))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2097,U_2098),U_2099) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2097,U_2100),U_2101)
| ~ class_Orderings_Olinorder(U_2097) ),
inference(definitional_conversion,[status(esa)],[f_514_2]) ).
cnf(f_514_4,plain,
( U_2099 = U_2101
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2097),U_2100),U_2101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2097),U_2098),U_2099))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2097,U_2098),U_2099) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2097,U_2100),U_2101)
| ~ class_Orderings_Olinorder(U_2097) ),
inference(clausify,[status(thm)],[f_514_3]) ).
fof(f_515_1,plain,
! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
( V_x_2 = V_z_2
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE]) ).
fof(f_515_2,plain,
! [U_2106,U_2105,U_2104,U_2103,U_2102] :
( U_2106 = U_2105
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2102,U_2103,U_2104,U_2105,c_Orderings_Obot__class_Obot(tc_fun(U_2102,tc_HOL_Obool))),U_2106)) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_2106,U_2105] :
( ! [U_2104,U_2103,U_2102] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2102,U_2103,U_2104,U_2105,c_Orderings_Obot__class_Obot(tc_fun(U_2102,tc_HOL_Obool))),U_2106))
| U_2106 = U_2105 ),
inference(miniscope,[status(thm)],[f_515_2]) ).
fof(f_515_4,plain,
! [U_2103,U_2104,U_2105,U_2106,U_2102] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2102,U_2103,U_2104,U_2105,c_Orderings_Obot__class_Obot(tc_fun(U_2102,tc_HOL_Obool))),U_2106))
| U_2106 = U_2105 ),
inference(definitional_conversion,[status(esa)],[f_515_3]) ).
cnf(f_515_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2102,U_2103,U_2104,U_2105,c_Orderings_Obot__class_Obot(tc_fun(U_2102,tc_HOL_Obool))),U_2106))
| U_2106 = U_2105 ),
inference(clausify,[status(thm)],[f_515_4]) ).
fof(f_516_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_fold__graph_OemptyI]) ).
fof(f_516_2,plain,
! [U_2110,U_2109,U_2108,U_2107] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2107,U_2108,U_2109,U_2110,c_Orderings_Obot__class_Obot(tc_fun(U_2107,tc_HOL_Obool))),U_2110)),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
! [U_2107,U_2108,U_2109,U_2110] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2107,U_2108,U_2109,U_2110,c_Orderings_Obot__class_Obot(tc_fun(U_2107,tc_HOL_Obool))),U_2110)),
inference(definitional_conversion,[status(esa)],[f_516_2]) ).
cnf(f_516_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2107,U_2108,U_2109,U_2110,c_Orderings_Obot__class_Obot(tc_fun(U_2107,tc_HOL_Obool))),U_2110)),
inference(clausify,[status(thm)],[f_516_3]) ).
fof(f_517_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).
fof(f_517_2,plain,
! [U_2114,U_2113,U_2112,U_2111] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2111,U_2112,U_2113,U_2114,c_Orderings_Obot__class_Obot(tc_fun(U_2111,tc_HOL_Obool))),U_2114)),
inference(variable_rename,[status(thm)],[f_517_1]) ).
fof(f_517_3,plain,
! [U_2111,U_2113,U_2112,U_2114] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2111,U_2112,U_2113,U_2114,c_Orderings_Obot__class_Obot(tc_fun(U_2111,tc_HOL_Obool))),U_2114)),
inference(definitional_conversion,[status(esa)],[f_517_2]) ).
cnf(f_517_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2111,U_2112,U_2113,U_2114,c_Orderings_Obot__class_Obot(tc_fun(U_2111,tc_HOL_Obool))),U_2114)),
inference(clausify,[status(thm)],[f_517_3]) ).
fof(f_518_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__inf__bot]) ).
fof(f_518_2,plain,
! [U_2116,U_2115] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2115),hAPP(c_Groups_Ouminus__class_Ouminus(U_2115),U_2116)),U_2116) = c_Orderings_Obot__class_Obot(U_2115)
| ~ class_Lattices_Oboolean__algebra(U_2115) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
fof(f_518_3,plain,
! [U_2115,U_2116] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2115),hAPP(c_Groups_Ouminus__class_Ouminus(U_2115),U_2116)),U_2116) = c_Orderings_Obot__class_Obot(U_2115)
| ~ class_Lattices_Oboolean__algebra(U_2115) ),
inference(definitional_conversion,[status(esa)],[f_518_2]) ).
cnf(f_518_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2115),hAPP(c_Groups_Ouminus__class_Ouminus(U_2115),U_2116)),U_2116) = c_Orderings_Obot__class_Obot(U_2115)
| ~ class_Lattices_Oboolean__algebra(U_2115) ),
inference(clausify,[status(thm)],[f_518_3]) ).
fof(f_519_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__compl__bot]) ).
fof(f_519_2,plain,
! [U_2118,U_2117] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2117),U_2118),hAPP(c_Groups_Ouminus__class_Ouminus(U_2117),U_2118)) = c_Orderings_Obot__class_Obot(U_2117)
| ~ class_Lattices_Oboolean__algebra(U_2117) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
fof(f_519_3,plain,
! [U_2117,U_2118] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2117),U_2118),hAPP(c_Groups_Ouminus__class_Ouminus(U_2117),U_2118)) = c_Orderings_Obot__class_Obot(U_2117)
| ~ class_Lattices_Oboolean__algebra(U_2117) ),
inference(definitional_conversion,[status(esa)],[f_519_2]) ).
cnf(f_519_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2117),U_2118),hAPP(c_Groups_Ouminus__class_Ouminus(U_2117),U_2118)) = c_Orderings_Obot__class_Obot(U_2117)
| ~ class_Lattices_Oboolean__algebra(U_2117) ),
inference(clausify,[status(thm)],[f_519_3]) ).
fof(f_520_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq]) ).
fof(f_520_2,plain,
! [U_2121,U_2120,U_2119] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2119),U_2120),U_2121) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2119),U_2120),hAPP(c_Groups_Ouminus__class_Ouminus(U_2119),U_2121))
| ~ class_Lattices_Oboolean__algebra(U_2119) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
! [U_2119,U_2120,U_2121] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2119),U_2120),U_2121) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2119),U_2120),hAPP(c_Groups_Ouminus__class_Ouminus(U_2119),U_2121))
| ~ class_Lattices_Oboolean__algebra(U_2119) ),
inference(definitional_conversion,[status(esa)],[f_520_2]) ).
cnf(f_520_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2119),U_2120),U_2121) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2119),U_2120),hAPP(c_Groups_Ouminus__class_Ouminus(U_2119),U_2121))
| ~ class_Lattices_Oboolean__algebra(U_2119) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_1,plain,
! [T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__top__eq]) ).
fof(f_521_2,plain,
! [U_2122] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2122),c_Orderings_Otop__class_Otop(U_2122)) = c_Orderings_Obot__class_Obot(U_2122)
| ~ class_Lattices_Oboolean__algebra(U_2122) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
! [U_2122] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2122),c_Orderings_Otop__class_Otop(U_2122)) = c_Orderings_Obot__class_Obot(U_2122)
| ~ class_Lattices_Oboolean__algebra(U_2122) ),
inference(definitional_conversion,[status(esa)],[f_521_2]) ).
cnf(f_521_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2122),c_Orderings_Otop__class_Otop(U_2122)) = c_Orderings_Obot__class_Obot(U_2122)
| ~ class_Lattices_Oboolean__algebra(U_2122) ),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_1,plain,
! [T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__bot__eq]) ).
fof(f_522_2,plain,
! [U_2123] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2123),c_Orderings_Obot__class_Obot(U_2123)) = c_Orderings_Otop__class_Otop(U_2123)
| ~ class_Lattices_Oboolean__algebra(U_2123) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
! [U_2123] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2123),c_Orderings_Obot__class_Obot(U_2123)) = c_Orderings_Otop__class_Otop(U_2123)
| ~ class_Lattices_Oboolean__algebra(U_2123) ),
inference(definitional_conversion,[status(esa)],[f_522_2]) ).
cnf(f_522_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2123),c_Orderings_Obot__class_Obot(U_2123)) = c_Orderings_Otop__class_Otop(U_2123)
| ~ class_Lattices_Oboolean__algebra(U_2123) ),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__sup]) ).
fof(f_523_2,plain,
! [U_2126,U_2125,U_2124] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2124),U_2125),U_2126)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2124),hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),U_2125)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),U_2126))
| ~ class_Lattices_Oboolean__algebra(U_2124) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
! [U_2124,U_2125,U_2126] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2124),U_2125),U_2126)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2124),hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),U_2125)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),U_2126))
| ~ class_Lattices_Oboolean__algebra(U_2124) ),
inference(definitional_conversion,[status(esa)],[f_523_2]) ).
cnf(f_523_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2124),U_2125),U_2126)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2124),hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),U_2125)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2124),U_2126))
| ~ class_Lattices_Oboolean__algebra(U_2124) ),
inference(clausify,[status(thm)],[f_523_3]) ).
fof(f_524_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__inf]) ).
fof(f_524_2,plain,
! [U_2129,U_2128,U_2127] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2127),U_2128),U_2129)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2127),hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),U_2128)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),U_2129))
| ~ class_Lattices_Oboolean__algebra(U_2127) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
! [U_2127,U_2128,U_2129] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2127),U_2128),U_2129)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2127),hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),U_2128)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),U_2129))
| ~ class_Lattices_Oboolean__algebra(U_2127) ),
inference(definitional_conversion,[status(esa)],[f_524_2]) ).
cnf(f_524_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2127),U_2128),U_2129)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2127),hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),U_2128)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2127),U_2129))
| ~ class_Lattices_Oboolean__algebra(U_2127) ),
inference(clausify,[status(thm)],[f_524_3]) ).
fof(f_525_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__sup__top]) ).
fof(f_525_2,plain,
! [U_2131,U_2130] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2130),hAPP(c_Groups_Ouminus__class_Ouminus(U_2130),U_2131)),U_2131) = c_Orderings_Otop__class_Otop(U_2130)
| ~ class_Lattices_Oboolean__algebra(U_2130) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
fof(f_525_3,plain,
! [U_2130,U_2131] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2130),hAPP(c_Groups_Ouminus__class_Ouminus(U_2130),U_2131)),U_2131) = c_Orderings_Otop__class_Otop(U_2130)
| ~ class_Lattices_Oboolean__algebra(U_2130) ),
inference(definitional_conversion,[status(esa)],[f_525_2]) ).
cnf(f_525_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2130),hAPP(c_Groups_Ouminus__class_Ouminus(U_2130),U_2131)),U_2131) = c_Orderings_Otop__class_Otop(U_2130)
| ~ class_Lattices_Oboolean__algebra(U_2130) ),
inference(clausify,[status(thm)],[f_525_3]) ).
fof(f_526_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sup__compl__top]) ).
fof(f_526_2,plain,
! [U_2133,U_2132] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2132),U_2133),hAPP(c_Groups_Ouminus__class_Ouminus(U_2132),U_2133)) = c_Orderings_Otop__class_Otop(U_2132)
| ~ class_Lattices_Oboolean__algebra(U_2132) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
fof(f_526_3,plain,
! [U_2132,U_2133] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2132),U_2133),hAPP(c_Groups_Ouminus__class_Ouminus(U_2132),U_2133)) = c_Orderings_Otop__class_Otop(U_2132)
| ~ class_Lattices_Oboolean__algebra(U_2132) ),
inference(definitional_conversion,[status(esa)],[f_526_2]) ).
cnf(f_526_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2132),U_2133),hAPP(c_Groups_Ouminus__class_Ouminus(U_2132),U_2133)) = c_Orderings_Otop__class_Otop(U_2132)
| ~ class_Lattices_Oboolean__algebra(U_2132) ),
inference(clausify,[status(thm)],[f_526_3]) ).
fof(f_527_1,plain,
! [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(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)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq]) ).
fof(f_527_2,plain,
! [U_2135,U_2134] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2134,tc_HOL_Obool)),U_2135),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2134,tc_HOL_Obool)),U_2135)))
| U_2135 != c_Orderings_Obot__class_Obot(tc_fun(U_2134,tc_HOL_Obool)) )
& ( U_2135 = c_Orderings_Obot__class_Obot(tc_fun(U_2134,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2134,tc_HOL_Obool)),U_2135),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2134,tc_HOL_Obool)),U_2135))) ) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
fof(f_527_3,plain,
( ! [U_2139,U_2137] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2137,tc_HOL_Obool)),U_2139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2137,tc_HOL_Obool)),U_2139)))
| U_2139 != c_Orderings_Obot__class_Obot(tc_fun(U_2137,tc_HOL_Obool)) )
& ! [U_2138,U_2136] :
( U_2138 = c_Orderings_Obot__class_Obot(tc_fun(U_2136,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2136,tc_HOL_Obool)),U_2138),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2136,tc_HOL_Obool)),U_2138))) ) ),
inference(miniscope,[status(thm)],[f_527_2]) ).
fof(f_527_4,plain,
( ! [U_2137,U_2139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2137,tc_HOL_Obool)),U_2139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2137,tc_HOL_Obool)),U_2139)))
| U_2139 != c_Orderings_Obot__class_Obot(tc_fun(U_2137,tc_HOL_Obool)) )
& ! [U_2138,U_2136] :
( U_2138 = c_Orderings_Obot__class_Obot(tc_fun(U_2136,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2136,tc_HOL_Obool)),U_2138),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2136,tc_HOL_Obool)),U_2138))) ) ),
inference(definitional_conversion,[status(esa)],[f_527_3]) ).
cnf(f_527_5,plain,
( U_2138 = c_Orderings_Obot__class_Obot(tc_fun(U_2136,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2136,tc_HOL_Obool)),U_2138),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2136,tc_HOL_Obool)),U_2138))) ),
inference(clausify,[status(thm)],[f_527_4]) ).
cnf(f_527_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2137,tc_HOL_Obool)),U_2139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2137,tc_HOL_Obool)),U_2139)))
| U_2139 != c_Orderings_Obot__class_Obot(tc_fun(U_2137,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_527_4]) ).
fof(f_528_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__empty__eq]) ).
fof(f_528_2,plain,
! [U_2140] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2140,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2140,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2140,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
! [U_2140] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2140,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2140,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2140,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_528_2]) ).
cnf(f_528_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2140,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2140,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2140,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_528_3]) ).
fof(f_529_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__UNIV__eq]) ).
fof(f_529_2,plain,
! [U_2141] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2141,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2141,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2141,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
! [U_2141] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2141,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2141,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2141,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_529_2]) ).
cnf(f_529_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2141,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2141,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2141,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_529_3]) ).
fof(f_530_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__disjoint]) ).
fof(f_530_2,plain,
! [U_2143,U_2142] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2142,tc_HOL_Obool)),U_2143),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2142,tc_HOL_Obool)),U_2143)) = c_Orderings_Obot__class_Obot(tc_fun(U_2142,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
! [U_2142,U_2143] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2142,tc_HOL_Obool)),U_2143),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2142,tc_HOL_Obool)),U_2143)) = c_Orderings_Obot__class_Obot(tc_fun(U_2142,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_530_2]) ).
cnf(f_530_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2142,tc_HOL_Obool)),U_2143),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2142,tc_HOL_Obool)),U_2143)) = c_Orderings_Obot__class_Obot(tc_fun(U_2142,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__disjoint2]) ).
fof(f_531_2,plain,
! [U_2145,U_2144] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2144,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2144,tc_HOL_Obool)),U_2145)),U_2145) = c_Orderings_Obot__class_Obot(tc_fun(U_2144,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
! [U_2144,U_2145] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2144,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2144,tc_HOL_Obool)),U_2145)),U_2145) = c_Orderings_Obot__class_Obot(tc_fun(U_2144,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_531_2]) ).
cnf(f_531_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2144,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2144,tc_HOL_Obool)),U_2145)),U_2145) = c_Orderings_Obot__class_Obot(tc_fun(U_2144,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_531_3]) ).
fof(f_532_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__partition]) ).
fof(f_532_2,plain,
! [U_2147,U_2146] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2146,tc_HOL_Obool)),U_2147),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2146,tc_HOL_Obool)),U_2147)) = c_Orderings_Otop__class_Otop(tc_fun(U_2146,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
! [U_2146,U_2147] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2146,tc_HOL_Obool)),U_2147),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2146,tc_HOL_Obool)),U_2147)) = c_Orderings_Otop__class_Otop(tc_fun(U_2146,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_532_2]) ).
cnf(f_532_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2146,tc_HOL_Obool)),U_2147),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2146,tc_HOL_Obool)),U_2147)) = c_Orderings_Otop__class_Otop(tc_fun(U_2146,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_532_3]) ).
fof(f_533_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__partition2]) ).
fof(f_533_2,plain,
! [U_2149,U_2148] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2148,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2148,tc_HOL_Obool)),U_2149)),U_2149) = c_Orderings_Otop__class_Otop(tc_fun(U_2148,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
! [U_2148,U_2149] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2148,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2148,tc_HOL_Obool)),U_2149)),U_2149) = c_Orderings_Otop__class_Otop(tc_fun(U_2148,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_533_2]) ).
cnf(f_533_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2148,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2148,tc_HOL_Obool)),U_2149)),U_2149) = c_Orderings_Otop__class_Otop(tc_fun(U_2148,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_533_3]) ).
fof(f_534_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__Int]) ).
fof(f_534_2,plain,
! [U_2152,U_2151,U_2150] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2150,tc_HOL_Obool)),U_2151),U_2152)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2150,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),U_2151)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),U_2152)),
inference(variable_rename,[status(thm)],[f_534_1]) ).
fof(f_534_3,plain,
! [U_2150,U_2151,U_2152] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2150,tc_HOL_Obool)),U_2151),U_2152)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2150,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),U_2151)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),U_2152)),
inference(definitional_conversion,[status(esa)],[f_534_2]) ).
cnf(f_534_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2150,tc_HOL_Obool)),U_2151),U_2152)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2150,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),U_2151)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,tc_HOL_Obool)),U_2152)),
inference(clausify,[status(thm)],[f_534_3]) ).
fof(f_535_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__Un]) ).
fof(f_535_2,plain,
! [U_2155,U_2154,U_2153] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2153,tc_HOL_Obool)),U_2154),U_2155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2153,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),U_2154)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),U_2155)),
inference(variable_rename,[status(thm)],[f_535_1]) ).
fof(f_535_3,plain,
! [U_2153,U_2154,U_2155] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2153,tc_HOL_Obool)),U_2154),U_2155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2153,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),U_2154)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),U_2155)),
inference(definitional_conversion,[status(esa)],[f_535_2]) ).
cnf(f_535_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2153,tc_HOL_Obool)),U_2154),U_2155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2153,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),U_2154)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2153,tc_HOL_Obool)),U_2155)),
inference(clausify,[status(thm)],[f_535_3]) ).
fof(f_536_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).
fof(f_536_2,plain,
! [U_2157,U_2156] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2156,tc_HOL_Obool)),U_2157) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2156,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2156,tc_HOL_Obool))),U_2157),
inference(variable_rename,[status(thm)],[f_536_1]) ).
fof(f_536_3,plain,
! [U_2156,U_2157] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2156,tc_HOL_Obool)),U_2157) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2156,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2156,tc_HOL_Obool))),U_2157),
inference(definitional_conversion,[status(esa)],[f_536_2]) ).
cnf(f_536_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2156,tc_HOL_Obool)),U_2157) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2156,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2156,tc_HOL_Obool))),U_2157),
inference(clausify,[status(thm)],[f_536_3]) ).
fof(f_537_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Compl__Diff__eq]) ).
fof(f_537_2,plain,
! [U_2160,U_2159,U_2158] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2158,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2158,tc_HOL_Obool)),U_2159),U_2160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2158,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2158,tc_HOL_Obool)),U_2159)),U_2160),
inference(variable_rename,[status(thm)],[f_537_1]) ).
fof(f_537_3,plain,
! [U_2158,U_2159,U_2160] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2158,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2158,tc_HOL_Obool)),U_2159),U_2160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2158,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2158,tc_HOL_Obool)),U_2159)),U_2160),
inference(definitional_conversion,[status(esa)],[f_537_2]) ).
cnf(f_537_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2158,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2158,tc_HOL_Obool)),U_2159),U_2160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2158,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2158,tc_HOL_Obool)),U_2159)),U_2160),
inference(clausify,[status(thm)],[f_537_3]) ).
fof(f_538_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Diff__eq]) ).
fof(f_538_2,plain,
! [U_2163,U_2162,U_2161] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2161,tc_HOL_Obool)),U_2162),U_2163) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2161,tc_HOL_Obool)),U_2162),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2161,tc_HOL_Obool)),U_2163)),
inference(variable_rename,[status(thm)],[f_538_1]) ).
fof(f_538_3,plain,
! [U_2161,U_2162,U_2163] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2161,tc_HOL_Obool)),U_2162),U_2163) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2161,tc_HOL_Obool)),U_2162),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2161,tc_HOL_Obool)),U_2163)),
inference(definitional_conversion,[status(esa)],[f_538_2]) ).
cnf(f_538_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2161,tc_HOL_Obool)),U_2162),U_2163) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2161,tc_HOL_Obool)),U_2162),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2161,tc_HOL_Obool)),U_2163)),
inference(clausify,[status(thm)],[f_538_3]) ).
fof(f_539_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Diff__Compl]) ).
fof(f_539_2,plain,
! [U_2166,U_2165,U_2164] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2164,tc_HOL_Obool)),U_2165),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2164,tc_HOL_Obool)),U_2166)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2164,tc_HOL_Obool)),U_2165),U_2166),
inference(variable_rename,[status(thm)],[f_539_1]) ).
fof(f_539_3,plain,
! [U_2164,U_2165,U_2166] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2164,tc_HOL_Obool)),U_2165),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2164,tc_HOL_Obool)),U_2166)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2164,tc_HOL_Obool)),U_2165),U_2166),
inference(definitional_conversion,[status(esa)],[f_539_2]) ).
cnf(f_539_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2164,tc_HOL_Obool)),U_2165),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2164,tc_HOL_Obool)),U_2166)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2164,tc_HOL_Obool)),U_2165),U_2166),
inference(clausify,[status(thm)],[f_539_3]) ).
fof(f_540_1,plain,
! [V_k_2,T_b] :
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Compl__atLeast]) ).
fof(f_540_2,plain,
! [U_2168,U_2167] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2167,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2167),U_2168)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2167),U_2168)
| ~ class_Orderings_Olinorder(U_2167) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
fof(f_540_3,plain,
! [U_2167,U_2168] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2167,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2167),U_2168)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2167),U_2168)
| ~ class_Orderings_Olinorder(U_2167) ),
inference(definitional_conversion,[status(esa)],[f_540_2]) ).
cnf(f_540_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2167,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2167),U_2168)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2167),U_2168)
| ~ class_Orderings_Olinorder(U_2167) ),
inference(clausify,[status(thm)],[f_540_3]) ).
fof(f_541_1,plain,
! [V_k_2,T_b] :
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Compl__lessThan]) ).
fof(f_541_2,plain,
! [U_2170,U_2169] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2169,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2169),U_2170)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2169),U_2170)
| ~ class_Orderings_Olinorder(U_2169) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
fof(f_541_3,plain,
! [U_2169,U_2170] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2169,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2169),U_2170)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2169),U_2170)
| ~ class_Orderings_Olinorder(U_2169) ),
inference(definitional_conversion,[status(esa)],[f_541_2]) ).
cnf(f_541_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2169,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2169),U_2170)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2169),U_2170)
| ~ class_Orderings_Olinorder(U_2169) ),
inference(clausify,[status(thm)],[f_541_3]) ).
fof(f_542_1,plain,
! [V_a_2,V_b_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty]) ).
fof(f_542_2,plain,
! [U_2173,U_2172,U_2171] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2171,U_2173),U_2172) = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2172),U_2173))
| ~ class_Orderings_Oorder(U_2171) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
fof(f_542_3,plain,
! [U_2171,U_2172,U_2173] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2171,U_2173),U_2172) = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2172),U_2173))
| ~ class_Orderings_Oorder(U_2171) ),
inference(definitional_conversion,[status(esa)],[f_542_2]) ).
cnf(f_542_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2171,U_2173),U_2172) = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2172),U_2173))
| ~ class_Orderings_Oorder(U_2171) ),
inference(clausify,[status(thm)],[f_542_3]) ).
fof(f_543_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| 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) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).
fof(f_543_2,plain,
! [U_2176,U_2175,U_2174] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_2174,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2174,U_2175),U_2176)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),U_2176)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),U_2176))
| c_Orderings_Obot__class_Obot(tc_fun(U_2174,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2174,U_2175),U_2176) ) )
| ~ class_Orderings_Oorder(U_2174) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
fof(f_543_3,plain,
( ! [U_2174,U_2175,U_2176] :
( c_Orderings_Obot__class_Obot(tc_fun(U_2174,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2174,U_2175),U_2176)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),U_2176))
| ~ sP157(U_2174,U_2175,U_2176) )
& ! [U_2174,U_2175,U_2176] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),U_2176))
| c_Orderings_Obot__class_Obot(tc_fun(U_2174,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2174,U_2175),U_2176)
| ~ sP157(U_2174,U_2175,U_2176) )
& ! [U_2174,U_2175,U_2176] :
( sP157(U_2174,U_2175,U_2176)
| ~ class_Orderings_Oorder(U_2174) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157])],[f_543_2]) ).
cnf(f_543_4,plain,
( sP157(U_2174,U_2175,U_2176)
| ~ class_Orderings_Oorder(U_2174) ),
inference(clausify,[status(thm)],[f_543_3]) ).
cnf(f_543_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),U_2176))
| c_Orderings_Obot__class_Obot(tc_fun(U_2174,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2174,U_2175),U_2176)
| ~ sP157(U_2174,U_2175,U_2176) ),
inference(clausify,[status(thm)],[f_543_3]) ).
cnf(f_543_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_2174,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2174,U_2175),U_2176)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),U_2176))
| ~ sP157(U_2174,U_2175,U_2176) ),
inference(clausify,[status(thm)],[f_543_3]) ).
fof(f_544_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| 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)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).
fof(f_544_2,plain,
! [U_2179,U_2178,U_2177] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2177,U_2178),U_2179) = c_Orderings_Obot__class_Obot(tc_fun(U_2177,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2177),U_2178),U_2179)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2177),U_2178),U_2179))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2177,U_2178),U_2179) != c_Orderings_Obot__class_Obot(tc_fun(U_2177,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_2177) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
fof(f_544_3,plain,
( ! [U_2179,U_2177,U_2178] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2177,U_2178),U_2179) = c_Orderings_Obot__class_Obot(tc_fun(U_2177,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2177),U_2178),U_2179))
| ~ sP158(U_2179,U_2177,U_2178) )
& ! [U_2179,U_2177,U_2178] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2177),U_2178),U_2179))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2177,U_2178),U_2179) != c_Orderings_Obot__class_Obot(tc_fun(U_2177,tc_HOL_Obool))
| ~ sP158(U_2179,U_2177,U_2178) )
& ! [U_2179,U_2177,U_2178] :
( sP158(U_2179,U_2177,U_2178)
| ~ class_Orderings_Oorder(U_2177) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158])],[f_544_2]) ).
cnf(f_544_4,plain,
( sP158(U_2179,U_2177,U_2178)
| ~ class_Orderings_Oorder(U_2177) ),
inference(clausify,[status(thm)],[f_544_3]) ).
cnf(f_544_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2177),U_2178),U_2179))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2177,U_2178),U_2179) != c_Orderings_Obot__class_Obot(tc_fun(U_2177,tc_HOL_Obool))
| ~ sP158(U_2179,U_2177,U_2178) ),
inference(clausify,[status(thm)],[f_544_3]) ).
cnf(f_544_6,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2177,U_2178),U_2179) = c_Orderings_Obot__class_Obot(tc_fun(U_2177,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2177),U_2178),U_2179))
| ~ sP158(U_2179,U_2177,U_2178) ),
inference(clausify,[status(thm)],[f_544_3]) ).
fof(f_545_1,plain,
! [V_k_2,T_b] :
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Compl__atMost]) ).
fof(f_545_2,plain,
! [U_2181,U_2180] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2180,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_2180),U_2181)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2180),U_2181)
| ~ class_Orderings_Olinorder(U_2180) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
fof(f_545_3,plain,
! [U_2181,U_2180] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2180,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_2180),U_2181)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2180),U_2181)
| ~ class_Orderings_Olinorder(U_2180) ),
inference(definitional_conversion,[status(esa)],[f_545_2]) ).
cnf(f_545_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2180,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_2180),U_2181)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2180),U_2181)
| ~ class_Orderings_Olinorder(U_2180) ),
inference(clausify,[status(thm)],[f_545_3]) ).
fof(f_546_1,plain,
! [V_k_2,T_b] :
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan]) ).
fof(f_546_2,plain,
! [U_2183,U_2182] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2182,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2182),U_2183)) = hAPP(c_SetInterval_Oord__class_OatMost(U_2182),U_2183)
| ~ class_Orderings_Olinorder(U_2182) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
fof(f_546_3,plain,
! [U_2182,U_2183] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2182,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2182),U_2183)) = hAPP(c_SetInterval_Oord__class_OatMost(U_2182),U_2183)
| ~ class_Orderings_Olinorder(U_2182) ),
inference(definitional_conversion,[status(esa)],[f_546_2]) ).
cnf(f_546_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2182,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2182),U_2183)) = hAPP(c_SetInterval_Oord__class_OatMost(U_2182),U_2183)
| ~ class_Orderings_Olinorder(U_2182) ),
inference(clausify,[status(thm)],[f_546_3]) ).
fof(f_547_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
| ~ 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_ca_2),V_d_2)))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff]) ).
fof(f_547_2,plain,
! [U_2188,U_2187,U_2186,U_2185,U_2184] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2186),U_2188))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2187),U_2185)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2186),U_2185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2184,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2184,U_2185),U_2186)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2184,U_2187),U_2188)))
| ~ class_Orderings_Olinorder(U_2184) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
fof(f_547_3,plain,
( ! [U_2184,U_2185,U_2186,U_2187,U_2188] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2186),U_2188))
| ~ sP159(U_2184,U_2185,U_2186,U_2187,U_2188) )
& ! [U_2184,U_2185,U_2186,U_2187,U_2188] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2187),U_2185))
| ~ sP159(U_2184,U_2185,U_2186,U_2187,U_2188) )
& ! [U_2184,U_2185,U_2186,U_2187,U_2188] :
( sP159(U_2184,U_2185,U_2186,U_2187,U_2188)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2186),U_2185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2184,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2184,U_2185),U_2186)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2184,U_2187),U_2188)))
| ~ class_Orderings_Olinorder(U_2184) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159])],[f_547_2]) ).
cnf(f_547_4,plain,
( sP159(U_2184,U_2185,U_2186,U_2187,U_2188)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2186),U_2185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2184,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2184,U_2185),U_2186)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2184,U_2187),U_2188)))
| ~ class_Orderings_Olinorder(U_2184) ),
inference(clausify,[status(thm)],[f_547_3]) ).
cnf(f_547_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2187),U_2185))
| ~ sP159(U_2184,U_2185,U_2186,U_2187,U_2188) ),
inference(clausify,[status(thm)],[f_547_3]) ).
cnf(f_547_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2186),U_2188))
| ~ sP159(U_2184,U_2185,U_2186,U_2187,U_2188) ),
inference(clausify,[status(thm)],[f_547_3]) ).
fof(f_548_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J]) ).
fof(f_548_2,plain,
! [U_2192,U_2191,U_2190,U_2189] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2189,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2190),U_2191)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2191),U_2192)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2190),U_2192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2189),U_2191),U_2192))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2189),U_2190),U_2191))
| ~ class_Orderings_Olinorder(U_2189) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
! [U_2189,U_2190,U_2191,U_2192] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2189,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2190),U_2191)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2191),U_2192)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2190),U_2192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2189),U_2191),U_2192))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2189),U_2190),U_2191))
| ~ class_Orderings_Olinorder(U_2189) ),
inference(definitional_conversion,[status(esa)],[f_548_2]) ).
cnf(f_548_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2189,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2190),U_2191)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2191),U_2192)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2189,U_2190),U_2192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2189),U_2191),U_2192))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2189),U_2190),U_2191))
| ~ class_Orderings_Olinorder(U_2189) ),
inference(clausify,[status(thm)],[f_548_3]) ).
fof(f_549_1,plain,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph_OinsertI]) ).
fof(f_549_2,plain,
! [U_2199,U_2198,U_2197,U_2196,U_2195,U_2194,U_2193] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2193,U_2196,U_2197,U_2198,hAPP(hAPP(c_Set_Oinsert(U_2193),U_2194),U_2195)),hAPP(hAPP(U_2197,U_2194),U_2199)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2193,U_2196,U_2197,U_2198,U_2195),U_2199))
| hBOOL(hAPP(hAPP(c_member(U_2193),U_2194),U_2195)) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
! [U_2194,U_2193,U_2195,U_2196,U_2197,U_2198,U_2199] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2193,U_2196,U_2197,U_2198,hAPP(hAPP(c_Set_Oinsert(U_2193),U_2194),U_2195)),hAPP(hAPP(U_2197,U_2194),U_2199)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2193,U_2196,U_2197,U_2198,U_2195),U_2199))
| hBOOL(hAPP(hAPP(c_member(U_2193),U_2194),U_2195)) ),
inference(definitional_conversion,[status(esa)],[f_549_2]) ).
cnf(f_549_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2193,U_2196,U_2197,U_2198,hAPP(hAPP(c_Set_Oinsert(U_2193),U_2194),U_2195)),hAPP(hAPP(U_2197,U_2194),U_2199)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2193,U_2196,U_2197,U_2198,U_2195),U_2199))
| hBOOL(hAPP(hAPP(c_member(U_2193),U_2194),U_2195)) ),
inference(clausify,[status(thm)],[f_549_3]) ).
fof(f_550_1,plain,
! [V_m_2,V_n_2,V_i_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__diff]) ).
fof(f_550_2,plain,
! [U_2203,U_2202,U_2201,U_2200] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2200,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2201),U_2203)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2201),U_2202)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2202),U_2203)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2200),U_2201),U_2202))
| ~ class_Orderings_Olinorder(U_2200) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
! [U_2201,U_2200,U_2202,U_2203] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2200,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2201),U_2203)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2201),U_2202)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2202),U_2203)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2200),U_2201),U_2202))
| ~ class_Orderings_Olinorder(U_2200) ),
inference(definitional_conversion,[status(esa)],[f_550_2]) ).
cnf(f_550_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2200,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2201),U_2203)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2201),U_2202)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2200,U_2202),U_2203)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2200),U_2201),U_2202))
| ~ class_Orderings_Olinorder(U_2200) ),
inference(clausify,[status(thm)],[f_550_3]) ).
fof(f_551_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J]) ).
fof(f_551_2,plain,
! [U_2207,U_2206,U_2205,U_2204] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2204,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2204,U_2205),U_2206)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2204,U_2206),U_2207)) = c_Orderings_Obot__class_Obot(tc_fun(U_2204,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2204) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
fof(f_551_3,plain,
! [U_2204,U_2205,U_2206,U_2207] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2204,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2204,U_2205),U_2206)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2204,U_2206),U_2207)) = c_Orderings_Obot__class_Obot(tc_fun(U_2204,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2204) ),
inference(definitional_conversion,[status(esa)],[f_551_2]) ).
cnf(f_551_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2204,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2204,U_2205),U_2206)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2204,U_2206),U_2207)) = c_Orderings_Obot__class_Obot(tc_fun(U_2204,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2204) ),
inference(clausify,[status(thm)],[f_551_3]) ).
fof(f_552_1,plain,
! [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_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ 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))) )
& ( 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)))
| 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl]) ).
fof(f_552_2,plain,
! [U_2210,U_2209,U_2208] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2208,tc_HOL_Obool)),U_2209),U_2210) = c_Orderings_Obot__class_Obot(tc_fun(U_2208,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2208,tc_HOL_Obool)),U_2209),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2208,tc_HOL_Obool)),U_2210))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2208,tc_HOL_Obool)),U_2209),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2208,tc_HOL_Obool)),U_2210)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2208,tc_HOL_Obool)),U_2209),U_2210) != c_Orderings_Obot__class_Obot(tc_fun(U_2208,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
fof(f_552_3,plain,
( ! [U_2216,U_2214,U_2212] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2212,tc_HOL_Obool)),U_2214),U_2216) = c_Orderings_Obot__class_Obot(tc_fun(U_2212,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2212,tc_HOL_Obool)),U_2216))) )
& ! [U_2215,U_2213,U_2211] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),U_2213),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2211,tc_HOL_Obool)),U_2215)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2211,tc_HOL_Obool)),U_2213),U_2215) != c_Orderings_Obot__class_Obot(tc_fun(U_2211,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_552_2]) ).
fof(f_552_4,plain,
( ! [U_2212,U_2214,U_2216] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2212,tc_HOL_Obool)),U_2214),U_2216) = c_Orderings_Obot__class_Obot(tc_fun(U_2212,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2212,tc_HOL_Obool)),U_2216))) )
& ! [U_2213,U_2211,U_2215] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),U_2213),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2211,tc_HOL_Obool)),U_2215)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2211,tc_HOL_Obool)),U_2213),U_2215) != c_Orderings_Obot__class_Obot(tc_fun(U_2211,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_552_3]) ).
cnf(f_552_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),U_2213),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2211,tc_HOL_Obool)),U_2215)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2211,tc_HOL_Obool)),U_2213),U_2215) != c_Orderings_Obot__class_Obot(tc_fun(U_2211,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_552_4]) ).
cnf(f_552_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2212,tc_HOL_Obool)),U_2214),U_2216) = c_Orderings_Obot__class_Obot(tc_fun(U_2212,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2212,tc_HOL_Obool)),U_2216))) ),
inference(clausify,[status(thm)],[f_552_4]) ).
fof(f_553_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J]) ).
fof(f_553_2,plain,
! [U_2220,U_2219,U_2218,U_2217] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2217,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2217,U_2218),U_2219)),c_SetInterval_Oord__class_OatLeastAtMost(U_2217,U_2219,U_2220)) = c_SetInterval_Oord__class_OatLeastAtMost(U_2217,U_2218,U_2220)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2219),U_2220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2218),U_2219))
| ~ class_Orderings_Olinorder(U_2217) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
fof(f_553_3,plain,
! [U_2217,U_2218,U_2219,U_2220] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2217,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2217,U_2218),U_2219)),c_SetInterval_Oord__class_OatLeastAtMost(U_2217,U_2219,U_2220)) = c_SetInterval_Oord__class_OatLeastAtMost(U_2217,U_2218,U_2220)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2219),U_2220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2218),U_2219))
| ~ class_Orderings_Olinorder(U_2217) ),
inference(definitional_conversion,[status(esa)],[f_553_2]) ).
cnf(f_553_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2217,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2217,U_2218),U_2219)),c_SetInterval_Oord__class_OatLeastAtMost(U_2217,U_2219,U_2220)) = c_SetInterval_Oord__class_OatLeastAtMost(U_2217,U_2218,U_2220)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2219),U_2220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2218),U_2219))
| ~ class_Orderings_Olinorder(U_2217) ),
inference(clausify,[status(thm)],[f_553_3]) ).
fof(f_554_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J]) ).
fof(f_554_2,plain,
! [U_2224,U_2223,U_2222,U_2221] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2221,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2221,U_2222),U_2223)),c_SetInterval_Oord__class_OatLeastAtMost(U_2221,U_2223,U_2224)) = c_Orderings_Obot__class_Obot(tc_fun(U_2221,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2221) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
! [U_2222,U_2223,U_2221,U_2224] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2221,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2221,U_2222),U_2223)),c_SetInterval_Oord__class_OatLeastAtMost(U_2221,U_2223,U_2224)) = c_Orderings_Obot__class_Obot(tc_fun(U_2221,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2221) ),
inference(definitional_conversion,[status(esa)],[f_554_2]) ).
cnf(f_554_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2221,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2221,U_2222),U_2223)),c_SetInterval_Oord__class_OatLeastAtMost(U_2221,U_2223,U_2224)) = c_Orderings_Obot__class_Obot(tc_fun(U_2221,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2221) ),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J]) ).
fof(f_555_2,plain,
! [U_2227,U_2226,U_2225] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2225,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2225),U_2226)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2225,U_2226),U_2227)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2225),U_2227)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2225),U_2226),U_2227))
| ~ class_Orderings_Olinorder(U_2225) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
fof(f_555_3,plain,
! [U_2225,U_2226,U_2227] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2225,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2225),U_2226)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2225,U_2226),U_2227)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2225),U_2227)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2225),U_2226),U_2227))
| ~ class_Orderings_Olinorder(U_2225) ),
inference(definitional_conversion,[status(esa)],[f_555_2]) ).
cnf(f_555_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2225,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2225),U_2226)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2225,U_2226),U_2227)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2225),U_2227)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2225),U_2226),U_2227))
| ~ class_Orderings_Olinorder(U_2225) ),
inference(clausify,[status(thm)],[f_555_3]) ).
fof(f_556_1,plain,
! [V_u_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J]) ).
fof(f_556_2,plain,
! [U_2230,U_2229,U_2228] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2228,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2228),U_2229)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2228,U_2229),U_2230)) = c_Orderings_Obot__class_Obot(tc_fun(U_2228,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2228) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
fof(f_556_3,plain,
! [U_2228,U_2229,U_2230] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2228,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2228),U_2229)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2228,U_2229),U_2230)) = c_Orderings_Obot__class_Obot(tc_fun(U_2228,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2228) ),
inference(definitional_conversion,[status(esa)],[f_556_2]) ).
cnf(f_556_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2228,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2228),U_2229)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2228,U_2229),U_2230)) = c_Orderings_Obot__class_Obot(tc_fun(U_2228,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2228) ),
inference(clausify,[status(thm)],[f_556_3]) ).
fof(f_557_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( 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))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J]) ).
fof(f_557_2,plain,
! [U_2234,U_2233,U_2232,U_2231] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2231,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_2231,U_2232,U_2233)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2231,U_2233),U_2234)) = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2231) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
fof(f_557_3,plain,
! [U_2231,U_2232,U_2233,U_2234] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2231,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_2231,U_2232,U_2233)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2231,U_2233),U_2234)) = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2231) ),
inference(definitional_conversion,[status(esa)],[f_557_2]) ).
cnf(f_557_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2231,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_2231,U_2232,U_2233)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2231,U_2233),U_2234)) = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2231) ),
inference(clausify,[status(thm)],[f_557_3]) ).
fof(f_558_1,plain,
! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set_Ointros]) ).
fof(f_558_2,plain,
! [U_2239,U_2238,U_2237,U_2236,U_2235] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2235,U_2236,hAPP(hAPP(c_Set_Oinsert(U_2235),U_2237),U_2238)),U_2239))
| hBOOL(hAPP(hAPP(c_member(U_2235),U_2237),U_2238))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2235,U_2235,U_2236,U_2237,U_2238),U_2239)) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
! [U_2235,U_2236,U_2237,U_2238,U_2239] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2235,U_2236,hAPP(hAPP(c_Set_Oinsert(U_2235),U_2237),U_2238)),U_2239))
| hBOOL(hAPP(hAPP(c_member(U_2235),U_2237),U_2238))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2235,U_2235,U_2236,U_2237,U_2238),U_2239)) ),
inference(definitional_conversion,[status(esa)],[f_558_2]) ).
cnf(f_558_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2235,U_2236,hAPP(hAPP(c_Set_Oinsert(U_2235),U_2237),U_2238)),U_2239))
| hBOOL(hAPP(hAPP(c_member(U_2235),U_2237),U_2238))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2235,U_2235,U_2236,U_2237,U_2238),U_2239)) ),
inference(clausify,[status(thm)],[f_558_3]) ).
fof(f_559_1,plain,
! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ 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))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__permute__diff]) ).
fof(f_559_2,plain,
! [U_2244,U_2243,U_2242,U_2241,U_2240] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2240,U_2240,c_Groups_Otimes__class_Otimes(U_2240),U_2244,hAPP(hAPP(c_Set_Oinsert(U_2240),U_2241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2240,tc_HOL_Obool)),U_2242),hAPP(hAPP(c_Set_Oinsert(U_2240),U_2244),c_Orderings_Obot__class_Obot(tc_fun(U_2240,tc_HOL_Obool)))))),U_2243))
| hBOOL(hAPP(hAPP(c_member(U_2240),U_2241),U_2242))
| ~ hBOOL(hAPP(hAPP(c_member(U_2240),U_2244),U_2242))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2240,U_2240,c_Groups_Otimes__class_Otimes(U_2240),U_2241,U_2242),U_2243))
| ~ class_Groups_Oab__semigroup__mult(U_2240) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
fof(f_559_3,plain,
! [U_2240,U_2241,U_2242,U_2243,U_2244] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2240,U_2240,c_Groups_Otimes__class_Otimes(U_2240),U_2244,hAPP(hAPP(c_Set_Oinsert(U_2240),U_2241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2240,tc_HOL_Obool)),U_2242),hAPP(hAPP(c_Set_Oinsert(U_2240),U_2244),c_Orderings_Obot__class_Obot(tc_fun(U_2240,tc_HOL_Obool)))))),U_2243))
| hBOOL(hAPP(hAPP(c_member(U_2240),U_2241),U_2242))
| ~ hBOOL(hAPP(hAPP(c_member(U_2240),U_2244),U_2242))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2240,U_2240,c_Groups_Otimes__class_Otimes(U_2240),U_2241,U_2242),U_2243))
| ~ class_Groups_Oab__semigroup__mult(U_2240) ),
inference(definitional_conversion,[status(esa)],[f_559_2]) ).
cnf(f_559_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2240,U_2240,c_Groups_Otimes__class_Otimes(U_2240),U_2244,hAPP(hAPP(c_Set_Oinsert(U_2240),U_2241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2240,tc_HOL_Obool)),U_2242),hAPP(hAPP(c_Set_Oinsert(U_2240),U_2244),c_Orderings_Obot__class_Obot(tc_fun(U_2240,tc_HOL_Obool)))))),U_2243))
| hBOOL(hAPP(hAPP(c_member(U_2240),U_2241),U_2242))
| ~ hBOOL(hAPP(hAPP(c_member(U_2240),U_2244),U_2242))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2240,U_2240,c_Groups_Otimes__class_Otimes(U_2240),U_2241,U_2242),U_2243))
| ~ class_Groups_Oab__semigroup__mult(U_2240) ),
inference(clausify,[status(thm)],[f_559_3]) ).
fof(f_560_1,plain,
! [V_x_2,V_F_2,V_f_2,T_b] :
( 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
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton]) ).
fof(f_560_2,plain,
! [U_2248,U_2247,U_2246,U_2245] :
( hAPP(U_2247,hAPP(hAPP(c_Set_Oinsert(U_2245),U_2248),c_Orderings_Obot__class_Obot(tc_fun(U_2245,tc_HOL_Obool)))) = U_2248
| ~ c_Finite__Set_Ofolding__one(U_2245,U_2246,U_2247) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
fof(f_560_3,plain,
! [U_2248,U_2247,U_2246,U_2245] :
( hAPP(U_2247,hAPP(hAPP(c_Set_Oinsert(U_2245),U_2248),c_Orderings_Obot__class_Obot(tc_fun(U_2245,tc_HOL_Obool)))) = U_2248
| ~ c_Finite__Set_Ofolding__one(U_2245,U_2246,U_2247) ),
inference(definitional_conversion,[status(esa)],[f_560_2]) ).
cnf(f_560_4,plain,
( hAPP(U_2247,hAPP(hAPP(c_Set_Oinsert(U_2245),U_2248),c_Orderings_Obot__class_Obot(tc_fun(U_2245,tc_HOL_Obool)))) = U_2248
| ~ c_Finite__Set_Ofolding__one(U_2245,U_2246,U_2247) ),
inference(clausify,[status(thm)],[f_560_3]) ).
fof(f_561_1,plain,
! [V_b_2,V_a_2,V_f_2,T_b] :
( ( 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))
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set__sing]) ).
fof(f_561_2,plain,
! [U_2252,U_2251,U_2250,U_2249] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2249,U_2250,hAPP(hAPP(c_Set_Oinsert(U_2249),U_2251),c_Orderings_Obot__class_Obot(tc_fun(U_2249,tc_HOL_Obool)))),U_2252))
| U_2251 != U_2252 )
& ( U_2251 = U_2252
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2249,U_2250,hAPP(hAPP(c_Set_Oinsert(U_2249),U_2251),c_Orderings_Obot__class_Obot(tc_fun(U_2249,tc_HOL_Obool)))),U_2252)) ) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
fof(f_561_3,plain,
( ! [U_2260,U_2258] :
( ! [U_2256,U_2254] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2254,U_2256,hAPP(hAPP(c_Set_Oinsert(U_2254),U_2258),c_Orderings_Obot__class_Obot(tc_fun(U_2254,tc_HOL_Obool)))),U_2260))
| U_2258 != U_2260 )
& ! [U_2259,U_2257] :
( ! [U_2255,U_2253] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2253,U_2255,hAPP(hAPP(c_Set_Oinsert(U_2253),U_2257),c_Orderings_Obot__class_Obot(tc_fun(U_2253,tc_HOL_Obool)))),U_2259))
| U_2257 = U_2259 ) ),
inference(miniscope,[status(thm)],[f_561_2]) ).
fof(f_561_4,plain,
( ! [U_2254,U_2260,U_2256,U_2258] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2254,U_2256,hAPP(hAPP(c_Set_Oinsert(U_2254),U_2258),c_Orderings_Obot__class_Obot(tc_fun(U_2254,tc_HOL_Obool)))),U_2260))
| U_2258 != U_2260 )
& ! [U_2257,U_2255,U_2253,U_2259] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2253,U_2255,hAPP(hAPP(c_Set_Oinsert(U_2253),U_2257),c_Orderings_Obot__class_Obot(tc_fun(U_2253,tc_HOL_Obool)))),U_2259))
| U_2257 = U_2259 ) ),
inference(definitional_conversion,[status(esa)],[f_561_3]) ).
cnf(f_561_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2253,U_2255,hAPP(hAPP(c_Set_Oinsert(U_2253),U_2257),c_Orderings_Obot__class_Obot(tc_fun(U_2253,tc_HOL_Obool)))),U_2259))
| U_2257 = U_2259 ),
inference(clausify,[status(thm)],[f_561_4]) ).
cnf(f_561_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2254,U_2256,hAPP(hAPP(c_Set_Oinsert(U_2254),U_2258),c_Orderings_Obot__class_Obot(tc_fun(U_2254,tc_HOL_Obool)))),U_2260))
| U_2258 != U_2260 ),
inference(clausify,[status(thm)],[f_561_4]) ).
fof(f_562_1,plain,
! [T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ! [B_x,B_B] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B))
| V_A_2 != hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B) ) )
& ( ? [B_x,B_B] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B))
& V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_nonempty__iff]) ).
fof(f_562_2,plain,
! [U_2266,U_2265] :
( ( U_2265 != c_Orderings_Obot__class_Obot(tc_fun(U_2266,tc_HOL_Obool))
| ! [U_2264,U_2263] :
( hBOOL(hAPP(hAPP(c_member(U_2266),U_2264),U_2263))
| U_2265 != hAPP(hAPP(c_Set_Oinsert(U_2266),U_2264),U_2263) ) )
& ( ? [U_2262,U_2261] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2266),U_2262),U_2261))
& U_2265 = hAPP(hAPP(c_Set_Oinsert(U_2266),U_2262),U_2261) )
| U_2265 = c_Orderings_Obot__class_Obot(tc_fun(U_2266,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
fof(f_562_3,plain,
( ! [U_2270,U_2268] :
( U_2268 != c_Orderings_Obot__class_Obot(tc_fun(U_2270,tc_HOL_Obool))
| ! [U_2264,U_2263] :
( hBOOL(hAPP(hAPP(c_member(U_2270),U_2264),U_2263))
| U_2268 != hAPP(hAPP(c_Set_Oinsert(U_2270),U_2264),U_2263) ) )
& ! [U_2269,U_2267] :
( ? [U_2262,U_2261] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2269),U_2262),U_2261))
& U_2267 = hAPP(hAPP(c_Set_Oinsert(U_2269),U_2262),U_2261) )
| U_2267 = c_Orderings_Obot__class_Obot(tc_fun(U_2269,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_562_2]) ).
fof(f_562_4,plain,
( ! [U_2270,U_2268] :
( U_2268 != c_Orderings_Obot__class_Obot(tc_fun(U_2270,tc_HOL_Obool))
| ! [U_2264,U_2263] :
( hBOOL(hAPP(hAPP(c_member(U_2270),U_2264),U_2263))
| U_2268 != hAPP(hAPP(c_Set_Oinsert(U_2270),U_2264),U_2263) ) )
& ! [U_2269,U_2267] :
( ? [U_2261] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2269),sK50(U_2269,U_2267)),U_2261))
& U_2267 = hAPP(hAPP(c_Set_Oinsert(U_2269),sK50(U_2269,U_2267)),U_2261) )
| U_2267 = c_Orderings_Obot__class_Obot(tc_fun(U_2269,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_2262,sK50(U_2269,U_2267))],[f_562_3]) ).
fof(f_562_5,plain,
( ! [U_2270,U_2268] :
( U_2268 != c_Orderings_Obot__class_Obot(tc_fun(U_2270,tc_HOL_Obool))
| ! [U_2264,U_2263] :
( hBOOL(hAPP(hAPP(c_member(U_2270),U_2264),U_2263))
| U_2268 != hAPP(hAPP(c_Set_Oinsert(U_2270),U_2264),U_2263) ) )
& ! [U_2269,U_2267] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_2269),sK50(U_2269,U_2267)),sK51(U_2269,U_2267)))
& U_2267 = hAPP(hAPP(c_Set_Oinsert(U_2269),sK50(U_2269,U_2267)),sK51(U_2269,U_2267)) )
| U_2267 = c_Orderings_Obot__class_Obot(tc_fun(U_2269,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_2261,sK51(U_2269,U_2267))],[f_562_4]) ).
fof(f_562_6,plain,
( ! [U_2267,U_2269] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2269),sK50(U_2269,U_2267)),sK51(U_2269,U_2267)))
| ~ sP160(U_2267,U_2269) )
& ! [U_2267,U_2269] :
( U_2267 = hAPP(hAPP(c_Set_Oinsert(U_2269),sK50(U_2269,U_2267)),sK51(U_2269,U_2267))
| ~ sP160(U_2267,U_2269) )
& ! [U_2263,U_2264,U_2268,U_2270] :
( U_2268 != c_Orderings_Obot__class_Obot(tc_fun(U_2270,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2270),U_2264),U_2263))
| U_2268 != hAPP(hAPP(c_Set_Oinsert(U_2270),U_2264),U_2263) )
& ! [U_2267,U_2269] :
( sP160(U_2267,U_2269)
| U_2267 = c_Orderings_Obot__class_Obot(tc_fun(U_2269,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_562_5]) ).
cnf(f_562_7,plain,
( sP160(U_2267,U_2269)
| U_2267 = c_Orderings_Obot__class_Obot(tc_fun(U_2269,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_562_6]) ).
cnf(f_562_8,plain,
( U_2268 != c_Orderings_Obot__class_Obot(tc_fun(U_2270,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2270),U_2264),U_2263))
| U_2268 != hAPP(hAPP(c_Set_Oinsert(U_2270),U_2264),U_2263) ),
inference(clausify,[status(thm)],[f_562_6]) ).
cnf(f_562_9,plain,
( U_2267 = hAPP(hAPP(c_Set_Oinsert(U_2269),sK50(U_2269,U_2267)),sK51(U_2269,U_2267))
| ~ sP160(U_2267,U_2269) ),
inference(clausify,[status(thm)],[f_562_6]) ).
cnf(f_562_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2269),sK50(U_2269,U_2267)),sK51(U_2269,U_2267)))
| ~ sP160(U_2267,U_2269) ),
inference(clausify,[status(thm)],[f_562_6]) ).
fof(f_563_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Pow__insert]) ).
fof(f_563_2,plain,
! [U_2273,U_2272,U_2271] : hAPP(c_Set_OPow(U_2271),hAPP(hAPP(c_Set_Oinsert(U_2271),U_2272),U_2273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_2271,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_2271),U_2273)),hAPP(c_Set_Oimage(tc_fun(U_2271,tc_HOL_Obool),tc_fun(U_2271,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_2271),U_2272)),hAPP(c_Set_OPow(U_2271),U_2273))),
inference(variable_rename,[status(thm)],[f_563_1]) ).
fof(f_563_3,plain,
! [U_2271,U_2272,U_2273] : hAPP(c_Set_OPow(U_2271),hAPP(hAPP(c_Set_Oinsert(U_2271),U_2272),U_2273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_2271,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_2271),U_2273)),hAPP(c_Set_Oimage(tc_fun(U_2271,tc_HOL_Obool),tc_fun(U_2271,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_2271),U_2272)),hAPP(c_Set_OPow(U_2271),U_2273))),
inference(definitional_conversion,[status(esa)],[f_563_2]) ).
cnf(f_563_4,plain,
hAPP(c_Set_OPow(U_2271),hAPP(hAPP(c_Set_Oinsert(U_2271),U_2272),U_2273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_2271,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_2271),U_2273)),hAPP(c_Set_Oimage(tc_fun(U_2271,tc_HOL_Obool),tc_fun(U_2271,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_2271),U_2272)),hAPP(c_Set_OPow(U_2271),U_2273))),
inference(clausify,[status(thm)],[f_563_3]) ).
fof(f_564_1,plain,
! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( ? [B_y_H] :
( 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))
& V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux]) ).
fof(f_564_2,plain,
! [U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275] :
( ? [U_2274] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2275,U_2276,U_2277,U_2278,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2279),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2281),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool))))),U_2274))
& U_2280 = hAPP(hAPP(U_2277,U_2281),U_2274) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2275),U_2281),U_2279))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2275,U_2276,U_2277,U_2278,U_2279),U_2280))
| ~ c_Finite__Set_Ofun__left__comm(U_2275,U_2276,U_2277) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
fof(f_564_3,plain,
! [U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2275,U_2276,U_2277,U_2278,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2279),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2281),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool))))),sK52(U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275)))
& U_2280 = hAPP(hAPP(U_2277,U_2281),sK52(U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2275),U_2281),U_2279))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2275,U_2276,U_2277,U_2278,U_2279),U_2280))
| ~ c_Finite__Set_Ofun__left__comm(U_2275,U_2276,U_2277) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_2274,sK52(U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275))],[f_564_2]) ).
fof(f_564_4,plain,
( ! [U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2275,U_2276,U_2277,U_2278,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2279),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2281),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool))))),sK52(U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275)))
| ~ sP161(U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281) )
& ! [U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281] :
( U_2280 = hAPP(hAPP(U_2277,U_2281),sK52(U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275))
| ~ sP161(U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281) )
& ! [U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281] :
( sP161(U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281)
| ~ hBOOL(hAPP(hAPP(c_member(U_2275),U_2281),U_2279))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2275,U_2276,U_2277,U_2278,U_2279),U_2280))
| ~ c_Finite__Set_Ofun__left__comm(U_2275,U_2276,U_2277) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_564_3]) ).
cnf(f_564_5,plain,
( sP161(U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281)
| ~ hBOOL(hAPP(hAPP(c_member(U_2275),U_2281),U_2279))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2275,U_2276,U_2277,U_2278,U_2279),U_2280))
| ~ c_Finite__Set_Ofun__left__comm(U_2275,U_2276,U_2277) ),
inference(clausify,[status(thm)],[f_564_4]) ).
cnf(f_564_6,plain,
( U_2280 = hAPP(hAPP(U_2277,U_2281),sK52(U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275))
| ~ sP161(U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281) ),
inference(clausify,[status(thm)],[f_564_4]) ).
cnf(f_564_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2275,U_2276,U_2277,U_2278,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2279),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2281),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool))))),sK52(U_2281,U_2280,U_2279,U_2278,U_2277,U_2276,U_2275)))
| ~ sP161(U_2275,U_2276,U_2277,U_2278,U_2279,U_2280,U_2281) ),
inference(clausify,[status(thm)],[f_564_4]) ).
fof(f_565_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem]) ).
fof(f_565_2,plain,
! [U_2283,U_2282] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2282),U_2283),U_2283) = U_2283
| ~ class_Lattices_Olattice(U_2282) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
! [U_2283,U_2282] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2282),U_2283),U_2283) = U_2283
| ~ class_Lattices_Olattice(U_2282) ),
inference(definitional_conversion,[status(esa)],[f_565_2]) ).
cnf(f_565_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2282),U_2283),U_2283) = U_2283
| ~ class_Lattices_Olattice(U_2282) ),
inference(clausify,[status(thm)],[f_565_3]) ).
fof(f_566_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x
| ~ class_Lattices_Olattice(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem]) ).
fof(f_566_2,plain,
! [U_2285,U_2284] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2284),U_2285),U_2285) = U_2285
| ~ class_Lattices_Olattice(U_2284) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
fof(f_566_3,plain,
! [U_2284,U_2285] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2284),U_2285),U_2285) = U_2285
| ~ class_Lattices_Olattice(U_2284) ),
inference(definitional_conversion,[status(esa)],[f_566_2]) ).
cnf(f_566_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2284),U_2285),U_2285) = U_2285
| ~ class_Lattices_Olattice(U_2284) ),
inference(clausify,[status(thm)],[f_566_3]) ).
fof(f_567_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(f_567_2,plain,
! [U_2288,U_2287,U_2286] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2286),U_2288),U_2287))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2286),U_2287),U_2288))
| U_2287 = U_2288
| ~ class_Rings_Olinordered__idom(U_2286) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
! [U_2286,U_2287,U_2288] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2286),U_2288),U_2287))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2286),U_2287),U_2288))
| U_2287 = U_2288
| ~ class_Rings_Olinordered__idom(U_2286) ),
inference(definitional_conversion,[status(esa)],[f_567_2]) ).
cnf(f_567_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2286),U_2288),U_2287))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2286),U_2287),U_2288))
| U_2287 = U_2288
| ~ class_Rings_Olinordered__idom(U_2286) ),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_1,plain,
! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| V_b_2 != hAPP(V_f_2,V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_image__eqI]) ).
fof(f_568_2,plain,
! [U_2294,U_2293,U_2292,U_2291,U_2290,U_2289] :
( hBOOL(hAPP(hAPP(c_member(U_2294),U_2289),hAPP(c_Set_Oimage(U_2292,U_2294,U_2290),U_2293)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2292),U_2291),U_2293))
| U_2289 != hAPP(U_2290,U_2291) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
fof(f_568_3,plain,
! [U_2289,U_2291,U_2290,U_2292,U_2293,U_2294] :
( hBOOL(hAPP(hAPP(c_member(U_2294),U_2289),hAPP(c_Set_Oimage(U_2292,U_2294,U_2290),U_2293)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2292),U_2291),U_2293))
| U_2289 != hAPP(U_2290,U_2291) ),
inference(definitional_conversion,[status(esa)],[f_568_2]) ).
cnf(f_568_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2294),U_2289),hAPP(c_Set_Oimage(U_2292,U_2294,U_2290),U_2293)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2292),U_2291),U_2293))
| U_2289 != hAPP(U_2290,U_2291) ),
inference(clausify,[status(thm)],[f_568_3]) ).
fof(f_569_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_double__complement]) ).
fof(f_569_2,plain,
! [U_2296,U_2295] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2295,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2295,tc_HOL_Obool)),U_2296)) = U_2296,
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
! [U_2295,U_2296] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2295,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2295,tc_HOL_Obool)),U_2296)) = U_2296,
inference(definitional_conversion,[status(esa)],[f_569_2]) ).
cnf(f_569_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2295,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2295,tc_HOL_Obool)),U_2296)) = U_2296,
inference(clausify,[status(thm)],[f_569_3]) ).
fof(f_570_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( 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)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_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_b,tc_HOL_Obool)),V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff]) ).
fof(f_570_2,plain,
! [U_2299,U_2298,U_2297] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2297,tc_HOL_Obool)),U_2298) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2297,tc_HOL_Obool)),U_2299)
| U_2298 != U_2299 )
& ( U_2298 = U_2299
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2297,tc_HOL_Obool)),U_2298) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2297,tc_HOL_Obool)),U_2299) ) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
fof(f_570_3,plain,
( ! [U_2305,U_2303] :
( ! [U_2301] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2301,tc_HOL_Obool)),U_2303) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2301,tc_HOL_Obool)),U_2305)
| U_2303 != U_2305 )
& ! [U_2304,U_2302] :
( ! [U_2300] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2300,tc_HOL_Obool)),U_2302) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2300,tc_HOL_Obool)),U_2304)
| U_2302 = U_2304 ) ),
inference(miniscope,[status(thm)],[f_570_2]) ).
fof(f_570_4,plain,
( ! [U_2305,U_2301,U_2303] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2301,tc_HOL_Obool)),U_2303) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2301,tc_HOL_Obool)),U_2305)
| U_2303 != U_2305 )
& ! [U_2304,U_2300,U_2302] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2300,tc_HOL_Obool)),U_2302) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2300,tc_HOL_Obool)),U_2304)
| U_2302 = U_2304 ) ),
inference(definitional_conversion,[status(esa)],[f_570_3]) ).
cnf(f_570_5,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2300,tc_HOL_Obool)),U_2302) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2300,tc_HOL_Obool)),U_2304)
| U_2302 = U_2304 ),
inference(clausify,[status(thm)],[f_570_4]) ).
cnf(f_570_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2301,tc_HOL_Obool)),U_2303) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2301,tc_HOL_Obool)),U_2305)
| U_2303 != U_2305 ),
inference(clausify,[status(thm)],[f_570_4]) ).
fof(f_571_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( 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)
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_image__Pow__surj]) ).
fof(f_571_2,plain,
! [U_2310,U_2309,U_2308,U_2307,U_2306] :
( hAPP(c_Set_Oimage(tc_fun(U_2306,tc_HOL_Obool),tc_fun(U_2307,tc_HOL_Obool),c_Set_Oimage(U_2306,U_2307,U_2308)),hAPP(c_Set_OPow(U_2306),U_2309)) = hAPP(c_Set_OPow(U_2307),U_2310)
| hAPP(c_Set_Oimage(U_2306,U_2307,U_2308),U_2309) != U_2310 ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
! [U_2306,U_2307,U_2308,U_2309,U_2310] :
( hAPP(c_Set_Oimage(tc_fun(U_2306,tc_HOL_Obool),tc_fun(U_2307,tc_HOL_Obool),c_Set_Oimage(U_2306,U_2307,U_2308)),hAPP(c_Set_OPow(U_2306),U_2309)) = hAPP(c_Set_OPow(U_2307),U_2310)
| hAPP(c_Set_Oimage(U_2306,U_2307,U_2308),U_2309) != U_2310 ),
inference(definitional_conversion,[status(esa)],[f_571_2]) ).
cnf(f_571_4,plain,
( hAPP(c_Set_Oimage(tc_fun(U_2306,tc_HOL_Obool),tc_fun(U_2307,tc_HOL_Obool),c_Set_Oimage(U_2306,U_2307,U_2308)),hAPP(c_Set_OPow(U_2306),U_2309)) = hAPP(c_Set_OPow(U_2307),U_2310)
| hAPP(c_Set_Oimage(U_2306,U_2307,U_2308),U_2309) != U_2310 ),
inference(clausify,[status(thm)],[f_571_3]) ).
fof(f_572_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__idem]) ).
fof(f_572_2,plain,
! [U_2313,U_2312,U_2311] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),U_2313)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),U_2313)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2311) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
! [U_2312,U_2311,U_2313] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),U_2313)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),U_2313)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2311) ),
inference(definitional_conversion,[status(esa)],[f_572_2]) ).
cnf(f_572_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),U_2313)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2311),U_2312),U_2313)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2311) ),
inference(clausify,[status(thm)],[f_572_3]) ).
fof(f_573_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__idem]) ).
fof(f_573_2,plain,
! [U_2315,U_2314] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2315),U_2315) = U_2315
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2314) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
fof(f_573_3,plain,
! [U_2314,U_2315] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2315),U_2315) = U_2315
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2314) ),
inference(definitional_conversion,[status(esa)],[f_573_2]) ).
cnf(f_573_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2315),U_2315) = U_2315
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2314) ),
inference(clausify,[status(thm)],[f_573_3]) ).
fof(f_574_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times_Oidem]) ).
fof(f_574_2,plain,
! [U_2317,U_2316] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2316),U_2317),U_2317) = U_2317
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2316) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
! [U_2316,U_2317] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2316),U_2317),U_2317) = U_2317
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2316) ),
inference(definitional_conversion,[status(esa)],[f_574_2]) ).
cnf(f_574_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2316),U_2317),U_2317) = U_2317
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2316) ),
inference(clausify,[status(thm)],[f_574_3]) ).
fof(f_575_1,plain,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
( 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))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm]) ).
fof(f_575_2,plain,
! [U_2323,U_2322,U_2321,U_2320,U_2319,U_2318] :
( hAPP(hAPP(U_2320,U_2321),hAPP(hAPP(U_2320,U_2322),U_2323)) = hAPP(hAPP(U_2320,U_2322),hAPP(hAPP(U_2320,U_2321),U_2323))
| ~ c_Finite__Set_Ofun__left__comm(U_2318,U_2319,U_2320) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
! [U_2323,U_2322,U_2321,U_2320] :
( ! [U_2319,U_2318] : ~ c_Finite__Set_Ofun__left__comm(U_2318,U_2319,U_2320)
| hAPP(hAPP(U_2320,U_2321),hAPP(hAPP(U_2320,U_2322),U_2323)) = hAPP(hAPP(U_2320,U_2322),hAPP(hAPP(U_2320,U_2321),U_2323)) ),
inference(miniscope,[status(thm)],[f_575_2]) ).
fof(f_575_4,plain,
! [U_2318,U_2319,U_2320,U_2321,U_2322,U_2323] :
( ~ c_Finite__Set_Ofun__left__comm(U_2318,U_2319,U_2320)
| hAPP(hAPP(U_2320,U_2321),hAPP(hAPP(U_2320,U_2322),U_2323)) = hAPP(hAPP(U_2320,U_2322),hAPP(hAPP(U_2320,U_2321),U_2323)) ),
inference(definitional_conversion,[status(esa)],[f_575_3]) ).
cnf(f_575_5,plain,
( ~ c_Finite__Set_Ofun__left__comm(U_2318,U_2319,U_2320)
| hAPP(hAPP(U_2320,U_2321),hAPP(hAPP(U_2320,U_2322),U_2323)) = hAPP(hAPP(U_2320,U_2322),hAPP(hAPP(U_2320,U_2321),U_2323)) ),
inference(clausify,[status(thm)],[f_575_4]) ).
fof(f_576_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Oab__semigroup__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J]) ).
fof(f_576_2,plain,
! [U_2327,U_2326,U_2325,U_2324] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),U_2326)),U_2327) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2326),U_2327))
| ~ class_Groups_Oab__semigroup__mult(U_2324) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
! [U_2324,U_2325,U_2326,U_2327] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),U_2326)),U_2327) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2326),U_2327))
| ~ class_Groups_Oab__semigroup__mult(U_2324) ),
inference(definitional_conversion,[status(esa)],[f_576_2]) ).
cnf(f_576_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),U_2326)),U_2327) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2326),U_2327))
| ~ class_Groups_Oab__semigroup__mult(U_2324) ),
inference(clausify,[status(thm)],[f_576_3]) ).
fof(f_577_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm]) ).
fof(f_577_2,plain,
! [U_2328] :
( c_Finite__Set_Ofun__left__comm(U_2328,U_2328,c_Groups_Otimes__class_Otimes(U_2328))
| ~ class_Groups_Oab__semigroup__mult(U_2328) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
! [U_2328] :
( c_Finite__Set_Ofun__left__comm(U_2328,U_2328,c_Groups_Otimes__class_Otimes(U_2328))
| ~ class_Groups_Oab__semigroup__mult(U_2328) ),
inference(definitional_conversion,[status(esa)],[f_577_2]) ).
cnf(f_577_4,plain,
( c_Finite__Set_Ofun__left__comm(U_2328,U_2328,c_Groups_Otimes__class_Otimes(U_2328))
| ~ class_Groups_Oab__semigroup__mult(U_2328) ),
inference(clausify,[status(thm)],[f_577_3]) ).
fof(f_578_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__right]) ).
fof(f_578_2,plain,
! [U_2331,U_2330,U_2329] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2329),U_2330),U_2331)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2329),U_2330),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2331))
| ~ class_Rings_Oring(U_2329) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
fof(f_578_3,plain,
! [U_2329,U_2330,U_2331] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2329),U_2330),U_2331)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2329),U_2330),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2331))
| ~ class_Rings_Oring(U_2329) ),
inference(definitional_conversion,[status(esa)],[f_578_2]) ).
cnf(f_578_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2329),U_2330),U_2331)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2329),U_2330),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2331))
| ~ class_Rings_Oring(U_2329) ),
inference(clausify,[status(thm)],[f_578_3]) ).
fof(f_579_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__left]) ).
fof(f_579_2,plain,
! [U_2334,U_2333,U_2332] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2332),U_2333),U_2334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2332),hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),U_2333)),U_2334)
| ~ class_Rings_Oring(U_2332) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
fof(f_579_3,plain,
! [U_2332,U_2333,U_2334] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2332),U_2333),U_2334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2332),hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),U_2333)),U_2334)
| ~ class_Rings_Oring(U_2332) ),
inference(definitional_conversion,[status(esa)],[f_579_2]) ).
cnf(f_579_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2332),U_2333),U_2334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2332),hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),U_2333)),U_2334)
| ~ class_Rings_Oring(U_2332) ),
inference(clausify,[status(thm)],[f_579_3]) ).
fof(f_580_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__commute]) ).
fof(f_580_2,plain,
! [U_2337,U_2336,U_2335] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2335),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2336)),U_2337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2335),U_2336),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2337))
| ~ class_Rings_Oring(U_2335) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
! [U_2335,U_2336,U_2337] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2335),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2336)),U_2337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2335),U_2336),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2337))
| ~ class_Rings_Oring(U_2335) ),
inference(definitional_conversion,[status(esa)],[f_580_2]) ).
cnf(f_580_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2335),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2336)),U_2337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2335),U_2336),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2337))
| ~ class_Rings_Oring(U_2335) ),
inference(clausify,[status(thm)],[f_580_3]) ).
fof(f_581_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__minus]) ).
fof(f_581_2,plain,
! [U_2340,U_2339,U_2338] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2339)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340)
| ~ class_Rings_Oring(U_2338) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
! [U_2338,U_2339,U_2340] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2339)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340)
| ~ class_Rings_Oring(U_2338) ),
inference(definitional_conversion,[status(esa)],[f_581_2]) ).
cnf(f_581_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2339)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340)
| ~ class_Rings_Oring(U_2338) ),
inference(clausify,[status(thm)],[f_581_3]) ).
fof(f_582_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)
| ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
& V_a_2 != V_b_2 ) )
& ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| V_a_2 = V_b_2
| 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) ) )
| ~ class_Rings_Oidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).
fof(f_582_2,plain,
! [U_2343,U_2342,U_2341] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2343),U_2343)
| ( U_2342 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2343)
& U_2342 != U_2343 ) )
& ( U_2342 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2343)
| U_2342 = U_2343
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2342) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2343),U_2343) ) )
| ~ class_Rings_Oidom(U_2341) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
fof(f_582_3,plain,
( ! [U_2341,U_2342,U_2343] :
( U_2342 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2343)
| ~ sP162(U_2341,U_2342,U_2343) )
& ! [U_2341,U_2342,U_2343] :
( U_2342 != U_2343
| ~ sP162(U_2341,U_2342,U_2343) )
& ! [U_2341,U_2342,U_2343] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2343),U_2343)
| sP162(U_2341,U_2342,U_2343)
| ~ sP163(U_2341,U_2342,U_2343) )
& ! [U_2341,U_2342,U_2343] :
( U_2342 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2343)
| U_2342 = U_2343
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2342) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2343),U_2343)
| ~ sP163(U_2341,U_2342,U_2343) )
& ! [U_2341,U_2342,U_2343] :
( sP163(U_2341,U_2342,U_2343)
| ~ class_Rings_Oidom(U_2341) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162,sP163])],[f_582_2]) ).
cnf(f_582_4,plain,
( sP163(U_2341,U_2342,U_2343)
| ~ class_Rings_Oidom(U_2341) ),
inference(clausify,[status(thm)],[f_582_3]) ).
cnf(f_582_5,plain,
( U_2342 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2343)
| U_2342 = U_2343
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2342) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2343),U_2343)
| ~ sP163(U_2341,U_2342,U_2343) ),
inference(clausify,[status(thm)],[f_582_3]) ).
cnf(f_582_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2343),U_2343)
| sP162(U_2341,U_2342,U_2343)
| ~ sP163(U_2341,U_2342,U_2343) ),
inference(clausify,[status(thm)],[f_582_3]) ).
cnf(f_582_7,plain,
( U_2342 != U_2343
| ~ sP162(U_2341,U_2342,U_2343) ),
inference(clausify,[status(thm)],[f_582_3]) ).
cnf(f_582_8,plain,
( U_2342 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2343)
| ~ sP162(U_2341,U_2342,U_2343) ),
inference(clausify,[status(thm)],[f_582_3]) ).
fof(f_583_1,plain,
! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ! [B_x] :
( V_z_2 != hAPP(V_f_2,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( V_z_2 = hAPP(V_f_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_image__iff]) ).
fof(f_583_2,plain,
! [U_2350,U_2349,U_2348,U_2347,U_2346] :
( ( hBOOL(hAPP(hAPP(c_member(U_2346),U_2347),hAPP(c_Set_Oimage(U_2348,U_2346,U_2349),U_2350)))
| ! [U_2345] :
( U_2347 != hAPP(U_2349,U_2345)
| ~ hBOOL(hAPP(hAPP(c_member(U_2348),U_2345),U_2350)) ) )
& ( ? [U_2344] :
( U_2347 = hAPP(U_2349,U_2344)
& hBOOL(hAPP(hAPP(c_member(U_2348),U_2344),U_2350)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2346),U_2347),hAPP(c_Set_Oimage(U_2348,U_2346,U_2349),U_2350))) ) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
fof(f_583_3,plain,
( ! [U_2360,U_2358,U_2356,U_2354] :
( ! [U_2352] : hBOOL(hAPP(hAPP(c_member(U_2352),U_2354),hAPP(c_Set_Oimage(U_2356,U_2352,U_2358),U_2360)))
| ! [U_2345] :
( U_2354 != hAPP(U_2358,U_2345)
| ~ hBOOL(hAPP(hAPP(c_member(U_2356),U_2345),U_2360)) ) )
& ! [U_2359,U_2357,U_2355,U_2353] :
( ! [U_2351] : ~ hBOOL(hAPP(hAPP(c_member(U_2351),U_2353),hAPP(c_Set_Oimage(U_2355,U_2351,U_2357),U_2359)))
| ? [U_2344] :
( U_2353 = hAPP(U_2357,U_2344)
& hBOOL(hAPP(hAPP(c_member(U_2355),U_2344),U_2359)) ) ) ),
inference(miniscope,[status(thm)],[f_583_2]) ).
fof(f_583_4,plain,
( ! [U_2360,U_2358,U_2356,U_2354] :
( ! [U_2352] : hBOOL(hAPP(hAPP(c_member(U_2352),U_2354),hAPP(c_Set_Oimage(U_2356,U_2352,U_2358),U_2360)))
| ! [U_2345] :
( U_2354 != hAPP(U_2358,U_2345)
| ~ hBOOL(hAPP(hAPP(c_member(U_2356),U_2345),U_2360)) ) )
& ! [U_2359,U_2357,U_2355,U_2353] :
( ! [U_2351] : ~ hBOOL(hAPP(hAPP(c_member(U_2351),U_2353),hAPP(c_Set_Oimage(U_2355,U_2351,U_2357),U_2359)))
| ( U_2353 = hAPP(U_2357,sK53(U_2359,U_2357,U_2355,U_2353))
& hBOOL(hAPP(hAPP(c_member(U_2355),sK53(U_2359,U_2357,U_2355,U_2353)),U_2359)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_2344,sK53(U_2359,U_2357,U_2355,U_2353))],[f_583_3]) ).
fof(f_583_5,plain,
( ! [U_2357,U_2355,U_2353,U_2359] :
( U_2353 = hAPP(U_2357,sK53(U_2359,U_2357,U_2355,U_2353))
| ~ sP164(U_2357,U_2355,U_2353,U_2359) )
& ! [U_2357,U_2355,U_2353,U_2359] :
( hBOOL(hAPP(hAPP(c_member(U_2355),sK53(U_2359,U_2357,U_2355,U_2353)),U_2359))
| ~ sP164(U_2357,U_2355,U_2353,U_2359) )
& ! [U_2345,U_2360,U_2354,U_2352,U_2358,U_2356] :
( hBOOL(hAPP(hAPP(c_member(U_2352),U_2354),hAPP(c_Set_Oimage(U_2356,U_2352,U_2358),U_2360)))
| U_2354 != hAPP(U_2358,U_2345)
| ~ hBOOL(hAPP(hAPP(c_member(U_2356),U_2345),U_2360)) )
& ! [U_2357,U_2351,U_2355,U_2353,U_2359] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2351),U_2353),hAPP(c_Set_Oimage(U_2355,U_2351,U_2357),U_2359)))
| sP164(U_2357,U_2355,U_2353,U_2359) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_583_4]) ).
cnf(f_583_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2351),U_2353),hAPP(c_Set_Oimage(U_2355,U_2351,U_2357),U_2359)))
| sP164(U_2357,U_2355,U_2353,U_2359) ),
inference(clausify,[status(thm)],[f_583_5]) ).
cnf(f_583_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_2352),U_2354),hAPP(c_Set_Oimage(U_2356,U_2352,U_2358),U_2360)))
| U_2354 != hAPP(U_2358,U_2345)
| ~ hBOOL(hAPP(hAPP(c_member(U_2356),U_2345),U_2360)) ),
inference(clausify,[status(thm)],[f_583_5]) ).
cnf(f_583_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_2355),sK53(U_2359,U_2357,U_2355,U_2353)),U_2359))
| ~ sP164(U_2357,U_2355,U_2353,U_2359) ),
inference(clausify,[status(thm)],[f_583_5]) ).
cnf(f_583_9,plain,
( U_2353 = hAPP(U_2357,sK53(U_2359,U_2357,U_2355,U_2353))
| ~ sP164(U_2357,U_2355,U_2353,U_2359) ),
inference(clausify,[status(thm)],[f_583_5]) ).
fof(f_584_1,plain,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_imageI]) ).
fof(f_584_2,plain,
! [U_2365,U_2364,U_2363,U_2362,U_2361] :
( hBOOL(hAPP(hAPP(c_member(U_2364),hAPP(U_2365,U_2362)),hAPP(c_Set_Oimage(U_2361,U_2364,U_2365),U_2363)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2361),U_2362),U_2363)) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
fof(f_584_3,plain,
! [U_2363,U_2361,U_2362,U_2364,U_2365] :
( hBOOL(hAPP(hAPP(c_member(U_2364),hAPP(U_2365,U_2362)),hAPP(c_Set_Oimage(U_2361,U_2364,U_2365),U_2363)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2361),U_2362),U_2363)) ),
inference(definitional_conversion,[status(esa)],[f_584_2]) ).
cnf(f_584_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2364),hAPP(U_2365,U_2362)),hAPP(c_Set_Oimage(U_2361,U_2364,U_2365),U_2363)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2361),U_2362),U_2363)) ),
inference(clausify,[status(thm)],[f_584_3]) ).
fof(f_585_1,plain,
! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| V_b_2 != hAPP(V_f_2,V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__image__eqI]) ).
fof(f_585_2,plain,
! [U_2371,U_2370,U_2369,U_2368,U_2367,U_2366] :
( hBOOL(hAPP(hAPP(c_member(U_2371),U_2369),hAPP(c_Set_Oimage(U_2366,U_2371,U_2370),U_2368)))
| U_2369 != hAPP(U_2370,U_2367)
| ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2368)) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
fof(f_585_3,plain,
! [U_2366,U_2367,U_2368,U_2369,U_2370,U_2371] :
( hBOOL(hAPP(hAPP(c_member(U_2371),U_2369),hAPP(c_Set_Oimage(U_2366,U_2371,U_2370),U_2368)))
| U_2369 != hAPP(U_2370,U_2367)
| ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2368)) ),
inference(definitional_conversion,[status(esa)],[f_585_2]) ).
cnf(f_585_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2371),U_2369),hAPP(c_Set_Oimage(U_2366,U_2371,U_2370),U_2368)))
| U_2369 != hAPP(U_2370,U_2367)
| ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2368)) ),
inference(clausify,[status(thm)],[f_585_3]) ).
fof(f_586_1,plain,
! [V_A_2,V_f_2,T_b,T_c] :
( ( 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))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__is__empty]) ).
fof(f_586_2,plain,
! [U_2375,U_2374,U_2373,U_2372] :
( ( hAPP(c_Set_Oimage(U_2372,U_2373,U_2374),U_2375) = c_Orderings_Obot__class_Obot(tc_fun(U_2373,tc_HOL_Obool))
| U_2375 != c_Orderings_Obot__class_Obot(tc_fun(U_2372,tc_HOL_Obool)) )
& ( U_2375 = c_Orderings_Obot__class_Obot(tc_fun(U_2372,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_2372,U_2373,U_2374),U_2375) != c_Orderings_Obot__class_Obot(tc_fun(U_2373,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
fof(f_586_3,plain,
( ! [U_2383,U_2381,U_2379,U_2377] :
( hAPP(c_Set_Oimage(U_2377,U_2379,U_2381),U_2383) = c_Orderings_Obot__class_Obot(tc_fun(U_2379,tc_HOL_Obool))
| U_2383 != c_Orderings_Obot__class_Obot(tc_fun(U_2377,tc_HOL_Obool)) )
& ! [U_2382,U_2380,U_2378,U_2376] :
( U_2382 = c_Orderings_Obot__class_Obot(tc_fun(U_2376,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_2376,U_2378,U_2380),U_2382) != c_Orderings_Obot__class_Obot(tc_fun(U_2378,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_586_2]) ).
fof(f_586_4,plain,
( ! [U_2377,U_2383,U_2379,U_2381] :
( hAPP(c_Set_Oimage(U_2377,U_2379,U_2381),U_2383) = c_Orderings_Obot__class_Obot(tc_fun(U_2379,tc_HOL_Obool))
| U_2383 != c_Orderings_Obot__class_Obot(tc_fun(U_2377,tc_HOL_Obool)) )
& ! [U_2380,U_2378,U_2382,U_2376] :
( U_2382 = c_Orderings_Obot__class_Obot(tc_fun(U_2376,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_2376,U_2378,U_2380),U_2382) != c_Orderings_Obot__class_Obot(tc_fun(U_2378,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_586_3]) ).
cnf(f_586_5,plain,
( U_2382 = c_Orderings_Obot__class_Obot(tc_fun(U_2376,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_2376,U_2378,U_2380),U_2382) != c_Orderings_Obot__class_Obot(tc_fun(U_2378,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_586_4]) ).
cnf(f_586_6,plain,
( hAPP(c_Set_Oimage(U_2377,U_2379,U_2381),U_2383) = c_Orderings_Obot__class_Obot(tc_fun(U_2379,tc_HOL_Obool))
| U_2383 != c_Orderings_Obot__class_Obot(tc_fun(U_2377,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_586_4]) ).
fof(f_587_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__empty]) ).
fof(f_587_2,plain,
! [U_2386,U_2385,U_2384] : hAPP(c_Set_Oimage(U_2384,U_2385,U_2386),c_Orderings_Obot__class_Obot(tc_fun(U_2384,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2385,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_587_1]) ).
fof(f_587_3,plain,
! [U_2384,U_2385,U_2386] : hAPP(c_Set_Oimage(U_2384,U_2385,U_2386),c_Orderings_Obot__class_Obot(tc_fun(U_2384,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2385,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_587_2]) ).
cnf(f_587_4,plain,
hAPP(c_Set_Oimage(U_2384,U_2385,U_2386),c_Orderings_Obot__class_Obot(tc_fun(U_2384,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2385,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_587_3]) ).
fof(f_588_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( ( 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)
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( V_A_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)) != hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_empty__is__image]) ).
fof(f_588_2,plain,
! [U_2390,U_2389,U_2388,U_2387] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_2387,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_2388,U_2387,U_2389),U_2390)
| U_2390 != c_Orderings_Obot__class_Obot(tc_fun(U_2388,tc_HOL_Obool)) )
& ( U_2390 = c_Orderings_Obot__class_Obot(tc_fun(U_2388,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(U_2387,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_2388,U_2387,U_2389),U_2390) ) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
( ! [U_2398,U_2396,U_2394] :
( ! [U_2392] : c_Orderings_Obot__class_Obot(tc_fun(U_2392,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_2394,U_2392,U_2396),U_2398)
| U_2398 != c_Orderings_Obot__class_Obot(tc_fun(U_2394,tc_HOL_Obool)) )
& ! [U_2397,U_2395,U_2393] :
( ! [U_2391] : c_Orderings_Obot__class_Obot(tc_fun(U_2391,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_2393,U_2391,U_2395),U_2397)
| U_2397 = c_Orderings_Obot__class_Obot(tc_fun(U_2393,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_588_2]) ).
fof(f_588_4,plain,
( ! [U_2396,U_2398,U_2392,U_2394] :
( c_Orderings_Obot__class_Obot(tc_fun(U_2392,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_2394,U_2392,U_2396),U_2398)
| U_2398 != c_Orderings_Obot__class_Obot(tc_fun(U_2394,tc_HOL_Obool)) )
& ! [U_2391,U_2397,U_2393,U_2395] :
( c_Orderings_Obot__class_Obot(tc_fun(U_2391,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_2393,U_2391,U_2395),U_2397)
| U_2397 = c_Orderings_Obot__class_Obot(tc_fun(U_2393,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_588_3]) ).
cnf(f_588_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_2391,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_2393,U_2391,U_2395),U_2397)
| U_2397 = c_Orderings_Obot__class_Obot(tc_fun(U_2393,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_588_4]) ).
cnf(f_588_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_2392,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_2394,U_2392,U_2396),U_2398)
| U_2398 != c_Orderings_Obot__class_Obot(tc_fun(U_2394,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_588_4]) ).
fof(f_589_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__insert]) ).
fof(f_589_2,plain,
! [U_2403,U_2402,U_2401,U_2400,U_2399] : hAPP(c_Set_Oimage(U_2399,U_2400,U_2401),hAPP(hAPP(c_Set_Oinsert(U_2399),U_2402),U_2403)) = hAPP(hAPP(c_Set_Oinsert(U_2400),hAPP(U_2401,U_2402)),hAPP(c_Set_Oimage(U_2399,U_2400,U_2401),U_2403)),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
! [U_2399,U_2400,U_2401,U_2402,U_2403] : hAPP(c_Set_Oimage(U_2399,U_2400,U_2401),hAPP(hAPP(c_Set_Oinsert(U_2399),U_2402),U_2403)) = hAPP(hAPP(c_Set_Oinsert(U_2400),hAPP(U_2401,U_2402)),hAPP(c_Set_Oimage(U_2399,U_2400,U_2401),U_2403)),
inference(definitional_conversion,[status(esa)],[f_589_2]) ).
cnf(f_589_4,plain,
hAPP(c_Set_Oimage(U_2399,U_2400,U_2401),hAPP(hAPP(c_Set_Oinsert(U_2399),U_2402),U_2403)) = hAPP(hAPP(c_Set_Oinsert(U_2400),hAPP(U_2401,U_2402)),hAPP(c_Set_Oimage(U_2399,U_2400,U_2401),U_2403)),
inference(clausify,[status(thm)],[f_589_3]) ).
fof(f_590_1,plain,
! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__mono]) ).
fof(f_590_2,plain,
! [U_2408,U_2407,U_2406,U_2405,U_2404] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2407,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2404,U_2407,U_2408),U_2405)),hAPP(c_Set_Oimage(U_2404,U_2407,U_2408),U_2406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2404,tc_HOL_Obool)),U_2405),U_2406)) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
fof(f_590_3,plain,
! [U_2404,U_2405,U_2406,U_2407,U_2408] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2407,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2404,U_2407,U_2408),U_2405)),hAPP(c_Set_Oimage(U_2404,U_2407,U_2408),U_2406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2404,tc_HOL_Obool)),U_2405),U_2406)) ),
inference(definitional_conversion,[status(esa)],[f_590_2]) ).
cnf(f_590_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2407,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2404,U_2407,U_2408),U_2405)),hAPP(c_Set_Oimage(U_2404,U_2407,U_2408),U_2406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2404,tc_HOL_Obool)),U_2405),U_2406)) ),
inference(clausify,[status(thm)],[f_590_3]) ).
fof(f_591_1,plain,
! [V_A_2,V_f_2,T_c,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(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ! [B_AA] :
( V_B_2 != hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) )
& ( ? [B_AA] :
( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__image__iff]) ).
fof(f_591_2,plain,
! [U_2415,U_2414,U_2413,U_2412,U_2411] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2411,tc_HOL_Obool)),U_2412),hAPP(c_Set_Oimage(U_2413,U_2411,U_2414),U_2415)))
| ! [U_2410] :
( U_2412 != hAPP(c_Set_Oimage(U_2413,U_2411,U_2414),U_2410)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2413,tc_HOL_Obool)),U_2410),U_2415)) ) )
& ( ? [U_2409] :
( U_2412 = hAPP(c_Set_Oimage(U_2413,U_2411,U_2414),U_2409)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2413,tc_HOL_Obool)),U_2409),U_2415)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2411,tc_HOL_Obool)),U_2412),hAPP(c_Set_Oimage(U_2413,U_2411,U_2414),U_2415))) ) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
fof(f_591_3,plain,
( ! [U_2425,U_2423,U_2421,U_2419,U_2417] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2417,tc_HOL_Obool)),U_2419),hAPP(c_Set_Oimage(U_2421,U_2417,U_2423),U_2425)))
| ! [U_2410] :
( U_2419 != hAPP(c_Set_Oimage(U_2421,U_2417,U_2423),U_2410)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2421,tc_HOL_Obool)),U_2410),U_2425)) ) )
& ! [U_2424,U_2422,U_2420,U_2418,U_2416] :
( ? [U_2409] :
( U_2418 = hAPP(c_Set_Oimage(U_2420,U_2416,U_2422),U_2409)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2420,tc_HOL_Obool)),U_2409),U_2424)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2416,tc_HOL_Obool)),U_2418),hAPP(c_Set_Oimage(U_2420,U_2416,U_2422),U_2424))) ) ),
inference(miniscope,[status(thm)],[f_591_2]) ).
fof(f_591_4,plain,
( ! [U_2425,U_2423,U_2421,U_2419,U_2417] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2417,tc_HOL_Obool)),U_2419),hAPP(c_Set_Oimage(U_2421,U_2417,U_2423),U_2425)))
| ! [U_2410] :
( U_2419 != hAPP(c_Set_Oimage(U_2421,U_2417,U_2423),U_2410)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2421,tc_HOL_Obool)),U_2410),U_2425)) ) )
& ! [U_2424,U_2422,U_2420,U_2418,U_2416] :
( ( U_2418 = hAPP(c_Set_Oimage(U_2420,U_2416,U_2422),sK54(U_2424,U_2422,U_2420,U_2418,U_2416))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2420,tc_HOL_Obool)),sK54(U_2424,U_2422,U_2420,U_2418,U_2416)),U_2424)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2416,tc_HOL_Obool)),U_2418),hAPP(c_Set_Oimage(U_2420,U_2416,U_2422),U_2424))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_2409,sK54(U_2424,U_2422,U_2420,U_2418,U_2416))],[f_591_3]) ).
fof(f_591_5,plain,
( ! [U_2418,U_2416,U_2420,U_2424,U_2422] :
( U_2418 = hAPP(c_Set_Oimage(U_2420,U_2416,U_2422),sK54(U_2424,U_2422,U_2420,U_2418,U_2416))
| ~ sP165(U_2418,U_2416,U_2420,U_2424,U_2422) )
& ! [U_2418,U_2416,U_2420,U_2424,U_2422] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2420,tc_HOL_Obool)),sK54(U_2424,U_2422,U_2420,U_2418,U_2416)),U_2424))
| ~ sP165(U_2418,U_2416,U_2420,U_2424,U_2422) )
& ! [U_2410,U_2425,U_2419,U_2417,U_2423,U_2421] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2417,tc_HOL_Obool)),U_2419),hAPP(c_Set_Oimage(U_2421,U_2417,U_2423),U_2425)))
| U_2419 != hAPP(c_Set_Oimage(U_2421,U_2417,U_2423),U_2410)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2421,tc_HOL_Obool)),U_2410),U_2425)) )
& ! [U_2418,U_2416,U_2420,U_2424,U_2422] :
( sP165(U_2418,U_2416,U_2420,U_2424,U_2422)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2416,tc_HOL_Obool)),U_2418),hAPP(c_Set_Oimage(U_2420,U_2416,U_2422),U_2424))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_591_4]) ).
cnf(f_591_6,plain,
( sP165(U_2418,U_2416,U_2420,U_2424,U_2422)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2416,tc_HOL_Obool)),U_2418),hAPP(c_Set_Oimage(U_2420,U_2416,U_2422),U_2424))) ),
inference(clausify,[status(thm)],[f_591_5]) ).
cnf(f_591_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2417,tc_HOL_Obool)),U_2419),hAPP(c_Set_Oimage(U_2421,U_2417,U_2423),U_2425)))
| U_2419 != hAPP(c_Set_Oimage(U_2421,U_2417,U_2423),U_2410)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2421,tc_HOL_Obool)),U_2410),U_2425)) ),
inference(clausify,[status(thm)],[f_591_5]) ).
cnf(f_591_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2420,tc_HOL_Obool)),sK54(U_2424,U_2422,U_2420,U_2418,U_2416)),U_2424))
| ~ sP165(U_2418,U_2416,U_2420,U_2424,U_2422) ),
inference(clausify,[status(thm)],[f_591_5]) ).
cnf(f_591_9,plain,
( U_2418 = hAPP(c_Set_Oimage(U_2420,U_2416,U_2422),sK54(U_2424,U_2422,U_2420,U_2418,U_2416))
| ~ sP165(U_2418,U_2416,U_2420,U_2424,U_2422) ),
inference(clausify,[status(thm)],[f_591_5]) ).
fof(f_592_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__Un]) ).
fof(f_592_2,plain,
! [U_2430,U_2429,U_2428,U_2427,U_2426] : hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2426,tc_HOL_Obool)),U_2429),U_2430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2427,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),U_2429)),hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),U_2430)),
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
! [U_2426,U_2427,U_2428,U_2429,U_2430] : hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2426,tc_HOL_Obool)),U_2429),U_2430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2427,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),U_2429)),hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),U_2430)),
inference(definitional_conversion,[status(esa)],[f_592_2]) ).
cnf(f_592_4,plain,
hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2426,tc_HOL_Obool)),U_2429),U_2430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2427,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),U_2429)),hAPP(c_Set_Oimage(U_2426,U_2427,U_2428),U_2430)),
inference(clausify,[status(thm)],[f_592_3]) ).
fof(f_593_1,plain,
! [V_B_2,V_A_2,V_f_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(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)))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_image__Pow__mono]) ).
fof(f_593_2,plain,
! [U_2435,U_2434,U_2433,U_2432,U_2431] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2431,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_2432,tc_HOL_Obool),tc_fun(U_2431,tc_HOL_Obool),c_Set_Oimage(U_2432,U_2431,U_2433)),hAPP(c_Set_OPow(U_2432),U_2434))),hAPP(c_Set_OPow(U_2431),U_2435)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2431,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2432,U_2431,U_2433),U_2434)),U_2435)) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
! [U_2431,U_2432,U_2433,U_2434,U_2435] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2431,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_2432,tc_HOL_Obool),tc_fun(U_2431,tc_HOL_Obool),c_Set_Oimage(U_2432,U_2431,U_2433)),hAPP(c_Set_OPow(U_2432),U_2434))),hAPP(c_Set_OPow(U_2431),U_2435)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2431,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2432,U_2431,U_2433),U_2434)),U_2435)) ),
inference(definitional_conversion,[status(esa)],[f_593_2]) ).
cnf(f_593_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2431,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_2432,tc_HOL_Obool),tc_fun(U_2431,tc_HOL_Obool),c_Set_Oimage(U_2432,U_2431,U_2433)),hAPP(c_Set_OPow(U_2432),U_2434))),hAPP(c_Set_OPow(U_2431),U_2435)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2431,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2432,U_2431,U_2433),U_2434)),U_2435)) ),
inference(clausify,[status(thm)],[f_593_3]) ).
fof(f_594_1,plain,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__image]) ).
fof(f_594_2,plain,
! [U_2440,U_2439,U_2438,U_2437,U_2436] :
( hAPP(hAPP(c_Set_Oinsert(U_2439),hAPP(U_2440,U_2437)),hAPP(c_Set_Oimage(U_2436,U_2439,U_2440),U_2438)) = hAPP(c_Set_Oimage(U_2436,U_2439,U_2440),U_2438)
| ~ hBOOL(hAPP(hAPP(c_member(U_2436),U_2437),U_2438)) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
fof(f_594_3,plain,
! [U_2437,U_2436,U_2438,U_2439,U_2440] :
( hAPP(hAPP(c_Set_Oinsert(U_2439),hAPP(U_2440,U_2437)),hAPP(c_Set_Oimage(U_2436,U_2439,U_2440),U_2438)) = hAPP(c_Set_Oimage(U_2436,U_2439,U_2440),U_2438)
| ~ hBOOL(hAPP(hAPP(c_member(U_2436),U_2437),U_2438)) ),
inference(definitional_conversion,[status(esa)],[f_594_2]) ).
cnf(f_594_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_2439),hAPP(U_2440,U_2437)),hAPP(c_Set_Oimage(U_2436,U_2439,U_2440),U_2438)) = hAPP(c_Set_Oimage(U_2436,U_2439,U_2440),U_2438)
| ~ hBOOL(hAPP(hAPP(c_member(U_2436),U_2437),U_2438)) ),
inference(clausify,[status(thm)],[f_594_3]) ).
fof(f_595_1,plain,
! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
( 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)))))
| V_b_2 != hAPP(V_f_2,V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_range__eqI]) ).
fof(f_595_2,plain,
! [U_2445,U_2444,U_2443,U_2442,U_2441] :
( hBOOL(hAPP(hAPP(c_member(U_2444),U_2441),hAPP(c_Set_Oimage(U_2445,U_2444,U_2442),c_Orderings_Otop__class_Otop(tc_fun(U_2445,tc_HOL_Obool)))))
| U_2441 != hAPP(U_2442,U_2443) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
fof(f_595_3,plain,
! [U_2441,U_2442,U_2443,U_2444,U_2445] :
( hBOOL(hAPP(hAPP(c_member(U_2444),U_2441),hAPP(c_Set_Oimage(U_2445,U_2444,U_2442),c_Orderings_Otop__class_Otop(tc_fun(U_2445,tc_HOL_Obool)))))
| U_2441 != hAPP(U_2442,U_2443) ),
inference(definitional_conversion,[status(esa)],[f_595_2]) ).
cnf(f_595_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2444),U_2441),hAPP(c_Set_Oimage(U_2445,U_2444,U_2442),c_Orderings_Otop__class_Otop(tc_fun(U_2445,tc_HOL_Obool)))))
| U_2441 != hAPP(U_2442,U_2443) ),
inference(clausify,[status(thm)],[f_595_3]) ).
fof(f_596_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_rangeI]) ).
fof(f_596_2,plain,
! [U_2449,U_2448,U_2447,U_2446] : hBOOL(hAPP(hAPP(c_member(U_2446),hAPP(U_2447,U_2448)),hAPP(c_Set_Oimage(U_2449,U_2446,U_2447),c_Orderings_Otop__class_Otop(tc_fun(U_2449,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
! [U_2446,U_2447,U_2448,U_2449] : hBOOL(hAPP(hAPP(c_member(U_2446),hAPP(U_2447,U_2448)),hAPP(c_Set_Oimage(U_2449,U_2446,U_2447),c_Orderings_Otop__class_Otop(tc_fun(U_2449,tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_596_2]) ).
cnf(f_596_4,plain,
hBOOL(hAPP(hAPP(c_member(U_2446),hAPP(U_2447,U_2448)),hAPP(c_Set_Oimage(U_2449,U_2446,U_2447),c_Orderings_Otop__class_Otop(tc_fun(U_2449,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_596_3]) ).
fof(f_597_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_image__Int__subset]) ).
fof(f_597_2,plain,
! [U_2454,U_2453,U_2452,U_2451,U_2450] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2450,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2451,tc_HOL_Obool)),U_2453),U_2454))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2450,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),U_2453)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),U_2454)))),
inference(variable_rename,[status(thm)],[f_597_1]) ).
fof(f_597_3,plain,
! [U_2450,U_2451,U_2452,U_2453,U_2454] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2450,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2451,tc_HOL_Obool)),U_2453),U_2454))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2450,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),U_2453)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),U_2454)))),
inference(definitional_conversion,[status(esa)],[f_597_2]) ).
cnf(f_597_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2450,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2451,tc_HOL_Obool)),U_2453),U_2454))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2450,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),U_2453)),hAPP(c_Set_Oimage(U_2451,U_2450,U_2452),U_2454)))),
inference(clausify,[status(thm)],[f_597_3]) ).
fof(f_598_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_image__diff__subset]) ).
fof(f_598_2,plain,
! [U_2459,U_2458,U_2457,U_2456,U_2455] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2455,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2455,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),U_2458)),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),U_2459))),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2456,tc_HOL_Obool)),U_2458),U_2459)))),
inference(variable_rename,[status(thm)],[f_598_1]) ).
fof(f_598_3,plain,
! [U_2455,U_2456,U_2457,U_2458,U_2459] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2455,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2455,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),U_2458)),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),U_2459))),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2456,tc_HOL_Obool)),U_2458),U_2459)))),
inference(definitional_conversion,[status(esa)],[f_598_2]) ).
cnf(f_598_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2455,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2455,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),U_2458)),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),U_2459))),hAPP(c_Set_Oimage(U_2456,U_2455,U_2457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2456,tc_HOL_Obool)),U_2458),U_2459)))),
inference(clausify,[status(thm)],[f_598_3]) ).
fof(f_599_1,plain,
! [V_y_2,V_x_2,T_b] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost]) ).
fof(f_599_2,plain,
! [U_2462,U_2461,U_2460] :
( hAPP(c_Set_Oimage(U_2460,U_2460,c_Groups_Ouminus__class_Ouminus(U_2460)),c_SetInterval_Oord__class_OatLeastAtMost(U_2460,U_2461,U_2462)) = c_SetInterval_Oord__class_OatLeastAtMost(U_2460,hAPP(c_Groups_Ouminus__class_Ouminus(U_2460),U_2462),hAPP(c_Groups_Ouminus__class_Ouminus(U_2460),U_2461))
| ~ class_Groups_Oordered__ab__group__add(U_2460) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
fof(f_599_3,plain,
! [U_2460,U_2461,U_2462] :
( hAPP(c_Set_Oimage(U_2460,U_2460,c_Groups_Ouminus__class_Ouminus(U_2460)),c_SetInterval_Oord__class_OatLeastAtMost(U_2460,U_2461,U_2462)) = c_SetInterval_Oord__class_OatLeastAtMost(U_2460,hAPP(c_Groups_Ouminus__class_Ouminus(U_2460),U_2462),hAPP(c_Groups_Ouminus__class_Ouminus(U_2460),U_2461))
| ~ class_Groups_Oordered__ab__group__add(U_2460) ),
inference(definitional_conversion,[status(esa)],[f_599_2]) ).
cnf(f_599_4,plain,
( hAPP(c_Set_Oimage(U_2460,U_2460,c_Groups_Ouminus__class_Ouminus(U_2460)),c_SetInterval_Oord__class_OatLeastAtMost(U_2460,U_2461,U_2462)) = c_SetInterval_Oord__class_OatLeastAtMost(U_2460,hAPP(c_Groups_Ouminus__class_Ouminus(U_2460),U_2462),hAPP(c_Groups_Ouminus__class_Ouminus(U_2460),U_2461))
| ~ class_Groups_Oordered__ab__group__add(U_2460) ),
inference(clausify,[status(thm)],[f_599_3]) ).
fof(f_600_1,plain,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( 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))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image]) ).
fof(f_600_2,plain,
! [U_2467,U_2466,U_2465,U_2464,U_2463] :
( hAPP(c_Set_Oimage(U_2464,U_2463,U_2466),U_2467) = c_Orderings_Otop__class_Otop(tc_fun(U_2463,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(U_2463,U_2464,U_2465,U_2466,U_2467) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
fof(f_600_3,plain,
! [U_2463,U_2464,U_2465,U_2466,U_2467] :
( hAPP(c_Set_Oimage(U_2464,U_2463,U_2466),U_2467) = c_Orderings_Otop__class_Otop(tc_fun(U_2463,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(U_2463,U_2464,U_2465,U_2466,U_2467) ),
inference(definitional_conversion,[status(esa)],[f_600_2]) ).
cnf(f_600_4,plain,
( hAPP(c_Set_Oimage(U_2464,U_2463,U_2466),U_2467) = c_Orderings_Otop__class_Otop(tc_fun(U_2463,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(U_2463,U_2464,U_2465,U_2466,U_2467) ),
inference(clausify,[status(thm)],[f_600_3]) ).
fof(f_601_1,plain,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( 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
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range]) ).
fof(f_601_2,plain,
! [U_2472,U_2471,U_2470,U_2469,U_2468] :
( hAPP(c_Set_Oimage(U_2468,U_2469,U_2470),c_Orderings_Otop__class_Otop(tc_fun(U_2468,tc_HOL_Obool))) = U_2472
| ~ c_Typedef_Otype__definition(U_2468,U_2469,U_2470,U_2471,U_2472) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
fof(f_601_3,plain,
! [U_2469,U_2468,U_2470,U_2471,U_2472] :
( hAPP(c_Set_Oimage(U_2468,U_2469,U_2470),c_Orderings_Otop__class_Otop(tc_fun(U_2468,tc_HOL_Obool))) = U_2472
| ~ c_Typedef_Otype__definition(U_2468,U_2469,U_2470,U_2471,U_2472) ),
inference(definitional_conversion,[status(esa)],[f_601_2]) ).
cnf(f_601_4,plain,
( hAPP(c_Set_Oimage(U_2468,U_2469,U_2470),c_Orderings_Otop__class_Otop(tc_fun(U_2468,tc_HOL_Obool))) = U_2472
| ~ c_Typedef_Otype__definition(U_2468,U_2469,U_2470,U_2471,U_2472) ),
inference(clausify,[status(thm)],[f_601_3]) ).
fof(f_602_1,plain,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( V_y_2 = V_x_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ]) ).
fof(f_602_2,plain,
! [U_2479,U_2478,U_2477,U_2476,U_2475,U_2474,U_2473] :
( U_2479 = U_2478
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2473,U_2474,U_2475,U_2476,U_2477),U_2479))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2473,U_2474,U_2475,U_2476,U_2477),U_2478))
| ~ c_Finite__Set_Ofun__left__comm(U_2473,U_2474,U_2475) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
fof(f_602_3,plain,
! [U_2473,U_2474,U_2475,U_2476,U_2477,U_2478,U_2479] :
( U_2479 = U_2478
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2473,U_2474,U_2475,U_2476,U_2477),U_2479))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2473,U_2474,U_2475,U_2476,U_2477),U_2478))
| ~ c_Finite__Set_Ofun__left__comm(U_2473,U_2474,U_2475) ),
inference(definitional_conversion,[status(esa)],[f_602_2]) ).
cnf(f_602_4,plain,
( U_2479 = U_2478
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2473,U_2474,U_2475,U_2476,U_2477),U_2479))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2473,U_2474,U_2475,U_2476,U_2477),U_2478))
| ~ c_Finite__Set_Ofun__left__comm(U_2473,U_2474,U_2475) ),
inference(clausify,[status(thm)],[f_602_3]) ).
fof(f_603_1,plain,
! [V_y_2,V_x_2,T_b] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan]) ).
fof(f_603_2,plain,
! [U_2482,U_2481,U_2480] :
( hAPP(c_Set_Oimage(U_2480,U_2480,c_Groups_Ouminus__class_Ouminus(U_2480)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_2480,U_2481,U_2482)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_2480,hAPP(c_Groups_Ouminus__class_Ouminus(U_2480),U_2482),hAPP(c_Groups_Ouminus__class_Ouminus(U_2480),U_2481))
| ~ class_Groups_Oordered__ab__group__add(U_2480) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
fof(f_603_3,plain,
! [U_2480,U_2481,U_2482] :
( hAPP(c_Set_Oimage(U_2480,U_2480,c_Groups_Ouminus__class_Ouminus(U_2480)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_2480,U_2481,U_2482)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_2480,hAPP(c_Groups_Ouminus__class_Ouminus(U_2480),U_2482),hAPP(c_Groups_Ouminus__class_Ouminus(U_2480),U_2481))
| ~ class_Groups_Oordered__ab__group__add(U_2480) ),
inference(definitional_conversion,[status(esa)],[f_603_2]) ).
cnf(f_603_4,plain,
( hAPP(c_Set_Oimage(U_2480,U_2480,c_Groups_Ouminus__class_Ouminus(U_2480)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_2480,U_2481,U_2482)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_2480,hAPP(c_Groups_Ouminus__class_Ouminus(U_2480),U_2482),hAPP(c_Groups_Ouminus__class_Ouminus(U_2480),U_2481))
| ~ class_Groups_Oordered__ab__group__add(U_2480) ),
inference(clausify,[status(thm)],[f_603_3]) ).
fof(f_604_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_empty__fold1SetE]) ).
fof(f_604_2,plain,
! [U_2485,U_2484,U_2483] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2483,U_2484,c_Orderings_Obot__class_Obot(tc_fun(U_2483,tc_HOL_Obool))),U_2485)),
inference(variable_rename,[status(thm)],[f_604_1]) ).
fof(f_604_3,plain,
! [U_2483,U_2484,U_2485] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2483,U_2484,c_Orderings_Obot__class_Obot(tc_fun(U_2483,tc_HOL_Obool))),U_2485)),
inference(definitional_conversion,[status(esa)],[f_604_2]) ).
cnf(f_604_4,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2483,U_2484,c_Orderings_Obot__class_Obot(tc_fun(U_2483,tc_HOL_Obool))),U_2485)),
inference(clausify,[status(thm)],[f_604_3]) ).
fof(f_605_1,plain,
! [V_x_2,V_A_2,V_f_2,T_b] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty]) ).
fof(f_605_2,plain,
! [U_2489,U_2488,U_2487,U_2486] :
( U_2488 != c_Orderings_Obot__class_Obot(tc_fun(U_2486,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2486,U_2487,U_2488),U_2489)) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
fof(f_605_3,plain,
! [U_2486,U_2487,U_2488,U_2489] :
( U_2488 != c_Orderings_Obot__class_Obot(tc_fun(U_2486,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2486,U_2487,U_2488),U_2489)) ),
inference(definitional_conversion,[status(esa)],[f_605_2]) ).
cnf(f_605_4,plain,
( U_2488 != c_Orderings_Obot__class_Obot(tc_fun(U_2486,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2486,U_2487,U_2488),U_2489)) ),
inference(clausify,[status(thm)],[f_605_3]) ).
fof(f_606_1,plain,
! [V_y_2,V_x_2,T_b] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan]) ).
fof(f_606_2,plain,
! [U_2492,U_2491,U_2490] :
( hAPP(c_Set_Oimage(U_2490,U_2490,c_Groups_Ouminus__class_Ouminus(U_2490)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2490,U_2491),U_2492)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_2490,hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),U_2492),hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),U_2491))
| ~ class_Groups_Oordered__ab__group__add(U_2490) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
fof(f_606_3,plain,
! [U_2490,U_2491,U_2492] :
( hAPP(c_Set_Oimage(U_2490,U_2490,c_Groups_Ouminus__class_Ouminus(U_2490)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2490,U_2491),U_2492)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_2490,hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),U_2492),hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),U_2491))
| ~ class_Groups_Oordered__ab__group__add(U_2490) ),
inference(definitional_conversion,[status(esa)],[f_606_2]) ).
cnf(f_606_4,plain,
( hAPP(c_Set_Oimage(U_2490,U_2490,c_Groups_Ouminus__class_Ouminus(U_2490)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2490,U_2491),U_2492)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_2490,hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),U_2492),hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),U_2491))
| ~ class_Groups_Oordered__ab__group__add(U_2490) ),
inference(clausify,[status(thm)],[f_606_3]) ).
fof(f_607_1,plain,
! [V_y_2,V_x_2,T_b] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost]) ).
fof(f_607_2,plain,
! [U_2495,U_2494,U_2493] :
( hAPP(c_Set_Oimage(U_2493,U_2493,c_Groups_Ouminus__class_Ouminus(U_2493)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_2493,U_2494,U_2495)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2493,hAPP(c_Groups_Ouminus__class_Ouminus(U_2493),U_2495)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2493),U_2494))
| ~ class_Groups_Oordered__ab__group__add(U_2493) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
fof(f_607_3,plain,
! [U_2493,U_2494,U_2495] :
( hAPP(c_Set_Oimage(U_2493,U_2493,c_Groups_Ouminus__class_Ouminus(U_2493)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_2493,U_2494,U_2495)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2493,hAPP(c_Groups_Ouminus__class_Ouminus(U_2493),U_2495)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2493),U_2494))
| ~ class_Groups_Oordered__ab__group__add(U_2493) ),
inference(definitional_conversion,[status(esa)],[f_607_2]) ).
cnf(f_607_4,plain,
( hAPP(c_Set_Oimage(U_2493,U_2493,c_Groups_Ouminus__class_Ouminus(U_2493)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_2493,U_2494,U_2495)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2493,hAPP(c_Groups_Ouminus__class_Ouminus(U_2493),U_2495)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2493),U_2494))
| ~ class_Groups_Oordered__ab__group__add(U_2493) ),
inference(clausify,[status(thm)],[f_607_3]) ).
fof(f_608_1,plain,
! [V_x_2,T_b] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan]) ).
fof(f_608_2,plain,
! [U_2497,U_2496] :
( hAPP(c_Set_Oimage(U_2496,U_2496,c_Groups_Ouminus__class_Ouminus(U_2496)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2496),U_2497)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2496),hAPP(c_Groups_Ouminus__class_Ouminus(U_2496),U_2497))
| ~ class_Groups_Oordered__ab__group__add(U_2496) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
fof(f_608_3,plain,
! [U_2496,U_2497] :
( hAPP(c_Set_Oimage(U_2496,U_2496,c_Groups_Ouminus__class_Ouminus(U_2496)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2496),U_2497)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2496),hAPP(c_Groups_Ouminus__class_Ouminus(U_2496),U_2497))
| ~ class_Groups_Oordered__ab__group__add(U_2496) ),
inference(definitional_conversion,[status(esa)],[f_608_2]) ).
cnf(f_608_4,plain,
( hAPP(c_Set_Oimage(U_2496,U_2496,c_Groups_Ouminus__class_Ouminus(U_2496)),hAPP(c_SetInterval_Oord__class_OlessThan(U_2496),U_2497)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2496),hAPP(c_Groups_Ouminus__class_Ouminus(U_2496),U_2497))
| ~ class_Groups_Oordered__ab__group__add(U_2496) ),
inference(clausify,[status(thm)],[f_608_3]) ).
fof(f_609_1,plain,
! [V_x_2,T_b] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan]) ).
fof(f_609_2,plain,
! [U_2499,U_2498] :
( hAPP(c_Set_Oimage(U_2498,U_2498,c_Groups_Ouminus__class_Ouminus(U_2498)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2498),U_2499)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2498),hAPP(c_Groups_Ouminus__class_Ouminus(U_2498),U_2499))
| ~ class_Groups_Oordered__ab__group__add(U_2498) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
fof(f_609_3,plain,
! [U_2499,U_2498] :
( hAPP(c_Set_Oimage(U_2498,U_2498,c_Groups_Ouminus__class_Ouminus(U_2498)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2498),U_2499)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2498),hAPP(c_Groups_Ouminus__class_Ouminus(U_2498),U_2499))
| ~ class_Groups_Oordered__ab__group__add(U_2498) ),
inference(definitional_conversion,[status(esa)],[f_609_2]) ).
cnf(f_609_4,plain,
( hAPP(c_Set_Oimage(U_2498,U_2498,c_Groups_Ouminus__class_Ouminus(U_2498)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2498),U_2499)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_2498),hAPP(c_Groups_Ouminus__class_Ouminus(U_2498),U_2499))
| ~ class_Groups_Oordered__ab__group__add(U_2498) ),
inference(clausify,[status(thm)],[f_609_3]) ).
fof(f_610_1,plain,
! [V_x_2,T_b] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast]) ).
fof(f_610_2,plain,
! [U_2501,U_2500] :
( hAPP(c_Set_Oimage(U_2500,U_2500,c_Groups_Ouminus__class_Ouminus(U_2500)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2500),U_2501)) = hAPP(c_SetInterval_Oord__class_OatMost(U_2500),hAPP(c_Groups_Ouminus__class_Ouminus(U_2500),U_2501))
| ~ class_Groups_Oordered__ab__group__add(U_2500) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
fof(f_610_3,plain,
! [U_2500,U_2501] :
( hAPP(c_Set_Oimage(U_2500,U_2500,c_Groups_Ouminus__class_Ouminus(U_2500)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2500),U_2501)) = hAPP(c_SetInterval_Oord__class_OatMost(U_2500),hAPP(c_Groups_Ouminus__class_Ouminus(U_2500),U_2501))
| ~ class_Groups_Oordered__ab__group__add(U_2500) ),
inference(definitional_conversion,[status(esa)],[f_610_2]) ).
cnf(f_610_4,plain,
( hAPP(c_Set_Oimage(U_2500,U_2500,c_Groups_Ouminus__class_Ouminus(U_2500)),hAPP(c_SetInterval_Oord__class_OatLeast(U_2500),U_2501)) = hAPP(c_SetInterval_Oord__class_OatMost(U_2500),hAPP(c_Groups_Ouminus__class_Ouminus(U_2500),U_2501))
| ~ class_Groups_Oordered__ab__group__add(U_2500) ),
inference(clausify,[status(thm)],[f_610_3]) ).
fof(f_611_1,plain,
! [V_x_2,T_b] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost]) ).
fof(f_611_2,plain,
! [U_2503,U_2502] :
( hAPP(c_Set_Oimage(U_2502,U_2502,c_Groups_Ouminus__class_Ouminus(U_2502)),hAPP(c_SetInterval_Oord__class_OatMost(U_2502),U_2503)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2502),hAPP(c_Groups_Ouminus__class_Ouminus(U_2502),U_2503))
| ~ class_Groups_Oordered__ab__group__add(U_2502) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
! [U_2502,U_2503] :
( hAPP(c_Set_Oimage(U_2502,U_2502,c_Groups_Ouminus__class_Ouminus(U_2502)),hAPP(c_SetInterval_Oord__class_OatMost(U_2502),U_2503)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2502),hAPP(c_Groups_Ouminus__class_Ouminus(U_2502),U_2503))
| ~ class_Groups_Oordered__ab__group__add(U_2502) ),
inference(definitional_conversion,[status(esa)],[f_611_2]) ).
cnf(f_611_4,plain,
( hAPP(c_Set_Oimage(U_2502,U_2502,c_Groups_Ouminus__class_Ouminus(U_2502)),hAPP(c_SetInterval_Oord__class_OatMost(U_2502),U_2503)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_2502),hAPP(c_Groups_Ouminus__class_Ouminus(U_2502),U_2503))
| ~ class_Groups_Oordered__ab__group__add(U_2502) ),
inference(clausify,[status(thm)],[f_611_3]) ).
fof(f_612_1,plain,
! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
( 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)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
| ~ 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))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__insert__swap]) ).
fof(f_612_2,plain,
! [U_2508,U_2507,U_2506,U_2505,U_2504] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2504,U_2504,c_Groups_Otimes__class_Otimes(U_2504),U_2508,hAPP(hAPP(c_Set_Oinsert(U_2504),U_2505),U_2506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2504),U_2508),U_2507)))
| hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),U_2506))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2504,U_2504,c_Groups_Otimes__class_Otimes(U_2504),U_2505,U_2506),U_2507))
| ~ class_Groups_Oab__semigroup__mult(U_2504) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
! [U_2504,U_2505,U_2506,U_2507,U_2508] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2504,U_2504,c_Groups_Otimes__class_Otimes(U_2504),U_2508,hAPP(hAPP(c_Set_Oinsert(U_2504),U_2505),U_2506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2504),U_2508),U_2507)))
| hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),U_2506))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2504,U_2504,c_Groups_Otimes__class_Otimes(U_2504),U_2505,U_2506),U_2507))
| ~ class_Groups_Oab__semigroup__mult(U_2504) ),
inference(definitional_conversion,[status(esa)],[f_612_2]) ).
cnf(f_612_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2504,U_2504,c_Groups_Otimes__class_Otimes(U_2504),U_2508,hAPP(hAPP(c_Set_Oinsert(U_2504),U_2505),U_2506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2504),U_2508),U_2507)))
| hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),U_2506))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2504,U_2504,c_Groups_Otimes__class_Otimes(U_2504),U_2505,U_2506),U_2507))
| ~ class_Groups_Oab__semigroup__mult(U_2504) ),
inference(clausify,[status(thm)],[f_612_3]) ).
fof(f_613_1,plain,
! [V_A_2,V_f_2,T_b,T_c] :
( 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))))
| 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)) ),
inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset]) ).
fof(f_613_2,plain,
! [U_2512,U_2511,U_2510,U_2509] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2510,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2510,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),U_2512))),hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2509,tc_HOL_Obool)),U_2512))))
| hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),c_Orderings_Otop__class_Otop(tc_fun(U_2509,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2510,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
fof(f_613_3,plain,
! [U_2510,U_2511,U_2512,U_2509] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2510,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2510,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),U_2512))),hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2509,tc_HOL_Obool)),U_2512))))
| hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),c_Orderings_Otop__class_Otop(tc_fun(U_2509,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2510,tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_613_2]) ).
cnf(f_613_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2510,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2510,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),U_2512))),hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2509,tc_HOL_Obool)),U_2512))))
| hAPP(c_Set_Oimage(U_2509,U_2510,U_2511),c_Orderings_Otop__class_Otop(tc_fun(U_2509,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2510,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_613_3]) ).
fof(f_614_1,plain,
! [V_A_2,T_b,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),
inference(fof_nnf,[status(thm)],[fact_Cantors__paradox]) ).
fof(f_614_2,plain,
! [U_2515,U_2514,U_2513] : hAPP(c_Set_Oimage(U_2514,tc_fun(U_2514,tc_HOL_Obool),U_2513),U_2515) != hAPP(c_Set_OPow(U_2514),U_2515),
inference(variable_rename,[status(thm)],[f_614_1]) ).
fof(f_614_3,plain,
! [U_2513,U_2514,U_2515] : hAPP(c_Set_Oimage(U_2514,tc_fun(U_2514,tc_HOL_Obool),U_2513),U_2515) != hAPP(c_Set_OPow(U_2514),U_2515),
inference(definitional_conversion,[status(esa)],[f_614_2]) ).
cnf(f_614_4,plain,
hAPP(c_Set_Oimage(U_2514,tc_fun(U_2514,tc_HOL_Obool),U_2513),U_2515) != hAPP(c_Set_OPow(U_2514),U_2515),
inference(clausify,[status(thm)],[f_614_3]) ).
fof(f_615_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( hAPP(V_F_2,V_A_2) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove]) ).
fof(f_615_2,plain,
! [U_2520,U_2519,U_2518,U_2517,U_2516] :
( ( ( hAPP(U_2518,U_2519) = hAPP(hAPP(U_2517,U_2520),hAPP(U_2518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool)) )
& ( hAPP(U_2518,U_2519) = U_2520
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2516),U_2520),U_2519))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2516),U_2519))
| ~ c_Finite__Set_Ofolding__one(U_2516,U_2517,U_2518) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
fof(f_615_3,plain,
( ! [U_2516,U_2517,U_2518,U_2519,U_2520] :
( hAPP(U_2518,U_2519) = hAPP(hAPP(U_2517,U_2520),hAPP(U_2518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool))
| ~ sP166(U_2516,U_2517,U_2518,U_2519,U_2520) )
& ! [U_2516,U_2517,U_2518,U_2519,U_2520] :
( hAPP(U_2518,U_2519) = U_2520
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool))
| ~ sP166(U_2516,U_2517,U_2518,U_2519,U_2520) )
& ! [U_2516,U_2517,U_2518,U_2519,U_2520] :
( sP166(U_2516,U_2517,U_2518,U_2519,U_2520)
| ~ hBOOL(hAPP(hAPP(c_member(U_2516),U_2520),U_2519))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2516),U_2519))
| ~ c_Finite__Set_Ofolding__one(U_2516,U_2517,U_2518) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_615_2]) ).
cnf(f_615_4,plain,
( sP166(U_2516,U_2517,U_2518,U_2519,U_2520)
| ~ hBOOL(hAPP(hAPP(c_member(U_2516),U_2520),U_2519))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2516),U_2519))
| ~ c_Finite__Set_Ofolding__one(U_2516,U_2517,U_2518) ),
inference(clausify,[status(thm)],[f_615_3]) ).
cnf(f_615_5,plain,
( hAPP(U_2518,U_2519) = U_2520
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool))
| ~ sP166(U_2516,U_2517,U_2518,U_2519,U_2520) ),
inference(clausify,[status(thm)],[f_615_3]) ).
cnf(f_615_6,plain,
( hAPP(U_2518,U_2519) = hAPP(hAPP(U_2517,U_2520),hAPP(U_2518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2516,tc_HOL_Obool)),U_2519),hAPP(hAPP(c_Set_Oinsert(U_2516),U_2520),c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2516,tc_HOL_Obool))
| ~ sP166(U_2516,U_2517,U_2518,U_2519,U_2520) ),
inference(clausify,[status(thm)],[f_615_3]) ).
fof(f_616_1,plain,
! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
( ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
& hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) )
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE]) ).
fof(f_616_2,plain,
! [U_2527,U_2526,U_2525,U_2524,U_2523] :
( ? [U_2522,U_2521] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2523),U_2522),U_2521))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2523,U_2523,U_2524,U_2522,U_2521),U_2527))
& hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526) = hAPP(hAPP(c_Set_Oinsert(U_2523),U_2522),U_2521) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2523,U_2524,hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526)),U_2527)) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
fof(f_616_3,plain,
! [U_2527,U_2526,U_2525,U_2524,U_2523] :
( ? [U_2521] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2523),sK55(U_2527,U_2526,U_2525,U_2524,U_2523)),U_2521))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2523,U_2523,U_2524,sK55(U_2527,U_2526,U_2525,U_2524,U_2523),U_2521),U_2527))
& hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526) = hAPP(hAPP(c_Set_Oinsert(U_2523),sK55(U_2527,U_2526,U_2525,U_2524,U_2523)),U_2521) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2523,U_2524,hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526)),U_2527)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_2522,sK55(U_2527,U_2526,U_2525,U_2524,U_2523))],[f_616_2]) ).
fof(f_616_4,plain,
! [U_2527,U_2526,U_2525,U_2524,U_2523] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_2523),sK55(U_2527,U_2526,U_2525,U_2524,U_2523)),sK56(U_2527,U_2526,U_2525,U_2524,U_2523)))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2523,U_2523,U_2524,sK55(U_2527,U_2526,U_2525,U_2524,U_2523),sK56(U_2527,U_2526,U_2525,U_2524,U_2523)),U_2527))
& hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526) = hAPP(hAPP(c_Set_Oinsert(U_2523),sK55(U_2527,U_2526,U_2525,U_2524,U_2523)),sK56(U_2527,U_2526,U_2525,U_2524,U_2523)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2523,U_2524,hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526)),U_2527)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_2521,sK56(U_2527,U_2526,U_2525,U_2524,U_2523))],[f_616_3]) ).
fof(f_616_5,plain,
( ! [U_2524,U_2525,U_2527,U_2526,U_2523] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2523),sK55(U_2527,U_2526,U_2525,U_2524,U_2523)),sK56(U_2527,U_2526,U_2525,U_2524,U_2523)))
| ~ sP167(U_2524,U_2525,U_2527,U_2526,U_2523) )
& ! [U_2524,U_2525,U_2527,U_2526,U_2523] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2523,U_2523,U_2524,sK55(U_2527,U_2526,U_2525,U_2524,U_2523),sK56(U_2527,U_2526,U_2525,U_2524,U_2523)),U_2527))
| ~ sP167(U_2524,U_2525,U_2527,U_2526,U_2523) )
& ! [U_2524,U_2525,U_2527,U_2526,U_2523] :
( hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526) = hAPP(hAPP(c_Set_Oinsert(U_2523),sK55(U_2527,U_2526,U_2525,U_2524,U_2523)),sK56(U_2527,U_2526,U_2525,U_2524,U_2523))
| ~ sP167(U_2524,U_2525,U_2527,U_2526,U_2523) )
& ! [U_2524,U_2525,U_2527,U_2526,U_2523] :
( sP167(U_2524,U_2525,U_2527,U_2526,U_2523)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2523,U_2524,hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526)),U_2527)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_616_4]) ).
cnf(f_616_6,plain,
( sP167(U_2524,U_2525,U_2527,U_2526,U_2523)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2523,U_2524,hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526)),U_2527)) ),
inference(clausify,[status(thm)],[f_616_5]) ).
cnf(f_616_7,plain,
( hAPP(hAPP(c_Set_Oinsert(U_2523),U_2525),U_2526) = hAPP(hAPP(c_Set_Oinsert(U_2523),sK55(U_2527,U_2526,U_2525,U_2524,U_2523)),sK56(U_2527,U_2526,U_2525,U_2524,U_2523))
| ~ sP167(U_2524,U_2525,U_2527,U_2526,U_2523) ),
inference(clausify,[status(thm)],[f_616_5]) ).
cnf(f_616_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2523,U_2523,U_2524,sK55(U_2527,U_2526,U_2525,U_2524,U_2523),sK56(U_2527,U_2526,U_2525,U_2524,U_2523)),U_2527))
| ~ sP167(U_2524,U_2525,U_2527,U_2526,U_2523) ),
inference(clausify,[status(thm)],[f_616_5]) ).
cnf(f_616_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2523),sK55(U_2527,U_2526,U_2525,U_2524,U_2523)),sK56(U_2527,U_2526,U_2525,U_2524,U_2523)))
| ~ sP167(U_2524,U_2525,U_2527,U_2526,U_2523) ),
inference(clausify,[status(thm)],[f_616_5]) ).
fof(f_617_1,plain,
! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
( ( 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))
| ! [B_a,B_A] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
| hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) != hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) )
& ( ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
& hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) )
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set_Oequations]) ).
fof(f_617_2,plain,
! [U_2536,U_2535,U_2534,U_2533,U_2532] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2532,U_2533,hAPP(hAPP(c_Set_Oinsert(U_2532),U_2534),U_2535)),U_2536))
| ! [U_2531,U_2530] :
( hBOOL(hAPP(hAPP(c_member(U_2532),U_2531),U_2530))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2532,U_2532,U_2533,U_2531,U_2530),U_2536))
| hAPP(hAPP(c_Set_Oinsert(U_2532),U_2534),U_2535) != hAPP(hAPP(c_Set_Oinsert(U_2532),U_2531),U_2530) ) )
& ( ? [U_2529,U_2528] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2532),U_2529),U_2528))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2532,U_2532,U_2533,U_2529,U_2528),U_2536))
& hAPP(hAPP(c_Set_Oinsert(U_2532),U_2534),U_2535) = hAPP(hAPP(c_Set_Oinsert(U_2532),U_2529),U_2528) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2532,U_2533,hAPP(hAPP(c_Set_Oinsert(U_2532),U_2534),U_2535)),U_2536)) ) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
fof(f_617_3,plain,
( ! [U_2546,U_2544,U_2542,U_2540,U_2538] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2538,U_2540,hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544)),U_2546))
| ! [U_2531,U_2530] :
( hBOOL(hAPP(hAPP(c_member(U_2538),U_2531),U_2530))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2538,U_2538,U_2540,U_2531,U_2530),U_2546))
| hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544) != hAPP(hAPP(c_Set_Oinsert(U_2538),U_2531),U_2530) ) )
& ! [U_2545,U_2543,U_2541,U_2539,U_2537] :
( ? [U_2529,U_2528] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2537),U_2529),U_2528))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2537,U_2537,U_2539,U_2529,U_2528),U_2545))
& hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543) = hAPP(hAPP(c_Set_Oinsert(U_2537),U_2529),U_2528) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2537,U_2539,hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543)),U_2545)) ) ),
inference(miniscope,[status(thm)],[f_617_2]) ).
fof(f_617_4,plain,
( ! [U_2546,U_2544,U_2542,U_2540,U_2538] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2538,U_2540,hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544)),U_2546))
| ! [U_2531,U_2530] :
( hBOOL(hAPP(hAPP(c_member(U_2538),U_2531),U_2530))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2538,U_2538,U_2540,U_2531,U_2530),U_2546))
| hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544) != hAPP(hAPP(c_Set_Oinsert(U_2538),U_2531),U_2530) ) )
& ! [U_2545,U_2543,U_2541,U_2539,U_2537] :
( ? [U_2528] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2537),sK57(U_2545,U_2543,U_2541,U_2539,U_2537)),U_2528))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2537,U_2537,U_2539,sK57(U_2545,U_2543,U_2541,U_2539,U_2537),U_2528),U_2545))
& hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543) = hAPP(hAPP(c_Set_Oinsert(U_2537),sK57(U_2545,U_2543,U_2541,U_2539,U_2537)),U_2528) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2537,U_2539,hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543)),U_2545)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_2529,sK57(U_2545,U_2543,U_2541,U_2539,U_2537))],[f_617_3]) ).
fof(f_617_5,plain,
( ! [U_2546,U_2544,U_2542,U_2540,U_2538] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2538,U_2540,hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544)),U_2546))
| ! [U_2531,U_2530] :
( hBOOL(hAPP(hAPP(c_member(U_2538),U_2531),U_2530))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2538,U_2538,U_2540,U_2531,U_2530),U_2546))
| hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544) != hAPP(hAPP(c_Set_Oinsert(U_2538),U_2531),U_2530) ) )
& ! [U_2545,U_2543,U_2541,U_2539,U_2537] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_2537),sK57(U_2545,U_2543,U_2541,U_2539,U_2537)),sK58(U_2545,U_2543,U_2541,U_2539,U_2537)))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2537,U_2537,U_2539,sK57(U_2545,U_2543,U_2541,U_2539,U_2537),sK58(U_2545,U_2543,U_2541,U_2539,U_2537)),U_2545))
& hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543) = hAPP(hAPP(c_Set_Oinsert(U_2537),sK57(U_2545,U_2543,U_2541,U_2539,U_2537)),sK58(U_2545,U_2543,U_2541,U_2539,U_2537)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2537,U_2539,hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543)),U_2545)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_2528,sK58(U_2545,U_2543,U_2541,U_2539,U_2537))],[f_617_4]) ).
fof(f_617_6,plain,
( ! [U_2541,U_2539,U_2545,U_2543,U_2537] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2537),sK57(U_2545,U_2543,U_2541,U_2539,U_2537)),sK58(U_2545,U_2543,U_2541,U_2539,U_2537)))
| ~ sP168(U_2541,U_2539,U_2545,U_2543,U_2537) )
& ! [U_2541,U_2539,U_2545,U_2543,U_2537] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2537,U_2537,U_2539,sK57(U_2545,U_2543,U_2541,U_2539,U_2537),sK58(U_2545,U_2543,U_2541,U_2539,U_2537)),U_2545))
| ~ sP168(U_2541,U_2539,U_2545,U_2543,U_2537) )
& ! [U_2541,U_2539,U_2545,U_2543,U_2537] :
( hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543) = hAPP(hAPP(c_Set_Oinsert(U_2537),sK57(U_2545,U_2543,U_2541,U_2539,U_2537)),sK58(U_2545,U_2543,U_2541,U_2539,U_2537))
| ~ sP168(U_2541,U_2539,U_2545,U_2543,U_2537) )
& ! [U_2544,U_2540,U_2530,U_2531,U_2538,U_2542,U_2546] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2538,U_2540,hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544)),U_2546))
| hBOOL(hAPP(hAPP(c_member(U_2538),U_2531),U_2530))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2538,U_2538,U_2540,U_2531,U_2530),U_2546))
| hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544) != hAPP(hAPP(c_Set_Oinsert(U_2538),U_2531),U_2530) )
& ! [U_2541,U_2539,U_2545,U_2543,U_2537] :
( sP168(U_2541,U_2539,U_2545,U_2543,U_2537)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2537,U_2539,hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543)),U_2545)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168])],[f_617_5]) ).
cnf(f_617_7,plain,
( sP168(U_2541,U_2539,U_2545,U_2543,U_2537)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2537,U_2539,hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543)),U_2545)) ),
inference(clausify,[status(thm)],[f_617_6]) ).
cnf(f_617_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_2538,U_2540,hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544)),U_2546))
| hBOOL(hAPP(hAPP(c_member(U_2538),U_2531),U_2530))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2538,U_2538,U_2540,U_2531,U_2530),U_2546))
| hAPP(hAPP(c_Set_Oinsert(U_2538),U_2542),U_2544) != hAPP(hAPP(c_Set_Oinsert(U_2538),U_2531),U_2530) ),
inference(clausify,[status(thm)],[f_617_6]) ).
cnf(f_617_9,plain,
( hAPP(hAPP(c_Set_Oinsert(U_2537),U_2541),U_2543) = hAPP(hAPP(c_Set_Oinsert(U_2537),sK57(U_2545,U_2543,U_2541,U_2539,U_2537)),sK58(U_2545,U_2543,U_2541,U_2539,U_2537))
| ~ sP168(U_2541,U_2539,U_2545,U_2543,U_2537) ),
inference(clausify,[status(thm)],[f_617_6]) ).
cnf(f_617_10,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2537,U_2537,U_2539,sK57(U_2545,U_2543,U_2541,U_2539,U_2537),sK58(U_2545,U_2543,U_2541,U_2539,U_2537)),U_2545))
| ~ sP168(U_2541,U_2539,U_2545,U_2543,U_2537) ),
inference(clausify,[status(thm)],[f_617_6]) ).
cnf(f_617_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2537),sK57(U_2545,U_2543,U_2541,U_2539,U_2537)),sK58(U_2545,U_2543,U_2541,U_2539,U_2537)))
| ~ sP168(U_2541,U_2539,U_2545,U_2543,U_2537) ),
inference(clausify,[status(thm)],[f_617_6]) ).
fof(f_618_1,plain,
! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
( ? [B_y] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y))
& V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ 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))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).
fof(f_618_2,plain,
! [U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548] :
( ? [U_2547] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2548,U_2549,U_2550,U_2551,U_2553),U_2547))
& U_2554 = hAPP(hAPP(U_2550,U_2552),U_2547) )
| hBOOL(hAPP(hAPP(c_member(U_2548),U_2552),U_2553))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2548,U_2549,U_2550,U_2551,hAPP(hAPP(c_Set_Oinsert(U_2548),U_2552),U_2553)),U_2554))
| ~ c_Finite__Set_Ofun__left__comm(U_2548,U_2549,U_2550) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
fof(f_618_3,plain,
! [U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2548,U_2549,U_2550,U_2551,U_2553),sK59(U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548)))
& U_2554 = hAPP(hAPP(U_2550,U_2552),sK59(U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548)) )
| hBOOL(hAPP(hAPP(c_member(U_2548),U_2552),U_2553))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2548,U_2549,U_2550,U_2551,hAPP(hAPP(c_Set_Oinsert(U_2548),U_2552),U_2553)),U_2554))
| ~ c_Finite__Set_Ofun__left__comm(U_2548,U_2549,U_2550) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_2547,sK59(U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548))],[f_618_2]) ).
fof(f_618_4,plain,
( ! [U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2548,U_2549,U_2550,U_2551,U_2553),sK59(U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548)))
| ~ sP169(U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549) )
& ! [U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549] :
( U_2554 = hAPP(hAPP(U_2550,U_2552),sK59(U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548))
| ~ sP169(U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549) )
& ! [U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549] :
( sP169(U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549)
| hBOOL(hAPP(hAPP(c_member(U_2548),U_2552),U_2553))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2548,U_2549,U_2550,U_2551,hAPP(hAPP(c_Set_Oinsert(U_2548),U_2552),U_2553)),U_2554))
| ~ c_Finite__Set_Ofun__left__comm(U_2548,U_2549,U_2550) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP169])],[f_618_3]) ).
cnf(f_618_5,plain,
( sP169(U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549)
| hBOOL(hAPP(hAPP(c_member(U_2548),U_2552),U_2553))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2548,U_2549,U_2550,U_2551,hAPP(hAPP(c_Set_Oinsert(U_2548),U_2552),U_2553)),U_2554))
| ~ c_Finite__Set_Ofun__left__comm(U_2548,U_2549,U_2550) ),
inference(clausify,[status(thm)],[f_618_4]) ).
cnf(f_618_6,plain,
( U_2554 = hAPP(hAPP(U_2550,U_2552),sK59(U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548))
| ~ sP169(U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549) ),
inference(clausify,[status(thm)],[f_618_4]) ).
cnf(f_618_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2548,U_2549,U_2550,U_2551,U_2553),sK59(U_2554,U_2553,U_2552,U_2551,U_2550,U_2549,U_2548)))
| ~ sP169(U_2550,U_2548,U_2551,U_2552,U_2553,U_2554,U_2549) ),
inference(clausify,[status(thm)],[f_618_4]) ).
fof(f_619_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter]) ).
fof(f_619_2,plain,
! [U_2559,U_2558,U_2557,U_2556,U_2555] :
( hAPP(hAPP(U_2556,hAPP(U_2557,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559))),hAPP(U_2557,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559))) = hAPP(hAPP(U_2556,hAPP(U_2557,U_2558)),hAPP(U_2557,U_2559))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559) = c_Orderings_Obot__class_Obot(tc_fun(U_2555,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2555),U_2559))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2555),U_2558))
| ~ c_Finite__Set_Ofolding__one(U_2555,U_2556,U_2557) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
! [U_2556,U_2557,U_2555,U_2558,U_2559] :
( hAPP(hAPP(U_2556,hAPP(U_2557,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559))),hAPP(U_2557,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559))) = hAPP(hAPP(U_2556,hAPP(U_2557,U_2558)),hAPP(U_2557,U_2559))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559) = c_Orderings_Obot__class_Obot(tc_fun(U_2555,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2555),U_2559))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2555),U_2558))
| ~ c_Finite__Set_Ofolding__one(U_2555,U_2556,U_2557) ),
inference(definitional_conversion,[status(esa)],[f_619_2]) ).
cnf(f_619_4,plain,
( hAPP(hAPP(U_2556,hAPP(U_2557,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559))),hAPP(U_2557,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559))) = hAPP(hAPP(U_2556,hAPP(U_2557,U_2558)),hAPP(U_2557,U_2559))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2555,tc_HOL_Obool)),U_2558),U_2559) = c_Orderings_Obot__class_Obot(tc_fun(U_2555,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2555),U_2559))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2555),U_2558))
| ~ c_Finite__Set_Ofolding__one(U_2555,U_2556,U_2557) ),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( 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))
| 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint]) ).
fof(f_620_2,plain,
! [U_2564,U_2563,U_2562,U_2561,U_2560] :
( hAPP(U_2562,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2560,tc_HOL_Obool)),U_2563),U_2564)) = hAPP(hAPP(U_2561,hAPP(U_2562,U_2563)),hAPP(U_2562,U_2564))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2560,tc_HOL_Obool)),U_2563),U_2564) != c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| U_2564 = c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2560),U_2564))
| U_2563 = c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2560),U_2563))
| ~ c_Finite__Set_Ofolding__one(U_2560,U_2561,U_2562) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
fof(f_620_3,plain,
! [U_2560,U_2561,U_2562,U_2563,U_2564] :
( hAPP(U_2562,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2560,tc_HOL_Obool)),U_2563),U_2564)) = hAPP(hAPP(U_2561,hAPP(U_2562,U_2563)),hAPP(U_2562,U_2564))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2560,tc_HOL_Obool)),U_2563),U_2564) != c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| U_2564 = c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2560),U_2564))
| U_2563 = c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2560),U_2563))
| ~ c_Finite__Set_Ofolding__one(U_2560,U_2561,U_2562) ),
inference(definitional_conversion,[status(esa)],[f_620_2]) ).
cnf(f_620_4,plain,
( hAPP(U_2562,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2560,tc_HOL_Obool)),U_2563),U_2564)) = hAPP(hAPP(U_2561,hAPP(U_2562,U_2563)),hAPP(U_2562,U_2564))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2560,tc_HOL_Obool)),U_2563),U_2564) != c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| U_2564 = c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2560),U_2564))
| U_2563 = c_Orderings_Obot__class_Obot(tc_fun(U_2560,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2560),U_2563))
| ~ c_Finite__Set_Ofolding__one(U_2560,U_2561,U_2562) ),
inference(clausify,[status(thm)],[f_620_3]) ).
fof(f_621_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove]) ).
fof(f_621_2,plain,
! [U_2569,U_2568,U_2567,U_2566,U_2565] :
( ( ( hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),U_2568)) = hAPP(hAPP(U_2566,U_2569),hAPP(U_2567,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool)) )
& ( hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),U_2568)) = U_2569
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2565),U_2568))
| ~ c_Finite__Set_Ofolding__one(U_2565,U_2566,U_2567) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
( ! [U_2568,U_2567,U_2566,U_2565,U_2569] :
( hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),U_2568)) = hAPP(hAPP(U_2566,U_2569),hAPP(U_2567,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool))
| ~ sP170(U_2568,U_2567,U_2566,U_2565,U_2569) )
& ! [U_2568,U_2567,U_2566,U_2565,U_2569] :
( hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),U_2568)) = U_2569
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool))
| ~ sP170(U_2568,U_2567,U_2566,U_2565,U_2569) )
& ! [U_2568,U_2567,U_2566,U_2565,U_2569] :
( sP170(U_2568,U_2567,U_2566,U_2565,U_2569)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2565),U_2568))
| ~ c_Finite__Set_Ofolding__one(U_2565,U_2566,U_2567) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_621_2]) ).
cnf(f_621_4,plain,
( sP170(U_2568,U_2567,U_2566,U_2565,U_2569)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2565),U_2568))
| ~ c_Finite__Set_Ofolding__one(U_2565,U_2566,U_2567) ),
inference(clausify,[status(thm)],[f_621_3]) ).
cnf(f_621_5,plain,
( hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),U_2568)) = U_2569
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool))
| ~ sP170(U_2568,U_2567,U_2566,U_2565,U_2569) ),
inference(clausify,[status(thm)],[f_621_3]) ).
cnf(f_621_6,plain,
( hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),U_2568)) = hAPP(hAPP(U_2566,U_2569),hAPP(U_2567,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2565,tc_HOL_Obool)),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2565),U_2569),c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2565,tc_HOL_Obool))
| ~ sP170(U_2568,U_2567,U_2566,U_2565,U_2569) ),
inference(clausify,[status(thm)],[f_621_3]) ).
fof(f_622_1,plain,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_finite_OemptyI]) ).
fof(f_622_2,plain,
! [U_2570] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_2570),c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
! [U_2570] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_2570),c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_622_2]) ).
cnf(f_622_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_2570),c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_622_3]) ).
fof(f_623_1,plain,
! [V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite_OinsertI]) ).
fof(f_623_2,plain,
! [U_2573,U_2572,U_2571] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2571),hAPP(hAPP(c_Set_Oinsert(U_2571),U_2573),U_2572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2571),U_2572)) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
! [U_2572,U_2571,U_2573] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2571),hAPP(hAPP(c_Set_Oinsert(U_2571),U_2573),U_2572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2571),U_2572)) ),
inference(definitional_conversion,[status(esa)],[f_623_2]) ).
cnf(f_623_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2571),hAPP(hAPP(c_Set_Oinsert(U_2571),U_2573),U_2572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2571),U_2572)) ),
inference(clausify,[status(thm)],[f_623_3]) ).
fof(f_624_1,plain,
! [V_h_2,T_c,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__imageI]) ).
fof(f_624_2,plain,
! [U_2577,U_2576,U_2575,U_2574] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2576),hAPP(c_Set_Oimage(U_2574,U_2576,U_2577),U_2575)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2574),U_2575)) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
fof(f_624_3,plain,
! [U_2574,U_2575,U_2576,U_2577] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2576),hAPP(c_Set_Oimage(U_2574,U_2576,U_2577),U_2575)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2574),U_2575)) ),
inference(definitional_conversion,[status(esa)],[f_624_2]) ).
cnf(f_624_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2576),hAPP(c_Set_Oimage(U_2574,U_2576,U_2577),U_2575)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2574),U_2575)) ),
inference(clausify,[status(thm)],[f_624_3]) ).
fof(f_625_1,plain,
! [V_Ga_2,V_F_2,T_b] :
( 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_Ga_2)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Int]) ).
fof(f_625_2,plain,
! [U_2580,U_2579,U_2578] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2578,tc_HOL_Obool)),U_2579),U_2580)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),U_2580))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),U_2579)) ) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
( ! [U_2578,U_2579,U_2580] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),U_2580))
| ~ sP171(U_2578,U_2579,U_2580) )
& ! [U_2578,U_2579,U_2580] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),U_2579))
| ~ sP171(U_2578,U_2579,U_2580) )
& ! [U_2578,U_2579,U_2580] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2578,tc_HOL_Obool)),U_2579),U_2580)))
| sP171(U_2578,U_2579,U_2580) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171])],[f_625_2]) ).
cnf(f_625_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2578,tc_HOL_Obool)),U_2579),U_2580)))
| sP171(U_2578,U_2579,U_2580) ),
inference(clausify,[status(thm)],[f_625_3]) ).
cnf(f_625_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),U_2579))
| ~ sP171(U_2578,U_2579,U_2580) ),
inference(clausify,[status(thm)],[f_625_3]) ).
cnf(f_625_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2578),U_2580))
| ~ sP171(U_2578,U_2579,U_2580) ),
inference(clausify,[status(thm)],[f_625_3]) ).
fof(f_626_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff]) ).
fof(f_626_2,plain,
! [U_2583,U_2582,U_2581] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2581,tc_HOL_Obool)),U_2582),U_2583)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2581),U_2582)) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
fof(f_626_3,plain,
! [U_2581,U_2582,U_2583] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2581,tc_HOL_Obool)),U_2582),U_2583)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2581),U_2582)) ),
inference(definitional_conversion,[status(esa)],[f_626_2]) ).
cnf(f_626_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2581,tc_HOL_Obool)),U_2582),U_2583)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2581),U_2582)) ),
inference(clausify,[status(thm)],[f_626_3]) ).
fof(f_627_1,plain,
! [V_M_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Inter]) ).
fof(f_627_2,plain,
! [U_2586,U_2585] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2585),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2585,tc_HOL_Obool),U_2586)))
| ! [U_2584] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2585),U_2584))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2585,tc_HOL_Obool)),U_2584),U_2586)) ) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
fof(f_627_3,plain,
! [U_2584,U_2585,U_2586] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2585),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2585,tc_HOL_Obool),U_2586)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2585),U_2584))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2585,tc_HOL_Obool)),U_2584),U_2586)) ),
inference(definitional_conversion,[status(esa)],[f_627_2]) ).
cnf(f_627_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2585),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2585,tc_HOL_Obool),U_2586)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2585),U_2584))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2585,tc_HOL_Obool)),U_2584),U_2586)) ),
inference(clausify,[status(thm)],[f_627_3]) ).
fof(f_628_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( ( ( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__UN]) ).
fof(f_628_2,plain,
! [U_2592,U_2591,U_2590,U_2589] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2589,tc_fun(U_2591,tc_HOL_Obool)),U_2590),U_2592)))
| ? [U_2588] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(U_2592,U_2588)))
& hBOOL(hAPP(hAPP(c_member(U_2589),U_2588),U_2590)) ) )
& ( ! [U_2587] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(U_2592,U_2587)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2589),U_2587),U_2590)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2589,tc_fun(U_2591,tc_HOL_Obool)),U_2590),U_2592))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2589),U_2590)) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
fof(f_628_3,plain,
! [U_2592,U_2591,U_2590,U_2589] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2589,tc_fun(U_2591,tc_HOL_Obool)),U_2590),U_2592)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(U_2592,sK60(U_2592,U_2591,U_2590,U_2589))))
& hBOOL(hAPP(hAPP(c_member(U_2589),sK60(U_2592,U_2591,U_2590,U_2589)),U_2590)) ) )
& ( ! [U_2587] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(U_2592,U_2587)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2589),U_2587),U_2590)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2589,tc_fun(U_2591,tc_HOL_Obool)),U_2590),U_2592))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2589),U_2590)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_2588,sK60(U_2592,U_2591,U_2590,U_2589))],[f_628_2]) ).
fof(f_628_4,plain,
( ! [U_2589,U_2590,U_2591,U_2592] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(U_2592,sK60(U_2592,U_2591,U_2590,U_2589))))
| ~ sP172(U_2589,U_2590,U_2591,U_2592) )
& ! [U_2589,U_2590,U_2591,U_2592] :
( hBOOL(hAPP(hAPP(c_member(U_2589),sK60(U_2592,U_2591,U_2590,U_2589)),U_2590))
| ~ sP172(U_2589,U_2590,U_2591,U_2592) )
& ! [U_2587,U_2589,U_2590,U_2591,U_2592] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2589,tc_fun(U_2591,tc_HOL_Obool)),U_2590),U_2592)))
| sP172(U_2589,U_2590,U_2591,U_2592)
| ~ sP173(U_2587,U_2589,U_2590,U_2591,U_2592) )
& ! [U_2587,U_2589,U_2590,U_2591,U_2592] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(U_2592,U_2587)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2589),U_2587),U_2590))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2589,tc_fun(U_2591,tc_HOL_Obool)),U_2590),U_2592)))
| ~ sP173(U_2587,U_2589,U_2590,U_2591,U_2592) )
& ! [U_2587,U_2589,U_2590,U_2591,U_2592] :
( sP173(U_2587,U_2589,U_2590,U_2591,U_2592)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2589),U_2590)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172,sP173])],[f_628_3]) ).
cnf(f_628_5,plain,
( sP173(U_2587,U_2589,U_2590,U_2591,U_2592)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2589),U_2590)) ),
inference(clausify,[status(thm)],[f_628_4]) ).
cnf(f_628_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(U_2592,U_2587)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2589),U_2587),U_2590))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2589,tc_fun(U_2591,tc_HOL_Obool)),U_2590),U_2592)))
| ~ sP173(U_2587,U_2589,U_2590,U_2591,U_2592) ),
inference(clausify,[status(thm)],[f_628_4]) ).
cnf(f_628_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2589,tc_fun(U_2591,tc_HOL_Obool)),U_2590),U_2592)))
| sP172(U_2589,U_2590,U_2591,U_2592)
| ~ sP173(U_2587,U_2589,U_2590,U_2591,U_2592) ),
inference(clausify,[status(thm)],[f_628_4]) ).
cnf(f_628_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_2589),sK60(U_2592,U_2591,U_2590,U_2589)),U_2590))
| ~ sP172(U_2589,U_2590,U_2591,U_2592) ),
inference(clausify,[status(thm)],[f_628_4]) ).
cnf(f_628_9,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),hAPP(U_2592,sK60(U_2592,U_2591,U_2590,U_2589))))
| ~ sP172(U_2589,U_2590,U_2591,U_2592) ),
inference(clausify,[status(thm)],[f_628_4]) ).
fof(f_629_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Finite__Set_Ofinite(T_b) ),
inference(fof_nnf,[status(thm)],[fact_finite]) ).
fof(f_629_2,plain,
! [U_2594,U_2593] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2593),U_2594))
| ~ class_Finite__Set_Ofinite(U_2593) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
fof(f_629_3,plain,
! [U_2593,U_2594] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2593),U_2594))
| ~ class_Finite__Set_Ofinite(U_2593) ),
inference(definitional_conversion,[status(esa)],[f_629_2]) ).
cnf(f_629_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2593),U_2594))
| ~ class_Finite__Set_Ofinite(U_2593) ),
inference(clausify,[status(thm)],[f_629_3]) ).
fof(f_630_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Finite__Set_Ofinite(T_b) ),
inference(fof_nnf,[status(thm)],[fact_finite__code]) ).
fof(f_630_2,plain,
! [U_2596,U_2595] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2595),U_2596))
| ~ class_Finite__Set_Ofinite(U_2595) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
! [U_2595,U_2596] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2595),U_2596))
| ~ class_Finite__Set_Ofinite(U_2595) ),
inference(definitional_conversion,[status(esa)],[f_630_2]) ).
cnf(f_630_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2595),U_2596))
| ~ class_Finite__Set_Ofinite(U_2595) ),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_1,plain,
! [T_c,T_b] :
( 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))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV]) ).
fof(f_631_2,plain,
! [U_2598,U_2597] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_2597,U_2598)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_2597,U_2598),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2598),c_Orderings_Otop__class_Otop(tc_fun(U_2598,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2597),c_Orderings_Otop__class_Otop(tc_fun(U_2597,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
fof(f_631_3,plain,
! [U_2597,U_2598] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_2597,U_2598)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_2597,U_2598),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2598),c_Orderings_Otop__class_Otop(tc_fun(U_2598,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2597),c_Orderings_Otop__class_Otop(tc_fun(U_2597,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_631_2]) ).
cnf(f_631_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_2597,U_2598)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_2597,U_2598),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2598),c_Orderings_Otop__class_Otop(tc_fun(U_2598,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2597),c_Orderings_Otop__class_Otop(tc_fun(U_2597,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_631_3]) ).
fof(f_632_1,plain,
! [T_b] :
( ( 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))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV]) ).
fof(f_632_2,plain,
! [U_2599] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2599)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2599),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2599),c_Orderings_Otop__class_Otop(tc_fun(U_2599,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2599),c_Orderings_Otop__class_Otop(tc_fun(U_2599,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2599)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2599),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
fof(f_632_3,plain,
( ! [U_2601] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2601)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2601),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2601),c_Orderings_Otop__class_Otop(tc_fun(U_2601,tc_HOL_Obool)))) )
& ! [U_2600] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2600),c_Orderings_Otop__class_Otop(tc_fun(U_2600,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2600)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2600),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_632_2]) ).
fof(f_632_4,plain,
( ! [U_2601] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2601)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2601),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2601),c_Orderings_Otop__class_Otop(tc_fun(U_2601,tc_HOL_Obool)))) )
& ! [U_2600] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2600),c_Orderings_Otop__class_Otop(tc_fun(U_2600,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2600)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2600),tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa)],[f_632_3]) ).
cnf(f_632_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2600),c_Orderings_Otop__class_Otop(tc_fun(U_2600,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2600)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2600),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_632_4]) ).
cnf(f_632_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2601)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2601),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2601),c_Orderings_Otop__class_Otop(tc_fun(U_2601,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_632_4]) ).
fof(f_633_1,plain,
! [T_c,T_b] :
( ( 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))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff]) ).
fof(f_633_2,plain,
! [U_2603,U_2602] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2602,U_2603)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2602,U_2603),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2603),c_Orderings_Otop__class_Otop(tc_fun(U_2603,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2602),c_Orderings_Otop__class_Otop(tc_fun(U_2602,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2603),c_Orderings_Otop__class_Otop(tc_fun(U_2603,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2602),c_Orderings_Otop__class_Otop(tc_fun(U_2602,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2602,U_2603)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2602,U_2603),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
( ! [U_2607,U_2605] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2605,U_2607)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2605,U_2607),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2607),c_Orderings_Otop__class_Otop(tc_fun(U_2607,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2605),c_Orderings_Otop__class_Otop(tc_fun(U_2605,tc_HOL_Obool)))) )
& ! [U_2606,U_2604] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2606),c_Orderings_Otop__class_Otop(tc_fun(U_2606,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2604),c_Orderings_Otop__class_Otop(tc_fun(U_2604,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2604,U_2606)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2604,U_2606),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_633_2]) ).
fof(f_633_4,plain,
( ! [U_2606,U_2604] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2606),c_Orderings_Otop__class_Otop(tc_fun(U_2606,tc_HOL_Obool))))
| ~ sP174(U_2606,U_2604) )
& ! [U_2606,U_2604] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2604),c_Orderings_Otop__class_Otop(tc_fun(U_2604,tc_HOL_Obool))))
| ~ sP174(U_2606,U_2604) )
& ! [U_2607,U_2605] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2605,U_2607)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2605,U_2607),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2607),c_Orderings_Otop__class_Otop(tc_fun(U_2607,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2605),c_Orderings_Otop__class_Otop(tc_fun(U_2605,tc_HOL_Obool)))) )
& ! [U_2606,U_2604] :
( sP174(U_2606,U_2604)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2604,U_2606)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2604,U_2606),tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_633_3]) ).
cnf(f_633_5,plain,
( sP174(U_2606,U_2604)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2604,U_2606)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2604,U_2606),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_633_4]) ).
cnf(f_633_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2605,U_2607)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2605,U_2607),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2607),c_Orderings_Otop__class_Otop(tc_fun(U_2607,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2605),c_Orderings_Otop__class_Otop(tc_fun(U_2605,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_633_4]) ).
cnf(f_633_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2604),c_Orderings_Otop__class_Otop(tc_fun(U_2604,tc_HOL_Obool))))
| ~ sP174(U_2606,U_2604) ),
inference(clausify,[status(thm)],[f_633_4]) ).
cnf(f_633_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2606),c_Orderings_Otop__class_Otop(tc_fun(U_2606,tc_HOL_Obool))))
| ~ sP174(U_2606,U_2604) ),
inference(clausify,[status(thm)],[f_633_4]) ).
fof(f_634_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UnionD]) ).
fof(f_634_2,plain,
! [U_2609,U_2608] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2608,tc_HOL_Obool)),U_2609))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2608,tc_HOL_Obool),U_2609))) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
fof(f_634_3,plain,
! [U_2609,U_2608] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2608,tc_HOL_Obool)),U_2609))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2608,tc_HOL_Obool),U_2609))) ),
inference(definitional_conversion,[status(esa)],[f_634_2]) ).
cnf(f_634_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2608,tc_HOL_Obool)),U_2609))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2608,tc_HOL_Obool),U_2609))) ),
inference(clausify,[status(thm)],[f_634_3]) ).
fof(f_635_1,plain,
! [V_A_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff]) ).
fof(f_635_2,plain,
! [U_2611,U_2610] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2610,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2610),U_2611)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2610),U_2611)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2610),U_2611))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2610,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2610),U_2611))) ) ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
fof(f_635_3,plain,
( ! [U_2615,U_2613] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2613,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2613),U_2615)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2613),U_2615)) )
& ! [U_2614,U_2612] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2612),U_2614))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2612,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2612),U_2614))) ) ),
inference(miniscope,[status(thm)],[f_635_2]) ).
fof(f_635_4,plain,
( ! [U_2613,U_2615] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2613,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2613),U_2615)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2613),U_2615)) )
& ! [U_2612,U_2614] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2612),U_2614))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2612,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2612),U_2614))) ) ),
inference(definitional_conversion,[status(esa)],[f_635_3]) ).
cnf(f_635_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2612),U_2614))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2612,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2612),U_2614))) ),
inference(clausify,[status(thm)],[f_635_4]) ).
cnf(f_635_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2613,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2613),U_2615)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2613),U_2615)) ),
inference(clausify,[status(thm)],[f_635_4]) ).
fof(f_636_1,plain,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_finite_Oequations_I1_J]) ).
fof(f_636_2,plain,
! [U_2616] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_2616),c_Orderings_Obot__class_Obot(tc_fun(U_2616,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
! [U_2616] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_2616),c_Orderings_Obot__class_Obot(tc_fun(U_2616,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_636_2]) ).
cnf(f_636_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_2616),c_Orderings_Obot__class_Obot(tc_fun(U_2616,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_636_3]) ).
fof(f_637_1,plain,
! [V_A_2,V_a_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__insert]) ).
fof(f_637_2,plain,
! [U_2619,U_2618,U_2617] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),hAPP(hAPP(c_Set_Oinsert(U_2617),U_2618),U_2619)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),U_2619)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),U_2619))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),hAPP(hAPP(c_Set_Oinsert(U_2617),U_2618),U_2619))) ) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
( ! [U_2625,U_2623,U_2621] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2621),hAPP(hAPP(c_Set_Oinsert(U_2621),U_2623),U_2625)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2621),U_2625)) )
& ! [U_2624,U_2622,U_2620] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),U_2624))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),hAPP(hAPP(c_Set_Oinsert(U_2620),U_2622),U_2624))) ) ),
inference(miniscope,[status(thm)],[f_637_2]) ).
fof(f_637_4,plain,
( ! [U_2621,U_2623,U_2625] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2621),hAPP(hAPP(c_Set_Oinsert(U_2621),U_2623),U_2625)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2621),U_2625)) )
& ! [U_2622,U_2624,U_2620] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),U_2624))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),hAPP(hAPP(c_Set_Oinsert(U_2620),U_2622),U_2624))) ) ),
inference(definitional_conversion,[status(esa)],[f_637_3]) ).
cnf(f_637_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),U_2624))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),hAPP(hAPP(c_Set_Oinsert(U_2620),U_2622),U_2624))) ),
inference(clausify,[status(thm)],[f_637_4]) ).
cnf(f_637_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2621),hAPP(hAPP(c_Set_Oinsert(U_2621),U_2623),U_2625)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2621),U_2625)) ),
inference(clausify,[status(thm)],[f_637_4]) ).
fof(f_638_1,plain,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ 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)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2]) ).
fof(f_638_2,plain,
! [U_2627,U_2626] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2627),c_Orderings_Otop__class_Otop(tc_fun(U_2627,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2626,U_2627)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2626,U_2627),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
! [U_2627] :
( ! [U_2626] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2626,U_2627)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2626,U_2627),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_2627),c_Orderings_Otop__class_Otop(tc_fun(U_2627,tc_HOL_Obool)))) ),
inference(miniscope,[status(thm)],[f_638_2]) ).
fof(f_638_4,plain,
! [U_2626,U_2627] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2626,U_2627)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2626,U_2627),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_2627),c_Orderings_Otop__class_Otop(tc_fun(U_2627,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_638_3]) ).
cnf(f_638_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2626,U_2627)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2626,U_2627),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_2627),c_Orderings_Otop__class_Otop(tc_fun(U_2627,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_638_4]) ).
fof(f_639_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__subset]) ).
fof(f_639_2,plain,
! [U_2630,U_2629,U_2628] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2628),U_2629))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2628),U_2630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2628,tc_HOL_Obool)),U_2629),U_2630)) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
fof(f_639_3,plain,
! [U_2628,U_2629,U_2630] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2628),U_2629))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2628),U_2630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2628,tc_HOL_Obool)),U_2629),U_2630)) ),
inference(definitional_conversion,[status(esa)],[f_639_2]) ).
cnf(f_639_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2628),U_2629))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2628),U_2630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2628,tc_HOL_Obool)),U_2629),U_2630)) ),
inference(clausify,[status(thm)],[f_639_3]) ).
fof(f_640_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__finite__subset]) ).
fof(f_640_2,plain,
! [U_2633,U_2632,U_2631] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2631),U_2633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2631,tc_HOL_Obool)),U_2633),U_2632))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2631),U_2632)) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
fof(f_640_3,plain,
! [U_2631,U_2632,U_2633] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2631),U_2633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2631,tc_HOL_Obool)),U_2633),U_2632))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2631),U_2632)) ),
inference(definitional_conversion,[status(esa)],[f_640_2]) ).
cnf(f_640_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2631),U_2633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2631,tc_HOL_Obool)),U_2633),U_2632))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2631),U_2632)) ),
inference(clausify,[status(thm)],[f_640_3]) ).
fof(f_641_1,plain,
! [T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(T_b) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV]) ).
fof(f_641_2,plain,
! [U_2634] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2634),c_Orderings_Otop__class_Otop(tc_fun(U_2634,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_2634) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
! [U_2634] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2634),c_Orderings_Otop__class_Otop(tc_fun(U_2634,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_2634) ),
inference(definitional_conversion,[status(esa)],[f_641_2]) ).
cnf(f_641_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2634),c_Orderings_Otop__class_Otop(tc_fun(U_2634,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_2634) ),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_1,plain,
! [V_Ga_2,V_F_2,T_b] :
( 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_Ga_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__UnI]) ).
fof(f_642_2,plain,
! [U_2637,U_2636,U_2635] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2635,tc_HOL_Obool)),U_2636),U_2637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2637))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2636)) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
fof(f_642_3,plain,
! [U_2635,U_2636,U_2637] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2635,tc_HOL_Obool)),U_2636),U_2637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2637))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2636)) ),
inference(definitional_conversion,[status(esa)],[f_642_2]) ).
cnf(f_642_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2635,tc_HOL_Obool)),U_2636),U_2637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2637))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2636)) ),
inference(clausify,[status(thm)],[f_642_3]) ).
fof(f_643_1,plain,
! [V_Ga_2,V_F_2,T_b] :
( ( 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_Ga_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
| ~ 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_Ga_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Un]) ).
fof(f_643_2,plain,
! [U_2640,U_2639,U_2638] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2638,tc_HOL_Obool)),U_2639),U_2640)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),U_2640))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),U_2639)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),U_2640))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),U_2639)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2638,tc_HOL_Obool)),U_2639),U_2640))) ) ),
inference(variable_rename,[status(thm)],[f_643_1]) ).
fof(f_643_3,plain,
( ! [U_2646,U_2644,U_2642] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2642,tc_HOL_Obool)),U_2644),U_2646)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2646))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2644)) )
& ! [U_2645,U_2643,U_2641] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2645))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2643)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2641,tc_HOL_Obool)),U_2643),U_2645))) ) ),
inference(miniscope,[status(thm)],[f_643_2]) ).
fof(f_643_4,plain,
( ! [U_2643,U_2641,U_2645] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2645))
| ~ sP175(U_2643,U_2641,U_2645) )
& ! [U_2643,U_2641,U_2645] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2643))
| ~ sP175(U_2643,U_2641,U_2645) )
& ! [U_2646,U_2644,U_2642] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2642,tc_HOL_Obool)),U_2644),U_2646)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2646))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2644)) )
& ! [U_2643,U_2641,U_2645] :
( sP175(U_2643,U_2641,U_2645)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2641,tc_HOL_Obool)),U_2643),U_2645))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_643_3]) ).
cnf(f_643_5,plain,
( sP175(U_2643,U_2641,U_2645)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2641,tc_HOL_Obool)),U_2643),U_2645))) ),
inference(clausify,[status(thm)],[f_643_4]) ).
cnf(f_643_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2642,tc_HOL_Obool)),U_2644),U_2646)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2646))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2644)) ),
inference(clausify,[status(thm)],[f_643_4]) ).
cnf(f_643_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2643))
| ~ sP175(U_2643,U_2641,U_2645) ),
inference(clausify,[status(thm)],[f_643_4]) ).
cnf(f_643_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2645))
| ~ sP175(U_2643,U_2641,U_2645) ),
inference(clausify,[status(thm)],[f_643_4]) ).
fof(f_644_1,plain,
! [V_A_2,V_B_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff2]) ).
fof(f_644_2,plain,
! [U_2649,U_2648,U_2647] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2647,tc_HOL_Obool)),U_2649),U_2648)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2649)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2649))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2647,tc_HOL_Obool)),U_2649),U_2648))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2648)) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
fof(f_644_3,plain,
( ! [U_2647,U_2649,U_2648] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2647,tc_HOL_Obool)),U_2649),U_2648)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2649))
| ~ sP176(U_2647,U_2649,U_2648) )
& ! [U_2647,U_2649,U_2648] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2649))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2647,tc_HOL_Obool)),U_2649),U_2648)))
| ~ sP176(U_2647,U_2649,U_2648) )
& ! [U_2647,U_2649,U_2648] :
( sP176(U_2647,U_2649,U_2648)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2648)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_644_2]) ).
cnf(f_644_4,plain,
( sP176(U_2647,U_2649,U_2648)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2648)) ),
inference(clausify,[status(thm)],[f_644_3]) ).
cnf(f_644_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2649))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2647,tc_HOL_Obool)),U_2649),U_2648)))
| ~ sP176(U_2647,U_2649,U_2648) ),
inference(clausify,[status(thm)],[f_644_3]) ).
cnf(f_644_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2647,tc_HOL_Obool)),U_2649),U_2648)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2647),U_2649))
| ~ sP176(U_2647,U_2649,U_2648) ),
inference(clausify,[status(thm)],[f_644_3]) ).
fof(f_645_1,plain,
! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite]) ).
fof(f_645_2,plain,
! [U_2655,U_2654,U_2653,U_2652,U_2651,U_2650] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2650),U_2654))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2650,U_2651,U_2652,U_2653,U_2654),U_2655)) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
! [U_2652,U_2651,U_2654,U_2650,U_2653,U_2655] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2650),U_2654))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2650,U_2651,U_2652,U_2653,U_2654),U_2655)) ),
inference(definitional_conversion,[status(esa)],[f_645_2]) ).
cnf(f_645_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2650),U_2654))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2650,U_2651,U_2652,U_2653,U_2654),U_2655)) ),
inference(clausify,[status(thm)],[f_645_3]) ).
fof(f_646_1,plain,
! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__surj]) ).
fof(f_646_2,plain,
! [U_2660,U_2659,U_2658,U_2657,U_2656] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2658),U_2659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2658,tc_HOL_Obool)),U_2659),hAPP(c_Set_Oimage(U_2656,U_2658,U_2660),U_2657)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2656),U_2657)) ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
fof(f_646_3,plain,
! [U_2657,U_2656,U_2658,U_2659,U_2660] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2658),U_2659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2658,tc_HOL_Obool)),U_2659),hAPP(c_Set_Oimage(U_2656,U_2658,U_2660),U_2657)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2656),U_2657)) ),
inference(definitional_conversion,[status(esa)],[f_646_2]) ).
cnf(f_646_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2658),U_2659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2658,tc_HOL_Obool)),U_2659),hAPP(c_Set_Oimage(U_2656,U_2658,U_2660),U_2657)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2656),U_2657)) ),
inference(clausify,[status(thm)],[f_646_3]) ).
fof(f_647_1,plain,
! [V_B_2,V_a_2,V_A_2,T_b] :
( ( 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))))
| ~ 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))) )
& ( 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)))
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert]) ).
fof(f_647_2,plain,
! [U_2664,U_2663,U_2662,U_2661] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2661,tc_HOL_Obool)),U_2662),hAPP(hAPP(c_Set_Oinsert(U_2661),U_2663),U_2664))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2661,tc_HOL_Obool)),U_2662),U_2664))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2661,tc_HOL_Obool)),U_2662),U_2664)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2661,tc_HOL_Obool)),U_2662),hAPP(hAPP(c_Set_Oinsert(U_2661),U_2663),U_2664)))) ) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
fof(f_647_3,plain,
( ! [U_2672,U_2670,U_2668,U_2666] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2666,tc_HOL_Obool)),U_2668),hAPP(hAPP(c_Set_Oinsert(U_2666),U_2670),U_2672))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2666,tc_HOL_Obool)),U_2668),U_2672))) )
& ! [U_2671,U_2669,U_2667,U_2665] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2665,tc_HOL_Obool)),U_2667),U_2671)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2665,tc_HOL_Obool)),U_2667),hAPP(hAPP(c_Set_Oinsert(U_2665),U_2669),U_2671)))) ) ),
inference(miniscope,[status(thm)],[f_647_2]) ).
fof(f_647_4,plain,
( ! [U_2666,U_2668,U_2670,U_2672] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2666,tc_HOL_Obool)),U_2668),hAPP(hAPP(c_Set_Oinsert(U_2666),U_2670),U_2672))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2666,tc_HOL_Obool)),U_2668),U_2672))) )
& ! [U_2667,U_2669,U_2671,U_2665] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2665,tc_HOL_Obool)),U_2667),U_2671)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2665,tc_HOL_Obool)),U_2667),hAPP(hAPP(c_Set_Oinsert(U_2665),U_2669),U_2671)))) ) ),
inference(definitional_conversion,[status(esa)],[f_647_3]) ).
cnf(f_647_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2665,tc_HOL_Obool)),U_2667),U_2671)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2665,tc_HOL_Obool)),U_2667),hAPP(hAPP(c_Set_Oinsert(U_2665),U_2669),U_2671)))) ),
inference(clausify,[status(thm)],[f_647_4]) ).
cnf(f_647_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2666,tc_HOL_Obool)),U_2668),hAPP(hAPP(c_Set_Oinsert(U_2666),U_2670),U_2672))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2666,tc_HOL_Obool)),U_2668),U_2672))) ),
inference(clausify,[status(thm)],[f_647_4]) ).
fof(f_648_1,plain,
! [V_A_2,T_b] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__compl]) ).
fof(f_648_2,plain,
! [U_2674,U_2673] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2673,tc_HOL_Obool)),U_2674)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),c_Orderings_Otop__class_Otop(tc_fun(U_2673,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),c_Orderings_Otop__class_Otop(tc_fun(U_2673,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2673,tc_HOL_Obool)),U_2674))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),U_2674)) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
fof(f_648_3,plain,
( ! [U_2673,U_2674] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2673,tc_HOL_Obool)),U_2674)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),c_Orderings_Otop__class_Otop(tc_fun(U_2673,tc_HOL_Obool))))
| ~ sP177(U_2673,U_2674) )
& ! [U_2673,U_2674] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),c_Orderings_Otop__class_Otop(tc_fun(U_2673,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2673,tc_HOL_Obool)),U_2674)))
| ~ sP177(U_2673,U_2674) )
& ! [U_2673,U_2674] :
( sP177(U_2673,U_2674)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),U_2674)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_648_2]) ).
cnf(f_648_4,plain,
( sP177(U_2673,U_2674)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),U_2674)) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),c_Orderings_Otop__class_Otop(tc_fun(U_2673,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2673,tc_HOL_Obool)),U_2674)))
| ~ sP177(U_2673,U_2674) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2673,tc_HOL_Obool)),U_2674)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2673),c_Orderings_Otop__class_Otop(tc_fun(U_2673,tc_HOL_Obool))))
| ~ sP177(U_2673,U_2674) ),
inference(clausify,[status(thm)],[f_648_3]) ).
fof(f_649_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert]) ).
fof(f_649_2,plain,
! [U_2679,U_2678,U_2677,U_2676,U_2675] :
( hAPP(U_2677,hAPP(hAPP(c_Set_Oinsert(U_2675),U_2679),U_2678)) = hAPP(hAPP(U_2676,U_2679),hAPP(U_2677,U_2678))
| U_2678 = c_Orderings_Obot__class_Obot(tc_fun(U_2675,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2675),U_2679),U_2678))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2675),U_2678))
| ~ c_Finite__Set_Ofolding__one(U_2675,U_2676,U_2677) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
fof(f_649_3,plain,
! [U_2675,U_2676,U_2677,U_2678,U_2679] :
( hAPP(U_2677,hAPP(hAPP(c_Set_Oinsert(U_2675),U_2679),U_2678)) = hAPP(hAPP(U_2676,U_2679),hAPP(U_2677,U_2678))
| U_2678 = c_Orderings_Obot__class_Obot(tc_fun(U_2675,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2675),U_2679),U_2678))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2675),U_2678))
| ~ c_Finite__Set_Ofolding__one(U_2675,U_2676,U_2677) ),
inference(definitional_conversion,[status(esa)],[f_649_2]) ).
cnf(f_649_4,plain,
( hAPP(U_2677,hAPP(hAPP(c_Set_Oinsert(U_2675),U_2679),U_2678)) = hAPP(hAPP(U_2676,U_2679),hAPP(U_2677,U_2678))
| U_2678 = c_Orderings_Obot__class_Obot(tc_fun(U_2675,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2675),U_2679),U_2678))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2675),U_2678))
| ~ c_Finite__Set_Ofolding__one(U_2675,U_2676,U_2677) ),
inference(clausify,[status(thm)],[f_649_3]) ).
fof(f_650_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove]) ).
fof(f_650_2,plain,
! [U_2687,U_2686,U_2685,U_2684,U_2683,U_2682,U_2681,U_2680] :
( hAPP(U_2685,U_2686) = hAPP(hAPP(U_2682,hAPP(U_2684,U_2687)),hAPP(U_2685,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2681,tc_HOL_Obool)),U_2686),hAPP(hAPP(c_Set_Oinsert(U_2681),U_2687),c_Orderings_Obot__class_Obot(tc_fun(U_2681,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2681),U_2687),U_2686))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2681),U_2686))
| ~ c_Finite__Set_Ofolding__image__simple(U_2680,U_2681,U_2682,U_2683,U_2684,U_2685) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
fof(f_650_3,plain,
! [U_2687,U_2686,U_2685,U_2684,U_2683,U_2682,U_2681] :
( ! [U_2680] : ~ c_Finite__Set_Ofolding__image__simple(U_2680,U_2681,U_2682,U_2683,U_2684,U_2685)
| hAPP(U_2685,U_2686) = hAPP(hAPP(U_2682,hAPP(U_2684,U_2687)),hAPP(U_2685,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2681,tc_HOL_Obool)),U_2686),hAPP(hAPP(c_Set_Oinsert(U_2681),U_2687),c_Orderings_Obot__class_Obot(tc_fun(U_2681,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2681),U_2687),U_2686))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2681),U_2686)) ),
inference(miniscope,[status(thm)],[f_650_2]) ).
fof(f_650_4,plain,
! [U_2681,U_2680,U_2682,U_2683,U_2684,U_2685,U_2686,U_2687] :
( ~ c_Finite__Set_Ofolding__image__simple(U_2680,U_2681,U_2682,U_2683,U_2684,U_2685)
| hAPP(U_2685,U_2686) = hAPP(hAPP(U_2682,hAPP(U_2684,U_2687)),hAPP(U_2685,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2681,tc_HOL_Obool)),U_2686),hAPP(hAPP(c_Set_Oinsert(U_2681),U_2687),c_Orderings_Obot__class_Obot(tc_fun(U_2681,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2681),U_2687),U_2686))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2681),U_2686)) ),
inference(definitional_conversion,[status(esa)],[f_650_3]) ).
cnf(f_650_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_2680,U_2681,U_2682,U_2683,U_2684,U_2685)
| hAPP(U_2685,U_2686) = hAPP(hAPP(U_2682,hAPP(U_2684,U_2687)),hAPP(U_2685,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2681,tc_HOL_Obool)),U_2686),hAPP(hAPP(c_Set_Oinsert(U_2681),U_2687),c_Orderings_Obot__class_Obot(tc_fun(U_2681,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2681),U_2687),U_2686))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2681),U_2686)) ),
inference(clausify,[status(thm)],[f_650_4]) ).
fof(f_651_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint]) ).
fof(f_651_2,plain,
! [U_2695,U_2694,U_2693,U_2692,U_2691,U_2690,U_2689,U_2688] :
( hAPP(U_2693,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2689,tc_HOL_Obool)),U_2694),U_2695)) = hAPP(hAPP(U_2690,hAPP(U_2693,U_2694)),hAPP(U_2693,U_2695))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2689,tc_HOL_Obool)),U_2694),U_2695) != c_Orderings_Obot__class_Obot(tc_fun(U_2689,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2689),U_2695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2689),U_2694))
| ~ c_Finite__Set_Ofolding__image__simple(U_2688,U_2689,U_2690,U_2691,U_2692,U_2693) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
fof(f_651_3,plain,
! [U_2695,U_2694,U_2693,U_2692,U_2691,U_2690,U_2689] :
( ! [U_2688] : ~ c_Finite__Set_Ofolding__image__simple(U_2688,U_2689,U_2690,U_2691,U_2692,U_2693)
| hAPP(U_2693,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2689,tc_HOL_Obool)),U_2694),U_2695)) = hAPP(hAPP(U_2690,hAPP(U_2693,U_2694)),hAPP(U_2693,U_2695))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2689,tc_HOL_Obool)),U_2694),U_2695) != c_Orderings_Obot__class_Obot(tc_fun(U_2689,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2689),U_2695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2689),U_2694)) ),
inference(miniscope,[status(thm)],[f_651_2]) ).
fof(f_651_4,plain,
! [U_2689,U_2688,U_2690,U_2691,U_2692,U_2693,U_2694,U_2695] :
( ~ c_Finite__Set_Ofolding__image__simple(U_2688,U_2689,U_2690,U_2691,U_2692,U_2693)
| hAPP(U_2693,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2689,tc_HOL_Obool)),U_2694),U_2695)) = hAPP(hAPP(U_2690,hAPP(U_2693,U_2694)),hAPP(U_2693,U_2695))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2689,tc_HOL_Obool)),U_2694),U_2695) != c_Orderings_Obot__class_Obot(tc_fun(U_2689,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2689),U_2695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2689),U_2694)) ),
inference(definitional_conversion,[status(esa)],[f_651_3]) ).
cnf(f_651_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_2688,U_2689,U_2690,U_2691,U_2692,U_2693)
| hAPP(U_2693,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2689,tc_HOL_Obool)),U_2694),U_2695)) = hAPP(hAPP(U_2690,hAPP(U_2693,U_2694)),hAPP(U_2693,U_2695))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2689,tc_HOL_Obool)),U_2694),U_2695) != c_Orderings_Obot__class_Obot(tc_fun(U_2689,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2689),U_2695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2689),U_2694)) ),
inference(clausify,[status(thm)],[f_651_4]) ).
fof(f_652_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove]) ).
fof(f_652_2,plain,
! [U_2703,U_2702,U_2701,U_2700,U_2699,U_2698,U_2697,U_2696] :
( hAPP(U_2701,hAPP(hAPP(c_Set_Oinsert(U_2697),U_2703),U_2702)) = hAPP(hAPP(U_2698,hAPP(U_2700,U_2703)),hAPP(U_2701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2697,tc_HOL_Obool)),U_2702),hAPP(hAPP(c_Set_Oinsert(U_2697),U_2703),c_Orderings_Obot__class_Obot(tc_fun(U_2697,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2697),U_2702))
| ~ c_Finite__Set_Ofolding__image__simple(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
fof(f_652_3,plain,
! [U_2703,U_2702,U_2701,U_2700,U_2699,U_2698,U_2697] :
( ! [U_2696] : ~ c_Finite__Set_Ofolding__image__simple(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701)
| hAPP(U_2701,hAPP(hAPP(c_Set_Oinsert(U_2697),U_2703),U_2702)) = hAPP(hAPP(U_2698,hAPP(U_2700,U_2703)),hAPP(U_2701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2697,tc_HOL_Obool)),U_2702),hAPP(hAPP(c_Set_Oinsert(U_2697),U_2703),c_Orderings_Obot__class_Obot(tc_fun(U_2697,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2697),U_2702)) ),
inference(miniscope,[status(thm)],[f_652_2]) ).
fof(f_652_4,plain,
! [U_2697,U_2696,U_2698,U_2699,U_2700,U_2701,U_2702,U_2703] :
( ~ c_Finite__Set_Ofolding__image__simple(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701)
| hAPP(U_2701,hAPP(hAPP(c_Set_Oinsert(U_2697),U_2703),U_2702)) = hAPP(hAPP(U_2698,hAPP(U_2700,U_2703)),hAPP(U_2701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2697,tc_HOL_Obool)),U_2702),hAPP(hAPP(c_Set_Oinsert(U_2697),U_2703),c_Orderings_Obot__class_Obot(tc_fun(U_2697,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2697),U_2702)) ),
inference(definitional_conversion,[status(esa)],[f_652_3]) ).
cnf(f_652_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701)
| hAPP(U_2701,hAPP(hAPP(c_Set_Oinsert(U_2697),U_2703),U_2702)) = hAPP(hAPP(U_2698,hAPP(U_2700,U_2703)),hAPP(U_2701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2697,tc_HOL_Obool)),U_2702),hAPP(hAPP(c_Set_Oinsert(U_2697),U_2703),c_Orderings_Obot__class_Obot(tc_fun(U_2697,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2697),U_2702)) ),
inference(clausify,[status(thm)],[f_652_4]) ).
fof(f_653_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove]) ).
fof(f_653_2,plain,
! [U_2706,U_2705,U_2704] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_2704,U_2705) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2704),U_2706),c_Big__Operators_Olattice__class_OInf__fin(U_2704,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(U_2704,U_2705) = U_2706
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2704),U_2706),U_2705))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2704),U_2705))
| ~ class_Lattices_Olattice(U_2704) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
( ! [U_2704,U_2706,U_2705] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2704,U_2705) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2704),U_2706),c_Big__Operators_Olattice__class_OInf__fin(U_2704,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool))
| ~ sP178(U_2704,U_2706,U_2705) )
& ! [U_2704,U_2706,U_2705] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2704,U_2705) = U_2706
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool))
| ~ sP178(U_2704,U_2706,U_2705) )
& ! [U_2704,U_2706,U_2705] :
( sP178(U_2704,U_2706,U_2705)
| ~ hBOOL(hAPP(hAPP(c_member(U_2704),U_2706),U_2705))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2704),U_2705))
| ~ class_Lattices_Olattice(U_2704) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_653_2]) ).
cnf(f_653_4,plain,
( sP178(U_2704,U_2706,U_2705)
| ~ hBOOL(hAPP(hAPP(c_member(U_2704),U_2706),U_2705))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2704),U_2705))
| ~ class_Lattices_Olattice(U_2704) ),
inference(clausify,[status(thm)],[f_653_3]) ).
cnf(f_653_5,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2704,U_2705) = U_2706
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool))
| ~ sP178(U_2704,U_2706,U_2705) ),
inference(clausify,[status(thm)],[f_653_3]) ).
cnf(f_653_6,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2704,U_2705) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2704),U_2706),c_Big__Operators_Olattice__class_OInf__fin(U_2704,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2705),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2704,tc_HOL_Obool))
| ~ sP178(U_2704,U_2706,U_2705) ),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove]) ).
fof(f_654_2,plain,
! [U_2709,U_2708,U_2707] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_2707,U_2708) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2707),U_2709),c_Big__Operators_Olattice__class_OSup__fin(U_2707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(U_2707,U_2708) = U_2709
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2707),U_2709),U_2708))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2707),U_2708))
| ~ class_Lattices_Olattice(U_2707) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
fof(f_654_3,plain,
( ! [U_2709,U_2707,U_2708] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2707,U_2708) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2707),U_2709),c_Big__Operators_Olattice__class_OSup__fin(U_2707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool))
| ~ sP179(U_2709,U_2707,U_2708) )
& ! [U_2709,U_2707,U_2708] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2707,U_2708) = U_2709
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool))
| ~ sP179(U_2709,U_2707,U_2708) )
& ! [U_2709,U_2707,U_2708] :
( sP179(U_2709,U_2707,U_2708)
| ~ hBOOL(hAPP(hAPP(c_member(U_2707),U_2709),U_2708))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2707),U_2708))
| ~ class_Lattices_Olattice(U_2707) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_654_2]) ).
cnf(f_654_4,plain,
( sP179(U_2709,U_2707,U_2708)
| ~ hBOOL(hAPP(hAPP(c_member(U_2707),U_2709),U_2708))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2707),U_2708))
| ~ class_Lattices_Olattice(U_2707) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_5,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2707,U_2708) = U_2709
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool))
| ~ sP179(U_2709,U_2707,U_2708) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_6,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2707,U_2708) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2707),U_2709),c_Big__Operators_Olattice__class_OSup__fin(U_2707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2707,tc_HOL_Obool)),U_2708),hAPP(hAPP(c_Set_Oinsert(U_2707),U_2709),c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2707,tc_HOL_Obool))
| ~ sP179(U_2709,U_2707,U_2708) ),
inference(clausify,[status(thm)],[f_654_3]) ).
fof(f_655_1,plain,
! [V_A_2,V_F_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2))
| ? [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))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed]) ).
fof(f_655_2,plain,
! [U_2715,U_2714,U_2713,U_2712] :
( hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(U_2714,U_2715)),U_2715))
| ? [U_2711,U_2710] : ~ hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(hAPP(U_2713,U_2711),U_2710)),hAPP(hAPP(c_Set_Oinsert(U_2712),U_2711),hAPP(hAPP(c_Set_Oinsert(U_2712),U_2710),c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))))))
| U_2715 = c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2712),U_2715))
| ~ c_Finite__Set_Ofolding__one(U_2712,U_2713,U_2714) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
! [U_2715,U_2714,U_2713,U_2712] :
( hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(U_2714,U_2715)),U_2715))
| ? [U_2710] : ~ hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(hAPP(U_2713,sK61(U_2715,U_2714,U_2713,U_2712)),U_2710)),hAPP(hAPP(c_Set_Oinsert(U_2712),sK61(U_2715,U_2714,U_2713,U_2712)),hAPP(hAPP(c_Set_Oinsert(U_2712),U_2710),c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))))))
| U_2715 = c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2712),U_2715))
| ~ c_Finite__Set_Ofolding__one(U_2712,U_2713,U_2714) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_2711,sK61(U_2715,U_2714,U_2713,U_2712))],[f_655_2]) ).
fof(f_655_4,plain,
! [U_2715,U_2714,U_2713,U_2712] :
( hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(U_2714,U_2715)),U_2715))
| ~ hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(hAPP(U_2713,sK61(U_2715,U_2714,U_2713,U_2712)),sK62(U_2715,U_2714,U_2713,U_2712))),hAPP(hAPP(c_Set_Oinsert(U_2712),sK61(U_2715,U_2714,U_2713,U_2712)),hAPP(hAPP(c_Set_Oinsert(U_2712),sK62(U_2715,U_2714,U_2713,U_2712)),c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))))))
| U_2715 = c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2712),U_2715))
| ~ c_Finite__Set_Ofolding__one(U_2712,U_2713,U_2714) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_2710,sK62(U_2715,U_2714,U_2713,U_2712))],[f_655_3]) ).
fof(f_655_5,plain,
! [U_2713,U_2712,U_2715,U_2714] :
( hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(U_2714,U_2715)),U_2715))
| ~ hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(hAPP(U_2713,sK61(U_2715,U_2714,U_2713,U_2712)),sK62(U_2715,U_2714,U_2713,U_2712))),hAPP(hAPP(c_Set_Oinsert(U_2712),sK61(U_2715,U_2714,U_2713,U_2712)),hAPP(hAPP(c_Set_Oinsert(U_2712),sK62(U_2715,U_2714,U_2713,U_2712)),c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))))))
| U_2715 = c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2712),U_2715))
| ~ c_Finite__Set_Ofolding__one(U_2712,U_2713,U_2714) ),
inference(definitional_conversion,[status(esa)],[f_655_4]) ).
cnf(f_655_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(U_2714,U_2715)),U_2715))
| ~ hBOOL(hAPP(hAPP(c_member(U_2712),hAPP(hAPP(U_2713,sK61(U_2715,U_2714,U_2713,U_2712)),sK62(U_2715,U_2714,U_2713,U_2712))),hAPP(hAPP(c_Set_Oinsert(U_2712),sK61(U_2715,U_2714,U_2713,U_2712)),hAPP(hAPP(c_Set_Oinsert(U_2712),sK62(U_2715,U_2714,U_2713,U_2712)),c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))))))
| U_2715 = c_Orderings_Obot__class_Obot(tc_fun(U_2712,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2712),U_2715))
| ~ c_Finite__Set_Ofolding__one(U_2712,U_2713,U_2714) ),
inference(clausify,[status(thm)],[f_655_5]) ).
fof(f_656_1,plain,
! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( ( hAPP(c_Set_Oimage(T_b,T_c,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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hAPP(c_Set_Oimage(T_b,T_c,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))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__image]) ).
fof(f_656_2,plain,
! [U_2721,U_2720,U_2719,U_2718,U_2717,U_2716] :
( ( hAPP(c_Set_Oimage(U_2716,U_2719,c_Fun_Ofun__upd(U_2716,U_2719,U_2720,U_2717,U_2721)),U_2718) = hAPP(c_Set_Oimage(U_2716,U_2719,U_2720),U_2718)
| hBOOL(hAPP(hAPP(c_member(U_2716),U_2717),U_2718)) )
& ( hAPP(c_Set_Oimage(U_2716,U_2719,c_Fun_Ofun__upd(U_2716,U_2719,U_2720,U_2717,U_2721)),U_2718) = hAPP(hAPP(c_Set_Oinsert(U_2719),U_2721),hAPP(c_Set_Oimage(U_2716,U_2719,U_2720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2716,tc_HOL_Obool)),U_2718),hAPP(hAPP(c_Set_Oinsert(U_2716),U_2717),c_Orderings_Obot__class_Obot(tc_fun(U_2716,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2716),U_2717),U_2718)) ) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
fof(f_656_3,plain,
( ! [U_2733,U_2731,U_2729,U_2727,U_2725,U_2723] :
( hAPP(c_Set_Oimage(U_2723,U_2729,c_Fun_Ofun__upd(U_2723,U_2729,U_2731,U_2725,U_2733)),U_2727) = hAPP(c_Set_Oimage(U_2723,U_2729,U_2731),U_2727)
| hBOOL(hAPP(hAPP(c_member(U_2723),U_2725),U_2727)) )
& ! [U_2732,U_2730,U_2728,U_2726,U_2724,U_2722] :
( hAPP(c_Set_Oimage(U_2722,U_2728,c_Fun_Ofun__upd(U_2722,U_2728,U_2730,U_2724,U_2732)),U_2726) = hAPP(hAPP(c_Set_Oinsert(U_2728),U_2732),hAPP(c_Set_Oimage(U_2722,U_2728,U_2730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2722,tc_HOL_Obool)),U_2726),hAPP(hAPP(c_Set_Oinsert(U_2722),U_2724),c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2722),U_2724),U_2726)) ) ),
inference(miniscope,[status(thm)],[f_656_2]) ).
fof(f_656_4,plain,
( ! [U_2725,U_2723,U_2727,U_2729,U_2731,U_2733] :
( hAPP(c_Set_Oimage(U_2723,U_2729,c_Fun_Ofun__upd(U_2723,U_2729,U_2731,U_2725,U_2733)),U_2727) = hAPP(c_Set_Oimage(U_2723,U_2729,U_2731),U_2727)
| hBOOL(hAPP(hAPP(c_member(U_2723),U_2725),U_2727)) )
& ! [U_2732,U_2730,U_2724,U_2728,U_2722,U_2726] :
( hAPP(c_Set_Oimage(U_2722,U_2728,c_Fun_Ofun__upd(U_2722,U_2728,U_2730,U_2724,U_2732)),U_2726) = hAPP(hAPP(c_Set_Oinsert(U_2728),U_2732),hAPP(c_Set_Oimage(U_2722,U_2728,U_2730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2722,tc_HOL_Obool)),U_2726),hAPP(hAPP(c_Set_Oinsert(U_2722),U_2724),c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2722),U_2724),U_2726)) ) ),
inference(definitional_conversion,[status(esa)],[f_656_3]) ).
cnf(f_656_5,plain,
( hAPP(c_Set_Oimage(U_2722,U_2728,c_Fun_Ofun__upd(U_2722,U_2728,U_2730,U_2724,U_2732)),U_2726) = hAPP(hAPP(c_Set_Oinsert(U_2728),U_2732),hAPP(c_Set_Oimage(U_2722,U_2728,U_2730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2722,tc_HOL_Obool)),U_2726),hAPP(hAPP(c_Set_Oinsert(U_2722),U_2724),c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2722),U_2724),U_2726)) ),
inference(clausify,[status(thm)],[f_656_4]) ).
cnf(f_656_6,plain,
( hAPP(c_Set_Oimage(U_2723,U_2729,c_Fun_Ofun__upd(U_2723,U_2729,U_2731,U_2725,U_2733)),U_2727) = hAPP(c_Set_Oimage(U_2723,U_2729,U_2731),U_2727)
| hBOOL(hAPP(hAPP(c_member(U_2723),U_2725),U_2727)) ),
inference(clausify,[status(thm)],[f_656_4]) ).
fof(f_657_1,plain,
! [V_Pa_2,V_A_2,T_b] :
( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ? [B_a,B_A] :
( ~ 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))))))
& hBOOL(hAPP(V_Pa_2,B_A))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) )
| ~ hBOOL(hAPP(V_Pa_2,V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__empty__induct]) ).
fof(f_657_2,plain,
! [U_2738,U_2737,U_2736] :
( hBOOL(hAPP(U_2738,c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))
| ? [U_2735,U_2734] :
( ~ hBOOL(hAPP(U_2738,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2736,tc_HOL_Obool)),U_2734),hAPP(hAPP(c_Set_Oinsert(U_2736),U_2735),c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))))
& hBOOL(hAPP(U_2738,U_2734))
& hBOOL(hAPP(hAPP(c_member(U_2736),U_2735),U_2734))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2734)) )
| ~ hBOOL(hAPP(U_2738,U_2737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2737)) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
! [U_2738,U_2737,U_2736] :
( hBOOL(hAPP(U_2738,c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))
| ? [U_2734] :
( ~ hBOOL(hAPP(U_2738,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2736,tc_HOL_Obool)),U_2734),hAPP(hAPP(c_Set_Oinsert(U_2736),sK63(U_2738,U_2737,U_2736)),c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))))
& hBOOL(hAPP(U_2738,U_2734))
& hBOOL(hAPP(hAPP(c_member(U_2736),sK63(U_2738,U_2737,U_2736)),U_2734))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2734)) )
| ~ hBOOL(hAPP(U_2738,U_2737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2737)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_2735,sK63(U_2738,U_2737,U_2736))],[f_657_2]) ).
fof(f_657_4,plain,
! [U_2738,U_2737,U_2736] :
( hBOOL(hAPP(U_2738,c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))
| ( ~ hBOOL(hAPP(U_2738,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2736,tc_HOL_Obool)),sK64(U_2738,U_2737,U_2736)),hAPP(hAPP(c_Set_Oinsert(U_2736),sK63(U_2738,U_2737,U_2736)),c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))))
& hBOOL(hAPP(U_2738,sK64(U_2738,U_2737,U_2736)))
& hBOOL(hAPP(hAPP(c_member(U_2736),sK63(U_2738,U_2737,U_2736)),sK64(U_2738,U_2737,U_2736)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),sK64(U_2738,U_2737,U_2736))) )
| ~ hBOOL(hAPP(U_2738,U_2737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2737)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_2734,sK64(U_2738,U_2737,U_2736))],[f_657_3]) ).
fof(f_657_5,plain,
( ! [U_2736,U_2737,U_2738] :
( ~ hBOOL(hAPP(U_2738,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2736,tc_HOL_Obool)),sK64(U_2738,U_2737,U_2736)),hAPP(hAPP(c_Set_Oinsert(U_2736),sK63(U_2738,U_2737,U_2736)),c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))))
| ~ sP180(U_2736,U_2737,U_2738) )
& ! [U_2736,U_2737,U_2738] :
( hBOOL(hAPP(U_2738,sK64(U_2738,U_2737,U_2736)))
| ~ sP180(U_2736,U_2737,U_2738) )
& ! [U_2736,U_2737,U_2738] :
( hBOOL(hAPP(hAPP(c_member(U_2736),sK63(U_2738,U_2737,U_2736)),sK64(U_2738,U_2737,U_2736)))
| ~ sP180(U_2736,U_2737,U_2738) )
& ! [U_2736,U_2737,U_2738] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),sK64(U_2738,U_2737,U_2736)))
| ~ sP180(U_2736,U_2737,U_2738) )
& ! [U_2736,U_2737,U_2738] :
( hBOOL(hAPP(U_2738,c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))
| sP180(U_2736,U_2737,U_2738)
| ~ hBOOL(hAPP(U_2738,U_2737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2737)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_657_4]) ).
cnf(f_657_6,plain,
( hBOOL(hAPP(U_2738,c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))
| sP180(U_2736,U_2737,U_2738)
| ~ hBOOL(hAPP(U_2738,U_2737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2737)) ),
inference(clausify,[status(thm)],[f_657_5]) ).
cnf(f_657_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),sK64(U_2738,U_2737,U_2736)))
| ~ sP180(U_2736,U_2737,U_2738) ),
inference(clausify,[status(thm)],[f_657_5]) ).
cnf(f_657_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_2736),sK63(U_2738,U_2737,U_2736)),sK64(U_2738,U_2737,U_2736)))
| ~ sP180(U_2736,U_2737,U_2738) ),
inference(clausify,[status(thm)],[f_657_5]) ).
cnf(f_657_9,plain,
( hBOOL(hAPP(U_2738,sK64(U_2738,U_2737,U_2736)))
| ~ sP180(U_2736,U_2737,U_2738) ),
inference(clausify,[status(thm)],[f_657_5]) ).
cnf(f_657_10,plain,
( ~ hBOOL(hAPP(U_2738,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2736,tc_HOL_Obool)),sK64(U_2738,U_2737,U_2736)),hAPP(hAPP(c_Set_Oinsert(U_2736),sK63(U_2738,U_2737,U_2736)),c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))))
| ~ sP180(U_2736,U_2737,U_2738) ),
inference(clausify,[status(thm)],[f_657_5]) ).
fof(f_658_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem]) ).
fof(f_658_2,plain,
! [U_2743,U_2742,U_2741,U_2740,U_2739] :
( hAPP(U_2741,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2739,tc_HOL_Obool)),U_2742),U_2743)) = hAPP(hAPP(U_2740,hAPP(U_2741,U_2742)),hAPP(U_2741,U_2743))
| U_2743 = c_Orderings_Obot__class_Obot(tc_fun(U_2739,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2739),U_2743))
| U_2742 = c_Orderings_Obot__class_Obot(tc_fun(U_2739,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2739),U_2742))
| ~ c_Finite__Set_Ofolding__one__idem(U_2739,U_2740,U_2741) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
! [U_2740,U_2741,U_2743,U_2742,U_2739] :
( hAPP(U_2741,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2739,tc_HOL_Obool)),U_2742),U_2743)) = hAPP(hAPP(U_2740,hAPP(U_2741,U_2742)),hAPP(U_2741,U_2743))
| U_2743 = c_Orderings_Obot__class_Obot(tc_fun(U_2739,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2739),U_2743))
| U_2742 = c_Orderings_Obot__class_Obot(tc_fun(U_2739,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2739),U_2742))
| ~ c_Finite__Set_Ofolding__one__idem(U_2739,U_2740,U_2741) ),
inference(definitional_conversion,[status(esa)],[f_658_2]) ).
cnf(f_658_4,plain,
( hAPP(U_2741,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2739,tc_HOL_Obool)),U_2742),U_2743)) = hAPP(hAPP(U_2740,hAPP(U_2741,U_2742)),hAPP(U_2741,U_2743))
| U_2743 = c_Orderings_Obot__class_Obot(tc_fun(U_2739,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2739),U_2743))
| U_2742 = c_Orderings_Obot__class_Obot(tc_fun(U_2739,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2739),U_2742))
| ~ c_Finite__Set_Ofolding__one__idem(U_2739,U_2740,U_2741) ),
inference(clausify,[status(thm)],[f_658_3]) ).
fof(f_659_1,plain,
! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_fun__upd__triv]) ).
fof(f_659_2,plain,
! [U_2747,U_2746,U_2745,U_2744] : c_Fun_Ofun__upd(U_2744,U_2745,U_2746,U_2747,hAPP(U_2746,U_2747)) = U_2746,
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
! [U_2747,U_2746,U_2744,U_2745] : c_Fun_Ofun__upd(U_2744,U_2745,U_2746,U_2747,hAPP(U_2746,U_2747)) = U_2746,
inference(definitional_conversion,[status(esa)],[f_659_2]) ).
cnf(f_659_4,plain,
c_Fun_Ofun__upd(U_2744,U_2745,U_2746,U_2747,hAPP(U_2746,U_2747)) = U_2746,
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_1,plain,
! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
( c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2
| hAPP(V_f_2,V_x_2) != V_y_2 ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__idem]) ).
fof(f_660_2,plain,
! [U_2752,U_2751,U_2750,U_2749,U_2748] :
( c_Fun_Ofun__upd(U_2751,U_2752,U_2748,U_2749,U_2750) = U_2748
| hAPP(U_2748,U_2749) != U_2750 ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
fof(f_660_3,plain,
! [U_2750,U_2749,U_2751,U_2748,U_2752] :
( c_Fun_Ofun__upd(U_2751,U_2752,U_2748,U_2749,U_2750) = U_2748
| hAPP(U_2748,U_2749) != U_2750 ),
inference(definitional_conversion,[status(esa)],[f_660_2]) ).
cnf(f_660_4,plain,
( c_Fun_Ofun__upd(U_2751,U_2752,U_2748,U_2749,U_2750) = U_2748
| hAPP(U_2748,U_2749) != U_2750 ),
inference(clausify,[status(thm)],[f_660_3]) ).
fof(f_661_1,plain,
! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
( 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)
| V_z_2 = V_x_2 ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__other]) ).
fof(f_661_2,plain,
! [U_2758,U_2757,U_2756,U_2755,U_2754,U_2753] :
( hAPP(c_Fun_Ofun__upd(U_2755,U_2756,U_2757,U_2754,U_2758),U_2753) = hAPP(U_2757,U_2753)
| U_2753 = U_2754 ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
! [U_2753,U_2754,U_2755,U_2756,U_2757,U_2758] :
( hAPP(c_Fun_Ofun__upd(U_2755,U_2756,U_2757,U_2754,U_2758),U_2753) = hAPP(U_2757,U_2753)
| U_2753 = U_2754 ),
inference(definitional_conversion,[status(esa)],[f_661_2]) ).
cnf(f_661_4,plain,
( hAPP(c_Fun_Ofun__upd(U_2755,U_2756,U_2757,U_2754,U_2758),U_2753) = hAPP(U_2757,U_2753)
| U_2753 = U_2754 ),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_1,plain,
! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
( c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2)
| V_a_2 = V_ca_2 ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__twist]) ).
fof(f_662_2,plain,
! [U_2765,U_2764,U_2763,U_2762,U_2761,U_2760,U_2759] :
( c_Fun_Ofun__upd(U_2761,U_2762,c_Fun_Ofun__upd(U_2761,U_2762,U_2763,U_2759,U_2764),U_2760,U_2765) = c_Fun_Ofun__upd(U_2761,U_2762,c_Fun_Ofun__upd(U_2761,U_2762,U_2763,U_2760,U_2765),U_2759,U_2764)
| U_2759 = U_2760 ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
! [U_2760,U_2759,U_2761,U_2762,U_2763,U_2764,U_2765] :
( c_Fun_Ofun__upd(U_2761,U_2762,c_Fun_Ofun__upd(U_2761,U_2762,U_2763,U_2759,U_2764),U_2760,U_2765) = c_Fun_Ofun__upd(U_2761,U_2762,c_Fun_Ofun__upd(U_2761,U_2762,U_2763,U_2760,U_2765),U_2759,U_2764)
| U_2759 = U_2760 ),
inference(definitional_conversion,[status(esa)],[f_662_2]) ).
cnf(f_662_4,plain,
( c_Fun_Ofun__upd(U_2761,U_2762,c_Fun_Ofun__upd(U_2761,U_2762,U_2763,U_2759,U_2764),U_2760,U_2765) = c_Fun_Ofun__upd(U_2761,U_2762,c_Fun_Ofun__upd(U_2761,U_2762,U_2763,U_2760,U_2765),U_2759,U_2764)
| U_2759 = U_2760 ),
inference(clausify,[status(thm)],[f_662_3]) ).
fof(f_663_1,plain,
! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
( ( 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)
| V_z_2 = V_x_2 )
& ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2
| V_z_2 != V_x_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__apply]) ).
fof(f_663_2,plain,
! [U_2771,U_2770,U_2769,U_2768,U_2767,U_2766] :
( ( hAPP(c_Fun_Ofun__upd(U_2768,U_2769,U_2770,U_2767,U_2771),U_2766) = hAPP(U_2770,U_2766)
| U_2766 = U_2767 )
& ( hAPP(c_Fun_Ofun__upd(U_2768,U_2769,U_2770,U_2767,U_2771),U_2766) = U_2771
| U_2766 != U_2767 ) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
( ! [U_2783,U_2781,U_2779,U_2777,U_2775,U_2773] :
( hAPP(c_Fun_Ofun__upd(U_2777,U_2779,U_2781,U_2775,U_2783),U_2773) = hAPP(U_2781,U_2773)
| U_2773 = U_2775 )
& ! [U_2782,U_2780,U_2778,U_2776,U_2774,U_2772] :
( hAPP(c_Fun_Ofun__upd(U_2776,U_2778,U_2780,U_2774,U_2782),U_2772) = U_2782
| U_2772 != U_2774 ) ),
inference(miniscope,[status(thm)],[f_663_2]) ).
fof(f_663_4,plain,
( ! [U_2773,U_2775,U_2777,U_2779,U_2781,U_2783] :
( hAPP(c_Fun_Ofun__upd(U_2777,U_2779,U_2781,U_2775,U_2783),U_2773) = hAPP(U_2781,U_2773)
| U_2773 = U_2775 )
& ! [U_2774,U_2778,U_2772,U_2776,U_2780,U_2782] :
( hAPP(c_Fun_Ofun__upd(U_2776,U_2778,U_2780,U_2774,U_2782),U_2772) = U_2782
| U_2772 != U_2774 ) ),
inference(definitional_conversion,[status(esa)],[f_663_3]) ).
cnf(f_663_5,plain,
( hAPP(c_Fun_Ofun__upd(U_2776,U_2778,U_2780,U_2774,U_2782),U_2772) = U_2782
| U_2772 != U_2774 ),
inference(clausify,[status(thm)],[f_663_4]) ).
cnf(f_663_6,plain,
( hAPP(c_Fun_Ofun__upd(U_2777,U_2779,U_2781,U_2775,U_2783),U_2773) = hAPP(U_2781,U_2773)
| U_2773 = U_2775 ),
inference(clausify,[status(thm)],[f_663_4]) ).
fof(f_664_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2,
inference(fof_nnf,[status(thm)],[fact_fun__upd__same]) ).
fof(f_664_2,plain,
! [U_2788,U_2787,U_2786,U_2785,U_2784] : hAPP(c_Fun_Ofun__upd(U_2784,U_2785,U_2786,U_2787,U_2788),U_2787) = U_2788,
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
! [U_2784,U_2785,U_2786,U_2787,U_2788] : hAPP(c_Fun_Ofun__upd(U_2784,U_2785,U_2786,U_2787,U_2788),U_2787) = U_2788,
inference(definitional_conversion,[status(esa)],[f_664_2]) ).
cnf(f_664_4,plain,
hAPP(c_Fun_Ofun__upd(U_2784,U_2785,U_2786,U_2787,U_2788),U_2787) = U_2788,
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_1,plain,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2),
inference(fof_nnf,[status(thm)],[fact_fun__upd__upd]) ).
fof(f_665_2,plain,
! [U_2794,U_2793,U_2792,U_2791,U_2790,U_2789] : c_Fun_Ofun__upd(U_2789,U_2790,c_Fun_Ofun__upd(U_2789,U_2790,U_2791,U_2792,U_2793),U_2792,U_2794) = c_Fun_Ofun__upd(U_2789,U_2790,U_2791,U_2792,U_2794),
inference(variable_rename,[status(thm)],[f_665_1]) ).
fof(f_665_3,plain,
! [U_2790,U_2789,U_2791,U_2792,U_2793,U_2794] : c_Fun_Ofun__upd(U_2789,U_2790,c_Fun_Ofun__upd(U_2789,U_2790,U_2791,U_2792,U_2793),U_2792,U_2794) = c_Fun_Ofun__upd(U_2789,U_2790,U_2791,U_2792,U_2794),
inference(definitional_conversion,[status(esa)],[f_665_2]) ).
cnf(f_665_4,plain,
c_Fun_Ofun__upd(U_2789,U_2790,c_Fun_Ofun__upd(U_2789,U_2790,U_2791,U_2792,U_2793),U_2792,U_2794) = c_Fun_Ofun__upd(U_2789,U_2790,U_2791,U_2792,U_2794),
inference(clausify,[status(thm)],[f_665_3]) ).
fof(f_666_1,plain,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
| hAPP(V_f_2,V_x_2) != V_y_2 )
& ( hAPP(V_f_2,V_x_2) = V_y_2
| c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) != V_f_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff]) ).
fof(f_666_2,plain,
! [U_2799,U_2798,U_2797,U_2796,U_2795] :
( ( c_Fun_Ofun__upd(U_2795,U_2796,U_2797,U_2798,U_2799) = U_2797
| hAPP(U_2797,U_2798) != U_2799 )
& ( hAPP(U_2797,U_2798) = U_2799
| c_Fun_Ofun__upd(U_2795,U_2796,U_2797,U_2798,U_2799) != U_2797 ) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
( ! [U_2809,U_2807,U_2805] :
( ! [U_2803,U_2801] : c_Fun_Ofun__upd(U_2801,U_2803,U_2805,U_2807,U_2809) = U_2805
| hAPP(U_2805,U_2807) != U_2809 )
& ! [U_2808,U_2806,U_2804] :
( ! [U_2802,U_2800] : c_Fun_Ofun__upd(U_2800,U_2802,U_2804,U_2806,U_2808) != U_2804
| hAPP(U_2804,U_2806) = U_2808 ) ),
inference(miniscope,[status(thm)],[f_666_2]) ).
fof(f_666_4,plain,
( ! [U_2809,U_2803,U_2801,U_2807,U_2805] :
( c_Fun_Ofun__upd(U_2801,U_2803,U_2805,U_2807,U_2809) = U_2805
| hAPP(U_2805,U_2807) != U_2809 )
& ! [U_2800,U_2802,U_2804,U_2806,U_2808] :
( c_Fun_Ofun__upd(U_2800,U_2802,U_2804,U_2806,U_2808) != U_2804
| hAPP(U_2804,U_2806) = U_2808 ) ),
inference(definitional_conversion,[status(esa)],[f_666_3]) ).
cnf(f_666_5,plain,
( c_Fun_Ofun__upd(U_2800,U_2802,U_2804,U_2806,U_2808) != U_2804
| hAPP(U_2804,U_2806) = U_2808 ),
inference(clausify,[status(thm)],[f_666_4]) ).
cnf(f_666_6,plain,
( c_Fun_Ofun__upd(U_2801,U_2803,U_2805,U_2807,U_2809) = U_2805
| hAPP(U_2805,U_2807) != U_2809 ),
inference(clausify,[status(thm)],[f_666_4]) ).
fof(f_667_1,plain,
! [V_x_2,V_F_2,V_f_2,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem]) ).
fof(f_667_2,plain,
! [U_2813,U_2812,U_2811,U_2810] :
( hAPP(hAPP(U_2811,U_2813),U_2813) = U_2813
| ~ c_Finite__Set_Ofolding__one__idem(U_2810,U_2811,U_2812) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
! [U_2813,U_2812,U_2811] :
( ! [U_2810] : ~ c_Finite__Set_Ofolding__one__idem(U_2810,U_2811,U_2812)
| hAPP(hAPP(U_2811,U_2813),U_2813) = U_2813 ),
inference(miniscope,[status(thm)],[f_667_2]) ).
fof(f_667_4,plain,
! [U_2811,U_2810,U_2812,U_2813] :
( ~ c_Finite__Set_Ofolding__one__idem(U_2810,U_2811,U_2812)
| hAPP(hAPP(U_2811,U_2813),U_2813) = U_2813 ),
inference(definitional_conversion,[status(esa)],[f_667_3]) ).
cnf(f_667_5,plain,
( ~ c_Finite__Set_Ofolding__one__idem(U_2810,U_2811,U_2812)
| hAPP(hAPP(U_2811,U_2813),U_2813) = U_2813 ),
inference(clausify,[status(thm)],[f_667_4]) ).
fof(f_668_1,plain,
! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
( ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ 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))) )
| ? [B_x] :
( ? [B_xa] :
( ~ hBOOL(hAPP(V_Pa_2,B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(V_Pa_2,B_xa))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& 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))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ball__UN]) ).
fof(f_668_2,plain,
! [U_2824,U_2823,U_2822,U_2821,U_2820] :
( ( ! [U_2819] :
( hBOOL(hAPP(U_2824,U_2819))
| ~ hBOOL(hAPP(hAPP(c_member(U_2820),U_2819),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2821,tc_fun(U_2820,tc_HOL_Obool)),U_2822),U_2823))) )
| ? [U_2818] :
( ? [U_2817] :
( ~ hBOOL(hAPP(U_2824,U_2817))
& hBOOL(hAPP(hAPP(c_member(U_2820),U_2817),hAPP(U_2823,U_2818))) )
& hBOOL(hAPP(hAPP(c_member(U_2821),U_2818),U_2822)) ) )
& ( ! [U_2816] :
( ! [U_2815] :
( hBOOL(hAPP(U_2824,U_2815))
| ~ hBOOL(hAPP(hAPP(c_member(U_2820),U_2815),hAPP(U_2823,U_2816))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2821),U_2816),U_2822)) )
| ? [U_2814] :
( ~ hBOOL(hAPP(U_2824,U_2814))
& hBOOL(hAPP(hAPP(c_member(U_2820),U_2814),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2821,tc_fun(U_2820,tc_HOL_Obool)),U_2822),U_2823))) ) ) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
( ! [U_2834,U_2832,U_2830,U_2828,U_2826] :
( ! [U_2819] :
( hBOOL(hAPP(U_2834,U_2819))
| ~ hBOOL(hAPP(hAPP(c_member(U_2826),U_2819),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2830),U_2832))) )
| ? [U_2818] :
( ? [U_2817] :
( ~ hBOOL(hAPP(U_2834,U_2817))
& hBOOL(hAPP(hAPP(c_member(U_2826),U_2817),hAPP(U_2832,U_2818))) )
& hBOOL(hAPP(hAPP(c_member(U_2828),U_2818),U_2830)) ) )
& ! [U_2833,U_2831,U_2829,U_2827,U_2825] :
( ! [U_2816] :
( ! [U_2815] :
( hBOOL(hAPP(U_2833,U_2815))
| ~ hBOOL(hAPP(hAPP(c_member(U_2825),U_2815),hAPP(U_2831,U_2816))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2827),U_2816),U_2829)) )
| ? [U_2814] :
( ~ hBOOL(hAPP(U_2833,U_2814))
& hBOOL(hAPP(hAPP(c_member(U_2825),U_2814),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2827,tc_fun(U_2825,tc_HOL_Obool)),U_2829),U_2831))) ) ) ),
inference(miniscope,[status(thm)],[f_668_2]) ).
fof(f_668_4,plain,
( ! [U_2834,U_2832,U_2830,U_2828,U_2826] :
( ! [U_2819] :
( hBOOL(hAPP(U_2834,U_2819))
| ~ hBOOL(hAPP(hAPP(c_member(U_2826),U_2819),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2830),U_2832))) )
| ? [U_2818] :
( ? [U_2817] :
( ~ hBOOL(hAPP(U_2834,U_2817))
& hBOOL(hAPP(hAPP(c_member(U_2826),U_2817),hAPP(U_2832,U_2818))) )
& hBOOL(hAPP(hAPP(c_member(U_2828),U_2818),U_2830)) ) )
& ! [U_2833,U_2831,U_2829,U_2827,U_2825] :
( ! [U_2816] :
( ! [U_2815] :
( hBOOL(hAPP(U_2833,U_2815))
| ~ hBOOL(hAPP(hAPP(c_member(U_2825),U_2815),hAPP(U_2831,U_2816))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2827),U_2816),U_2829)) )
| ( ~ hBOOL(hAPP(U_2833,sK65(U_2833,U_2831,U_2829,U_2827,U_2825)))
& hBOOL(hAPP(hAPP(c_member(U_2825),sK65(U_2833,U_2831,U_2829,U_2827,U_2825)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2827,tc_fun(U_2825,tc_HOL_Obool)),U_2829),U_2831))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_2814,sK65(U_2833,U_2831,U_2829,U_2827,U_2825))],[f_668_3]) ).
fof(f_668_5,plain,
( ! [U_2834,U_2832,U_2830,U_2828,U_2826] :
( ! [U_2819] :
( hBOOL(hAPP(U_2834,U_2819))
| ~ hBOOL(hAPP(hAPP(c_member(U_2826),U_2819),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2830),U_2832))) )
| ( ? [U_2817] :
( ~ hBOOL(hAPP(U_2834,U_2817))
& hBOOL(hAPP(hAPP(c_member(U_2826),U_2817),hAPP(U_2832,sK66(U_2834,U_2832,U_2830,U_2828,U_2826)))) )
& hBOOL(hAPP(hAPP(c_member(U_2828),sK66(U_2834,U_2832,U_2830,U_2828,U_2826)),U_2830)) ) )
& ! [U_2833,U_2831,U_2829,U_2827,U_2825] :
( ! [U_2816] :
( ! [U_2815] :
( hBOOL(hAPP(U_2833,U_2815))
| ~ hBOOL(hAPP(hAPP(c_member(U_2825),U_2815),hAPP(U_2831,U_2816))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2827),U_2816),U_2829)) )
| ( ~ hBOOL(hAPP(U_2833,sK65(U_2833,U_2831,U_2829,U_2827,U_2825)))
& hBOOL(hAPP(hAPP(c_member(U_2825),sK65(U_2833,U_2831,U_2829,U_2827,U_2825)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2827,tc_fun(U_2825,tc_HOL_Obool)),U_2829),U_2831))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_2818,sK66(U_2834,U_2832,U_2830,U_2828,U_2826))],[f_668_4]) ).
fof(f_668_6,plain,
( ! [U_2834,U_2832,U_2830,U_2828,U_2826] :
( ! [U_2819] :
( hBOOL(hAPP(U_2834,U_2819))
| ~ hBOOL(hAPP(hAPP(c_member(U_2826),U_2819),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2830),U_2832))) )
| ( ~ hBOOL(hAPP(U_2834,sK67(U_2834,U_2832,U_2830,U_2828,U_2826)))
& hBOOL(hAPP(hAPP(c_member(U_2826),sK67(U_2834,U_2832,U_2830,U_2828,U_2826)),hAPP(U_2832,sK66(U_2834,U_2832,U_2830,U_2828,U_2826))))
& hBOOL(hAPP(hAPP(c_member(U_2828),sK66(U_2834,U_2832,U_2830,U_2828,U_2826)),U_2830)) ) )
& ! [U_2833,U_2831,U_2829,U_2827,U_2825] :
( ! [U_2816] :
( ! [U_2815] :
( hBOOL(hAPP(U_2833,U_2815))
| ~ hBOOL(hAPP(hAPP(c_member(U_2825),U_2815),hAPP(U_2831,U_2816))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2827),U_2816),U_2829)) )
| ( ~ hBOOL(hAPP(U_2833,sK65(U_2833,U_2831,U_2829,U_2827,U_2825)))
& hBOOL(hAPP(hAPP(c_member(U_2825),sK65(U_2833,U_2831,U_2829,U_2827,U_2825)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2827,tc_fun(U_2825,tc_HOL_Obool)),U_2829),U_2831))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_2817,sK67(U_2834,U_2832,U_2830,U_2828,U_2826))],[f_668_5]) ).
fof(f_668_7,plain,
( ! [U_2826,U_2828,U_2830,U_2832,U_2834] :
( ~ hBOOL(hAPP(U_2834,sK67(U_2834,U_2832,U_2830,U_2828,U_2826)))
| ~ sP182(U_2826,U_2828,U_2830,U_2832,U_2834) )
& ! [U_2826,U_2828,U_2830,U_2832,U_2834] :
( hBOOL(hAPP(hAPP(c_member(U_2826),sK67(U_2834,U_2832,U_2830,U_2828,U_2826)),hAPP(U_2832,sK66(U_2834,U_2832,U_2830,U_2828,U_2826))))
| ~ sP182(U_2826,U_2828,U_2830,U_2832,U_2834) )
& ! [U_2826,U_2828,U_2830,U_2832,U_2834] :
( hBOOL(hAPP(hAPP(c_member(U_2828),sK66(U_2834,U_2832,U_2830,U_2828,U_2826)),U_2830))
| ~ sP182(U_2826,U_2828,U_2830,U_2832,U_2834) )
& ! [U_2831,U_2825,U_2829,U_2827,U_2833] :
( ~ hBOOL(hAPP(U_2833,sK65(U_2833,U_2831,U_2829,U_2827,U_2825)))
| ~ sP181(U_2831,U_2825,U_2829,U_2827,U_2833) )
& ! [U_2831,U_2825,U_2829,U_2827,U_2833] :
( hBOOL(hAPP(hAPP(c_member(U_2825),sK65(U_2833,U_2831,U_2829,U_2827,U_2825)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2827,tc_fun(U_2825,tc_HOL_Obool)),U_2829),U_2831)))
| ~ sP181(U_2831,U_2825,U_2829,U_2827,U_2833) )
& ! [U_2826,U_2819,U_2828,U_2830,U_2832,U_2834] :
( hBOOL(hAPP(U_2834,U_2819))
| ~ hBOOL(hAPP(hAPP(c_member(U_2826),U_2819),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2830),U_2832)))
| sP182(U_2826,U_2828,U_2830,U_2832,U_2834) )
& ! [U_2831,U_2815,U_2816,U_2825,U_2829,U_2827,U_2833] :
( hBOOL(hAPP(U_2833,U_2815))
| ~ hBOOL(hAPP(hAPP(c_member(U_2825),U_2815),hAPP(U_2831,U_2816)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2827),U_2816),U_2829))
| sP181(U_2831,U_2825,U_2829,U_2827,U_2833) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181,sP182])],[f_668_6]) ).
cnf(f_668_8,plain,
( hBOOL(hAPP(U_2833,U_2815))
| ~ hBOOL(hAPP(hAPP(c_member(U_2825),U_2815),hAPP(U_2831,U_2816)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2827),U_2816),U_2829))
| sP181(U_2831,U_2825,U_2829,U_2827,U_2833) ),
inference(clausify,[status(thm)],[f_668_7]) ).
cnf(f_668_9,plain,
( hBOOL(hAPP(U_2834,U_2819))
| ~ hBOOL(hAPP(hAPP(c_member(U_2826),U_2819),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2830),U_2832)))
| sP182(U_2826,U_2828,U_2830,U_2832,U_2834) ),
inference(clausify,[status(thm)],[f_668_7]) ).
cnf(f_668_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_2825),sK65(U_2833,U_2831,U_2829,U_2827,U_2825)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2827,tc_fun(U_2825,tc_HOL_Obool)),U_2829),U_2831)))
| ~ sP181(U_2831,U_2825,U_2829,U_2827,U_2833) ),
inference(clausify,[status(thm)],[f_668_7]) ).
cnf(f_668_11,plain,
( ~ hBOOL(hAPP(U_2833,sK65(U_2833,U_2831,U_2829,U_2827,U_2825)))
| ~ sP181(U_2831,U_2825,U_2829,U_2827,U_2833) ),
inference(clausify,[status(thm)],[f_668_7]) ).
cnf(f_668_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_2828),sK66(U_2834,U_2832,U_2830,U_2828,U_2826)),U_2830))
| ~ sP182(U_2826,U_2828,U_2830,U_2832,U_2834) ),
inference(clausify,[status(thm)],[f_668_7]) ).
cnf(f_668_13,plain,
( hBOOL(hAPP(hAPP(c_member(U_2826),sK67(U_2834,U_2832,U_2830,U_2828,U_2826)),hAPP(U_2832,sK66(U_2834,U_2832,U_2830,U_2828,U_2826))))
| ~ sP182(U_2826,U_2828,U_2830,U_2832,U_2834) ),
inference(clausify,[status(thm)],[f_668_7]) ).
cnf(f_668_14,plain,
( ~ hBOOL(hAPP(U_2834,sK67(U_2834,U_2832,U_2830,U_2828,U_2826)))
| ~ sP182(U_2826,U_2828,U_2830,U_2832,U_2834) ),
inference(clausify,[status(thm)],[f_668_7]) ).
fof(f_669_1,plain,
! [V_A_2,T_b] :
( 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)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup]) ).
fof(f_669_2,plain,
! [U_2836,U_2835] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2835),c_Big__Operators_Olattice__class_OInf__fin(U_2835,U_2836)),c_Big__Operators_Olattice__class_OSup__fin(U_2835,U_2836)))
| U_2836 = c_Orderings_Obot__class_Obot(tc_fun(U_2835,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2835),U_2836))
| ~ class_Lattices_Olattice(U_2835) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
fof(f_669_3,plain,
! [U_2836,U_2835] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2835),c_Big__Operators_Olattice__class_OInf__fin(U_2835,U_2836)),c_Big__Operators_Olattice__class_OSup__fin(U_2835,U_2836)))
| U_2836 = c_Orderings_Obot__class_Obot(tc_fun(U_2835,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2835),U_2836))
| ~ class_Lattices_Olattice(U_2835) ),
inference(definitional_conversion,[status(esa)],[f_669_2]) ).
cnf(f_669_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2835),c_Big__Operators_Olattice__class_OInf__fin(U_2835,U_2836)),c_Big__Operators_Olattice__class_OSup__fin(U_2835,U_2836)))
| U_2836 = c_Orderings_Obot__class_Obot(tc_fun(U_2835,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2835),U_2836))
| ~ class_Lattices_Olattice(U_2835) ),
inference(clausify,[status(thm)],[f_669_3]) ).
fof(f_670_1,plain,
! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty]) ).
fof(f_670_2,plain,
! [U_2842,U_2841,U_2840,U_2839,U_2838,U_2837] :
( hAPP(U_2842,c_Orderings_Obot__class_Obot(tc_fun(U_2838,tc_HOL_Obool))) = U_2840
| ~ c_Finite__Set_Ofolding__image__simple(U_2837,U_2838,U_2839,U_2840,U_2841,U_2842) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
fof(f_670_3,plain,
! [U_2842,U_2841,U_2840,U_2839,U_2838] :
( ! [U_2837] : ~ c_Finite__Set_Ofolding__image__simple(U_2837,U_2838,U_2839,U_2840,U_2841,U_2842)
| hAPP(U_2842,c_Orderings_Obot__class_Obot(tc_fun(U_2838,tc_HOL_Obool))) = U_2840 ),
inference(miniscope,[status(thm)],[f_670_2]) ).
fof(f_670_4,plain,
! [U_2840,U_2839,U_2841,U_2842,U_2838,U_2837] :
( ~ c_Finite__Set_Ofolding__image__simple(U_2837,U_2838,U_2839,U_2840,U_2841,U_2842)
| hAPP(U_2842,c_Orderings_Obot__class_Obot(tc_fun(U_2838,tc_HOL_Obool))) = U_2840 ),
inference(definitional_conversion,[status(esa)],[f_670_3]) ).
cnf(f_670_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_2837,U_2838,U_2839,U_2840,U_2841,U_2842)
| hAPP(U_2842,c_Orderings_Obot__class_Obot(tc_fun(U_2838,tc_HOL_Obool))) = U_2840 ),
inference(clausify,[status(thm)],[f_670_4]) ).
fof(f_671_1,plain,
! [V_x_2,T_b] :
( 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
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton]) ).
fof(f_671_2,plain,
! [U_2844,U_2843] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2843,hAPP(hAPP(c_Set_Oinsert(U_2843),U_2844),c_Orderings_Obot__class_Obot(tc_fun(U_2843,tc_HOL_Obool)))) = U_2844
| ~ class_Lattices_Olattice(U_2843) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
fof(f_671_3,plain,
! [U_2843,U_2844] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2843,hAPP(hAPP(c_Set_Oinsert(U_2843),U_2844),c_Orderings_Obot__class_Obot(tc_fun(U_2843,tc_HOL_Obool)))) = U_2844
| ~ class_Lattices_Olattice(U_2843) ),
inference(definitional_conversion,[status(esa)],[f_671_2]) ).
cnf(f_671_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2843,hAPP(hAPP(c_Set_Oinsert(U_2843),U_2844),c_Orderings_Obot__class_Obot(tc_fun(U_2843,tc_HOL_Obool)))) = U_2844
| ~ class_Lattices_Olattice(U_2843) ),
inference(clausify,[status(thm)],[f_671_3]) ).
fof(f_672_1,plain,
! [V_x_2,T_b] :
( 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
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton]) ).
fof(f_672_2,plain,
! [U_2846,U_2845] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2845,hAPP(hAPP(c_Set_Oinsert(U_2845),U_2846),c_Orderings_Obot__class_Obot(tc_fun(U_2845,tc_HOL_Obool)))) = U_2846
| ~ class_Lattices_Olattice(U_2845) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
! [U_2845,U_2846] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2845,hAPP(hAPP(c_Set_Oinsert(U_2845),U_2846),c_Orderings_Obot__class_Obot(tc_fun(U_2845,tc_HOL_Obool)))) = U_2846
| ~ class_Lattices_Olattice(U_2845) ),
inference(definitional_conversion,[status(esa)],[f_672_2]) ).
cnf(f_672_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2845,hAPP(hAPP(c_Set_Oinsert(U_2845),U_2846),c_Orderings_Obot__class_Obot(tc_fun(U_2845,tc_HOL_Obool)))) = U_2846
| ~ class_Lattices_Olattice(U_2845) ),
inference(clausify,[status(thm)],[f_672_3]) ).
fof(f_673_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem]) ).
fof(f_673_2,plain,
! [U_2849,U_2848,U_2847] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2849),c_Big__Operators_Olattice__class_OSup__fin(U_2847,U_2848)) = c_Big__Operators_Olattice__class_OSup__fin(U_2847,U_2848)
| ~ hBOOL(hAPP(hAPP(c_member(U_2847),U_2849),U_2848))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2847),U_2848))
| ~ class_Lattices_Olattice(U_2847) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
fof(f_673_3,plain,
! [U_2847,U_2848,U_2849] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2849),c_Big__Operators_Olattice__class_OSup__fin(U_2847,U_2848)) = c_Big__Operators_Olattice__class_OSup__fin(U_2847,U_2848)
| ~ hBOOL(hAPP(hAPP(c_member(U_2847),U_2849),U_2848))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2847),U_2848))
| ~ class_Lattices_Olattice(U_2847) ),
inference(definitional_conversion,[status(esa)],[f_673_2]) ).
cnf(f_673_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2849),c_Big__Operators_Olattice__class_OSup__fin(U_2847,U_2848)) = c_Big__Operators_Olattice__class_OSup__fin(U_2847,U_2848)
| ~ hBOOL(hAPP(hAPP(c_member(U_2847),U_2849),U_2848))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2847),U_2848))
| ~ class_Lattices_Olattice(U_2847) ),
inference(clausify,[status(thm)],[f_673_3]) ).
fof(f_674_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb]) ).
fof(f_674_2,plain,
! [U_2852,U_2851,U_2850] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2852),c_Big__Operators_Olattice__class_OInf__fin(U_2850,U_2851)) = U_2852
| ~ hBOOL(hAPP(hAPP(c_member(U_2850),U_2852),U_2851))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2850),U_2851))
| ~ class_Lattices_Olattice(U_2850) ),
inference(variable_rename,[status(thm)],[f_674_1]) ).
fof(f_674_3,plain,
! [U_2850,U_2851,U_2852] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2852),c_Big__Operators_Olattice__class_OInf__fin(U_2850,U_2851)) = U_2852
| ~ hBOOL(hAPP(hAPP(c_member(U_2850),U_2852),U_2851))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2850),U_2851))
| ~ class_Lattices_Olattice(U_2850) ),
inference(definitional_conversion,[status(esa)],[f_674_2]) ).
cnf(f_674_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2852),c_Big__Operators_Olattice__class_OInf__fin(U_2850,U_2851)) = U_2852
| ~ hBOOL(hAPP(hAPP(c_member(U_2850),U_2852),U_2851))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2850),U_2851))
| ~ class_Lattices_Olattice(U_2850) ),
inference(clausify,[status(thm)],[f_674_3]) ).
fof(f_675_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem]) ).
fof(f_675_2,plain,
! [U_2855,U_2854,U_2853] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2853),U_2855),c_Big__Operators_Olattice__class_OInf__fin(U_2853,U_2854)) = c_Big__Operators_Olattice__class_OInf__fin(U_2853,U_2854)
| ~ hBOOL(hAPP(hAPP(c_member(U_2853),U_2855),U_2854))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2853),U_2854))
| ~ class_Lattices_Olattice(U_2853) ),
inference(variable_rename,[status(thm)],[f_675_1]) ).
fof(f_675_3,plain,
! [U_2853,U_2854,U_2855] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2853),U_2855),c_Big__Operators_Olattice__class_OInf__fin(U_2853,U_2854)) = c_Big__Operators_Olattice__class_OInf__fin(U_2853,U_2854)
| ~ hBOOL(hAPP(hAPP(c_member(U_2853),U_2855),U_2854))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2853),U_2854))
| ~ class_Lattices_Olattice(U_2853) ),
inference(definitional_conversion,[status(esa)],[f_675_2]) ).
cnf(f_675_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2853),U_2855),c_Big__Operators_Olattice__class_OInf__fin(U_2853,U_2854)) = c_Big__Operators_Olattice__class_OInf__fin(U_2853,U_2854)
| ~ hBOOL(hAPP(hAPP(c_member(U_2853),U_2855),U_2854))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2853),U_2854))
| ~ class_Lattices_Olattice(U_2853) ),
inference(clausify,[status(thm)],[f_675_3]) ).
fof(f_676_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb]) ).
fof(f_676_2,plain,
! [U_2858,U_2857,U_2856] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2856),U_2858),c_Big__Operators_Olattice__class_OSup__fin(U_2856,U_2857)) = U_2858
| ~ hBOOL(hAPP(hAPP(c_member(U_2856),U_2858),U_2857))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2856),U_2857))
| ~ class_Lattices_Olattice(U_2856) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
fof(f_676_3,plain,
! [U_2856,U_2857,U_2858] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2856),U_2858),c_Big__Operators_Olattice__class_OSup__fin(U_2856,U_2857)) = U_2858
| ~ hBOOL(hAPP(hAPP(c_member(U_2856),U_2858),U_2857))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2856),U_2857))
| ~ class_Lattices_Olattice(U_2856) ),
inference(definitional_conversion,[status(esa)],[f_676_2]) ).
cnf(f_676_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2856),U_2858),c_Big__Operators_Olattice__class_OSup__fin(U_2856,U_2857)) = U_2858
| ~ hBOOL(hAPP(hAPP(c_member(U_2856),U_2858),U_2857))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2856),U_2857))
| ~ class_Lattices_Olattice(U_2856) ),
inference(clausify,[status(thm)],[f_676_3]) ).
fof(f_677_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup]) ).
fof(f_677_2,plain,
! [U_2860,U_2859] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2859,U_2860) = c_Complete__Lattice_OSup__class_OSup(U_2859,U_2860)
| U_2860 = c_Orderings_Obot__class_Obot(tc_fun(U_2859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2859),U_2860))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2859) ),
inference(variable_rename,[status(thm)],[f_677_1]) ).
fof(f_677_3,plain,
! [U_2859,U_2860] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2859,U_2860) = c_Complete__Lattice_OSup__class_OSup(U_2859,U_2860)
| U_2860 = c_Orderings_Obot__class_Obot(tc_fun(U_2859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2859),U_2860))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2859) ),
inference(definitional_conversion,[status(esa)],[f_677_2]) ).
cnf(f_677_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2859,U_2860) = c_Complete__Lattice_OSup__class_OSup(U_2859,U_2860)
| U_2860 = c_Orderings_Obot__class_Obot(tc_fun(U_2859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2859),U_2860))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2859) ),
inference(clausify,[status(thm)],[f_677_3]) ).
fof(f_678_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf]) ).
fof(f_678_2,plain,
! [U_2862,U_2861] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2861,U_2862) = c_Complete__Lattice_OInf__class_OInf(U_2861,U_2862)
| U_2862 = c_Orderings_Obot__class_Obot(tc_fun(U_2861,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2861),U_2862))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2861) ),
inference(variable_rename,[status(thm)],[f_678_1]) ).
fof(f_678_3,plain,
! [U_2861,U_2862] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2861,U_2862) = c_Complete__Lattice_OInf__class_OInf(U_2861,U_2862)
| U_2862 = c_Orderings_Obot__class_Obot(tc_fun(U_2861,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2861),U_2862))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2861) ),
inference(definitional_conversion,[status(esa)],[f_678_2]) ).
cnf(f_678_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2861,U_2862) = c_Complete__Lattice_OInf__class_OInf(U_2861,U_2862)
| U_2862 = c_Orderings_Obot__class_Obot(tc_fun(U_2861,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2861),U_2862))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2861) ),
inference(clausify,[status(thm)],[f_678_3]) ).
fof(f_679_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem]) ).
fof(f_679_2,plain,
! [U_2867,U_2866,U_2865,U_2864,U_2863] :
( hAPP(hAPP(U_2864,U_2867),hAPP(U_2865,U_2866)) = hAPP(U_2865,U_2866)
| ~ hBOOL(hAPP(hAPP(c_member(U_2863),U_2867),U_2866))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2863),U_2866))
| ~ c_Finite__Set_Ofolding__one__idem(U_2863,U_2864,U_2865) ),
inference(variable_rename,[status(thm)],[f_679_1]) ).
fof(f_679_3,plain,
! [U_2863,U_2864,U_2865,U_2866,U_2867] :
( hAPP(hAPP(U_2864,U_2867),hAPP(U_2865,U_2866)) = hAPP(U_2865,U_2866)
| ~ hBOOL(hAPP(hAPP(c_member(U_2863),U_2867),U_2866))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2863),U_2866))
| ~ c_Finite__Set_Ofolding__one__idem(U_2863,U_2864,U_2865) ),
inference(definitional_conversion,[status(esa)],[f_679_2]) ).
cnf(f_679_4,plain,
( hAPP(hAPP(U_2864,U_2867),hAPP(U_2865,U_2866)) = hAPP(U_2865,U_2866)
| ~ hBOOL(hAPP(hAPP(c_member(U_2863),U_2867),U_2866))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2863),U_2866))
| ~ c_Finite__Set_Ofolding__one__idem(U_2863,U_2864,U_2865) ),
inference(clausify,[status(thm)],[f_679_3]) ).
fof(f_680_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem]) ).
fof(f_680_2,plain,
! [U_2870,U_2869,U_2868] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2868,hAPP(hAPP(c_Set_Oinsert(U_2868),U_2870),U_2869)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2870),c_Big__Operators_Olattice__class_OSup__fin(U_2868,U_2869))
| U_2869 = c_Orderings_Obot__class_Obot(tc_fun(U_2868,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2868),U_2869))
| ~ class_Lattices_Olattice(U_2868) ),
inference(variable_rename,[status(thm)],[f_680_1]) ).
fof(f_680_3,plain,
! [U_2868,U_2869,U_2870] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2868,hAPP(hAPP(c_Set_Oinsert(U_2868),U_2870),U_2869)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2870),c_Big__Operators_Olattice__class_OSup__fin(U_2868,U_2869))
| U_2869 = c_Orderings_Obot__class_Obot(tc_fun(U_2868,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2868),U_2869))
| ~ class_Lattices_Olattice(U_2868) ),
inference(definitional_conversion,[status(esa)],[f_680_2]) ).
cnf(f_680_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2868,hAPP(hAPP(c_Set_Oinsert(U_2868),U_2870),U_2869)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2870),c_Big__Operators_Olattice__class_OSup__fin(U_2868,U_2869))
| U_2869 = c_Orderings_Obot__class_Obot(tc_fun(U_2868,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2868),U_2869))
| ~ class_Lattices_Olattice(U_2868) ),
inference(clausify,[status(thm)],[f_680_3]) ).
fof(f_681_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem]) ).
fof(f_681_2,plain,
! [U_2873,U_2872,U_2871] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2871,hAPP(hAPP(c_Set_Oinsert(U_2871),U_2873),U_2872)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2871),U_2873),c_Big__Operators_Olattice__class_OInf__fin(U_2871,U_2872))
| U_2872 = c_Orderings_Obot__class_Obot(tc_fun(U_2871,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2871),U_2872))
| ~ class_Lattices_Olattice(U_2871) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
! [U_2871,U_2872,U_2873] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2871,hAPP(hAPP(c_Set_Oinsert(U_2871),U_2873),U_2872)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2871),U_2873),c_Big__Operators_Olattice__class_OInf__fin(U_2871,U_2872))
| U_2872 = c_Orderings_Obot__class_Obot(tc_fun(U_2871,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2871),U_2872))
| ~ class_Lattices_Olattice(U_2871) ),
inference(definitional_conversion,[status(esa)],[f_681_2]) ).
cnf(f_681_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2871,hAPP(hAPP(c_Set_Oinsert(U_2871),U_2873),U_2872)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2871),U_2873),c_Big__Operators_Olattice__class_OInf__fin(U_2871,U_2872))
| U_2872 = c_Orderings_Obot__class_Obot(tc_fun(U_2871,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2871),U_2872))
| ~ class_Lattices_Olattice(U_2871) ),
inference(clausify,[status(thm)],[f_681_3]) ).
fof(f_682_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem]) ).
fof(f_682_2,plain,
! [U_2876,U_2875,U_2874] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2874),c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2876)),c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2875)) = c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2875)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2874,tc_HOL_Obool)),U_2876),U_2875))
| U_2876 = c_Orderings_Obot__class_Obot(tc_fun(U_2874,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2874),U_2875))
| ~ class_Lattices_Olattice(U_2874) ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
fof(f_682_3,plain,
! [U_2874,U_2875,U_2876] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2874),c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2876)),c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2875)) = c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2875)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2874,tc_HOL_Obool)),U_2876),U_2875))
| U_2876 = c_Orderings_Obot__class_Obot(tc_fun(U_2874,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2874),U_2875))
| ~ class_Lattices_Olattice(U_2874) ),
inference(definitional_conversion,[status(esa)],[f_682_2]) ).
cnf(f_682_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2874),c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2876)),c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2875)) = c_Big__Operators_Olattice__class_OSup__fin(U_2874,U_2875)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2874,tc_HOL_Obool)),U_2876),U_2875))
| U_2876 = c_Orderings_Obot__class_Obot(tc_fun(U_2874,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2874),U_2875))
| ~ class_Lattices_Olattice(U_2874) ),
inference(clausify,[status(thm)],[f_682_3]) ).
fof(f_683_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem]) ).
fof(f_683_2,plain,
! [U_2879,U_2878,U_2877] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2877),c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2879)),c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2878)) = c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2878)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2877,tc_HOL_Obool)),U_2879),U_2878))
| U_2879 = c_Orderings_Obot__class_Obot(tc_fun(U_2877,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2877),U_2878))
| ~ class_Lattices_Olattice(U_2877) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
fof(f_683_3,plain,
! [U_2877,U_2878,U_2879] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2877),c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2879)),c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2878)) = c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2878)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2877,tc_HOL_Obool)),U_2879),U_2878))
| U_2879 = c_Orderings_Obot__class_Obot(tc_fun(U_2877,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2877),U_2878))
| ~ class_Lattices_Olattice(U_2877) ),
inference(definitional_conversion,[status(esa)],[f_683_2]) ).
cnf(f_683_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2877),c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2879)),c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2878)) = c_Big__Operators_Olattice__class_OInf__fin(U_2877,U_2878)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2877,tc_HOL_Obool)),U_2879),U_2878))
| U_2879 = c_Orderings_Obot__class_Obot(tc_fun(U_2877,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2877),U_2878))
| ~ class_Lattices_Olattice(U_2877) ),
inference(clausify,[status(thm)],[f_683_3]) ).
fof(f_684_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem]) ).
fof(f_684_2,plain,
! [U_2882,U_2881,U_2880] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2880,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2880,tc_HOL_Obool)),U_2881),U_2882)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2880),c_Big__Operators_Olattice__class_OSup__fin(U_2880,U_2881)),c_Big__Operators_Olattice__class_OSup__fin(U_2880,U_2882))
| U_2882 = c_Orderings_Obot__class_Obot(tc_fun(U_2880,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2880),U_2882))
| U_2881 = c_Orderings_Obot__class_Obot(tc_fun(U_2880,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2880),U_2881))
| ~ class_Lattices_Olattice(U_2880) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
fof(f_684_3,plain,
! [U_2880,U_2881,U_2882] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2880,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2880,tc_HOL_Obool)),U_2881),U_2882)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2880),c_Big__Operators_Olattice__class_OSup__fin(U_2880,U_2881)),c_Big__Operators_Olattice__class_OSup__fin(U_2880,U_2882))
| U_2882 = c_Orderings_Obot__class_Obot(tc_fun(U_2880,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2880),U_2882))
| U_2881 = c_Orderings_Obot__class_Obot(tc_fun(U_2880,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2880),U_2881))
| ~ class_Lattices_Olattice(U_2880) ),
inference(definitional_conversion,[status(esa)],[f_684_2]) ).
cnf(f_684_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2880,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2880,tc_HOL_Obool)),U_2881),U_2882)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2880),c_Big__Operators_Olattice__class_OSup__fin(U_2880,U_2881)),c_Big__Operators_Olattice__class_OSup__fin(U_2880,U_2882))
| U_2882 = c_Orderings_Obot__class_Obot(tc_fun(U_2880,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2880),U_2882))
| U_2881 = c_Orderings_Obot__class_Obot(tc_fun(U_2880,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2880),U_2881))
| ~ class_Lattices_Olattice(U_2880) ),
inference(clausify,[status(thm)],[f_684_3]) ).
fof(f_685_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem]) ).
fof(f_685_2,plain,
! [U_2885,U_2884,U_2883] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2883,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2883,tc_HOL_Obool)),U_2884),U_2885)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2883),c_Big__Operators_Olattice__class_OInf__fin(U_2883,U_2884)),c_Big__Operators_Olattice__class_OInf__fin(U_2883,U_2885))
| U_2885 = c_Orderings_Obot__class_Obot(tc_fun(U_2883,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2883),U_2885))
| U_2884 = c_Orderings_Obot__class_Obot(tc_fun(U_2883,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2883),U_2884))
| ~ class_Lattices_Olattice(U_2883) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
fof(f_685_3,plain,
! [U_2883,U_2884,U_2885] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2883,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2883,tc_HOL_Obool)),U_2884),U_2885)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2883),c_Big__Operators_Olattice__class_OInf__fin(U_2883,U_2884)),c_Big__Operators_Olattice__class_OInf__fin(U_2883,U_2885))
| U_2885 = c_Orderings_Obot__class_Obot(tc_fun(U_2883,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2883),U_2885))
| U_2884 = c_Orderings_Obot__class_Obot(tc_fun(U_2883,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2883),U_2884))
| ~ class_Lattices_Olattice(U_2883) ),
inference(definitional_conversion,[status(esa)],[f_685_2]) ).
cnf(f_685_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2883,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2883,tc_HOL_Obool)),U_2884),U_2885)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2883),c_Big__Operators_Olattice__class_OInf__fin(U_2883,U_2884)),c_Big__Operators_Olattice__class_OInf__fin(U_2883,U_2885))
| U_2885 = c_Orderings_Obot__class_Obot(tc_fun(U_2883,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2883),U_2885))
| U_2884 = c_Orderings_Obot__class_Obot(tc_fun(U_2883,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2883),U_2884))
| ~ class_Lattices_Olattice(U_2883) ),
inference(clausify,[status(thm)],[f_685_3]) ).
fof(f_686_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(f_686_2,plain,
! [U_2893,U_2892,U_2891,U_2890,U_2889,U_2888,U_2887,U_2886] :
( hAPP(U_2891,hAPP(hAPP(c_Set_Oinsert(U_2887),U_2893),U_2892)) = hAPP(hAPP(U_2888,hAPP(U_2890,U_2893)),hAPP(U_2891,U_2892))
| hBOOL(hAPP(hAPP(c_member(U_2887),U_2893),U_2892))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2887),U_2892))
| ~ c_Finite__Set_Ofolding__image__simple(U_2886,U_2887,U_2888,U_2889,U_2890,U_2891) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
fof(f_686_3,plain,
! [U_2893,U_2892,U_2891,U_2890,U_2889,U_2888,U_2887] :
( ! [U_2886] : ~ c_Finite__Set_Ofolding__image__simple(U_2886,U_2887,U_2888,U_2889,U_2890,U_2891)
| hAPP(U_2891,hAPP(hAPP(c_Set_Oinsert(U_2887),U_2893),U_2892)) = hAPP(hAPP(U_2888,hAPP(U_2890,U_2893)),hAPP(U_2891,U_2892))
| hBOOL(hAPP(hAPP(c_member(U_2887),U_2893),U_2892))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2887),U_2892)) ),
inference(miniscope,[status(thm)],[f_686_2]) ).
fof(f_686_4,plain,
! [U_2887,U_2886,U_2888,U_2890,U_2892,U_2891,U_2889,U_2893] :
( ~ c_Finite__Set_Ofolding__image__simple(U_2886,U_2887,U_2888,U_2889,U_2890,U_2891)
| hAPP(U_2891,hAPP(hAPP(c_Set_Oinsert(U_2887),U_2893),U_2892)) = hAPP(hAPP(U_2888,hAPP(U_2890,U_2893)),hAPP(U_2891,U_2892))
| hBOOL(hAPP(hAPP(c_member(U_2887),U_2893),U_2892))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2887),U_2892)) ),
inference(definitional_conversion,[status(esa)],[f_686_3]) ).
cnf(f_686_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_2886,U_2887,U_2888,U_2889,U_2890,U_2891)
| hAPP(U_2891,hAPP(hAPP(c_Set_Oinsert(U_2887),U_2893),U_2892)) = hAPP(hAPP(U_2888,hAPP(U_2890,U_2893)),hAPP(U_2891,U_2892))
| hBOOL(hAPP(hAPP(c_member(U_2887),U_2893),U_2892))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2887),U_2892)) ),
inference(clausify,[status(thm)],[f_686_4]) ).
fof(f_687_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter]) ).
fof(f_687_2,plain,
! [U_2901,U_2900,U_2899,U_2898,U_2897,U_2896,U_2895,U_2894] :
( hAPP(hAPP(U_2896,hAPP(U_2899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2895,tc_HOL_Obool)),U_2900),U_2901))),hAPP(U_2899,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2895,tc_HOL_Obool)),U_2900),U_2901))) = hAPP(hAPP(U_2896,hAPP(U_2899,U_2900)),hAPP(U_2899,U_2901))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2895),U_2901))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2895),U_2900))
| ~ c_Finite__Set_Ofolding__image__simple(U_2894,U_2895,U_2896,U_2897,U_2898,U_2899) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
fof(f_687_3,plain,
! [U_2901,U_2900,U_2899,U_2898,U_2897,U_2896,U_2895] :
( ! [U_2894] : ~ c_Finite__Set_Ofolding__image__simple(U_2894,U_2895,U_2896,U_2897,U_2898,U_2899)
| hAPP(hAPP(U_2896,hAPP(U_2899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2895,tc_HOL_Obool)),U_2900),U_2901))),hAPP(U_2899,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2895,tc_HOL_Obool)),U_2900),U_2901))) = hAPP(hAPP(U_2896,hAPP(U_2899,U_2900)),hAPP(U_2899,U_2901))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2895),U_2901))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2895),U_2900)) ),
inference(miniscope,[status(thm)],[f_687_2]) ).
fof(f_687_4,plain,
! [U_2894,U_2895,U_2896,U_2897,U_2898,U_2899,U_2900,U_2901] :
( ~ c_Finite__Set_Ofolding__image__simple(U_2894,U_2895,U_2896,U_2897,U_2898,U_2899)
| hAPP(hAPP(U_2896,hAPP(U_2899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2895,tc_HOL_Obool)),U_2900),U_2901))),hAPP(U_2899,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2895,tc_HOL_Obool)),U_2900),U_2901))) = hAPP(hAPP(U_2896,hAPP(U_2899,U_2900)),hAPP(U_2899,U_2901))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2895),U_2901))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2895),U_2900)) ),
inference(definitional_conversion,[status(esa)],[f_687_3]) ).
cnf(f_687_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_2894,U_2895,U_2896,U_2897,U_2898,U_2899)
| hAPP(hAPP(U_2896,hAPP(U_2899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2895,tc_HOL_Obool)),U_2900),U_2901))),hAPP(U_2899,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2895,tc_HOL_Obool)),U_2900),U_2901))) = hAPP(hAPP(U_2896,hAPP(U_2899,U_2900)),hAPP(U_2899,U_2901))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2895),U_2901))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2895),U_2900)) ),
inference(clausify,[status(thm)],[f_687_4]) ).
fof(f_688_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert]) ).
fof(f_688_2,plain,
! [U_2904,U_2903,U_2902] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2902,hAPP(hAPP(c_Set_Oinsert(U_2902),U_2904),U_2903)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2902),U_2904),c_Big__Operators_Olattice__class_OSup__fin(U_2902,U_2903))
| U_2903 = c_Orderings_Obot__class_Obot(tc_fun(U_2902,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2902),U_2904),U_2903))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2902),U_2903))
| ~ class_Lattices_Olattice(U_2902) ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
fof(f_688_3,plain,
! [U_2902,U_2903,U_2904] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2902,hAPP(hAPP(c_Set_Oinsert(U_2902),U_2904),U_2903)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2902),U_2904),c_Big__Operators_Olattice__class_OSup__fin(U_2902,U_2903))
| U_2903 = c_Orderings_Obot__class_Obot(tc_fun(U_2902,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2902),U_2904),U_2903))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2902),U_2903))
| ~ class_Lattices_Olattice(U_2902) ),
inference(definitional_conversion,[status(esa)],[f_688_2]) ).
cnf(f_688_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2902,hAPP(hAPP(c_Set_Oinsert(U_2902),U_2904),U_2903)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2902),U_2904),c_Big__Operators_Olattice__class_OSup__fin(U_2902,U_2903))
| U_2903 = c_Orderings_Obot__class_Obot(tc_fun(U_2902,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2902),U_2904),U_2903))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2902),U_2903))
| ~ class_Lattices_Olattice(U_2902) ),
inference(clausify,[status(thm)],[f_688_3]) ).
fof(f_689_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert]) ).
fof(f_689_2,plain,
! [U_2907,U_2906,U_2905] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2905,hAPP(hAPP(c_Set_Oinsert(U_2905),U_2907),U_2906)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2905),U_2907),c_Big__Operators_Olattice__class_OInf__fin(U_2905,U_2906))
| U_2906 = c_Orderings_Obot__class_Obot(tc_fun(U_2905,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2905),U_2907),U_2906))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2905),U_2906))
| ~ class_Lattices_Olattice(U_2905) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
fof(f_689_3,plain,
! [U_2905,U_2906,U_2907] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2905,hAPP(hAPP(c_Set_Oinsert(U_2905),U_2907),U_2906)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2905),U_2907),c_Big__Operators_Olattice__class_OInf__fin(U_2905,U_2906))
| U_2906 = c_Orderings_Obot__class_Obot(tc_fun(U_2905,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2905),U_2907),U_2906))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2905),U_2906))
| ~ class_Lattices_Olattice(U_2905) ),
inference(definitional_conversion,[status(esa)],[f_689_2]) ).
cnf(f_689_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2905,hAPP(hAPP(c_Set_Oinsert(U_2905),U_2907),U_2906)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2905),U_2907),c_Big__Operators_Olattice__class_OInf__fin(U_2905,U_2906))
| U_2906 = c_Orderings_Obot__class_Obot(tc_fun(U_2905,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2905),U_2907),U_2906))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2905),U_2906))
| ~ class_Lattices_Olattice(U_2905) ),
inference(clausify,[status(thm)],[f_689_3]) ).
fof(f_690_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( 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
| 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)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove]) ).
fof(f_690_2,plain,
! [U_2910,U_2909,U_2908] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),U_2909)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2908),U_2910),c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),U_2909)) = U_2910
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2908),U_2909))
| ~ class_Lattices_Olattice(U_2908) ),
inference(variable_rename,[status(thm)],[f_690_1]) ).
fof(f_690_3,plain,
( ! [U_2908,U_2910,U_2909] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),U_2909)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2908),U_2910),c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool))
| ~ sP183(U_2908,U_2910,U_2909) )
& ! [U_2908,U_2910,U_2909] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),U_2909)) = U_2910
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool))
| ~ sP183(U_2908,U_2910,U_2909) )
& ! [U_2908,U_2910,U_2909] :
( sP183(U_2908,U_2910,U_2909)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2908),U_2909))
| ~ class_Lattices_Olattice(U_2908) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_690_2]) ).
cnf(f_690_4,plain,
( sP183(U_2908,U_2910,U_2909)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2908),U_2909))
| ~ class_Lattices_Olattice(U_2908) ),
inference(clausify,[status(thm)],[f_690_3]) ).
cnf(f_690_5,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),U_2909)) = U_2910
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool))
| ~ sP183(U_2908,U_2910,U_2909) ),
inference(clausify,[status(thm)],[f_690_3]) ).
cnf(f_690_6,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),U_2909)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2908),U_2910),c_Big__Operators_Olattice__class_OSup__fin(U_2908,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2908,tc_HOL_Obool)),U_2909),hAPP(hAPP(c_Set_Oinsert(U_2908),U_2910),c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2908,tc_HOL_Obool))
| ~ sP183(U_2908,U_2910,U_2909) ),
inference(clausify,[status(thm)],[f_690_3]) ).
fof(f_691_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( 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
| 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)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove]) ).
fof(f_691_2,plain,
! [U_2913,U_2912,U_2911] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),U_2912)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2911),U_2913),c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),U_2912)) = U_2913
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2911),U_2912))
| ~ class_Lattices_Olattice(U_2911) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
fof(f_691_3,plain,
( ! [U_2911,U_2912,U_2913] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),U_2912)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2911),U_2913),c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool))
| ~ sP184(U_2911,U_2912,U_2913) )
& ! [U_2911,U_2912,U_2913] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),U_2912)) = U_2913
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool))
| ~ sP184(U_2911,U_2912,U_2913) )
& ! [U_2911,U_2912,U_2913] :
( sP184(U_2911,U_2912,U_2913)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2911),U_2912))
| ~ class_Lattices_Olattice(U_2911) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_691_2]) ).
cnf(f_691_4,plain,
( sP184(U_2911,U_2912,U_2913)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2911),U_2912))
| ~ class_Lattices_Olattice(U_2911) ),
inference(clausify,[status(thm)],[f_691_3]) ).
cnf(f_691_5,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),U_2912)) = U_2913
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool))
| ~ sP184(U_2911,U_2912,U_2913) ),
inference(clausify,[status(thm)],[f_691_3]) ).
cnf(f_691_6,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),U_2912)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2911),U_2913),c_Big__Operators_Olattice__class_OInf__fin(U_2911,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2911,tc_HOL_Obool)),U_2912),hAPP(hAPP(c_Set_Oinsert(U_2911),U_2913),c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2911,tc_HOL_Obool))
| ~ sP184(U_2911,U_2912,U_2913) ),
inference(clausify,[status(thm)],[f_691_3]) ).
fof(f_692_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter]) ).
fof(f_692_2,plain,
! [U_2916,U_2915,U_2914] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2914),c_Big__Operators_Olattice__class_OSup__fin(U_2914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916))),c_Big__Operators_Olattice__class_OSup__fin(U_2914,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2914),c_Big__Operators_Olattice__class_OSup__fin(U_2914,U_2915)),c_Big__Operators_Olattice__class_OSup__fin(U_2914,U_2916))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916) = c_Orderings_Obot__class_Obot(tc_fun(U_2914,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2914),U_2916))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2914),U_2915))
| ~ class_Lattices_Olattice(U_2914) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
! [U_2914,U_2915,U_2916] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2914),c_Big__Operators_Olattice__class_OSup__fin(U_2914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916))),c_Big__Operators_Olattice__class_OSup__fin(U_2914,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2914),c_Big__Operators_Olattice__class_OSup__fin(U_2914,U_2915)),c_Big__Operators_Olattice__class_OSup__fin(U_2914,U_2916))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916) = c_Orderings_Obot__class_Obot(tc_fun(U_2914,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2914),U_2916))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2914),U_2915))
| ~ class_Lattices_Olattice(U_2914) ),
inference(definitional_conversion,[status(esa)],[f_692_2]) ).
cnf(f_692_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2914),c_Big__Operators_Olattice__class_OSup__fin(U_2914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916))),c_Big__Operators_Olattice__class_OSup__fin(U_2914,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2914),c_Big__Operators_Olattice__class_OSup__fin(U_2914,U_2915)),c_Big__Operators_Olattice__class_OSup__fin(U_2914,U_2916))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2914,tc_HOL_Obool)),U_2915),U_2916) = c_Orderings_Obot__class_Obot(tc_fun(U_2914,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2914),U_2916))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2914),U_2915))
| ~ class_Lattices_Olattice(U_2914) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint]) ).
fof(f_693_2,plain,
! [U_2919,U_2918,U_2917] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2917,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2917,tc_HOL_Obool)),U_2918),U_2919)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2917),c_Big__Operators_Olattice__class_OSup__fin(U_2917,U_2918)),c_Big__Operators_Olattice__class_OSup__fin(U_2917,U_2919))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2917,tc_HOL_Obool)),U_2918),U_2919) != c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| U_2919 = c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2917),U_2919))
| U_2918 = c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2917),U_2918))
| ~ class_Lattices_Olattice(U_2917) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
fof(f_693_3,plain,
! [U_2917,U_2918,U_2919] :
( c_Big__Operators_Olattice__class_OSup__fin(U_2917,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2917,tc_HOL_Obool)),U_2918),U_2919)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2917),c_Big__Operators_Olattice__class_OSup__fin(U_2917,U_2918)),c_Big__Operators_Olattice__class_OSup__fin(U_2917,U_2919))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2917,tc_HOL_Obool)),U_2918),U_2919) != c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| U_2919 = c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2917),U_2919))
| U_2918 = c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2917),U_2918))
| ~ class_Lattices_Olattice(U_2917) ),
inference(definitional_conversion,[status(esa)],[f_693_2]) ).
cnf(f_693_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_2917,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2917,tc_HOL_Obool)),U_2918),U_2919)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2917),c_Big__Operators_Olattice__class_OSup__fin(U_2917,U_2918)),c_Big__Operators_Olattice__class_OSup__fin(U_2917,U_2919))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2917,tc_HOL_Obool)),U_2918),U_2919) != c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| U_2919 = c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2917),U_2919))
| U_2918 = c_Orderings_Obot__class_Obot(tc_fun(U_2917,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2917),U_2918))
| ~ class_Lattices_Olattice(U_2917) ),
inference(clausify,[status(thm)],[f_693_3]) ).
fof(f_694_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter]) ).
fof(f_694_2,plain,
! [U_2922,U_2921,U_2920] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2920),c_Big__Operators_Olattice__class_OInf__fin(U_2920,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922))),c_Big__Operators_Olattice__class_OInf__fin(U_2920,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2920),c_Big__Operators_Olattice__class_OInf__fin(U_2920,U_2921)),c_Big__Operators_Olattice__class_OInf__fin(U_2920,U_2922))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922) = c_Orderings_Obot__class_Obot(tc_fun(U_2920,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2920),U_2922))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2920),U_2921))
| ~ class_Lattices_Olattice(U_2920) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
fof(f_694_3,plain,
! [U_2922,U_2921,U_2920] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2920),c_Big__Operators_Olattice__class_OInf__fin(U_2920,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922))),c_Big__Operators_Olattice__class_OInf__fin(U_2920,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2920),c_Big__Operators_Olattice__class_OInf__fin(U_2920,U_2921)),c_Big__Operators_Olattice__class_OInf__fin(U_2920,U_2922))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922) = c_Orderings_Obot__class_Obot(tc_fun(U_2920,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2920),U_2922))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2920),U_2921))
| ~ class_Lattices_Olattice(U_2920) ),
inference(definitional_conversion,[status(esa)],[f_694_2]) ).
cnf(f_694_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2920),c_Big__Operators_Olattice__class_OInf__fin(U_2920,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922))),c_Big__Operators_Olattice__class_OInf__fin(U_2920,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2920),c_Big__Operators_Olattice__class_OInf__fin(U_2920,U_2921)),c_Big__Operators_Olattice__class_OInf__fin(U_2920,U_2922))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2922) = c_Orderings_Obot__class_Obot(tc_fun(U_2920,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2920),U_2922))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2920),U_2921))
| ~ class_Lattices_Olattice(U_2920) ),
inference(clausify,[status(thm)],[f_694_3]) ).
fof(f_695_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint]) ).
fof(f_695_2,plain,
! [U_2925,U_2924,U_2923] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2923,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2923,tc_HOL_Obool)),U_2924),U_2925)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2923),c_Big__Operators_Olattice__class_OInf__fin(U_2923,U_2924)),c_Big__Operators_Olattice__class_OInf__fin(U_2923,U_2925))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2923,tc_HOL_Obool)),U_2924),U_2925) != c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| U_2925 = c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2923),U_2925))
| U_2924 = c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2923),U_2924))
| ~ class_Lattices_Olattice(U_2923) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
fof(f_695_3,plain,
! [U_2923,U_2924,U_2925] :
( c_Big__Operators_Olattice__class_OInf__fin(U_2923,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2923,tc_HOL_Obool)),U_2924),U_2925)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2923),c_Big__Operators_Olattice__class_OInf__fin(U_2923,U_2924)),c_Big__Operators_Olattice__class_OInf__fin(U_2923,U_2925))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2923,tc_HOL_Obool)),U_2924),U_2925) != c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| U_2925 = c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2923),U_2925))
| U_2924 = c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2923),U_2924))
| ~ class_Lattices_Olattice(U_2923) ),
inference(definitional_conversion,[status(esa)],[f_695_2]) ).
cnf(f_695_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_2923,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2923,tc_HOL_Obool)),U_2924),U_2925)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2923),c_Big__Operators_Olattice__class_OInf__fin(U_2923,U_2924)),c_Big__Operators_Olattice__class_OInf__fin(U_2923,U_2925))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2923,tc_HOL_Obool)),U_2924),U_2925) != c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| U_2925 = c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2923),U_2925))
| U_2924 = c_Orderings_Obot__class_Obot(tc_fun(U_2923,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2923),U_2924))
| ~ class_Lattices_Olattice(U_2923) ),
inference(clausify,[status(thm)],[f_695_3]) ).
fof(f_696_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem]) ).
fof(f_696_2,plain,
! [U_2930,U_2929,U_2928,U_2927,U_2926] :
( hAPP(U_2928,hAPP(hAPP(c_Set_Oinsert(U_2926),U_2930),U_2929)) = hAPP(hAPP(U_2927,U_2930),hAPP(U_2928,U_2929))
| U_2929 = c_Orderings_Obot__class_Obot(tc_fun(U_2926,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2926),U_2929))
| ~ c_Finite__Set_Ofolding__one__idem(U_2926,U_2927,U_2928) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
fof(f_696_3,plain,
! [U_2927,U_2926,U_2930,U_2929,U_2928] :
( hAPP(U_2928,hAPP(hAPP(c_Set_Oinsert(U_2926),U_2930),U_2929)) = hAPP(hAPP(U_2927,U_2930),hAPP(U_2928,U_2929))
| U_2929 = c_Orderings_Obot__class_Obot(tc_fun(U_2926,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2926),U_2929))
| ~ c_Finite__Set_Ofolding__one__idem(U_2926,U_2927,U_2928) ),
inference(definitional_conversion,[status(esa)],[f_696_2]) ).
cnf(f_696_4,plain,
( hAPP(U_2928,hAPP(hAPP(c_Set_Oinsert(U_2926),U_2930),U_2929)) = hAPP(hAPP(U_2927,U_2930),hAPP(U_2928,U_2929))
| U_2929 = c_Orderings_Obot__class_Obot(tc_fun(U_2926,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2926),U_2929))
| ~ c_Finite__Set_Ofolding__one__idem(U_2926,U_2927,U_2928) ),
inference(clausify,[status(thm)],[f_696_3]) ).
fof(f_697_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem]) ).
fof(f_697_2,plain,
! [U_2935,U_2934,U_2933,U_2932,U_2931] :
( hAPP(hAPP(U_2932,hAPP(U_2933,U_2935)),hAPP(U_2933,U_2934)) = hAPP(U_2933,U_2934)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2931,tc_HOL_Obool)),U_2935),U_2934))
| U_2935 = c_Orderings_Obot__class_Obot(tc_fun(U_2931,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2931),U_2934))
| ~ c_Finite__Set_Ofolding__one__idem(U_2931,U_2932,U_2933) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
fof(f_697_3,plain,
! [U_2932,U_2933,U_2934,U_2935,U_2931] :
( hAPP(hAPP(U_2932,hAPP(U_2933,U_2935)),hAPP(U_2933,U_2934)) = hAPP(U_2933,U_2934)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2931,tc_HOL_Obool)),U_2935),U_2934))
| U_2935 = c_Orderings_Obot__class_Obot(tc_fun(U_2931,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2931),U_2934))
| ~ c_Finite__Set_Ofolding__one__idem(U_2931,U_2932,U_2933) ),
inference(definitional_conversion,[status(esa)],[f_697_2]) ).
cnf(f_697_4,plain,
( hAPP(hAPP(U_2932,hAPP(U_2933,U_2935)),hAPP(U_2933,U_2934)) = hAPP(U_2933,U_2934)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2931,tc_HOL_Obool)),U_2935),U_2934))
| U_2935 = c_Orderings_Obot__class_Obot(tc_fun(U_2931,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2931),U_2934))
| ~ c_Finite__Set_Ofolding__one__idem(U_2931,U_2932,U_2933) ),
inference(clausify,[status(thm)],[f_697_3]) ).
fof(f_698_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2))
| ? [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))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed]) ).
fof(f_698_2,plain,
! [U_2939,U_2938] :
( hBOOL(hAPP(hAPP(c_member(U_2938),c_Big__Operators_Olattice__class_OInf__fin(U_2938,U_2939)),U_2939))
| ? [U_2937,U_2936] : ~ hBOOL(hAPP(hAPP(c_member(U_2938),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2938),U_2937),U_2936)),hAPP(hAPP(c_Set_Oinsert(U_2938),U_2937),hAPP(hAPP(c_Set_Oinsert(U_2938),U_2936),c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))))))
| U_2939 = c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2938),U_2939))
| ~ class_Lattices_Olattice(U_2938) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
fof(f_698_3,plain,
! [U_2939,U_2938] :
( hBOOL(hAPP(hAPP(c_member(U_2938),c_Big__Operators_Olattice__class_OInf__fin(U_2938,U_2939)),U_2939))
| ? [U_2936] : ~ hBOOL(hAPP(hAPP(c_member(U_2938),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2938),sK68(U_2939,U_2938)),U_2936)),hAPP(hAPP(c_Set_Oinsert(U_2938),sK68(U_2939,U_2938)),hAPP(hAPP(c_Set_Oinsert(U_2938),U_2936),c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))))))
| U_2939 = c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2938),U_2939))
| ~ class_Lattices_Olattice(U_2938) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_2937,sK68(U_2939,U_2938))],[f_698_2]) ).
fof(f_698_4,plain,
! [U_2939,U_2938] :
( hBOOL(hAPP(hAPP(c_member(U_2938),c_Big__Operators_Olattice__class_OInf__fin(U_2938,U_2939)),U_2939))
| ~ hBOOL(hAPP(hAPP(c_member(U_2938),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2938),sK68(U_2939,U_2938)),sK69(U_2939,U_2938))),hAPP(hAPP(c_Set_Oinsert(U_2938),sK68(U_2939,U_2938)),hAPP(hAPP(c_Set_Oinsert(U_2938),sK69(U_2939,U_2938)),c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))))))
| U_2939 = c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2938),U_2939))
| ~ class_Lattices_Olattice(U_2938) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_2936,sK69(U_2939,U_2938))],[f_698_3]) ).
fof(f_698_5,plain,
! [U_2938,U_2939] :
( hBOOL(hAPP(hAPP(c_member(U_2938),c_Big__Operators_Olattice__class_OInf__fin(U_2938,U_2939)),U_2939))
| ~ hBOOL(hAPP(hAPP(c_member(U_2938),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2938),sK68(U_2939,U_2938)),sK69(U_2939,U_2938))),hAPP(hAPP(c_Set_Oinsert(U_2938),sK68(U_2939,U_2938)),hAPP(hAPP(c_Set_Oinsert(U_2938),sK69(U_2939,U_2938)),c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))))))
| U_2939 = c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2938),U_2939))
| ~ class_Lattices_Olattice(U_2938) ),
inference(definitional_conversion,[status(esa)],[f_698_4]) ).
cnf(f_698_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2938),c_Big__Operators_Olattice__class_OInf__fin(U_2938,U_2939)),U_2939))
| ~ hBOOL(hAPP(hAPP(c_member(U_2938),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2938),sK68(U_2939,U_2938)),sK69(U_2939,U_2938))),hAPP(hAPP(c_Set_Oinsert(U_2938),sK68(U_2939,U_2938)),hAPP(hAPP(c_Set_Oinsert(U_2938),sK69(U_2939,U_2938)),c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))))))
| U_2939 = c_Orderings_Obot__class_Obot(tc_fun(U_2938,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2938),U_2939))
| ~ class_Lattices_Olattice(U_2938) ),
inference(clausify,[status(thm)],[f_698_5]) ).
fof(f_699_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2))
| ? [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))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed]) ).
fof(f_699_2,plain,
! [U_2943,U_2942] :
( hBOOL(hAPP(hAPP(c_member(U_2942),c_Big__Operators_Olattice__class_OSup__fin(U_2942,U_2943)),U_2943))
| ? [U_2941,U_2940] : ~ hBOOL(hAPP(hAPP(c_member(U_2942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2942),U_2941),U_2940)),hAPP(hAPP(c_Set_Oinsert(U_2942),U_2941),hAPP(hAPP(c_Set_Oinsert(U_2942),U_2940),c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))))))
| U_2943 = c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2942),U_2943))
| ~ class_Lattices_Olattice(U_2942) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
fof(f_699_3,plain,
! [U_2943,U_2942] :
( hBOOL(hAPP(hAPP(c_member(U_2942),c_Big__Operators_Olattice__class_OSup__fin(U_2942,U_2943)),U_2943))
| ? [U_2940] : ~ hBOOL(hAPP(hAPP(c_member(U_2942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2942),sK70(U_2943,U_2942)),U_2940)),hAPP(hAPP(c_Set_Oinsert(U_2942),sK70(U_2943,U_2942)),hAPP(hAPP(c_Set_Oinsert(U_2942),U_2940),c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))))))
| U_2943 = c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2942),U_2943))
| ~ class_Lattices_Olattice(U_2942) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_2941,sK70(U_2943,U_2942))],[f_699_2]) ).
fof(f_699_4,plain,
! [U_2943,U_2942] :
( hBOOL(hAPP(hAPP(c_member(U_2942),c_Big__Operators_Olattice__class_OSup__fin(U_2942,U_2943)),U_2943))
| ~ hBOOL(hAPP(hAPP(c_member(U_2942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2942),sK70(U_2943,U_2942)),sK71(U_2943,U_2942))),hAPP(hAPP(c_Set_Oinsert(U_2942),sK70(U_2943,U_2942)),hAPP(hAPP(c_Set_Oinsert(U_2942),sK71(U_2943,U_2942)),c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))))))
| U_2943 = c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2942),U_2943))
| ~ class_Lattices_Olattice(U_2942) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_2940,sK71(U_2943,U_2942))],[f_699_3]) ).
fof(f_699_5,plain,
! [U_2942,U_2943] :
( hBOOL(hAPP(hAPP(c_member(U_2942),c_Big__Operators_Olattice__class_OSup__fin(U_2942,U_2943)),U_2943))
| ~ hBOOL(hAPP(hAPP(c_member(U_2942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2942),sK70(U_2943,U_2942)),sK71(U_2943,U_2942))),hAPP(hAPP(c_Set_Oinsert(U_2942),sK70(U_2943,U_2942)),hAPP(hAPP(c_Set_Oinsert(U_2942),sK71(U_2943,U_2942)),c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))))))
| U_2943 = c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2942),U_2943))
| ~ class_Lattices_Olattice(U_2942) ),
inference(definitional_conversion,[status(esa)],[f_699_4]) ).
cnf(f_699_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2942),c_Big__Operators_Olattice__class_OSup__fin(U_2942,U_2943)),U_2943))
| ~ hBOOL(hAPP(hAPP(c_member(U_2942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2942),sK70(U_2943,U_2942)),sK71(U_2943,U_2942))),hAPP(hAPP(c_Set_Oinsert(U_2942),sK70(U_2943,U_2942)),hAPP(hAPP(c_Set_Oinsert(U_2942),sK71(U_2943,U_2942)),c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))))))
| U_2943 = c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2942),U_2943))
| ~ class_Lattices_Olattice(U_2942) ),
inference(clausify,[status(thm)],[f_699_5]) ).
fof(f_700_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
| ? [B_M] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Union]) ).
fof(f_700_2,plain,
! [U_2946,U_2945] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2945),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2945,tc_HOL_Obool),U_2946)))
| ? [U_2944] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2945),U_2944))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_2945,tc_HOL_Obool)),U_2944),U_2946)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2945,tc_HOL_Obool)),U_2946)) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
fof(f_700_3,plain,
! [U_2946,U_2945] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2945),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2945,tc_HOL_Obool),U_2946)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2945),sK72(U_2946,U_2945)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_2945,tc_HOL_Obool)),sK72(U_2946,U_2945)),U_2946)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2945,tc_HOL_Obool)),U_2946)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_2944,sK72(U_2946,U_2945))],[f_700_2]) ).
fof(f_700_4,plain,
( ! [U_2946,U_2945] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2945),sK72(U_2946,U_2945)))
| ~ sP185(U_2946,U_2945) )
& ! [U_2946,U_2945] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2945,tc_HOL_Obool)),sK72(U_2946,U_2945)),U_2946))
| ~ sP185(U_2946,U_2945) )
& ! [U_2946,U_2945] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2945),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2945,tc_HOL_Obool),U_2946)))
| sP185(U_2946,U_2945)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2945,tc_HOL_Obool)),U_2946)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_700_3]) ).
cnf(f_700_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2945),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2945,tc_HOL_Obool),U_2946)))
| sP185(U_2946,U_2945)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2945,tc_HOL_Obool)),U_2946)) ),
inference(clausify,[status(thm)],[f_700_4]) ).
cnf(f_700_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2945,tc_HOL_Obool)),sK72(U_2946,U_2945)),U_2946))
| ~ sP185(U_2946,U_2945) ),
inference(clausify,[status(thm)],[f_700_4]) ).
cnf(f_700_7,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2945),sK72(U_2946,U_2945)))
| ~ sP185(U_2946,U_2945) ),
inference(clausify,[status(thm)],[f_700_4]) ).
fof(f_701_1,plain,
! [V_N_2,V_h_2,T_b] :
( 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))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [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))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute]) ).
fof(f_701_2,plain,
! [U_2951,U_2950,U_2949] :
( hAPP(U_2950,c_Big__Operators_Olattice__class_OInf__fin(U_2949,U_2951)) = c_Big__Operators_Olattice__class_OInf__fin(U_2949,hAPP(c_Set_Oimage(U_2949,U_2949,U_2950),U_2951))
| U_2951 = c_Orderings_Obot__class_Obot(tc_fun(U_2949,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2949),U_2951))
| ? [U_2948,U_2947] : hAPP(U_2950,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),U_2948),U_2947)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),hAPP(U_2950,U_2948)),hAPP(U_2950,U_2947))
| ~ class_Lattices_Olattice(U_2949) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
fof(f_701_3,plain,
! [U_2951,U_2950,U_2949] :
( hAPP(U_2950,c_Big__Operators_Olattice__class_OInf__fin(U_2949,U_2951)) = c_Big__Operators_Olattice__class_OInf__fin(U_2949,hAPP(c_Set_Oimage(U_2949,U_2949,U_2950),U_2951))
| U_2951 = c_Orderings_Obot__class_Obot(tc_fun(U_2949,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2949),U_2951))
| ? [U_2947] : hAPP(U_2950,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),sK73(U_2951,U_2950,U_2949)),U_2947)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),hAPP(U_2950,sK73(U_2951,U_2950,U_2949))),hAPP(U_2950,U_2947))
| ~ class_Lattices_Olattice(U_2949) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_2948,sK73(U_2951,U_2950,U_2949))],[f_701_2]) ).
fof(f_701_4,plain,
! [U_2951,U_2950,U_2949] :
( hAPP(U_2950,c_Big__Operators_Olattice__class_OInf__fin(U_2949,U_2951)) = c_Big__Operators_Olattice__class_OInf__fin(U_2949,hAPP(c_Set_Oimage(U_2949,U_2949,U_2950),U_2951))
| U_2951 = c_Orderings_Obot__class_Obot(tc_fun(U_2949,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2949),U_2951))
| hAPP(U_2950,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),sK73(U_2951,U_2950,U_2949)),sK74(U_2951,U_2950,U_2949))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),hAPP(U_2950,sK73(U_2951,U_2950,U_2949))),hAPP(U_2950,sK74(U_2951,U_2950,U_2949)))
| ~ class_Lattices_Olattice(U_2949) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_2947,sK74(U_2951,U_2950,U_2949))],[f_701_3]) ).
fof(f_701_5,plain,
! [U_2949,U_2950,U_2951] :
( hAPP(U_2950,c_Big__Operators_Olattice__class_OInf__fin(U_2949,U_2951)) = c_Big__Operators_Olattice__class_OInf__fin(U_2949,hAPP(c_Set_Oimage(U_2949,U_2949,U_2950),U_2951))
| U_2951 = c_Orderings_Obot__class_Obot(tc_fun(U_2949,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2949),U_2951))
| hAPP(U_2950,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),sK73(U_2951,U_2950,U_2949)),sK74(U_2951,U_2950,U_2949))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),hAPP(U_2950,sK73(U_2951,U_2950,U_2949))),hAPP(U_2950,sK74(U_2951,U_2950,U_2949)))
| ~ class_Lattices_Olattice(U_2949) ),
inference(definitional_conversion,[status(esa)],[f_701_4]) ).
cnf(f_701_6,plain,
( hAPP(U_2950,c_Big__Operators_Olattice__class_OInf__fin(U_2949,U_2951)) = c_Big__Operators_Olattice__class_OInf__fin(U_2949,hAPP(c_Set_Oimage(U_2949,U_2949,U_2950),U_2951))
| U_2951 = c_Orderings_Obot__class_Obot(tc_fun(U_2949,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2949),U_2951))
| hAPP(U_2950,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),sK73(U_2951,U_2950,U_2949)),sK74(U_2951,U_2950,U_2949))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2949),hAPP(U_2950,sK73(U_2951,U_2950,U_2949))),hAPP(U_2950,sK74(U_2951,U_2950,U_2949)))
| ~ class_Lattices_Olattice(U_2949) ),
inference(clausify,[status(thm)],[f_701_5]) ).
fof(f_702_1,plain,
! [V_N_2,V_h_2,T_b] :
( 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))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [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))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute]) ).
fof(f_702_2,plain,
! [U_2956,U_2955,U_2954] :
( hAPP(U_2955,c_Big__Operators_Olattice__class_OSup__fin(U_2954,U_2956)) = c_Big__Operators_Olattice__class_OSup__fin(U_2954,hAPP(c_Set_Oimage(U_2954,U_2954,U_2955),U_2956))
| U_2956 = c_Orderings_Obot__class_Obot(tc_fun(U_2954,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2954),U_2956))
| ? [U_2953,U_2952] : hAPP(U_2955,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),U_2953),U_2952)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),hAPP(U_2955,U_2953)),hAPP(U_2955,U_2952))
| ~ class_Lattices_Olattice(U_2954) ),
inference(variable_rename,[status(thm)],[f_702_1]) ).
fof(f_702_3,plain,
! [U_2956,U_2955,U_2954] :
( hAPP(U_2955,c_Big__Operators_Olattice__class_OSup__fin(U_2954,U_2956)) = c_Big__Operators_Olattice__class_OSup__fin(U_2954,hAPP(c_Set_Oimage(U_2954,U_2954,U_2955),U_2956))
| U_2956 = c_Orderings_Obot__class_Obot(tc_fun(U_2954,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2954),U_2956))
| ? [U_2952] : hAPP(U_2955,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),sK75(U_2956,U_2955,U_2954)),U_2952)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),hAPP(U_2955,sK75(U_2956,U_2955,U_2954))),hAPP(U_2955,U_2952))
| ~ class_Lattices_Olattice(U_2954) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_2953,sK75(U_2956,U_2955,U_2954))],[f_702_2]) ).
fof(f_702_4,plain,
! [U_2956,U_2955,U_2954] :
( hAPP(U_2955,c_Big__Operators_Olattice__class_OSup__fin(U_2954,U_2956)) = c_Big__Operators_Olattice__class_OSup__fin(U_2954,hAPP(c_Set_Oimage(U_2954,U_2954,U_2955),U_2956))
| U_2956 = c_Orderings_Obot__class_Obot(tc_fun(U_2954,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2954),U_2956))
| hAPP(U_2955,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),sK75(U_2956,U_2955,U_2954)),sK76(U_2956,U_2955,U_2954))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),hAPP(U_2955,sK75(U_2956,U_2955,U_2954))),hAPP(U_2955,sK76(U_2956,U_2955,U_2954)))
| ~ class_Lattices_Olattice(U_2954) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_2952,sK76(U_2956,U_2955,U_2954))],[f_702_3]) ).
fof(f_702_5,plain,
! [U_2954,U_2955,U_2956] :
( hAPP(U_2955,c_Big__Operators_Olattice__class_OSup__fin(U_2954,U_2956)) = c_Big__Operators_Olattice__class_OSup__fin(U_2954,hAPP(c_Set_Oimage(U_2954,U_2954,U_2955),U_2956))
| U_2956 = c_Orderings_Obot__class_Obot(tc_fun(U_2954,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2954),U_2956))
| hAPP(U_2955,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),sK75(U_2956,U_2955,U_2954)),sK76(U_2956,U_2955,U_2954))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),hAPP(U_2955,sK75(U_2956,U_2955,U_2954))),hAPP(U_2955,sK76(U_2956,U_2955,U_2954)))
| ~ class_Lattices_Olattice(U_2954) ),
inference(definitional_conversion,[status(esa)],[f_702_4]) ).
cnf(f_702_6,plain,
( hAPP(U_2955,c_Big__Operators_Olattice__class_OSup__fin(U_2954,U_2956)) = c_Big__Operators_Olattice__class_OSup__fin(U_2954,hAPP(c_Set_Oimage(U_2954,U_2954,U_2955),U_2956))
| U_2956 = c_Orderings_Obot__class_Obot(tc_fun(U_2954,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2954),U_2956))
| hAPP(U_2955,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),sK75(U_2956,U_2955,U_2954)),sK76(U_2956,U_2955,U_2954))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2954),hAPP(U_2955,sK75(U_2956,U_2955,U_2954))),hAPP(U_2955,sK76(U_2956,U_2955,U_2954)))
| ~ class_Lattices_Olattice(U_2954) ),
inference(clausify,[status(thm)],[f_702_5]) ).
fof(f_703_1,plain,
! [V_Pa_2,V_A_2,V_F_2,T_b] :
( hBOOL(hAPP(V_Pa_2,V_F_2))
| ? [B_a,B_F] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F)))
& hBOOL(hAPP(V_Pa_2,B_F))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
| ~ hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__subset__induct]) ).
fof(f_703_2,plain,
! [U_2962,U_2961,U_2960,U_2959] :
( hBOOL(hAPP(U_2962,U_2960))
| ? [U_2958,U_2957] :
( ~ hBOOL(hAPP(U_2962,hAPP(hAPP(c_Set_Oinsert(U_2959),U_2958),U_2957)))
& hBOOL(hAPP(U_2962,U_2957))
& ~ hBOOL(hAPP(hAPP(c_member(U_2959),U_2958),U_2957))
& hBOOL(hAPP(hAPP(c_member(U_2959),U_2958),U_2961))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),U_2957)) )
| ~ hBOOL(hAPP(U_2962,c_Orderings_Obot__class_Obot(tc_fun(U_2959,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2959,tc_HOL_Obool)),U_2960),U_2961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),U_2960)) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
fof(f_703_3,plain,
! [U_2962,U_2961,U_2960,U_2959] :
( hBOOL(hAPP(U_2962,U_2960))
| ? [U_2957] :
( ~ hBOOL(hAPP(U_2962,hAPP(hAPP(c_Set_Oinsert(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),U_2957)))
& hBOOL(hAPP(U_2962,U_2957))
& ~ hBOOL(hAPP(hAPP(c_member(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),U_2957))
& hBOOL(hAPP(hAPP(c_member(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),U_2961))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),U_2957)) )
| ~ hBOOL(hAPP(U_2962,c_Orderings_Obot__class_Obot(tc_fun(U_2959,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2959,tc_HOL_Obool)),U_2960),U_2961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),U_2960)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_2958,sK77(U_2962,U_2961,U_2960,U_2959))],[f_703_2]) ).
fof(f_703_4,plain,
! [U_2962,U_2961,U_2960,U_2959] :
( hBOOL(hAPP(U_2962,U_2960))
| ( ~ hBOOL(hAPP(U_2962,hAPP(hAPP(c_Set_Oinsert(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),sK78(U_2962,U_2961,U_2960,U_2959))))
& hBOOL(hAPP(U_2962,sK78(U_2962,U_2961,U_2960,U_2959)))
& ~ hBOOL(hAPP(hAPP(c_member(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),sK78(U_2962,U_2961,U_2960,U_2959)))
& hBOOL(hAPP(hAPP(c_member(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),U_2961))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),sK78(U_2962,U_2961,U_2960,U_2959))) )
| ~ hBOOL(hAPP(U_2962,c_Orderings_Obot__class_Obot(tc_fun(U_2959,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2959,tc_HOL_Obool)),U_2960),U_2961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),U_2960)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_2957,sK78(U_2962,U_2961,U_2960,U_2959))],[f_703_3]) ).
fof(f_703_5,plain,
( ! [U_2959,U_2960,U_2961,U_2962] :
( ~ hBOOL(hAPP(U_2962,hAPP(hAPP(c_Set_Oinsert(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),sK78(U_2962,U_2961,U_2960,U_2959))))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) )
& ! [U_2959,U_2960,U_2961,U_2962] :
( hBOOL(hAPP(U_2962,sK78(U_2962,U_2961,U_2960,U_2959)))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) )
& ! [U_2959,U_2960,U_2961,U_2962] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),sK78(U_2962,U_2961,U_2960,U_2959)))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) )
& ! [U_2959,U_2960,U_2961,U_2962] :
( hBOOL(hAPP(hAPP(c_member(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),U_2961))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) )
& ! [U_2959,U_2960,U_2961,U_2962] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),sK78(U_2962,U_2961,U_2960,U_2959)))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) )
& ! [U_2959,U_2960,U_2961,U_2962] :
( hBOOL(hAPP(U_2962,U_2960))
| sP186(U_2959,U_2960,U_2961,U_2962)
| ~ hBOOL(hAPP(U_2962,c_Orderings_Obot__class_Obot(tc_fun(U_2959,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2959,tc_HOL_Obool)),U_2960),U_2961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),U_2960)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_703_4]) ).
cnf(f_703_6,plain,
( hBOOL(hAPP(U_2962,U_2960))
| sP186(U_2959,U_2960,U_2961,U_2962)
| ~ hBOOL(hAPP(U_2962,c_Orderings_Obot__class_Obot(tc_fun(U_2959,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2959,tc_HOL_Obool)),U_2960),U_2961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),U_2960)) ),
inference(clausify,[status(thm)],[f_703_5]) ).
cnf(f_703_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2959),sK78(U_2962,U_2961,U_2960,U_2959)))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) ),
inference(clausify,[status(thm)],[f_703_5]) ).
cnf(f_703_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),U_2961))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) ),
inference(clausify,[status(thm)],[f_703_5]) ).
cnf(f_703_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),sK78(U_2962,U_2961,U_2960,U_2959)))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) ),
inference(clausify,[status(thm)],[f_703_5]) ).
cnf(f_703_10,plain,
( hBOOL(hAPP(U_2962,sK78(U_2962,U_2961,U_2960,U_2959)))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) ),
inference(clausify,[status(thm)],[f_703_5]) ).
cnf(f_703_11,plain,
( ~ hBOOL(hAPP(U_2962,hAPP(hAPP(c_Set_Oinsert(U_2959),sK77(U_2962,U_2961,U_2960,U_2959)),sK78(U_2962,U_2961,U_2960,U_2959))))
| ~ sP186(U_2959,U_2960,U_2961,U_2962) ),
inference(clausify,[status(thm)],[f_703_5]) ).
fof(f_704_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( 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))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec]) ).
fof(f_704_2,plain,
! [U_2968,U_2967,U_2966,U_2965,U_2964,U_2963] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_2963,U_2964,U_2965),U_2968),U_2966) = hAPP(hAPP(U_2965,U_2967),hAPP(hAPP(c_Finite__Set_Ofold(U_2963,U_2964,U_2965),U_2968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2963,tc_HOL_Obool)),U_2966),hAPP(hAPP(c_Set_Oinsert(U_2963),U_2967),c_Orderings_Obot__class_Obot(tc_fun(U_2963,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2963),U_2967),U_2966))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2963),U_2966))
| ~ c_Finite__Set_Ofun__left__comm(U_2963,U_2964,U_2965) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
fof(f_704_3,plain,
! [U_2963,U_2964,U_2968,U_2965,U_2966,U_2967] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_2963,U_2964,U_2965),U_2968),U_2966) = hAPP(hAPP(U_2965,U_2967),hAPP(hAPP(c_Finite__Set_Ofold(U_2963,U_2964,U_2965),U_2968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2963,tc_HOL_Obool)),U_2966),hAPP(hAPP(c_Set_Oinsert(U_2963),U_2967),c_Orderings_Obot__class_Obot(tc_fun(U_2963,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2963),U_2967),U_2966))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2963),U_2966))
| ~ c_Finite__Set_Ofun__left__comm(U_2963,U_2964,U_2965) ),
inference(definitional_conversion,[status(esa)],[f_704_2]) ).
cnf(f_704_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_2963,U_2964,U_2965),U_2968),U_2966) = hAPP(hAPP(U_2965,U_2967),hAPP(hAPP(c_Finite__Set_Ofold(U_2963,U_2964,U_2965),U_2968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2963,tc_HOL_Obool)),U_2966),hAPP(hAPP(c_Set_Oinsert(U_2963),U_2967),c_Orderings_Obot__class_Obot(tc_fun(U_2963,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2963),U_2967),U_2966))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2963),U_2966))
| ~ c_Finite__Set_Ofun__left__comm(U_2963,U_2964,U_2965) ),
inference(clausify,[status(thm)],[f_704_3]) ).
fof(f_705_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__Un]) ).
fof(f_705_2,plain,
! [U_2971,U_2970,U_2969] :
( hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2969,tc_HOL_Obool)),U_2970),U_2971)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2969),hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),U_2970)),hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),U_2971))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2969,tc_HOL_Obool)),U_2970),U_2971) != c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| U_2971 = c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2969),U_2971))
| U_2970 = c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2969),U_2970))
| ~ class_Groups_Oab__semigroup__mult(U_2969) ),
inference(variable_rename,[status(thm)],[f_705_1]) ).
fof(f_705_3,plain,
! [U_2969,U_2970,U_2971] :
( hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2969,tc_HOL_Obool)),U_2970),U_2971)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2969),hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),U_2970)),hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),U_2971))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2969,tc_HOL_Obool)),U_2970),U_2971) != c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| U_2971 = c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2969),U_2971))
| U_2970 = c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2969),U_2970))
| ~ class_Groups_Oab__semigroup__mult(U_2969) ),
inference(definitional_conversion,[status(esa)],[f_705_2]) ).
cnf(f_705_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2969,tc_HOL_Obool)),U_2970),U_2971)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2969),hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),U_2970)),hAPP(c_Finite__Set_Ofold1(U_2969,c_Groups_Otimes__class_Otimes(U_2969)),U_2971))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2969,tc_HOL_Obool)),U_2970),U_2971) != c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| U_2971 = c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2969),U_2971))
| U_2970 = c_Orderings_Obot__class_Obot(tc_fun(U_2969,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2969),U_2970))
| ~ class_Groups_Oab__semigroup__mult(U_2969) ),
inference(clausify,[status(thm)],[f_705_3]) ).
fof(f_706_1,plain,
! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
( 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))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [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))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute]) ).
fof(f_706_2,plain,
! [U_2978,U_2977,U_2976,U_2975,U_2974] :
( hAPP(U_2977,hAPP(U_2976,U_2978)) = hAPP(U_2976,hAPP(c_Set_Oimage(U_2974,U_2974,U_2977),U_2978))
| U_2978 = c_Orderings_Obot__class_Obot(tc_fun(U_2974,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2974),U_2978))
| ? [U_2973,U_2972] : hAPP(U_2977,hAPP(hAPP(U_2975,U_2973),U_2972)) != hAPP(hAPP(U_2975,hAPP(U_2977,U_2973)),hAPP(U_2977,U_2972))
| ~ c_Finite__Set_Ofolding__one__idem(U_2974,U_2975,U_2976) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
fof(f_706_3,plain,
! [U_2978,U_2977,U_2976,U_2975,U_2974] :
( hAPP(U_2977,hAPP(U_2976,U_2978)) = hAPP(U_2976,hAPP(c_Set_Oimage(U_2974,U_2974,U_2977),U_2978))
| U_2978 = c_Orderings_Obot__class_Obot(tc_fun(U_2974,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2974),U_2978))
| ? [U_2972] : hAPP(U_2977,hAPP(hAPP(U_2975,sK79(U_2978,U_2977,U_2976,U_2975,U_2974)),U_2972)) != hAPP(hAPP(U_2975,hAPP(U_2977,sK79(U_2978,U_2977,U_2976,U_2975,U_2974))),hAPP(U_2977,U_2972))
| ~ c_Finite__Set_Ofolding__one__idem(U_2974,U_2975,U_2976) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_2973,sK79(U_2978,U_2977,U_2976,U_2975,U_2974))],[f_706_2]) ).
fof(f_706_4,plain,
! [U_2978,U_2977,U_2976,U_2975,U_2974] :
( hAPP(U_2977,hAPP(U_2976,U_2978)) = hAPP(U_2976,hAPP(c_Set_Oimage(U_2974,U_2974,U_2977),U_2978))
| U_2978 = c_Orderings_Obot__class_Obot(tc_fun(U_2974,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2974),U_2978))
| hAPP(U_2977,hAPP(hAPP(U_2975,sK79(U_2978,U_2977,U_2976,U_2975,U_2974)),sK80(U_2978,U_2977,U_2976,U_2975,U_2974))) != hAPP(hAPP(U_2975,hAPP(U_2977,sK79(U_2978,U_2977,U_2976,U_2975,U_2974))),hAPP(U_2977,sK80(U_2978,U_2977,U_2976,U_2975,U_2974)))
| ~ c_Finite__Set_Ofolding__one__idem(U_2974,U_2975,U_2976) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_2972,sK80(U_2978,U_2977,U_2976,U_2975,U_2974))],[f_706_3]) ).
fof(f_706_5,plain,
! [U_2974,U_2975,U_2976,U_2977,U_2978] :
( hAPP(U_2977,hAPP(U_2976,U_2978)) = hAPP(U_2976,hAPP(c_Set_Oimage(U_2974,U_2974,U_2977),U_2978))
| U_2978 = c_Orderings_Obot__class_Obot(tc_fun(U_2974,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2974),U_2978))
| hAPP(U_2977,hAPP(hAPP(U_2975,sK79(U_2978,U_2977,U_2976,U_2975,U_2974)),sK80(U_2978,U_2977,U_2976,U_2975,U_2974))) != hAPP(hAPP(U_2975,hAPP(U_2977,sK79(U_2978,U_2977,U_2976,U_2975,U_2974))),hAPP(U_2977,sK80(U_2978,U_2977,U_2976,U_2975,U_2974)))
| ~ c_Finite__Set_Ofolding__one__idem(U_2974,U_2975,U_2976) ),
inference(definitional_conversion,[status(esa)],[f_706_4]) ).
cnf(f_706_6,plain,
( hAPP(U_2977,hAPP(U_2976,U_2978)) = hAPP(U_2976,hAPP(c_Set_Oimage(U_2974,U_2974,U_2977),U_2978))
| U_2978 = c_Orderings_Obot__class_Obot(tc_fun(U_2974,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2974),U_2978))
| hAPP(U_2977,hAPP(hAPP(U_2975,sK79(U_2978,U_2977,U_2976,U_2975,U_2974)),sK80(U_2978,U_2977,U_2976,U_2975,U_2974))) != hAPP(hAPP(U_2975,hAPP(U_2977,sK79(U_2978,U_2977,U_2976,U_2975,U_2974))),hAPP(U_2977,sK80(U_2978,U_2977,U_2976,U_2975,U_2974)))
| ~ c_Finite__Set_Ofolding__one__idem(U_2974,U_2975,U_2976) ),
inference(clausify,[status(thm)],[f_706_5]) ).
fof(f_707_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_fold__empty]) ).
fof(f_707_2,plain,
! [U_2982,U_2981,U_2980,U_2979] : hAPP(hAPP(c_Finite__Set_Ofold(U_2979,U_2980,U_2981),U_2982),c_Orderings_Obot__class_Obot(tc_fun(U_2979,tc_HOL_Obool))) = U_2982,
inference(variable_rename,[status(thm)],[f_707_1]) ).
fof(f_707_3,plain,
! [U_2982,U_2981,U_2980,U_2979] : hAPP(hAPP(c_Finite__Set_Ofold(U_2979,U_2980,U_2981),U_2982),c_Orderings_Obot__class_Obot(tc_fun(U_2979,tc_HOL_Obool))) = U_2982,
inference(definitional_conversion,[status(esa)],[f_707_2]) ).
cnf(f_707_4,plain,
hAPP(hAPP(c_Finite__Set_Ofold(U_2979,U_2980,U_2981),U_2982),c_Orderings_Obot__class_Obot(tc_fun(U_2979,tc_HOL_Obool))) = U_2982,
inference(clausify,[status(thm)],[f_707_3]) ).
fof(f_708_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem]) ).
fof(f_708_2,plain,
! [U_2985,U_2984,U_2983] :
( hAPP(c_Finite__Set_Ofold1(U_2983,c_Groups_Otimes__class_Otimes(U_2983)),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),U_2984)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2983,U_2983,c_Groups_Otimes__class_Otimes(U_2983)),U_2985),U_2984)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2983),U_2984))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2983) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
fof(f_708_3,plain,
! [U_2983,U_2984,U_2985] :
( hAPP(c_Finite__Set_Ofold1(U_2983,c_Groups_Otimes__class_Otimes(U_2983)),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),U_2984)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2983,U_2983,c_Groups_Otimes__class_Otimes(U_2983)),U_2985),U_2984)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2983),U_2984))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2983) ),
inference(definitional_conversion,[status(esa)],[f_708_2]) ).
cnf(f_708_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_2983,c_Groups_Otimes__class_Otimes(U_2983)),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),U_2984)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2983,U_2983,c_Groups_Otimes__class_Otimes(U_2983)),U_2985),U_2984)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2983),U_2984))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2983) ),
inference(clausify,[status(thm)],[f_708_3]) ).
fof(f_709_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold]) ).
fof(f_709_2,plain,
! [U_2988,U_2987,U_2986] :
( hAPP(c_Finite__Set_Ofold1(U_2986,c_Groups_Otimes__class_Otimes(U_2986)),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),U_2987)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2986,U_2986,c_Groups_Otimes__class_Otimes(U_2986)),U_2988),U_2987)
| hBOOL(hAPP(hAPP(c_member(U_2986),U_2988),U_2987))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2986),U_2987))
| ~ class_Groups_Oab__semigroup__mult(U_2986) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
fof(f_709_3,plain,
! [U_2986,U_2987,U_2988] :
( hAPP(c_Finite__Set_Ofold1(U_2986,c_Groups_Otimes__class_Otimes(U_2986)),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),U_2987)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2986,U_2986,c_Groups_Otimes__class_Otimes(U_2986)),U_2988),U_2987)
| hBOOL(hAPP(hAPP(c_member(U_2986),U_2988),U_2987))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2986),U_2987))
| ~ class_Groups_Oab__semigroup__mult(U_2986) ),
inference(definitional_conversion,[status(esa)],[f_709_2]) ).
cnf(f_709_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_2986,c_Groups_Otimes__class_Otimes(U_2986)),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),U_2987)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2986,U_2986,c_Groups_Otimes__class_Otimes(U_2986)),U_2988),U_2987)
| hBOOL(hAPP(hAPP(c_member(U_2986),U_2988),U_2987))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2986),U_2987))
| ~ class_Groups_Oab__semigroup__mult(U_2986) ),
inference(clausify,[status(thm)],[f_709_3]) ).
fof(f_710_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm]) ).
fof(f_710_2,plain,
! [U_2994,U_2993,U_2992,U_2991,U_2990,U_2989] :
( hAPP(hAPP(U_2991,U_2993),hAPP(hAPP(c_Finite__Set_Ofold(U_2989,U_2990,U_2991),U_2994),U_2992)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2989,U_2990,U_2991),hAPP(hAPP(U_2991,U_2993),U_2994)),U_2992)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2989),U_2992))
| ~ c_Finite__Set_Ofun__left__comm(U_2989,U_2990,U_2991) ),
inference(variable_rename,[status(thm)],[f_710_1]) ).
fof(f_710_3,plain,
! [U_2989,U_2990,U_2991,U_2992,U_2993,U_2994] :
( hAPP(hAPP(U_2991,U_2993),hAPP(hAPP(c_Finite__Set_Ofold(U_2989,U_2990,U_2991),U_2994),U_2992)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2989,U_2990,U_2991),hAPP(hAPP(U_2991,U_2993),U_2994)),U_2992)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2989),U_2992))
| ~ c_Finite__Set_Ofun__left__comm(U_2989,U_2990,U_2991) ),
inference(definitional_conversion,[status(esa)],[f_710_2]) ).
cnf(f_710_4,plain,
( hAPP(hAPP(U_2991,U_2993),hAPP(hAPP(c_Finite__Set_Ofold(U_2989,U_2990,U_2991),U_2994),U_2992)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2989,U_2990,U_2991),hAPP(hAPP(U_2991,U_2993),U_2994)),U_2992)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2989),U_2992))
| ~ c_Finite__Set_Ofun__left__comm(U_2989,U_2990,U_2991) ),
inference(clausify,[status(thm)],[f_710_3]) ).
fof(f_711_1,plain,
! [V_a_2,V_f_2,T_b,V_g_2] :
( 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
| V_g_2 != c_Finite__Set_Ofold1(T_b,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def]) ).
fof(f_711_2,plain,
! [U_2998,U_2997,U_2996,U_2995] :
( hAPP(U_2995,hAPP(hAPP(c_Set_Oinsert(U_2996),U_2998),c_Orderings_Obot__class_Obot(tc_fun(U_2996,tc_HOL_Obool)))) = U_2998
| U_2995 != c_Finite__Set_Ofold1(U_2996,U_2997) ),
inference(variable_rename,[status(thm)],[f_711_1]) ).
fof(f_711_3,plain,
! [U_2995,U_2996,U_2997,U_2998] :
( hAPP(U_2995,hAPP(hAPP(c_Set_Oinsert(U_2996),U_2998),c_Orderings_Obot__class_Obot(tc_fun(U_2996,tc_HOL_Obool)))) = U_2998
| U_2995 != c_Finite__Set_Ofold1(U_2996,U_2997) ),
inference(definitional_conversion,[status(esa)],[f_711_2]) ).
cnf(f_711_4,plain,
( hAPP(U_2995,hAPP(hAPP(c_Set_Oinsert(U_2996),U_2998),c_Orderings_Obot__class_Obot(tc_fun(U_2996,tc_HOL_Obool)))) = U_2998
| U_2995 != c_Finite__Set_Ofold1(U_2996,U_2997) ),
inference(clausify,[status(thm)],[f_711_3]) ).
fof(f_712_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_fold1__singleton]) ).
fof(f_712_2,plain,
! [U_3001,U_3000,U_2999] : hAPP(c_Finite__Set_Ofold1(U_2999,U_3000),hAPP(hAPP(c_Set_Oinsert(U_2999),U_3001),c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool)))) = U_3001,
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
! [U_2999,U_3000,U_3001] : hAPP(c_Finite__Set_Ofold1(U_2999,U_3000),hAPP(hAPP(c_Set_Oinsert(U_2999),U_3001),c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool)))) = U_3001,
inference(definitional_conversion,[status(esa)],[f_712_2]) ).
cnf(f_712_4,plain,
hAPP(c_Finite__Set_Ofold1(U_2999,U_3000),hAPP(hAPP(c_Set_Oinsert(U_2999),U_3001),c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool)))) = U_3001,
inference(clausify,[status(thm)],[f_712_3]) ).
fof(f_713_1,plain,
! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality]) ).
fof(f_713_2,plain,
! [U_3007,U_3006,U_3005,U_3004,U_3003,U_3002] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3002,U_3003,U_3004),U_3005),U_3006) = U_3007
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3002,U_3003,U_3004,U_3005,U_3006),U_3007))
| ~ c_Finite__Set_Ofun__left__comm(U_3002,U_3003,U_3004) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
! [U_3002,U_3003,U_3004,U_3005,U_3006,U_3007] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3002,U_3003,U_3004),U_3005),U_3006) = U_3007
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3002,U_3003,U_3004,U_3005,U_3006),U_3007))
| ~ c_Finite__Set_Ofun__left__comm(U_3002,U_3003,U_3004) ),
inference(definitional_conversion,[status(esa)],[f_713_2]) ).
cnf(f_713_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3002,U_3003,U_3004),U_3005),U_3006) = U_3007
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3002,U_3003,U_3004,U_3005,U_3006),U_3007))
| ~ c_Finite__Set_Ofun__left__comm(U_3002,U_3003,U_3004) ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_1,plain,
! [V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold]) ).
fof(f_714_2,plain,
! [U_3011,U_3010,U_3009,U_3008] :
( hAPP(U_3010,U_3011) = hAPP(c_Finite__Set_Ofold1(U_3008,U_3009),U_3011)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3008),U_3011))
| ~ c_Finite__Set_Ofolding__one(U_3008,U_3009,U_3010) ),
inference(variable_rename,[status(thm)],[f_714_1]) ).
fof(f_714_3,plain,
! [U_3009,U_3010,U_3008,U_3011] :
( hAPP(U_3010,U_3011) = hAPP(c_Finite__Set_Ofold1(U_3008,U_3009),U_3011)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3008),U_3011))
| ~ c_Finite__Set_Ofolding__one(U_3008,U_3009,U_3010) ),
inference(definitional_conversion,[status(esa)],[f_714_2]) ).
cnf(f_714_4,plain,
( hAPP(U_3010,U_3011) = hAPP(c_Finite__Set_Ofold1(U_3008,U_3009),U_3011)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3008),U_3011))
| ~ c_Finite__Set_Ofolding__one(U_3008,U_3009,U_3010) ),
inference(clausify,[status(thm)],[f_714_3]) ).
fof(f_715_1,plain,
! [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_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_union__fold__insert]) ).
fof(f_715_2,plain,
! [U_3014,U_3013,U_3012] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),U_3013),U_3014) = hAPP(hAPP(c_Finite__Set_Ofold(U_3012,tc_fun(U_3012,tc_HOL_Obool),c_Set_Oinsert(U_3012)),U_3014),U_3013)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013)) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
fof(f_715_3,plain,
! [U_3012,U_3013,U_3014] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),U_3013),U_3014) = hAPP(hAPP(c_Finite__Set_Ofold(U_3012,tc_fun(U_3012,tc_HOL_Obool),c_Set_Oinsert(U_3012)),U_3014),U_3013)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013)) ),
inference(definitional_conversion,[status(esa)],[f_715_2]) ).
cnf(f_715_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),U_3013),U_3014) = hAPP(hAPP(c_Finite__Set_Ofold(U_3012,tc_fun(U_3012,tc_HOL_Obool),c_Set_Oinsert(U_3012)),U_3014),U_3013)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013)) ),
inference(clausify,[status(thm)],[f_715_3]) ).
fof(f_716_1,plain,
! [V_a_2,V_b_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__sup__insert]) ).
fof(f_716_2,plain,
! [U_3018,U_3017,U_3016,U_3015] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3015,U_3015,c_Lattices_Osemilattice__sup__class_Osup(U_3015)),U_3017),hAPP(hAPP(c_Set_Oinsert(U_3015),U_3018),U_3016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3015),U_3018),hAPP(hAPP(c_Finite__Set_Ofold(U_3015,U_3015,c_Lattices_Osemilattice__sup__class_Osup(U_3015)),U_3017),U_3016))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3015),U_3016))
| ~ class_Lattices_Osemilattice__sup(U_3015) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
fof(f_716_3,plain,
! [U_3015,U_3016,U_3017,U_3018] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3015,U_3015,c_Lattices_Osemilattice__sup__class_Osup(U_3015)),U_3017),hAPP(hAPP(c_Set_Oinsert(U_3015),U_3018),U_3016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3015),U_3018),hAPP(hAPP(c_Finite__Set_Ofold(U_3015,U_3015,c_Lattices_Osemilattice__sup__class_Osup(U_3015)),U_3017),U_3016))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3015),U_3016))
| ~ class_Lattices_Osemilattice__sup(U_3015) ),
inference(definitional_conversion,[status(esa)],[f_716_2]) ).
cnf(f_716_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3015,U_3015,c_Lattices_Osemilattice__sup__class_Osup(U_3015)),U_3017),hAPP(hAPP(c_Set_Oinsert(U_3015),U_3018),U_3016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3015),U_3018),hAPP(hAPP(c_Finite__Set_Ofold(U_3015,U_3015,c_Lattices_Osemilattice__sup__class_Osup(U_3015)),U_3017),U_3016))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3015),U_3016))
| ~ class_Lattices_Osemilattice__sup(U_3015) ),
inference(clausify,[status(thm)],[f_716_3]) ).
fof(f_717_1,plain,
! [V_a_2,V_b_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__inf__insert]) ).
fof(f_717_2,plain,
! [U_3022,U_3021,U_3020,U_3019] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3019,U_3019,c_Lattices_Osemilattice__inf__class_Oinf(U_3019)),U_3021),hAPP(hAPP(c_Set_Oinsert(U_3019),U_3022),U_3020)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3019),U_3022),hAPP(hAPP(c_Finite__Set_Ofold(U_3019,U_3019,c_Lattices_Osemilattice__inf__class_Oinf(U_3019)),U_3021),U_3020))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3019),U_3020))
| ~ class_Lattices_Osemilattice__inf(U_3019) ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
fof(f_717_3,plain,
! [U_3019,U_3020,U_3021,U_3022] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3019,U_3019,c_Lattices_Osemilattice__inf__class_Oinf(U_3019)),U_3021),hAPP(hAPP(c_Set_Oinsert(U_3019),U_3022),U_3020)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3019),U_3022),hAPP(hAPP(c_Finite__Set_Ofold(U_3019,U_3019,c_Lattices_Osemilattice__inf__class_Oinf(U_3019)),U_3021),U_3020))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3019),U_3020))
| ~ class_Lattices_Osemilattice__inf(U_3019) ),
inference(definitional_conversion,[status(esa)],[f_717_2]) ).
cnf(f_717_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3019,U_3019,c_Lattices_Osemilattice__inf__class_Oinf(U_3019)),U_3021),hAPP(hAPP(c_Set_Oinsert(U_3019),U_3022),U_3020)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3019),U_3022),hAPP(hAPP(c_Finite__Set_Ofold(U_3019,U_3019,c_Lattices_Osemilattice__inf__class_Oinf(U_3019)),U_3021),U_3020))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3019),U_3020))
| ~ class_Lattices_Osemilattice__inf(U_3019) ),
inference(clausify,[status(thm)],[f_717_3]) ).
fof(f_718_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup]) ).
fof(f_718_2,plain,
! [U_3025,U_3024,U_3023] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3023),U_3025),c_Complete__Lattice_OSup__class_OSup(U_3023,U_3024)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3023,U_3023,c_Lattices_Osemilattice__sup__class_Osup(U_3023)),U_3025),U_3024)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3023),U_3024))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3023) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
fof(f_718_3,plain,
! [U_3023,U_3024,U_3025] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3023),U_3025),c_Complete__Lattice_OSup__class_OSup(U_3023,U_3024)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3023,U_3023,c_Lattices_Osemilattice__sup__class_Osup(U_3023)),U_3025),U_3024)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3023),U_3024))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3023) ),
inference(definitional_conversion,[status(esa)],[f_718_2]) ).
cnf(f_718_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3023),U_3025),c_Complete__Lattice_OSup__class_OSup(U_3023,U_3024)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3023,U_3023,c_Lattices_Osemilattice__sup__class_Osup(U_3023)),U_3025),U_3024)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3023),U_3024))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3023) ),
inference(clausify,[status(thm)],[f_718_3]) ).
fof(f_719_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf]) ).
fof(f_719_2,plain,
! [U_3028,U_3027,U_3026] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3026),U_3028),c_Complete__Lattice_OInf__class_OInf(U_3026,U_3027)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3026,U_3026,c_Lattices_Osemilattice__inf__class_Oinf(U_3026)),U_3028),U_3027)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3026),U_3027))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3026) ),
inference(variable_rename,[status(thm)],[f_719_1]) ).
fof(f_719_3,plain,
! [U_3026,U_3027,U_3028] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3026),U_3028),c_Complete__Lattice_OInf__class_OInf(U_3026,U_3027)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3026,U_3026,c_Lattices_Osemilattice__inf__class_Oinf(U_3026)),U_3028),U_3027)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3026),U_3027))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3026) ),
inference(definitional_conversion,[status(esa)],[f_719_2]) ).
cnf(f_719_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3026),U_3028),c_Complete__Lattice_OInf__class_OInf(U_3026,U_3027)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3026,U_3026,c_Lattices_Osemilattice__inf__class_Oinf(U_3026)),U_3028),U_3027)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3026),U_3027))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3026) ),
inference(clausify,[status(thm)],[f_719_3]) ).
fof(f_720_1,plain,
! [V_z_2,V_A_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,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold]) ).
fof(f_720_2,plain,
! [U_3033,U_3032,U_3031,U_3030,U_3029] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3029,U_3030,U_3031,U_3033,U_3032),hAPP(hAPP(c_Finite__Set_Ofold(U_3029,U_3030,U_3031),U_3033),U_3032)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3029),U_3032))
| ~ c_Finite__Set_Ofun__left__comm(U_3029,U_3030,U_3031) ),
inference(variable_rename,[status(thm)],[f_720_1]) ).
fof(f_720_3,plain,
! [U_3029,U_3030,U_3031,U_3032,U_3033] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3029,U_3030,U_3031,U_3033,U_3032),hAPP(hAPP(c_Finite__Set_Ofold(U_3029,U_3030,U_3031),U_3033),U_3032)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3029),U_3032))
| ~ c_Finite__Set_Ofun__left__comm(U_3029,U_3030,U_3031) ),
inference(definitional_conversion,[status(esa)],[f_720_2]) ).
cnf(f_720_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3029,U_3030,U_3031,U_3033,U_3032),hAPP(hAPP(c_Finite__Set_Ofold(U_3029,U_3030,U_3031),U_3033),U_3032)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3029),U_3032))
| ~ c_Finite__Set_Ofun__left__comm(U_3029,U_3030,U_3031) ),
inference(clausify,[status(thm)],[f_720_3]) ).
fof(f_721_1,plain,
! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H]) ).
fof(f_721_2,plain,
! [U_3038,U_3037,U_3036,U_3035,U_3034] :
( hAPP(U_3036,hAPP(hAPP(c_Set_Oinsert(U_3034),U_3038),U_3037)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3034,U_3034,U_3035),U_3038),U_3037)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3034),U_3037))
| ~ c_Finite__Set_Ofolding__one__idem(U_3034,U_3035,U_3036) ),
inference(variable_rename,[status(thm)],[f_721_1]) ).
fof(f_721_3,plain,
! [U_3035,U_3034,U_3036,U_3037,U_3038] :
( hAPP(U_3036,hAPP(hAPP(c_Set_Oinsert(U_3034),U_3038),U_3037)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3034,U_3034,U_3035),U_3038),U_3037)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3034),U_3037))
| ~ c_Finite__Set_Ofolding__one__idem(U_3034,U_3035,U_3036) ),
inference(definitional_conversion,[status(esa)],[f_721_2]) ).
cnf(f_721_4,plain,
( hAPP(U_3036,hAPP(hAPP(c_Set_Oinsert(U_3034),U_3038),U_3037)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3034,U_3034,U_3035),U_3038),U_3037)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3034),U_3037))
| ~ c_Finite__Set_Ofolding__one__idem(U_3034,U_3035,U_3036) ),
inference(clausify,[status(thm)],[f_721_3]) ).
fof(f_722_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq]) ).
fof(f_722_2,plain,
! [U_3040,U_3039] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3039,U_3040) = hAPP(c_Finite__Set_Ofold1(U_3039,c_Lattices_Osemilattice__sup__class_Osup(U_3039)),U_3040)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3040))
| ~ class_Lattices_Olattice(U_3039) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
fof(f_722_3,plain,
! [U_3039,U_3040] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3039,U_3040) = hAPP(c_Finite__Set_Ofold1(U_3039,c_Lattices_Osemilattice__sup__class_Osup(U_3039)),U_3040)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3040))
| ~ class_Lattices_Olattice(U_3039) ),
inference(definitional_conversion,[status(esa)],[f_722_2]) ).
cnf(f_722_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3039,U_3040) = hAPP(c_Finite__Set_Ofold1(U_3039,c_Lattices_Osemilattice__sup__class_Osup(U_3039)),U_3040)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3040))
| ~ class_Lattices_Olattice(U_3039) ),
inference(clausify,[status(thm)],[f_722_3]) ).
fof(f_723_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq]) ).
fof(f_723_2,plain,
! [U_3042,U_3041] :
( c_Big__Operators_Olattice__class_OInf__fin(U_3041,U_3042) = hAPP(c_Finite__Set_Ofold1(U_3041,c_Lattices_Osemilattice__inf__class_Oinf(U_3041)),U_3042)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3041),U_3042))
| ~ class_Lattices_Olattice(U_3041) ),
inference(variable_rename,[status(thm)],[f_723_1]) ).
fof(f_723_3,plain,
! [U_3041,U_3042] :
( c_Big__Operators_Olattice__class_OInf__fin(U_3041,U_3042) = hAPP(c_Finite__Set_Ofold1(U_3041,c_Lattices_Osemilattice__inf__class_Oinf(U_3041)),U_3042)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3041),U_3042))
| ~ class_Lattices_Olattice(U_3041) ),
inference(definitional_conversion,[status(esa)],[f_723_2]) ).
cnf(f_723_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_3041,U_3042) = hAPP(c_Finite__Set_Ofold1(U_3041,c_Lattices_Osemilattice__inf__class_Oinf(U_3041)),U_3042)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3041),U_3042))
| ~ class_Lattices_Olattice(U_3041) ),
inference(clausify,[status(thm)],[f_723_3]) ).
fof(f_724_1,plain,
! [V_b_2,V_a_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup]) ).
fof(f_724_2,plain,
! [U_3046,U_3045,U_3044,U_3043] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3043),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3043),U_3045),U_3046)),hAPP(hAPP(c_Finite__Set_Ofold(U_3043,U_3043,c_Lattices_Osemilattice__sup__class_Osup(U_3043)),U_3046),U_3044)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3043),U_3045),U_3044))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3043),U_3044))
| ~ class_Lattices_Osemilattice__sup(U_3043) ),
inference(variable_rename,[status(thm)],[f_724_1]) ).
fof(f_724_3,plain,
! [U_3043,U_3044,U_3045,U_3046] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3043),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3043),U_3045),U_3046)),hAPP(hAPP(c_Finite__Set_Ofold(U_3043,U_3043,c_Lattices_Osemilattice__sup__class_Osup(U_3043)),U_3046),U_3044)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3043),U_3045),U_3044))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3043),U_3044))
| ~ class_Lattices_Osemilattice__sup(U_3043) ),
inference(definitional_conversion,[status(esa)],[f_724_2]) ).
cnf(f_724_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3043),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3043),U_3045),U_3046)),hAPP(hAPP(c_Finite__Set_Ofold(U_3043,U_3043,c_Lattices_Osemilattice__sup__class_Osup(U_3043)),U_3046),U_3044)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3043),U_3045),U_3044))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3043),U_3044))
| ~ class_Lattices_Osemilattice__sup(U_3043) ),
inference(clausify,[status(thm)],[f_724_3]) ).
fof(f_725_1,plain,
! [V_b_2,V_a_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf]) ).
fof(f_725_2,plain,
! [U_3050,U_3049,U_3048,U_3047] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3047),hAPP(hAPP(c_Finite__Set_Ofold(U_3047,U_3047,c_Lattices_Osemilattice__inf__class_Oinf(U_3047)),U_3050),U_3048)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3047),U_3049),U_3050)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3047),U_3049),U_3048))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3047),U_3048))
| ~ class_Lattices_Osemilattice__inf(U_3047) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
fof(f_725_3,plain,
! [U_3047,U_3048,U_3049,U_3050] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3047),hAPP(hAPP(c_Finite__Set_Ofold(U_3047,U_3047,c_Lattices_Osemilattice__inf__class_Oinf(U_3047)),U_3050),U_3048)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3047),U_3049),U_3050)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3047),U_3049),U_3048))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3047),U_3048))
| ~ class_Lattices_Osemilattice__inf(U_3047) ),
inference(definitional_conversion,[status(esa)],[f_725_2]) ).
cnf(f_725_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3047),hAPP(hAPP(c_Finite__Set_Ofold(U_3047,U_3047,c_Lattices_Osemilattice__inf__class_Oinf(U_3047)),U_3050),U_3048)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3047),U_3049),U_3050)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3047),U_3049),U_3048))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3047),U_3048))
| ~ class_Lattices_Osemilattice__inf(U_3047) ),
inference(clausify,[status(thm)],[f_725_3]) ).
fof(f_726_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup]) ).
fof(f_726_2,plain,
! [U_3052,U_3051] :
( c_Complete__Lattice_OSup__class_OSup(U_3051,U_3052) = hAPP(hAPP(c_Finite__Set_Ofold(U_3051,U_3051,c_Lattices_Osemilattice__sup__class_Osup(U_3051)),c_Orderings_Obot__class_Obot(U_3051)),U_3052)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3051),U_3052))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3051) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
fof(f_726_3,plain,
! [U_3051,U_3052] :
( c_Complete__Lattice_OSup__class_OSup(U_3051,U_3052) = hAPP(hAPP(c_Finite__Set_Ofold(U_3051,U_3051,c_Lattices_Osemilattice__sup__class_Osup(U_3051)),c_Orderings_Obot__class_Obot(U_3051)),U_3052)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3051),U_3052))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3051) ),
inference(definitional_conversion,[status(esa)],[f_726_2]) ).
cnf(f_726_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_3051,U_3052) = hAPP(hAPP(c_Finite__Set_Ofold(U_3051,U_3051,c_Lattices_Osemilattice__sup__class_Osup(U_3051)),c_Orderings_Obot__class_Obot(U_3051)),U_3052)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3051),U_3052))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3051) ),
inference(clausify,[status(thm)],[f_726_3]) ).
fof(f_727_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf]) ).
fof(f_727_2,plain,
! [U_3054,U_3053] :
( c_Complete__Lattice_OInf__class_OInf(U_3053,U_3054) = hAPP(hAPP(c_Finite__Set_Ofold(U_3053,U_3053,c_Lattices_Osemilattice__inf__class_Oinf(U_3053)),c_Orderings_Otop__class_Otop(U_3053)),U_3054)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3053),U_3054))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3053) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
fof(f_727_3,plain,
! [U_3053,U_3054] :
( c_Complete__Lattice_OInf__class_OInf(U_3053,U_3054) = hAPP(hAPP(c_Finite__Set_Ofold(U_3053,U_3053,c_Lattices_Osemilattice__inf__class_Oinf(U_3053)),c_Orderings_Otop__class_Otop(U_3053)),U_3054)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3053),U_3054))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3053) ),
inference(definitional_conversion,[status(esa)],[f_727_2]) ).
cnf(f_727_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_3053,U_3054) = hAPP(hAPP(c_Finite__Set_Ofold(U_3053,U_3053,c_Lattices_Osemilattice__inf__class_Oinf(U_3053)),c_Orderings_Otop__class_Otop(U_3053)),U_3054)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3053),U_3054))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_3053) ),
inference(clausify,[status(thm)],[f_727_3]) ).
fof(f_728_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H]) ).
fof(f_728_2,plain,
! [U_3057,U_3056,U_3055] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3055,hAPP(hAPP(c_Set_Oinsert(U_3055),U_3057),U_3056)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3055,U_3055,c_Lattices_Osemilattice__sup__class_Osup(U_3055)),U_3057),U_3056)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3055),U_3056))
| ~ class_Lattices_Olattice(U_3055) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
fof(f_728_3,plain,
! [U_3055,U_3056,U_3057] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3055,hAPP(hAPP(c_Set_Oinsert(U_3055),U_3057),U_3056)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3055,U_3055,c_Lattices_Osemilattice__sup__class_Osup(U_3055)),U_3057),U_3056)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3055),U_3056))
| ~ class_Lattices_Olattice(U_3055) ),
inference(definitional_conversion,[status(esa)],[f_728_2]) ).
cnf(f_728_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3055,hAPP(hAPP(c_Set_Oinsert(U_3055),U_3057),U_3056)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3055,U_3055,c_Lattices_Osemilattice__sup__class_Osup(U_3055)),U_3057),U_3056)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3055),U_3056))
| ~ class_Lattices_Olattice(U_3055) ),
inference(clausify,[status(thm)],[f_728_3]) ).
fof(f_729_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H]) ).
fof(f_729_2,plain,
! [U_3060,U_3059,U_3058] :
( c_Big__Operators_Olattice__class_OInf__fin(U_3058,hAPP(hAPP(c_Set_Oinsert(U_3058),U_3060),U_3059)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3058,U_3058,c_Lattices_Osemilattice__inf__class_Oinf(U_3058)),U_3060),U_3059)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3058),U_3059))
| ~ class_Lattices_Olattice(U_3058) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
fof(f_729_3,plain,
! [U_3058,U_3059,U_3060] :
( c_Big__Operators_Olattice__class_OInf__fin(U_3058,hAPP(hAPP(c_Set_Oinsert(U_3058),U_3060),U_3059)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3058,U_3058,c_Lattices_Osemilattice__inf__class_Oinf(U_3058)),U_3060),U_3059)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3058),U_3059))
| ~ class_Lattices_Olattice(U_3058) ),
inference(definitional_conversion,[status(esa)],[f_729_2]) ).
cnf(f_729_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_3058,hAPP(hAPP(c_Set_Oinsert(U_3058),U_3060),U_3059)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3058,U_3058,c_Lattices_Osemilattice__inf__class_Oinf(U_3058)),U_3060),U_3059)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3058),U_3059))
| ~ class_Lattices_Olattice(U_3058) ),
inference(clausify,[status(thm)],[f_729_3]) ).
fof(f_730_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).
fof(f_730_2,plain,
! [U_3066,U_3065,U_3064,U_3063,U_3062,U_3061] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3061,U_3062,U_3063),U_3066),hAPP(hAPP(c_Set_Oinsert(U_3061),U_3065),U_3064)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3061,U_3062,U_3063),hAPP(hAPP(U_3063,U_3065),U_3066)),U_3064)
| hBOOL(hAPP(hAPP(c_member(U_3061),U_3065),U_3064))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3061),U_3064))
| ~ c_Finite__Set_Ofun__left__comm(U_3061,U_3062,U_3063) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
fof(f_730_3,plain,
! [U_3061,U_3062,U_3063,U_3064,U_3065,U_3066] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3061,U_3062,U_3063),U_3066),hAPP(hAPP(c_Set_Oinsert(U_3061),U_3065),U_3064)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3061,U_3062,U_3063),hAPP(hAPP(U_3063,U_3065),U_3066)),U_3064)
| hBOOL(hAPP(hAPP(c_member(U_3061),U_3065),U_3064))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3061),U_3064))
| ~ c_Finite__Set_Ofun__left__comm(U_3061,U_3062,U_3063) ),
inference(definitional_conversion,[status(esa)],[f_730_2]) ).
cnf(f_730_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3061,U_3062,U_3063),U_3066),hAPP(hAPP(c_Set_Oinsert(U_3061),U_3065),U_3064)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3061,U_3062,U_3063),hAPP(hAPP(U_3063,U_3065),U_3066)),U_3064)
| hBOOL(hAPP(hAPP(c_member(U_3061),U_3065),U_3064))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3061),U_3064))
| ~ c_Finite__Set_Ofun__left__comm(U_3061,U_3062,U_3063) ),
inference(clausify,[status(thm)],[f_730_3]) ).
fof(f_731_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).
fof(f_731_2,plain,
! [U_3072,U_3071,U_3070,U_3069,U_3068,U_3067] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3067,U_3068,U_3069),U_3072),hAPP(hAPP(c_Set_Oinsert(U_3067),U_3071),U_3070)) = hAPP(hAPP(U_3069,U_3071),hAPP(hAPP(c_Finite__Set_Ofold(U_3067,U_3068,U_3069),U_3072),U_3070))
| hBOOL(hAPP(hAPP(c_member(U_3067),U_3071),U_3070))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3067),U_3070))
| ~ c_Finite__Set_Ofun__left__comm(U_3067,U_3068,U_3069) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
fof(f_731_3,plain,
! [U_3067,U_3068,U_3069,U_3070,U_3071,U_3072] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3067,U_3068,U_3069),U_3072),hAPP(hAPP(c_Set_Oinsert(U_3067),U_3071),U_3070)) = hAPP(hAPP(U_3069,U_3071),hAPP(hAPP(c_Finite__Set_Ofold(U_3067,U_3068,U_3069),U_3072),U_3070))
| hBOOL(hAPP(hAPP(c_member(U_3067),U_3071),U_3070))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3067),U_3070))
| ~ c_Finite__Set_Ofun__left__comm(U_3067,U_3068,U_3069) ),
inference(definitional_conversion,[status(esa)],[f_731_2]) ).
cnf(f_731_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3067,U_3068,U_3069),U_3072),hAPP(hAPP(c_Set_Oinsert(U_3067),U_3071),U_3070)) = hAPP(hAPP(U_3069,U_3071),hAPP(hAPP(c_Finite__Set_Ofold(U_3067,U_3068,U_3069),U_3072),U_3070))
| hBOOL(hAPP(hAPP(c_member(U_3067),U_3071),U_3070))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3067),U_3070))
| ~ c_Finite__Set_Ofun__left__comm(U_3067,U_3068,U_3069) ),
inference(clausify,[status(thm)],[f_731_3]) ).
fof(f_732_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).
fof(f_732_2,plain,
! [U_3077,U_3076,U_3075,U_3074,U_3073] :
( hAPP(U_3075,hAPP(hAPP(c_Set_Oinsert(U_3073),U_3077),U_3076)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3073,U_3073,U_3074),U_3077),U_3076)
| hBOOL(hAPP(hAPP(c_member(U_3073),U_3077),U_3076))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3073),U_3076))
| ~ c_Finite__Set_Ofolding__one(U_3073,U_3074,U_3075) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
fof(f_732_3,plain,
! [U_3073,U_3074,U_3075,U_3076,U_3077] :
( hAPP(U_3075,hAPP(hAPP(c_Set_Oinsert(U_3073),U_3077),U_3076)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3073,U_3073,U_3074),U_3077),U_3076)
| hBOOL(hAPP(hAPP(c_member(U_3073),U_3077),U_3076))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3073),U_3076))
| ~ c_Finite__Set_Ofolding__one(U_3073,U_3074,U_3075) ),
inference(definitional_conversion,[status(esa)],[f_732_2]) ).
cnf(f_732_4,plain,
( hAPP(U_3075,hAPP(hAPP(c_Set_Oinsert(U_3073),U_3077),U_3076)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3073,U_3073,U_3074),U_3077),U_3076)
| hBOOL(hAPP(hAPP(c_member(U_3073),U_3077),U_3076))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3073),U_3076))
| ~ c_Finite__Set_Ofolding__one(U_3073,U_3074,U_3075) ),
inference(clausify,[status(thm)],[f_732_3]) ).
fof(f_733_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__belowI]) ).
fof(f_733_2,plain,
! [U_3080,U_3079,U_3078] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3078),hAPP(c_Finite__Set_Ofold1(U_3078,c_Lattices_Osemilattice__inf__class_Oinf(U_3078)),U_3079)),U_3080))
| ~ hBOOL(hAPP(hAPP(c_member(U_3078),U_3080),U_3079))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3078),U_3079))
| ~ class_Lattices_Osemilattice__inf(U_3078) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
fof(f_733_3,plain,
! [U_3078,U_3079,U_3080] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3078),hAPP(c_Finite__Set_Ofold1(U_3078,c_Lattices_Osemilattice__inf__class_Oinf(U_3078)),U_3079)),U_3080))
| ~ hBOOL(hAPP(hAPP(c_member(U_3078),U_3080),U_3079))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3078),U_3079))
| ~ class_Lattices_Osemilattice__inf(U_3078) ),
inference(definitional_conversion,[status(esa)],[f_733_2]) ).
cnf(f_733_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3078),hAPP(c_Finite__Set_Ofold1(U_3078,c_Lattices_Osemilattice__inf__class_Oinf(U_3078)),U_3079)),U_3080))
| ~ hBOOL(hAPP(hAPP(c_member(U_3078),U_3080),U_3079))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3078),U_3079))
| ~ class_Lattices_Osemilattice__inf(U_3078) ),
inference(clausify,[status(thm)],[f_733_3]) ).
fof(f_734_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_below__fold1__iff]) ).
fof(f_734_2,plain,
! [U_3085,U_3084,U_3083] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),hAPP(c_Finite__Set_Ofold1(U_3083,c_Lattices_Osemilattice__inf__class_Oinf(U_3083)),U_3084)))
| ? [U_3082] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),U_3082))
& hBOOL(hAPP(hAPP(c_member(U_3083),U_3082),U_3084)) ) )
& ( ! [U_3081] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),U_3081))
| ~ hBOOL(hAPP(hAPP(c_member(U_3083),U_3081),U_3084)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),hAPP(c_Finite__Set_Ofold1(U_3083,c_Lattices_Osemilattice__inf__class_Oinf(U_3083)),U_3084))) ) )
| U_3084 = c_Orderings_Obot__class_Obot(tc_fun(U_3083,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3083),U_3084))
| ~ class_Lattices_Osemilattice__inf(U_3083) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
fof(f_734_3,plain,
! [U_3085,U_3084,U_3083] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),hAPP(c_Finite__Set_Ofold1(U_3083,c_Lattices_Osemilattice__inf__class_Oinf(U_3083)),U_3084)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),sK81(U_3085,U_3084,U_3083)))
& hBOOL(hAPP(hAPP(c_member(U_3083),sK81(U_3085,U_3084,U_3083)),U_3084)) ) )
& ( ! [U_3081] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),U_3081))
| ~ hBOOL(hAPP(hAPP(c_member(U_3083),U_3081),U_3084)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),hAPP(c_Finite__Set_Ofold1(U_3083,c_Lattices_Osemilattice__inf__class_Oinf(U_3083)),U_3084))) ) )
| U_3084 = c_Orderings_Obot__class_Obot(tc_fun(U_3083,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3083),U_3084))
| ~ class_Lattices_Osemilattice__inf(U_3083) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_3082,sK81(U_3085,U_3084,U_3083))],[f_734_2]) ).
fof(f_734_4,plain,
( ! [U_3083,U_3084,U_3085] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),sK81(U_3085,U_3084,U_3083)))
| ~ sP187(U_3083,U_3084,U_3085) )
& ! [U_3083,U_3084,U_3085] :
( hBOOL(hAPP(hAPP(c_member(U_3083),sK81(U_3085,U_3084,U_3083)),U_3084))
| ~ sP187(U_3083,U_3084,U_3085) )
& ! [U_3081,U_3083,U_3084,U_3085] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),hAPP(c_Finite__Set_Ofold1(U_3083,c_Lattices_Osemilattice__inf__class_Oinf(U_3083)),U_3084)))
| sP187(U_3083,U_3084,U_3085)
| ~ sP188(U_3081,U_3083,U_3084,U_3085) )
& ! [U_3081,U_3083,U_3084,U_3085] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),U_3081))
| ~ hBOOL(hAPP(hAPP(c_member(U_3083),U_3081),U_3084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),hAPP(c_Finite__Set_Ofold1(U_3083,c_Lattices_Osemilattice__inf__class_Oinf(U_3083)),U_3084)))
| ~ sP188(U_3081,U_3083,U_3084,U_3085) )
& ! [U_3081,U_3083,U_3084,U_3085] :
( sP188(U_3081,U_3083,U_3084,U_3085)
| U_3084 = c_Orderings_Obot__class_Obot(tc_fun(U_3083,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3083),U_3084))
| ~ class_Lattices_Osemilattice__inf(U_3083) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187,sP188])],[f_734_3]) ).
cnf(f_734_5,plain,
( sP188(U_3081,U_3083,U_3084,U_3085)
| U_3084 = c_Orderings_Obot__class_Obot(tc_fun(U_3083,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3083),U_3084))
| ~ class_Lattices_Osemilattice__inf(U_3083) ),
inference(clausify,[status(thm)],[f_734_4]) ).
cnf(f_734_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),U_3081))
| ~ hBOOL(hAPP(hAPP(c_member(U_3083),U_3081),U_3084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),hAPP(c_Finite__Set_Ofold1(U_3083,c_Lattices_Osemilattice__inf__class_Oinf(U_3083)),U_3084)))
| ~ sP188(U_3081,U_3083,U_3084,U_3085) ),
inference(clausify,[status(thm)],[f_734_4]) ).
cnf(f_734_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),hAPP(c_Finite__Set_Ofold1(U_3083,c_Lattices_Osemilattice__inf__class_Oinf(U_3083)),U_3084)))
| sP187(U_3083,U_3084,U_3085)
| ~ sP188(U_3081,U_3083,U_3084,U_3085) ),
inference(clausify,[status(thm)],[f_734_4]) ).
cnf(f_734_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_3083),sK81(U_3085,U_3084,U_3083)),U_3084))
| ~ sP187(U_3083,U_3084,U_3085) ),
inference(clausify,[status(thm)],[f_734_4]) ).
cnf(f_734_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3083),U_3085),sK81(U_3085,U_3084,U_3083)))
| ~ sP187(U_3083,U_3084,U_3085) ),
inference(clausify,[status(thm)],[f_734_4]) ).
fof(f_735_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem]) ).
fof(f_735_2,plain,
! [U_3088,U_3087,U_3086] :
( hAPP(c_Finite__Set_Ofold1(U_3086,c_Groups_Otimes__class_Otimes(U_3086)),hAPP(hAPP(c_Set_Oinsert(U_3086),U_3088),U_3087)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3086),U_3088),hAPP(c_Finite__Set_Ofold1(U_3086,c_Groups_Otimes__class_Otimes(U_3086)),U_3087))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3086),U_3087))
| U_3087 = c_Orderings_Obot__class_Obot(tc_fun(U_3086,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3086) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
fof(f_735_3,plain,
! [U_3088,U_3087,U_3086] :
( hAPP(c_Finite__Set_Ofold1(U_3086,c_Groups_Otimes__class_Otimes(U_3086)),hAPP(hAPP(c_Set_Oinsert(U_3086),U_3088),U_3087)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3086),U_3088),hAPP(c_Finite__Set_Ofold1(U_3086,c_Groups_Otimes__class_Otimes(U_3086)),U_3087))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3086),U_3087))
| U_3087 = c_Orderings_Obot__class_Obot(tc_fun(U_3086,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3086) ),
inference(definitional_conversion,[status(esa)],[f_735_2]) ).
cnf(f_735_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_3086,c_Groups_Otimes__class_Otimes(U_3086)),hAPP(hAPP(c_Set_Oinsert(U_3086),U_3088),U_3087)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3086),U_3088),hAPP(c_Finite__Set_Ofold1(U_3086,c_Groups_Otimes__class_Otimes(U_3086)),U_3087))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3086),U_3087))
| U_3087 = c_Orderings_Obot__class_Obot(tc_fun(U_3086,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3086) ),
inference(clausify,[status(thm)],[f_735_3]) ).
fof(f_736_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__Un2]) ).
fof(f_736_2,plain,
! [U_3091,U_3090,U_3089] :
( hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3089,tc_HOL_Obool)),U_3090),U_3091)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3089),hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),U_3090)),hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),U_3091))
| U_3091 = c_Orderings_Obot__class_Obot(tc_fun(U_3089,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3089),U_3091))
| U_3090 = c_Orderings_Obot__class_Obot(tc_fun(U_3089,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3089),U_3090))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3089) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
fof(f_736_3,plain,
! [U_3089,U_3091,U_3090] :
( hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3089,tc_HOL_Obool)),U_3090),U_3091)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3089),hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),U_3090)),hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),U_3091))
| U_3091 = c_Orderings_Obot__class_Obot(tc_fun(U_3089,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3089),U_3091))
| U_3090 = c_Orderings_Obot__class_Obot(tc_fun(U_3089,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3089),U_3090))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3089) ),
inference(definitional_conversion,[status(esa)],[f_736_2]) ).
cnf(f_736_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3089,tc_HOL_Obool)),U_3090),U_3091)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3089),hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),U_3090)),hAPP(c_Finite__Set_Ofold1(U_3089,c_Groups_Otimes__class_Otimes(U_3089)),U_3091))
| U_3091 = c_Orderings_Obot__class_Obot(tc_fun(U_3089,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3089),U_3091))
| U_3090 = c_Orderings_Obot__class_Obot(tc_fun(U_3089,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3089),U_3090))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3089) ),
inference(clausify,[status(thm)],[f_736_3]) ).
fof(f_737_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).
fof(f_737_2,plain,
! [U_3094,U_3093,U_3092] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3092,hAPP(hAPP(c_Set_Oinsert(U_3092),U_3094),U_3093)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3092,U_3092,c_Lattices_Osemilattice__sup__class_Osup(U_3092)),U_3094),U_3093)
| hBOOL(hAPP(hAPP(c_member(U_3092),U_3094),U_3093))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),U_3093))
| ~ class_Lattices_Olattice(U_3092) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
fof(f_737_3,plain,
! [U_3093,U_3094,U_3092] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3092,hAPP(hAPP(c_Set_Oinsert(U_3092),U_3094),U_3093)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3092,U_3092,c_Lattices_Osemilattice__sup__class_Osup(U_3092)),U_3094),U_3093)
| hBOOL(hAPP(hAPP(c_member(U_3092),U_3094),U_3093))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),U_3093))
| ~ class_Lattices_Olattice(U_3092) ),
inference(definitional_conversion,[status(esa)],[f_737_2]) ).
cnf(f_737_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3092,hAPP(hAPP(c_Set_Oinsert(U_3092),U_3094),U_3093)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3092,U_3092,c_Lattices_Osemilattice__sup__class_Osup(U_3092)),U_3094),U_3093)
| hBOOL(hAPP(hAPP(c_member(U_3092),U_3094),U_3093))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),U_3093))
| ~ class_Lattices_Olattice(U_3092) ),
inference(clausify,[status(thm)],[f_737_3]) ).
fof(f_738_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).
fof(f_738_2,plain,
! [U_3097,U_3096,U_3095] :
( c_Big__Operators_Olattice__class_OInf__fin(U_3095,hAPP(hAPP(c_Set_Oinsert(U_3095),U_3097),U_3096)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3095,U_3095,c_Lattices_Osemilattice__inf__class_Oinf(U_3095)),U_3097),U_3096)
| hBOOL(hAPP(hAPP(c_member(U_3095),U_3097),U_3096))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3095),U_3096))
| ~ class_Lattices_Olattice(U_3095) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
fof(f_738_3,plain,
! [U_3095,U_3096,U_3097] :
( c_Big__Operators_Olattice__class_OInf__fin(U_3095,hAPP(hAPP(c_Set_Oinsert(U_3095),U_3097),U_3096)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3095,U_3095,c_Lattices_Osemilattice__inf__class_Oinf(U_3095)),U_3097),U_3096)
| hBOOL(hAPP(hAPP(c_member(U_3095),U_3097),U_3096))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3095),U_3096))
| ~ class_Lattices_Olattice(U_3095) ),
inference(definitional_conversion,[status(esa)],[f_738_2]) ).
cnf(f_738_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_3095,hAPP(hAPP(c_Set_Oinsert(U_3095),U_3097),U_3096)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3095,U_3095,c_Lattices_Osemilattice__inf__class_Oinf(U_3095)),U_3097),U_3096)
| hBOOL(hAPP(hAPP(c_member(U_3095),U_3097),U_3096))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3095),U_3096))
| ~ class_Lattices_Olattice(U_3095) ),
inference(clausify,[status(thm)],[f_738_3]) ).
fof(f_739_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( 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))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove]) ).
fof(f_739_2,plain,
! [U_3103,U_3102,U_3101,U_3100,U_3099,U_3098] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3098,U_3099,U_3100),U_3102),hAPP(hAPP(c_Set_Oinsert(U_3098),U_3103),U_3101)) = hAPP(hAPP(U_3100,U_3103),hAPP(hAPP(c_Finite__Set_Ofold(U_3098,U_3099,U_3100),U_3102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3098,tc_HOL_Obool)),U_3101),hAPP(hAPP(c_Set_Oinsert(U_3098),U_3103),c_Orderings_Obot__class_Obot(tc_fun(U_3098,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3098),U_3101))
| ~ c_Finite__Set_Ofun__left__comm(U_3098,U_3099,U_3100) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
fof(f_739_3,plain,
! [U_3098,U_3099,U_3100,U_3101,U_3102,U_3103] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3098,U_3099,U_3100),U_3102),hAPP(hAPP(c_Set_Oinsert(U_3098),U_3103),U_3101)) = hAPP(hAPP(U_3100,U_3103),hAPP(hAPP(c_Finite__Set_Ofold(U_3098,U_3099,U_3100),U_3102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3098,tc_HOL_Obool)),U_3101),hAPP(hAPP(c_Set_Oinsert(U_3098),U_3103),c_Orderings_Obot__class_Obot(tc_fun(U_3098,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3098),U_3101))
| ~ c_Finite__Set_Ofun__left__comm(U_3098,U_3099,U_3100) ),
inference(definitional_conversion,[status(esa)],[f_739_2]) ).
cnf(f_739_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3098,U_3099,U_3100),U_3102),hAPP(hAPP(c_Set_Oinsert(U_3098),U_3103),U_3101)) = hAPP(hAPP(U_3100,U_3103),hAPP(hAPP(c_Finite__Set_Ofold(U_3098,U_3099,U_3100),U_3102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3098,tc_HOL_Obool)),U_3101),hAPP(hAPP(c_Set_Oinsert(U_3098),U_3103),c_Orderings_Obot__class_Obot(tc_fun(U_3098,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3098),U_3101))
| ~ c_Finite__Set_Ofun__left__comm(U_3098,U_3099,U_3100) ),
inference(clausify,[status(thm)],[f_739_3]) ).
fof(f_740_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__insert]) ).
fof(f_740_2,plain,
! [U_3106,U_3105,U_3104] :
( hAPP(c_Finite__Set_Ofold1(U_3104,c_Groups_Otimes__class_Otimes(U_3104)),hAPP(hAPP(c_Set_Oinsert(U_3104),U_3106),U_3105)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3106),hAPP(c_Finite__Set_Ofold1(U_3104,c_Groups_Otimes__class_Otimes(U_3104)),U_3105))
| hBOOL(hAPP(hAPP(c_member(U_3104),U_3106),U_3105))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3104),U_3105))
| U_3105 = c_Orderings_Obot__class_Obot(tc_fun(U_3104,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_3104) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
fof(f_740_3,plain,
! [U_3104,U_3105,U_3106] :
( hAPP(c_Finite__Set_Ofold1(U_3104,c_Groups_Otimes__class_Otimes(U_3104)),hAPP(hAPP(c_Set_Oinsert(U_3104),U_3106),U_3105)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3106),hAPP(c_Finite__Set_Ofold1(U_3104,c_Groups_Otimes__class_Otimes(U_3104)),U_3105))
| hBOOL(hAPP(hAPP(c_member(U_3104),U_3106),U_3105))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3104),U_3105))
| U_3105 = c_Orderings_Obot__class_Obot(tc_fun(U_3104,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_3104) ),
inference(definitional_conversion,[status(esa)],[f_740_2]) ).
cnf(f_740_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_3104,c_Groups_Otimes__class_Otimes(U_3104)),hAPP(hAPP(c_Set_Oinsert(U_3104),U_3106),U_3105)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3106),hAPP(c_Finite__Set_Ofold1(U_3104,c_Groups_Otimes__class_Otimes(U_3104)),U_3105))
| hBOOL(hAPP(hAPP(c_member(U_3104),U_3106),U_3105))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3104),U_3105))
| U_3105 = c_Orderings_Obot__class_Obot(tc_fun(U_3104,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_3104) ),
inference(clausify,[status(thm)],[f_740_3]) ).
fof(f_741_1,plain,
! [V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq]) ).
fof(f_741_2,plain,
! [U_3110,U_3109,U_3108,U_3107] :
( hAPP(U_3109,U_3110) = hAPP(c_Finite__Set_Ofold1(U_3107,U_3108),U_3110)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3107),U_3110))
| ~ c_Big__Operators_Osemilattice__big(U_3107,U_3108,U_3109) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
fof(f_741_3,plain,
! [U_3107,U_3108,U_3109,U_3110] :
( hAPP(U_3109,U_3110) = hAPP(c_Finite__Set_Ofold1(U_3107,U_3108),U_3110)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3107),U_3110))
| ~ c_Big__Operators_Osemilattice__big(U_3107,U_3108,U_3109) ),
inference(definitional_conversion,[status(esa)],[f_741_2]) ).
cnf(f_741_4,plain,
( hAPP(U_3109,U_3110) = hAPP(c_Finite__Set_Ofold1(U_3107,U_3108),U_3110)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3107),U_3110))
| ~ c_Big__Operators_Osemilattice__big(U_3107,U_3108,U_3109) ),
inference(clausify,[status(thm)],[f_741_3]) ).
fof(f_742_1,plain,
! [V_A_2,T_b] :
( 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))
| ? [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))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__in]) ).
fof(f_742_2,plain,
! [U_3114,U_3113] :
( hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(c_Finite__Set_Ofold1(U_3113,c_Groups_Otimes__class_Otimes(U_3113)),U_3114)),U_3114))
| ? [U_3112,U_3111] : ~ hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3113),U_3112),U_3111)),hAPP(hAPP(c_Set_Oinsert(U_3113),U_3112),hAPP(hAPP(c_Set_Oinsert(U_3113),U_3111),c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))))))
| U_3114 = c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),U_3114))
| ~ class_Groups_Oab__semigroup__mult(U_3113) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
fof(f_742_3,plain,
! [U_3114,U_3113] :
( hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(c_Finite__Set_Ofold1(U_3113,c_Groups_Otimes__class_Otimes(U_3113)),U_3114)),U_3114))
| ? [U_3111] : ~ hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3113),sK82(U_3114,U_3113)),U_3111)),hAPP(hAPP(c_Set_Oinsert(U_3113),sK82(U_3114,U_3113)),hAPP(hAPP(c_Set_Oinsert(U_3113),U_3111),c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))))))
| U_3114 = c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),U_3114))
| ~ class_Groups_Oab__semigroup__mult(U_3113) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_3112,sK82(U_3114,U_3113))],[f_742_2]) ).
fof(f_742_4,plain,
! [U_3114,U_3113] :
( hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(c_Finite__Set_Ofold1(U_3113,c_Groups_Otimes__class_Otimes(U_3113)),U_3114)),U_3114))
| ~ hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3113),sK82(U_3114,U_3113)),sK83(U_3114,U_3113))),hAPP(hAPP(c_Set_Oinsert(U_3113),sK82(U_3114,U_3113)),hAPP(hAPP(c_Set_Oinsert(U_3113),sK83(U_3114,U_3113)),c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))))))
| U_3114 = c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),U_3114))
| ~ class_Groups_Oab__semigroup__mult(U_3113) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_3111,sK83(U_3114,U_3113))],[f_742_3]) ).
fof(f_742_5,plain,
! [U_3113,U_3114] :
( hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(c_Finite__Set_Ofold1(U_3113,c_Groups_Otimes__class_Otimes(U_3113)),U_3114)),U_3114))
| ~ hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3113),sK82(U_3114,U_3113)),sK83(U_3114,U_3113))),hAPP(hAPP(c_Set_Oinsert(U_3113),sK82(U_3114,U_3113)),hAPP(hAPP(c_Set_Oinsert(U_3113),sK83(U_3114,U_3113)),c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))))))
| U_3114 = c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),U_3114))
| ~ class_Groups_Oab__semigroup__mult(U_3113) ),
inference(definitional_conversion,[status(esa)],[f_742_4]) ).
cnf(f_742_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(c_Finite__Set_Ofold1(U_3113,c_Groups_Otimes__class_Otimes(U_3113)),U_3114)),U_3114))
| ~ hBOOL(hAPP(hAPP(c_member(U_3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3113),sK82(U_3114,U_3113)),sK83(U_3114,U_3113))),hAPP(hAPP(c_Set_Oinsert(U_3113),sK82(U_3114,U_3113)),hAPP(hAPP(c_Set_Oinsert(U_3113),sK83(U_3114,U_3113)),c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))))))
| U_3114 = c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),U_3114))
| ~ class_Groups_Oab__semigroup__mult(U_3113) ),
inference(clausify,[status(thm)],[f_742_5]) ).
fof(f_743_1,plain,
! [V_N_2,V_h_2,T_b] :
( 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))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [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))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute]) ).
fof(f_743_2,plain,
! [U_3119,U_3118,U_3117] :
( hAPP(U_3118,hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),U_3119)) = hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),hAPP(c_Set_Oimage(U_3117,U_3117,U_3118),U_3119))
| U_3119 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3119))
| ? [U_3116,U_3115] : hAPP(U_3118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),U_3116),U_3115)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),hAPP(U_3118,U_3116)),hAPP(U_3118,U_3115))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3117) ),
inference(variable_rename,[status(thm)],[f_743_1]) ).
fof(f_743_3,plain,
! [U_3119,U_3118,U_3117] :
( hAPP(U_3118,hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),U_3119)) = hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),hAPP(c_Set_Oimage(U_3117,U_3117,U_3118),U_3119))
| U_3119 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3119))
| ? [U_3115] : hAPP(U_3118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),sK84(U_3119,U_3118,U_3117)),U_3115)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),hAPP(U_3118,sK84(U_3119,U_3118,U_3117))),hAPP(U_3118,U_3115))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_3116,sK84(U_3119,U_3118,U_3117))],[f_743_2]) ).
fof(f_743_4,plain,
! [U_3119,U_3118,U_3117] :
( hAPP(U_3118,hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),U_3119)) = hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),hAPP(c_Set_Oimage(U_3117,U_3117,U_3118),U_3119))
| U_3119 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3119))
| hAPP(U_3118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),sK84(U_3119,U_3118,U_3117)),sK85(U_3119,U_3118,U_3117))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),hAPP(U_3118,sK84(U_3119,U_3118,U_3117))),hAPP(U_3118,sK85(U_3119,U_3118,U_3117)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_3115,sK85(U_3119,U_3118,U_3117))],[f_743_3]) ).
fof(f_743_5,plain,
! [U_3117,U_3118,U_3119] :
( hAPP(U_3118,hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),U_3119)) = hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),hAPP(c_Set_Oimage(U_3117,U_3117,U_3118),U_3119))
| U_3119 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3119))
| hAPP(U_3118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),sK84(U_3119,U_3118,U_3117)),sK85(U_3119,U_3118,U_3117))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),hAPP(U_3118,sK84(U_3119,U_3118,U_3117))),hAPP(U_3118,sK85(U_3119,U_3118,U_3117)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3117) ),
inference(definitional_conversion,[status(esa)],[f_743_4]) ).
cnf(f_743_6,plain,
( hAPP(U_3118,hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),U_3119)) = hAPP(c_Finite__Set_Ofold1(U_3117,c_Groups_Otimes__class_Otimes(U_3117)),hAPP(c_Set_Oimage(U_3117,U_3117,U_3118),U_3119))
| U_3119 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3119))
| hAPP(U_3118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),sK84(U_3119,U_3118,U_3117)),sK85(U_3119,U_3118,U_3117))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3117),hAPP(U_3118,sK84(U_3119,U_3118,U_3117))),hAPP(U_3118,sK85(U_3119,U_3118,U_3117)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3117) ),
inference(clausify,[status(thm)],[f_743_5]) ).
fof(f_744_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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))
| ? [B_x] :
( hAPP(V_g_2,B_x) != V_z_2
& 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))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter__neutral]) ).
fof(f_744_2,plain,
! [U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122,U_3121] :
( hAPP(U_3126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128)) = hAPP(hAPP(U_3123,hAPP(U_3126,U_3127)),hAPP(U_3126,U_3128))
| ? [U_3120] :
( hAPP(U_3125,U_3120) != U_3124
& hBOOL(hAPP(hAPP(c_member(U_3122),U_3120),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3128))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3127))
| ~ c_Finite__Set_Ofolding__image__simple(U_3121,U_3122,U_3123,U_3124,U_3125,U_3126) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
fof(f_744_3,plain,
! [U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122] :
( ! [U_3121] : ~ c_Finite__Set_Ofolding__image__simple(U_3121,U_3122,U_3123,U_3124,U_3125,U_3126)
| hAPP(U_3126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128)) = hAPP(hAPP(U_3123,hAPP(U_3126,U_3127)),hAPP(U_3126,U_3128))
| ? [U_3120] :
( hAPP(U_3125,U_3120) != U_3124
& hBOOL(hAPP(hAPP(c_member(U_3122),U_3120),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3128))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3127)) ),
inference(miniscope,[status(thm)],[f_744_2]) ).
fof(f_744_4,plain,
! [U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122] :
( ! [U_3121] : ~ c_Finite__Set_Ofolding__image__simple(U_3121,U_3122,U_3123,U_3124,U_3125,U_3126)
| hAPP(U_3126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128)) = hAPP(hAPP(U_3123,hAPP(U_3126,U_3127)),hAPP(U_3126,U_3128))
| ( hAPP(U_3125,sK86(U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122)) != U_3124
& hBOOL(hAPP(hAPP(c_member(U_3122),sK86(U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3128))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3127)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_3120,sK86(U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122))],[f_744_3]) ).
fof(f_744_5,plain,
( ! [U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128] :
( hAPP(U_3125,sK86(U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122)) != U_3124
| ~ sP189(U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128) )
& ! [U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128] :
( hBOOL(hAPP(hAPP(c_member(U_3122),sK86(U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128)))
| ~ sP189(U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128) )
& ! [U_3121,U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128] :
( ~ c_Finite__Set_Ofolding__image__simple(U_3121,U_3122,U_3123,U_3124,U_3125,U_3126)
| hAPP(U_3126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128)) = hAPP(hAPP(U_3123,hAPP(U_3126,U_3127)),hAPP(U_3126,U_3128))
| sP189(U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3128))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3127)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_744_4]) ).
cnf(f_744_6,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_3121,U_3122,U_3123,U_3124,U_3125,U_3126)
| hAPP(U_3126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128)) = hAPP(hAPP(U_3123,hAPP(U_3126,U_3127)),hAPP(U_3126,U_3128))
| sP189(U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3128))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3122),U_3127)) ),
inference(clausify,[status(thm)],[f_744_5]) ).
cnf(f_744_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_3122),sK86(U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3122,tc_HOL_Obool)),U_3127),U_3128)))
| ~ sP189(U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128) ),
inference(clausify,[status(thm)],[f_744_5]) ).
cnf(f_744_8,plain,
( hAPP(U_3125,sK86(U_3128,U_3127,U_3126,U_3125,U_3124,U_3123,U_3122)) != U_3124
| ~ sP189(U_3122,U_3123,U_3124,U_3125,U_3126,U_3127,U_3128) ),
inference(clausify,[status(thm)],[f_744_5]) ).
fof(f_745_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem]) ).
fof(f_745_2,plain,
! [U_3134,U_3133,U_3132,U_3131,U_3130,U_3129] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3129,U_3130,U_3131),U_3133),hAPP(hAPP(c_Set_Oinsert(U_3129),U_3134),U_3132)) = hAPP(hAPP(U_3131,U_3134),hAPP(hAPP(c_Finite__Set_Ofold(U_3129,U_3130,U_3131),U_3133),U_3132))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3129),U_3132))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_3129,U_3130,U_3131) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
fof(f_745_3,plain,
! [U_3131,U_3132,U_3129,U_3134,U_3133,U_3130] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3129,U_3130,U_3131),U_3133),hAPP(hAPP(c_Set_Oinsert(U_3129),U_3134),U_3132)) = hAPP(hAPP(U_3131,U_3134),hAPP(hAPP(c_Finite__Set_Ofold(U_3129,U_3130,U_3131),U_3133),U_3132))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3129),U_3132))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_3129,U_3130,U_3131) ),
inference(definitional_conversion,[status(esa)],[f_745_2]) ).
cnf(f_745_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3129,U_3130,U_3131),U_3133),hAPP(hAPP(c_Set_Oinsert(U_3129),U_3134),U_3132)) = hAPP(hAPP(U_3131,U_3134),hAPP(hAPP(c_Finite__Set_Ofold(U_3129,U_3130,U_3131),U_3133),U_3132))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3129),U_3132))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_3129,U_3130,U_3131) ),
inference(clausify,[status(thm)],[f_745_3]) ).
fof(f_746_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2]) ).
fof(f_746_2,plain,
! [U_3140,U_3139,U_3138,U_3137,U_3136,U_3135] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3135,U_3136,U_3137),U_3139),hAPP(hAPP(c_Set_Oinsert(U_3135),U_3140),U_3138)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3135,U_3136,U_3137),hAPP(hAPP(U_3137,U_3140),U_3139)),U_3138)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3135),U_3138))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_3135,U_3136,U_3137) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
fof(f_746_3,plain,
! [U_3136,U_3135,U_3137,U_3138,U_3139,U_3140] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3135,U_3136,U_3137),U_3139),hAPP(hAPP(c_Set_Oinsert(U_3135),U_3140),U_3138)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3135,U_3136,U_3137),hAPP(hAPP(U_3137,U_3140),U_3139)),U_3138)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3135),U_3138))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_3135,U_3136,U_3137) ),
inference(definitional_conversion,[status(esa)],[f_746_2]) ).
cnf(f_746_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3135,U_3136,U_3137),U_3139),hAPP(hAPP(c_Set_Oinsert(U_3135),U_3140),U_3138)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3135,U_3136,U_3137),hAPP(hAPP(U_3137,U_3140),U_3139)),U_3138)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3135),U_3138))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_3135,U_3136,U_3137) ),
inference(clausify,[status(thm)],[f_746_3]) ).
fof(f_747_1,plain,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Rings_Oring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring]) ).
fof(f_747_2,plain,
! [U_3145,U_3144,U_3143,U_3142,U_3141] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3142,U_3141),U_3145),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3142,tc_HOL_Obool)),U_3143),hAPP(hAPP(c_Set_Oinsert(U_3142),U_3144),c_Orderings_Obot__class_Obot(tc_fun(U_3142,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3141),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3142,U_3141),U_3145),U_3143)),hAPP(U_3145,U_3144))
| ~ hBOOL(hAPP(hAPP(c_member(U_3142),U_3144),U_3143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3142),U_3143))
| ~ class_Rings_Oring(U_3141) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
fof(f_747_3,plain,
! [U_3141,U_3142,U_3143,U_3144,U_3145] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3142,U_3141),U_3145),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3142,tc_HOL_Obool)),U_3143),hAPP(hAPP(c_Set_Oinsert(U_3142),U_3144),c_Orderings_Obot__class_Obot(tc_fun(U_3142,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3141),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3142,U_3141),U_3145),U_3143)),hAPP(U_3145,U_3144))
| ~ hBOOL(hAPP(hAPP(c_member(U_3142),U_3144),U_3143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3142),U_3143))
| ~ class_Rings_Oring(U_3141) ),
inference(definitional_conversion,[status(esa)],[f_747_2]) ).
cnf(f_747_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3142,U_3141),U_3145),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3142,tc_HOL_Obool)),U_3143),hAPP(hAPP(c_Set_Oinsert(U_3142),U_3144),c_Orderings_Obot__class_Obot(tc_fun(U_3142,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3141),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3142,U_3141),U_3145),U_3143)),hAPP(U_3145,U_3144))
| ~ hBOOL(hAPP(hAPP(c_member(U_3142),U_3144),U_3143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3142),U_3143))
| ~ class_Rings_Oring(U_3141) ),
inference(clausify,[status(thm)],[f_747_3]) ).
fof(f_748_1,plain,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_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))))) = 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1]) ).
fof(f_748_2,plain,
! [U_3150,U_3149,U_3148,U_3147,U_3146] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3147,tc_HOL_Obool)),U_3148),hAPP(hAPP(c_Set_Oinsert(U_3147),U_3149),c_Orderings_Obot__class_Obot(tc_fun(U_3147,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),U_3148)
| hBOOL(hAPP(hAPP(c_member(U_3147),U_3149),U_3148)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3147,tc_HOL_Obool)),U_3148),hAPP(hAPP(c_Set_Oinsert(U_3147),U_3149),c_Orderings_Obot__class_Obot(tc_fun(U_3147,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3146),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),U_3148)),hAPP(U_3150,U_3149))
| ~ hBOOL(hAPP(hAPP(c_member(U_3147),U_3149),U_3148)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3147),U_3148))
| ~ class_Groups_Oab__group__add(U_3146) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
fof(f_748_3,plain,
( ! [U_3146,U_3147,U_3148,U_3149,U_3150] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3147,tc_HOL_Obool)),U_3148),hAPP(hAPP(c_Set_Oinsert(U_3147),U_3149),c_Orderings_Obot__class_Obot(tc_fun(U_3147,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),U_3148)
| hBOOL(hAPP(hAPP(c_member(U_3147),U_3149),U_3148))
| ~ sP190(U_3146,U_3147,U_3148,U_3149,U_3150) )
& ! [U_3146,U_3147,U_3148,U_3149,U_3150] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3147,tc_HOL_Obool)),U_3148),hAPP(hAPP(c_Set_Oinsert(U_3147),U_3149),c_Orderings_Obot__class_Obot(tc_fun(U_3147,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3146),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),U_3148)),hAPP(U_3150,U_3149))
| ~ hBOOL(hAPP(hAPP(c_member(U_3147),U_3149),U_3148))
| ~ sP190(U_3146,U_3147,U_3148,U_3149,U_3150) )
& ! [U_3146,U_3147,U_3148,U_3149,U_3150] :
( sP190(U_3146,U_3147,U_3148,U_3149,U_3150)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3147),U_3148))
| ~ class_Groups_Oab__group__add(U_3146) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190])],[f_748_2]) ).
cnf(f_748_4,plain,
( sP190(U_3146,U_3147,U_3148,U_3149,U_3150)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3147),U_3148))
| ~ class_Groups_Oab__group__add(U_3146) ),
inference(clausify,[status(thm)],[f_748_3]) ).
cnf(f_748_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3147,tc_HOL_Obool)),U_3148),hAPP(hAPP(c_Set_Oinsert(U_3147),U_3149),c_Orderings_Obot__class_Obot(tc_fun(U_3147,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3146),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),U_3148)),hAPP(U_3150,U_3149))
| ~ hBOOL(hAPP(hAPP(c_member(U_3147),U_3149),U_3148))
| ~ sP190(U_3146,U_3147,U_3148,U_3149,U_3150) ),
inference(clausify,[status(thm)],[f_748_3]) ).
cnf(f_748_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3147,tc_HOL_Obool)),U_3148),hAPP(hAPP(c_Set_Oinsert(U_3147),U_3149),c_Orderings_Obot__class_Obot(tc_fun(U_3147,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3147,U_3146),U_3150),U_3148)
| hBOOL(hAPP(hAPP(c_member(U_3147),U_3149),U_3148))
| ~ sP190(U_3146,U_3147,U_3148,U_3149,U_3150) ),
inference(clausify,[status(thm)],[f_748_3]) ).
fof(f_749_1,plain,
! [V_g_2,V_x_2,V_A_2,T_b,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_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))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oremove]) ).
fof(f_749_2,plain,
! [U_3155,U_3154,U_3153,U_3152,U_3151] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3152,U_3151),U_3155),U_3153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3151),hAPP(U_3155,U_3154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3152,U_3151),U_3155),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3152,tc_HOL_Obool)),U_3153),hAPP(hAPP(c_Set_Oinsert(U_3152),U_3154),c_Orderings_Obot__class_Obot(tc_fun(U_3152,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3152),U_3154),U_3153))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3152),U_3153))
| ~ class_Groups_Ocomm__monoid__mult(U_3151) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
fof(f_749_3,plain,
! [U_3153,U_3152,U_3155,U_3154,U_3151] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3152,U_3151),U_3155),U_3153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3151),hAPP(U_3155,U_3154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3152,U_3151),U_3155),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3152,tc_HOL_Obool)),U_3153),hAPP(hAPP(c_Set_Oinsert(U_3152),U_3154),c_Orderings_Obot__class_Obot(tc_fun(U_3152,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3152),U_3154),U_3153))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3152),U_3153))
| ~ class_Groups_Ocomm__monoid__mult(U_3151) ),
inference(definitional_conversion,[status(esa)],[f_749_2]) ).
cnf(f_749_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3152,U_3151),U_3155),U_3153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3151),hAPP(U_3155,U_3154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3152,U_3151),U_3155),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3152,tc_HOL_Obool)),U_3153),hAPP(hAPP(c_Set_Oinsert(U_3152),U_3154),c_Orderings_Obot__class_Obot(tc_fun(U_3152,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3152),U_3154),U_3153))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3152),U_3153))
| ~ class_Groups_Ocomm__monoid__mult(U_3151) ),
inference(clausify,[status(thm)],[f_749_3]) ).
fof(f_750_1,plain,
! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
( 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)
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem]) ).
fof(f_750_2,plain,
! [U_3160,U_3159,U_3158,U_3157,U_3156] :
( hAPP(hAPP(U_3158,U_3159),hAPP(hAPP(U_3158,U_3159),U_3160)) = hAPP(hAPP(U_3158,U_3159),U_3160)
| ~ c_Finite__Set_Ofun__left__comm__idem(U_3156,U_3157,U_3158) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
fof(f_750_3,plain,
! [U_3160,U_3159,U_3158] :
( ! [U_3157,U_3156] : ~ c_Finite__Set_Ofun__left__comm__idem(U_3156,U_3157,U_3158)
| hAPP(hAPP(U_3158,U_3159),hAPP(hAPP(U_3158,U_3159),U_3160)) = hAPP(hAPP(U_3158,U_3159),U_3160) ),
inference(miniscope,[status(thm)],[f_750_2]) ).
fof(f_750_4,plain,
! [U_3156,U_3159,U_3157,U_3158,U_3160] :
( ~ c_Finite__Set_Ofun__left__comm__idem(U_3156,U_3157,U_3158)
| hAPP(hAPP(U_3158,U_3159),hAPP(hAPP(U_3158,U_3159),U_3160)) = hAPP(hAPP(U_3158,U_3159),U_3160) ),
inference(definitional_conversion,[status(esa)],[f_750_3]) ).
cnf(f_750_5,plain,
( ~ c_Finite__Set_Ofun__left__comm__idem(U_3156,U_3157,U_3158)
| hAPP(hAPP(U_3158,U_3159),hAPP(hAPP(U_3158,U_3159),U_3160)) = hAPP(hAPP(U_3158,U_3159),U_3160) ),
inference(clausify,[status(thm)],[f_750_4]) ).
fof(f_751_1,plain,
! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl]) ).
fof(f_751_2,plain,
! [U_3165,U_3164,U_3163,U_3162,U_3161] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3161),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3162),U_3164))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3162),U_3163))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3163),U_3164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3163),U_3164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3162),U_3163))
| ~ class_Groups_Oab__group__add(U_3161) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
fof(f_751_3,plain,
! [U_3161,U_3162,U_3163,U_3164,U_3165] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3161),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3162),U_3164))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3162),U_3163))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3163),U_3164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3163),U_3164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3162),U_3163))
| ~ class_Groups_Oab__group__add(U_3161) ),
inference(definitional_conversion,[status(esa)],[f_751_2]) ).
cnf(f_751_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3161),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3162),U_3164))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3162),U_3163))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3161),U_3165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3163),U_3164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3163),U_3164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3162),U_3163))
| ~ class_Groups_Oab__group__add(U_3161) ),
inference(clausify,[status(thm)],[f_751_3]) ).
fof(f_752_1,plain,
! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__insert]) ).
fof(f_752_2,plain,
! [U_3166] : c_Finite__Set_Ofun__left__comm__idem(U_3166,tc_fun(U_3166,tc_HOL_Obool),c_Set_Oinsert(U_3166)),
inference(variable_rename,[status(thm)],[f_752_1]) ).
fof(f_752_3,plain,
! [U_3166] : c_Finite__Set_Ofun__left__comm__idem(U_3166,tc_fun(U_3166,tc_HOL_Obool),c_Set_Oinsert(U_3166)),
inference(definitional_conversion,[status(esa)],[f_752_2]) ).
cnf(f_752_4,plain,
c_Finite__Set_Ofun__left__comm__idem(U_3166,tc_fun(U_3166,tc_HOL_Obool),c_Set_Oinsert(U_3166)),
inference(clausify,[status(thm)],[f_752_3]) ).
fof(f_753_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem]) ).
fof(f_753_2,plain,
! [U_3167] :
( c_Finite__Set_Ofun__left__comm__idem(U_3167,U_3167,c_Groups_Otimes__class_Otimes(U_3167))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3167) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
fof(f_753_3,plain,
! [U_3167] :
( c_Finite__Set_Ofun__left__comm__idem(U_3167,U_3167,c_Groups_Otimes__class_Otimes(U_3167))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3167) ),
inference(definitional_conversion,[status(esa)],[f_753_2]) ).
cnf(f_753_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_3167,U_3167,c_Groups_Otimes__class_Otimes(U_3167))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3167) ),
inference(clausify,[status(thm)],[f_753_3]) ).
fof(f_754_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup]) ).
fof(f_754_2,plain,
! [U_3168] :
( c_Finite__Set_Ofun__left__comm__idem(U_3168,U_3168,c_Lattices_Osemilattice__sup__class_Osup(U_3168))
| ~ class_Lattices_Osemilattice__sup(U_3168) ),
inference(variable_rename,[status(thm)],[f_754_1]) ).
fof(f_754_3,plain,
! [U_3168] :
( c_Finite__Set_Ofun__left__comm__idem(U_3168,U_3168,c_Lattices_Osemilattice__sup__class_Osup(U_3168))
| ~ class_Lattices_Osemilattice__sup(U_3168) ),
inference(definitional_conversion,[status(esa)],[f_754_2]) ).
cnf(f_754_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_3168,U_3168,c_Lattices_Osemilattice__sup__class_Osup(U_3168))
| ~ class_Lattices_Osemilattice__sup(U_3168) ),
inference(clausify,[status(thm)],[f_754_3]) ).
fof(f_755_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf]) ).
fof(f_755_2,plain,
! [U_3169] :
( c_Finite__Set_Ofun__left__comm__idem(U_3169,U_3169,c_Lattices_Osemilattice__inf__class_Oinf(U_3169))
| ~ class_Lattices_Osemilattice__inf(U_3169) ),
inference(variable_rename,[status(thm)],[f_755_1]) ).
fof(f_755_3,plain,
! [U_3169] :
( c_Finite__Set_Ofun__left__comm__idem(U_3169,U_3169,c_Lattices_Osemilattice__inf__class_Oinf(U_3169))
| ~ class_Lattices_Osemilattice__inf(U_3169) ),
inference(definitional_conversion,[status(esa)],[f_755_2]) ).
cnf(f_755_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_3169,U_3169,c_Lattices_Osemilattice__inf__class_Oinf(U_3169))
| ~ class_Lattices_Osemilattice__inf(U_3169) ),
inference(clausify,[status(thm)],[f_755_3]) ).
fof(f_756_1,plain,
! [V_f_2,V_A_2,V_B_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat]) ).
fof(f_756_2,plain,
! [U_3173,U_3172,U_3171,U_3170] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3170,tc_HOL_Obool)),U_3172),U_3171)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),U_3172)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),U_3171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3170,tc_HOL_Obool)),U_3171),U_3172))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3170),U_3171)) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
fof(f_756_3,plain,
! [U_3170,U_3171,U_3172,U_3173] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3170,tc_HOL_Obool)),U_3172),U_3171)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),U_3172)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),U_3171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3170,tc_HOL_Obool)),U_3171),U_3172))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3170),U_3171)) ),
inference(definitional_conversion,[status(esa)],[f_756_2]) ).
cnf(f_756_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3170,tc_HOL_Obool)),U_3172),U_3171)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),U_3172)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3170,tc_Nat_Onat),U_3173),U_3171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3170,tc_HOL_Obool)),U_3171),U_3172))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3170),U_3171)) ),
inference(clausify,[status(thm)],[f_756_3]) ).
fof(f_757_1,plain,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert]) ).
fof(f_757_2,plain,
! [U_3178,U_3177,U_3176,U_3175,U_3174] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3175,U_3174),U_3178),hAPP(hAPP(c_Set_Oinsert(U_3175),U_3177),U_3176)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3174),hAPP(U_3178,U_3177)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3175,U_3174),U_3178),U_3176))
| hBOOL(hAPP(hAPP(c_member(U_3175),U_3177),U_3176))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3175),U_3176))
| ~ class_Groups_Ocomm__monoid__mult(U_3174) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
fof(f_757_3,plain,
! [U_3174,U_3175,U_3176,U_3177,U_3178] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3175,U_3174),U_3178),hAPP(hAPP(c_Set_Oinsert(U_3175),U_3177),U_3176)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3174),hAPP(U_3178,U_3177)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3175,U_3174),U_3178),U_3176))
| hBOOL(hAPP(hAPP(c_member(U_3175),U_3177),U_3176))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3175),U_3176))
| ~ class_Groups_Ocomm__monoid__mult(U_3174) ),
inference(definitional_conversion,[status(esa)],[f_757_2]) ).
cnf(f_757_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3175,U_3174),U_3178),hAPP(hAPP(c_Set_Oinsert(U_3175),U_3177),U_3176)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3174),hAPP(U_3178,U_3177)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3175,U_3174),U_3178),U_3176))
| hBOOL(hAPP(hAPP(c_member(U_3175),U_3177),U_3176))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3175),U_3176))
| ~ class_Groups_Ocomm__monoid__mult(U_3174) ),
inference(clausify,[status(thm)],[f_757_3]) ).
fof(f_758_1,plain,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__insert]) ).
fof(f_758_2,plain,
! [U_3183,U_3182,U_3181,U_3180,U_3179] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3180,U_3179),U_3183),hAPP(hAPP(c_Set_Oinsert(U_3180),U_3182),U_3181)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3179),hAPP(U_3183,U_3182)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3180,U_3179),U_3183),U_3181))
| hBOOL(hAPP(hAPP(c_member(U_3180),U_3182),U_3181))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),U_3181))
| ~ class_Groups_Ocomm__monoid__mult(U_3179) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
fof(f_758_3,plain,
! [U_3179,U_3180,U_3181,U_3182,U_3183] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3180,U_3179),U_3183),hAPP(hAPP(c_Set_Oinsert(U_3180),U_3182),U_3181)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3179),hAPP(U_3183,U_3182)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3180,U_3179),U_3183),U_3181))
| hBOOL(hAPP(hAPP(c_member(U_3180),U_3182),U_3181))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),U_3181))
| ~ class_Groups_Ocomm__monoid__mult(U_3179) ),
inference(definitional_conversion,[status(esa)],[f_758_2]) ).
cnf(f_758_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3180,U_3179),U_3183),hAPP(hAPP(c_Set_Oinsert(U_3180),U_3182),U_3181)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3179),hAPP(U_3183,U_3182)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3180,U_3179),U_3183),U_3181))
| hBOOL(hAPP(hAPP(c_member(U_3180),U_3182),U_3181))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),U_3181))
| ~ class_Groups_Ocomm__monoid__mult(U_3179) ),
inference(clausify,[status(thm)],[f_758_3]) ).
fof(f_759_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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_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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int]) ).
fof(f_759_2,plain,
! [U_3188,U_3187,U_3186,U_3185,U_3184] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3184),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3185,tc_HOL_Obool)),U_3186),U_3187))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3185,tc_HOL_Obool)),U_3186),U_3187))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3184),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),U_3186)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),U_3187))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),U_3187))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),U_3186))
| ~ class_Groups_Ocomm__monoid__mult(U_3184) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
fof(f_759_3,plain,
! [U_3184,U_3185,U_3186,U_3187,U_3188] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3184),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3185,tc_HOL_Obool)),U_3186),U_3187))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3185,tc_HOL_Obool)),U_3186),U_3187))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3184),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),U_3186)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),U_3187))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),U_3187))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),U_3186))
| ~ class_Groups_Ocomm__monoid__mult(U_3184) ),
inference(definitional_conversion,[status(esa)],[f_759_2]) ).
cnf(f_759_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3184),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3185,tc_HOL_Obool)),U_3186),U_3187))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3185,tc_HOL_Obool)),U_3186),U_3187))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3184),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),U_3186)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3185,U_3184),U_3188),U_3187))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),U_3187))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),U_3186))
| ~ class_Groups_Ocomm__monoid__mult(U_3184) ),
inference(clausify,[status(thm)],[f_759_3]) ).
fof(f_760_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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_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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter]) ).
fof(f_760_2,plain,
! [U_3193,U_3192,U_3191,U_3190,U_3189] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3189),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3190,tc_HOL_Obool)),U_3191),U_3192))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3190,tc_HOL_Obool)),U_3191),U_3192))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3189),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),U_3191)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),U_3192))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3190),U_3192))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3190),U_3191))
| ~ class_Groups_Ocomm__monoid__mult(U_3189) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
fof(f_760_3,plain,
! [U_3189,U_3190,U_3191,U_3192,U_3193] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3189),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3190,tc_HOL_Obool)),U_3191),U_3192))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3190,tc_HOL_Obool)),U_3191),U_3192))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3189),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),U_3191)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),U_3192))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3190),U_3192))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3190),U_3191))
| ~ class_Groups_Ocomm__monoid__mult(U_3189) ),
inference(definitional_conversion,[status(esa)],[f_760_2]) ).
cnf(f_760_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3189),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3190,tc_HOL_Obool)),U_3191),U_3192))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3190,tc_HOL_Obool)),U_3191),U_3192))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3189),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),U_3191)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3190,U_3189),U_3193),U_3192))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3190),U_3192))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3190),U_3191))
| ~ class_Groups_Ocomm__monoid__mult(U_3189) ),
inference(clausify,[status(thm)],[f_760_3]) ).
fof(f_761_1,plain,
! [V_f_2,V_A_2,V_a_2,T_b] :
( ( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1__nat]) ).
fof(f_761_2,plain,
! [U_3197,U_3196,U_3195,U_3194] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3194,tc_Nat_Onat),U_3197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3194,tc_HOL_Obool)),U_3196),hAPP(hAPP(c_Set_Oinsert(U_3194),U_3195),c_Orderings_Obot__class_Obot(tc_fun(U_3194,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3194,tc_Nat_Onat),U_3197),U_3196)
| hBOOL(hAPP(hAPP(c_member(U_3194),U_3195),U_3196)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3194,tc_Nat_Onat),U_3197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3194,tc_HOL_Obool)),U_3196),hAPP(hAPP(c_Set_Oinsert(U_3194),U_3195),c_Orderings_Obot__class_Obot(tc_fun(U_3194,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3194,tc_Nat_Onat),U_3197),U_3196)),hAPP(U_3197,U_3195))
| ~ hBOOL(hAPP(hAPP(c_member(U_3194),U_3195),U_3196)) ) ),
inference(variable_rename,[status(thm)],[f_761_1]) ).
fof(f_761_3,plain,
( ! [U_3205,U_3203,U_3201,U_3199] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3199,tc_Nat_Onat),U_3205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3199,tc_HOL_Obool)),U_3203),hAPP(hAPP(c_Set_Oinsert(U_3199),U_3201),c_Orderings_Obot__class_Obot(tc_fun(U_3199,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3199,tc_Nat_Onat),U_3205),U_3203)
| hBOOL(hAPP(hAPP(c_member(U_3199),U_3201),U_3203)) )
& ! [U_3204,U_3202,U_3200,U_3198] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3198,tc_Nat_Onat),U_3204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3198,tc_HOL_Obool)),U_3202),hAPP(hAPP(c_Set_Oinsert(U_3198),U_3200),c_Orderings_Obot__class_Obot(tc_fun(U_3198,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3198,tc_Nat_Onat),U_3204),U_3202)),hAPP(U_3204,U_3200))
| ~ hBOOL(hAPP(hAPP(c_member(U_3198),U_3200),U_3202)) ) ),
inference(miniscope,[status(thm)],[f_761_2]) ).
fof(f_761_4,plain,
( ! [U_3201,U_3199,U_3203,U_3205] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3199,tc_Nat_Onat),U_3205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3199,tc_HOL_Obool)),U_3203),hAPP(hAPP(c_Set_Oinsert(U_3199),U_3201),c_Orderings_Obot__class_Obot(tc_fun(U_3199,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3199,tc_Nat_Onat),U_3205),U_3203)
| hBOOL(hAPP(hAPP(c_member(U_3199),U_3201),U_3203)) )
& ! [U_3200,U_3204,U_3202,U_3198] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3198,tc_Nat_Onat),U_3204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3198,tc_HOL_Obool)),U_3202),hAPP(hAPP(c_Set_Oinsert(U_3198),U_3200),c_Orderings_Obot__class_Obot(tc_fun(U_3198,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3198,tc_Nat_Onat),U_3204),U_3202)),hAPP(U_3204,U_3200))
| ~ hBOOL(hAPP(hAPP(c_member(U_3198),U_3200),U_3202)) ) ),
inference(definitional_conversion,[status(esa)],[f_761_3]) ).
cnf(f_761_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3198,tc_Nat_Onat),U_3204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3198,tc_HOL_Obool)),U_3202),hAPP(hAPP(c_Set_Oinsert(U_3198),U_3200),c_Orderings_Obot__class_Obot(tc_fun(U_3198,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3198,tc_Nat_Onat),U_3204),U_3202)),hAPP(U_3204,U_3200))
| ~ hBOOL(hAPP(hAPP(c_member(U_3198),U_3200),U_3202)) ),
inference(clausify,[status(thm)],[f_761_4]) ).
cnf(f_761_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3199,tc_Nat_Onat),U_3205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3199,tc_HOL_Obool)),U_3203),hAPP(hAPP(c_Set_Oinsert(U_3199),U_3201),c_Orderings_Obot__class_Obot(tc_fun(U_3199,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3199,tc_Nat_Onat),U_3205),U_3203)
| hBOOL(hAPP(hAPP(c_member(U_3199),U_3201),U_3203)) ),
inference(clausify,[status(thm)],[f_761_4]) ).
fof(f_762_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff]) ).
fof(f_762_2,plain,
! [U_3210,U_3209,U_3208,U_3207,U_3206] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3207,tc_HOL_Obool)),U_3208),U_3209)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3206),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),U_3208)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),U_3209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3207,tc_HOL_Obool)),U_3209),U_3208))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3207),U_3208))
| ~ class_Groups_Oab__group__add(U_3206) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
! [U_3206,U_3207,U_3208,U_3209,U_3210] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3207,tc_HOL_Obool)),U_3208),U_3209)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3206),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),U_3208)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),U_3209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3207,tc_HOL_Obool)),U_3209),U_3208))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3207),U_3208))
| ~ class_Groups_Oab__group__add(U_3206) ),
inference(definitional_conversion,[status(esa)],[f_762_2]) ).
cnf(f_762_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3207,tc_HOL_Obool)),U_3208),U_3209)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3206),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),U_3208)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3207,U_3206),U_3210),U_3209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3207,tc_HOL_Obool)),U_3209),U_3208))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3207),U_3208))
| ~ class_Groups_Oab__group__add(U_3206) ),
inference(clausify,[status(thm)],[f_762_3]) ).
fof(f_763_1,plain,
! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
( 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))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove]) ).
fof(f_763_2,plain,
! [U_3215,U_3214,U_3213,U_3212,U_3211] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3212,U_3211),U_3214),hAPP(hAPP(c_Set_Oinsert(U_3212),U_3215),U_3213)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3211),hAPP(U_3214,U_3215)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3212,U_3211),U_3214),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3212,tc_HOL_Obool)),U_3213),hAPP(hAPP(c_Set_Oinsert(U_3212),U_3215),c_Orderings_Obot__class_Obot(tc_fun(U_3212,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3212),U_3213))
| ~ class_Groups_Ocomm__monoid__mult(U_3211) ),
inference(variable_rename,[status(thm)],[f_763_1]) ).
fof(f_763_3,plain,
! [U_3211,U_3212,U_3213,U_3214,U_3215] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3212,U_3211),U_3214),hAPP(hAPP(c_Set_Oinsert(U_3212),U_3215),U_3213)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3211),hAPP(U_3214,U_3215)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3212,U_3211),U_3214),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3212,tc_HOL_Obool)),U_3213),hAPP(hAPP(c_Set_Oinsert(U_3212),U_3215),c_Orderings_Obot__class_Obot(tc_fun(U_3212,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3212),U_3213))
| ~ class_Groups_Ocomm__monoid__mult(U_3211) ),
inference(definitional_conversion,[status(esa)],[f_763_2]) ).
cnf(f_763_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3212,U_3211),U_3214),hAPP(hAPP(c_Set_Oinsert(U_3212),U_3215),U_3213)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3211),hAPP(U_3214,U_3215)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3212,U_3211),U_3214),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3212,tc_HOL_Obool)),U_3213),hAPP(hAPP(c_Set_Oinsert(U_3212),U_3215),c_Orderings_Obot__class_Obot(tc_fun(U_3212,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3212),U_3213))
| ~ class_Groups_Ocomm__monoid__mult(U_3211) ),
inference(clausify,[status(thm)],[f_763_3]) ).
fof(f_764_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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_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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint]) ).
fof(f_764_2,plain,
! [U_3220,U_3219,U_3218,U_3217,U_3216] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3217,tc_HOL_Obool)),U_3218),U_3219)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3216),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),U_3218)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),U_3219))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3217,tc_HOL_Obool)),U_3218),U_3219) != c_Orderings_Obot__class_Obot(tc_fun(U_3217,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3218))
| ~ class_Groups_Ocomm__monoid__mult(U_3216) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
fof(f_764_3,plain,
! [U_3216,U_3217,U_3218,U_3219,U_3220] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3217,tc_HOL_Obool)),U_3218),U_3219)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3216),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),U_3218)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),U_3219))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3217,tc_HOL_Obool)),U_3218),U_3219) != c_Orderings_Obot__class_Obot(tc_fun(U_3217,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3218))
| ~ class_Groups_Ocomm__monoid__mult(U_3216) ),
inference(definitional_conversion,[status(esa)],[f_764_2]) ).
cnf(f_764_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3217,tc_HOL_Obool)),U_3218),U_3219)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3216),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),U_3218)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3217,U_3216),U_3220),U_3219))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3217,tc_HOL_Obool)),U_3218),U_3219) != c_Orderings_Obot__class_Obot(tc_fun(U_3217,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3218))
| ~ class_Groups_Ocomm__monoid__mult(U_3216) ),
inference(clausify,[status(thm)],[f_764_3]) ).
fof(f_765_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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_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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint]) ).
fof(f_765_2,plain,
! [U_3225,U_3224,U_3223,U_3222,U_3221] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3222,tc_HOL_Obool)),U_3223),U_3224)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3221),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),U_3223)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),U_3224))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3222,tc_HOL_Obool)),U_3223),U_3224) != c_Orderings_Obot__class_Obot(tc_fun(U_3222,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3222),U_3224))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3222),U_3223))
| ~ class_Groups_Ocomm__monoid__mult(U_3221) ),
inference(variable_rename,[status(thm)],[f_765_1]) ).
fof(f_765_3,plain,
! [U_3221,U_3222,U_3223,U_3224,U_3225] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3222,tc_HOL_Obool)),U_3223),U_3224)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3221),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),U_3223)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),U_3224))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3222,tc_HOL_Obool)),U_3223),U_3224) != c_Orderings_Obot__class_Obot(tc_fun(U_3222,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3222),U_3224))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3222),U_3223))
| ~ class_Groups_Ocomm__monoid__mult(U_3221) ),
inference(definitional_conversion,[status(esa)],[f_765_2]) ).
cnf(f_765_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3222,tc_HOL_Obool)),U_3223),U_3224)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3221),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),U_3223)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3222,U_3221),U_3225),U_3224))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3222,tc_HOL_Obool)),U_3223),U_3224) != c_Orderings_Obot__class_Obot(tc_fun(U_3222,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3222),U_3224))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3222),U_3223))
| ~ class_Groups_Ocomm__monoid__mult(U_3221) ),
inference(clausify,[status(thm)],[f_765_3]) ).
fof(f_766_1,plain,
! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__strict__mono]) ).
fof(f_766_2,plain,
! [U_3231,U_3230,U_3229,U_3228,U_3227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3227),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3228,U_3227),U_3230),U_3229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3228,U_3227),U_3231),U_3229)))
| ? [U_3226] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3227),hAPP(U_3230,U_3226)),hAPP(U_3231,U_3226)))
& hBOOL(hAPP(hAPP(c_member(U_3228),U_3226),U_3229)) )
| U_3229 = c_Orderings_Obot__class_Obot(tc_fun(U_3228,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3228),U_3229))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3227)
| ~ class_Groups_Ocomm__monoid__add(U_3227) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
fof(f_766_3,plain,
! [U_3231,U_3230,U_3229,U_3228,U_3227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3227),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3228,U_3227),U_3230),U_3229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3228,U_3227),U_3231),U_3229)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3227),hAPP(U_3230,sK87(U_3231,U_3230,U_3229,U_3228,U_3227))),hAPP(U_3231,sK87(U_3231,U_3230,U_3229,U_3228,U_3227))))
& hBOOL(hAPP(hAPP(c_member(U_3228),sK87(U_3231,U_3230,U_3229,U_3228,U_3227)),U_3229)) )
| U_3229 = c_Orderings_Obot__class_Obot(tc_fun(U_3228,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3228),U_3229))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3227)
| ~ class_Groups_Ocomm__monoid__add(U_3227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_3226,sK87(U_3231,U_3230,U_3229,U_3228,U_3227))],[f_766_2]) ).
fof(f_766_4,plain,
( ! [U_3227,U_3228,U_3229,U_3230,U_3231] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3227),hAPP(U_3230,sK87(U_3231,U_3230,U_3229,U_3228,U_3227))),hAPP(U_3231,sK87(U_3231,U_3230,U_3229,U_3228,U_3227))))
| ~ sP191(U_3227,U_3228,U_3229,U_3230,U_3231) )
& ! [U_3227,U_3228,U_3229,U_3230,U_3231] :
( hBOOL(hAPP(hAPP(c_member(U_3228),sK87(U_3231,U_3230,U_3229,U_3228,U_3227)),U_3229))
| ~ sP191(U_3227,U_3228,U_3229,U_3230,U_3231) )
& ! [U_3227,U_3228,U_3229,U_3230,U_3231] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3227),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3228,U_3227),U_3230),U_3229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3228,U_3227),U_3231),U_3229)))
| sP191(U_3227,U_3228,U_3229,U_3230,U_3231)
| U_3229 = c_Orderings_Obot__class_Obot(tc_fun(U_3228,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3228),U_3229))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3227)
| ~ class_Groups_Ocomm__monoid__add(U_3227) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191])],[f_766_3]) ).
cnf(f_766_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3227),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3228,U_3227),U_3230),U_3229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3228,U_3227),U_3231),U_3229)))
| sP191(U_3227,U_3228,U_3229,U_3230,U_3231)
| U_3229 = c_Orderings_Obot__class_Obot(tc_fun(U_3228,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3228),U_3229))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3227)
| ~ class_Groups_Ocomm__monoid__add(U_3227) ),
inference(clausify,[status(thm)],[f_766_4]) ).
cnf(f_766_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3228),sK87(U_3231,U_3230,U_3229,U_3228,U_3227)),U_3229))
| ~ sP191(U_3227,U_3228,U_3229,U_3230,U_3231) ),
inference(clausify,[status(thm)],[f_766_4]) ).
cnf(f_766_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3227),hAPP(U_3230,sK87(U_3231,U_3230,U_3229,U_3228,U_3227))),hAPP(U_3231,sK87(U_3231,U_3230,U_3229,U_3228,U_3227))))
| ~ sP191(U_3227,U_3228,U_3229,U_3230,U_3231) ),
inference(clausify,[status(thm)],[f_766_4]) ).
fof(f_767_1,plain,
! [V_f_2,V_a_2,V_A_2,T_b,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_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))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H]) ).
fof(f_767_2,plain,
! [U_3236,U_3235,U_3234,U_3233,U_3232] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3233,U_3232),U_3236),U_3234) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3232),hAPP(U_3236,U_3235)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3233,U_3232),U_3236),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3233,tc_HOL_Obool)),U_3234),hAPP(hAPP(c_Set_Oinsert(U_3233),U_3235),c_Orderings_Obot__class_Obot(tc_fun(U_3233,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3233),U_3235),U_3234))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3233),U_3234))
| ~ class_Groups_Ocomm__monoid__add(U_3232) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
fof(f_767_3,plain,
! [U_3232,U_3234,U_3233,U_3235,U_3236] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3233,U_3232),U_3236),U_3234) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3232),hAPP(U_3236,U_3235)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3233,U_3232),U_3236),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3233,tc_HOL_Obool)),U_3234),hAPP(hAPP(c_Set_Oinsert(U_3233),U_3235),c_Orderings_Obot__class_Obot(tc_fun(U_3233,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3233),U_3235),U_3234))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3233),U_3234))
| ~ class_Groups_Ocomm__monoid__add(U_3232) ),
inference(definitional_conversion,[status(esa)],[f_767_2]) ).
cnf(f_767_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3233,U_3232),U_3236),U_3234) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3232),hAPP(U_3236,U_3235)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3233,U_3232),U_3236),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3233,tc_HOL_Obool)),U_3234),hAPP(hAPP(c_Set_Oinsert(U_3233),U_3235),c_Orderings_Obot__class_Obot(tc_fun(U_3233,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3233),U_3235),U_3234))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3233),U_3234))
| ~ class_Groups_Ocomm__monoid__add(U_3232) ),
inference(clausify,[status(thm)],[f_767_3]) ).
fof(f_768_1,plain,
! [V_g_2,V_x_2,V_A_2,T_b,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_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))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oremove]) ).
fof(f_768_2,plain,
! [U_3241,U_3240,U_3239,U_3238,U_3237] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3238,U_3237),U_3241),U_3239) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3237),hAPP(U_3241,U_3240)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3238,U_3237),U_3241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3238,tc_HOL_Obool)),U_3239),hAPP(hAPP(c_Set_Oinsert(U_3238),U_3240),c_Orderings_Obot__class_Obot(tc_fun(U_3238,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3238),U_3240),U_3239))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3238),U_3239))
| ~ class_Groups_Ocomm__monoid__add(U_3237) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
fof(f_768_3,plain,
! [U_3237,U_3238,U_3239,U_3240,U_3241] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3238,U_3237),U_3241),U_3239) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3237),hAPP(U_3241,U_3240)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3238,U_3237),U_3241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3238,tc_HOL_Obool)),U_3239),hAPP(hAPP(c_Set_Oinsert(U_3238),U_3240),c_Orderings_Obot__class_Obot(tc_fun(U_3238,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3238),U_3240),U_3239))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3238),U_3239))
| ~ class_Groups_Ocomm__monoid__add(U_3237) ),
inference(definitional_conversion,[status(esa)],[f_768_2]) ).
cnf(f_768_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3238,U_3237),U_3241),U_3239) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3237),hAPP(U_3241,U_3240)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3238,U_3237),U_3241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3238,tc_HOL_Obool)),U_3239),hAPP(hAPP(c_Set_Oinsert(U_3238),U_3240),c_Orderings_Obot__class_Obot(tc_fun(U_3238,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3238),U_3240),U_3239))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3238),U_3239))
| ~ class_Groups_Ocomm__monoid__add(U_3237) ),
inference(clausify,[status(thm)],[f_768_3]) ).
fof(f_769_1,plain,
! [V_ca_2,V_b_2,V_A_2,T_b] :
( 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_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf]) ).
fof(f_769_2,plain,
! [U_3246,U_3245,U_3244,U_3243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3243),U_3245),U_3246)),hAPP(hAPP(c_Finite__Set_Ofold(U_3243,U_3243,c_Lattices_Osemilattice__inf__class_Oinf(U_3243)),U_3246),U_3244)))
| ? [U_3242] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3243),U_3245),U_3242))
& hBOOL(hAPP(hAPP(c_member(U_3243),U_3242),U_3244)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3243),U_3244))
| ~ class_Lattices_Osemilattice__inf(U_3243) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
fof(f_769_3,plain,
! [U_3246,U_3245,U_3244,U_3243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3243),U_3245),U_3246)),hAPP(hAPP(c_Finite__Set_Ofold(U_3243,U_3243,c_Lattices_Osemilattice__inf__class_Oinf(U_3243)),U_3246),U_3244)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3243),U_3245),sK88(U_3246,U_3245,U_3244,U_3243)))
& hBOOL(hAPP(hAPP(c_member(U_3243),sK88(U_3246,U_3245,U_3244,U_3243)),U_3244)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3243),U_3244))
| ~ class_Lattices_Osemilattice__inf(U_3243) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_3242,sK88(U_3246,U_3245,U_3244,U_3243))],[f_769_2]) ).
fof(f_769_4,plain,
( ! [U_3243,U_3244,U_3245,U_3246] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3243),U_3245),sK88(U_3246,U_3245,U_3244,U_3243)))
| ~ sP192(U_3243,U_3244,U_3245,U_3246) )
& ! [U_3243,U_3244,U_3245,U_3246] :
( hBOOL(hAPP(hAPP(c_member(U_3243),sK88(U_3246,U_3245,U_3244,U_3243)),U_3244))
| ~ sP192(U_3243,U_3244,U_3245,U_3246) )
& ! [U_3243,U_3244,U_3245,U_3246] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3243),U_3245),U_3246)),hAPP(hAPP(c_Finite__Set_Ofold(U_3243,U_3243,c_Lattices_Osemilattice__inf__class_Oinf(U_3243)),U_3246),U_3244)))
| sP192(U_3243,U_3244,U_3245,U_3246)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3243),U_3244))
| ~ class_Lattices_Osemilattice__inf(U_3243) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_769_3]) ).
cnf(f_769_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3243),U_3245),U_3246)),hAPP(hAPP(c_Finite__Set_Ofold(U_3243,U_3243,c_Lattices_Osemilattice__inf__class_Oinf(U_3243)),U_3246),U_3244)))
| sP192(U_3243,U_3244,U_3245,U_3246)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3243),U_3244))
| ~ class_Lattices_Osemilattice__inf(U_3243) ),
inference(clausify,[status(thm)],[f_769_4]) ).
cnf(f_769_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3243),sK88(U_3246,U_3245,U_3244,U_3243)),U_3244))
| ~ sP192(U_3243,U_3244,U_3245,U_3246) ),
inference(clausify,[status(thm)],[f_769_4]) ).
cnf(f_769_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3243),U_3245),sK88(U_3246,U_3245,U_3244,U_3243)))
| ~ sP192(U_3243,U_3244,U_3245,U_3246) ),
inference(clausify,[status(thm)],[f_769_4]) ).
fof(f_770_1,plain,
! [V_ca_2,V_b_2,V_A_2,T_b] :
( 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_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup]) ).
fof(f_770_2,plain,
! [U_3251,U_3250,U_3249,U_3248] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3248),hAPP(hAPP(c_Finite__Set_Ofold(U_3248,U_3248,c_Lattices_Osemilattice__sup__class_Osup(U_3248)),U_3251),U_3249)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3248),U_3250),U_3251)))
| ? [U_3247] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3248),U_3247),U_3250))
& hBOOL(hAPP(hAPP(c_member(U_3248),U_3247),U_3249)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3248),U_3249))
| ~ class_Lattices_Osemilattice__sup(U_3248) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
fof(f_770_3,plain,
! [U_3251,U_3250,U_3249,U_3248] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3248),hAPP(hAPP(c_Finite__Set_Ofold(U_3248,U_3248,c_Lattices_Osemilattice__sup__class_Osup(U_3248)),U_3251),U_3249)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3248),U_3250),U_3251)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3248),sK89(U_3251,U_3250,U_3249,U_3248)),U_3250))
& hBOOL(hAPP(hAPP(c_member(U_3248),sK89(U_3251,U_3250,U_3249,U_3248)),U_3249)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3248),U_3249))
| ~ class_Lattices_Osemilattice__sup(U_3248) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_3247,sK89(U_3251,U_3250,U_3249,U_3248))],[f_770_2]) ).
fof(f_770_4,plain,
( ! [U_3248,U_3249,U_3250,U_3251] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3248),sK89(U_3251,U_3250,U_3249,U_3248)),U_3250))
| ~ sP193(U_3248,U_3249,U_3250,U_3251) )
& ! [U_3248,U_3249,U_3250,U_3251] :
( hBOOL(hAPP(hAPP(c_member(U_3248),sK89(U_3251,U_3250,U_3249,U_3248)),U_3249))
| ~ sP193(U_3248,U_3249,U_3250,U_3251) )
& ! [U_3248,U_3249,U_3250,U_3251] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3248),hAPP(hAPP(c_Finite__Set_Ofold(U_3248,U_3248,c_Lattices_Osemilattice__sup__class_Osup(U_3248)),U_3251),U_3249)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3248),U_3250),U_3251)))
| sP193(U_3248,U_3249,U_3250,U_3251)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3248),U_3249))
| ~ class_Lattices_Osemilattice__sup(U_3248) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193])],[f_770_3]) ).
cnf(f_770_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3248),hAPP(hAPP(c_Finite__Set_Ofold(U_3248,U_3248,c_Lattices_Osemilattice__sup__class_Osup(U_3248)),U_3251),U_3249)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3248),U_3250),U_3251)))
| sP193(U_3248,U_3249,U_3250,U_3251)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3248),U_3249))
| ~ class_Lattices_Osemilattice__sup(U_3248) ),
inference(clausify,[status(thm)],[f_770_4]) ).
cnf(f_770_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3248),sK89(U_3251,U_3250,U_3249,U_3248)),U_3249))
| ~ sP193(U_3248,U_3249,U_3250,U_3251) ),
inference(clausify,[status(thm)],[f_770_4]) ).
cnf(f_770_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3248),sK89(U_3251,U_3250,U_3249,U_3248)),U_3250))
| ~ sP193(U_3248,U_3249,U_3250,U_3251) ),
inference(clausify,[status(thm)],[f_770_4]) ).
fof(f_771_1,plain,
! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
( 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_ca_2),V_d_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x)) )
| V_b_2 != V_d_2
| V_a_2 != V_ca_2
| ~ class_Orderings_Oord(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong]) ).
fof(f_771_2,plain,
! [U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3254,U_3253),U_3259),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_3254,U_3255),U_3257)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3254,U_3253),U_3260),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_3254,U_3256),U_3258))
| ? [U_3252] :
( hAPP(U_3259,U_3252) != hAPP(U_3260,U_3252)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3254),U_3252),U_3258))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3254),U_3256),U_3252)) )
| U_3257 != U_3258
| U_3255 != U_3256
| ~ class_Orderings_Oord(U_3254)
| ~ class_Groups_Ocomm__monoid__add(U_3253) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
fof(f_771_3,plain,
! [U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3254,U_3253),U_3259),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_3254,U_3255),U_3257)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3254,U_3253),U_3260),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_3254,U_3256),U_3258))
| ( hAPP(U_3259,sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253)) != hAPP(U_3260,sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3254),sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253)),U_3258))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3254),U_3256),sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253))) )
| U_3257 != U_3258
| U_3255 != U_3256
| ~ class_Orderings_Oord(U_3254)
| ~ class_Groups_Ocomm__monoid__add(U_3253) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_3252,sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253))],[f_771_2]) ).
fof(f_771_4,plain,
( ! [U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260] :
( hAPP(U_3259,sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253)) != hAPP(U_3260,sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253))
| ~ sP194(U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260) )
& ! [U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3254),sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253)),U_3258))
| ~ sP194(U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260) )
& ! [U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3254),U_3256),sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253)))
| ~ sP194(U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260) )
& ! [U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3254,U_3253),U_3259),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_3254,U_3255),U_3257)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3254,U_3253),U_3260),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_3254,U_3256),U_3258))
| sP194(U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260)
| U_3257 != U_3258
| U_3255 != U_3256
| ~ class_Orderings_Oord(U_3254)
| ~ class_Groups_Ocomm__monoid__add(U_3253) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194])],[f_771_3]) ).
cnf(f_771_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3254,U_3253),U_3259),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_3254,U_3255),U_3257)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3254,U_3253),U_3260),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_3254,U_3256),U_3258))
| sP194(U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260)
| U_3257 != U_3258
| U_3255 != U_3256
| ~ class_Orderings_Oord(U_3254)
| ~ class_Groups_Ocomm__monoid__add(U_3253) ),
inference(clausify,[status(thm)],[f_771_4]) ).
cnf(f_771_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3254),U_3256),sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253)))
| ~ sP194(U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260) ),
inference(clausify,[status(thm)],[f_771_4]) ).
cnf(f_771_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3254),sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253)),U_3258))
| ~ sP194(U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260) ),
inference(clausify,[status(thm)],[f_771_4]) ).
cnf(f_771_8,plain,
( hAPP(U_3259,sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253)) != hAPP(U_3260,sK90(U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254,U_3253))
| ~ sP194(U_3253,U_3254,U_3255,U_3256,U_3257,U_3258,U_3259,U_3260) ),
inference(clausify,[status(thm)],[f_771_4]) ).
fof(f_772_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem]) ).
fof(f_772_2,plain,
! [U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262,U_3261] :
( hAPP(U_3266,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3262,tc_HOL_Obool)),U_3267),U_3268)) = hAPP(hAPP(U_3263,hAPP(U_3266,U_3267)),hAPP(U_3266,U_3268))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3262),U_3268))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3262),U_3267))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_3261,U_3262,U_3263,U_3264,U_3265,U_3266) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
fof(f_772_3,plain,
! [U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262] :
( ! [U_3261] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_3261,U_3262,U_3263,U_3264,U_3265,U_3266)
| hAPP(U_3266,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3262,tc_HOL_Obool)),U_3267),U_3268)) = hAPP(hAPP(U_3263,hAPP(U_3266,U_3267)),hAPP(U_3266,U_3268))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3262),U_3268))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3262),U_3267)) ),
inference(miniscope,[status(thm)],[f_772_2]) ).
fof(f_772_4,plain,
! [U_3265,U_3266,U_3262,U_3264,U_3267,U_3268,U_3261,U_3263] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3261,U_3262,U_3263,U_3264,U_3265,U_3266)
| hAPP(U_3266,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3262,tc_HOL_Obool)),U_3267),U_3268)) = hAPP(hAPP(U_3263,hAPP(U_3266,U_3267)),hAPP(U_3266,U_3268))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3262),U_3268))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3262),U_3267)) ),
inference(definitional_conversion,[status(esa)],[f_772_3]) ).
cnf(f_772_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3261,U_3262,U_3263,U_3264,U_3265,U_3266)
| hAPP(U_3266,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3262,tc_HOL_Obool)),U_3267),U_3268)) = hAPP(hAPP(U_3263,hAPP(U_3266,U_3267)),hAPP(U_3266,U_3268))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3262),U_3268))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3262),U_3267)) ),
inference(clausify,[status(thm)],[f_772_4]) ).
fof(f_773_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem]) ).
fof(f_773_2,plain,
! [U_3276,U_3275,U_3274,U_3273,U_3272,U_3271,U_3270,U_3269] :
( hAPP(hAPP(U_3271,hAPP(U_3274,U_3276)),hAPP(U_3274,U_3275)) = hAPP(U_3274,U_3275)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3270,tc_HOL_Obool)),U_3276),U_3275))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3270),U_3275))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_3269,U_3270,U_3271,U_3272,U_3273,U_3274) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
fof(f_773_3,plain,
! [U_3276,U_3275,U_3274,U_3273,U_3272,U_3271,U_3270] :
( ! [U_3269] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_3269,U_3270,U_3271,U_3272,U_3273,U_3274)
| hAPP(hAPP(U_3271,hAPP(U_3274,U_3276)),hAPP(U_3274,U_3275)) = hAPP(U_3274,U_3275)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3270,tc_HOL_Obool)),U_3276),U_3275))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3270),U_3275)) ),
inference(miniscope,[status(thm)],[f_773_2]) ).
fof(f_773_4,plain,
! [U_3270,U_3269,U_3271,U_3272,U_3273,U_3274,U_3275,U_3276] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3269,U_3270,U_3271,U_3272,U_3273,U_3274)
| hAPP(hAPP(U_3271,hAPP(U_3274,U_3276)),hAPP(U_3274,U_3275)) = hAPP(U_3274,U_3275)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3270,tc_HOL_Obool)),U_3276),U_3275))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3270),U_3275)) ),
inference(definitional_conversion,[status(esa)],[f_773_3]) ).
cnf(f_773_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3269,U_3270,U_3271,U_3272,U_3273,U_3274)
| hAPP(hAPP(U_3271,hAPP(U_3274,U_3276)),hAPP(U_3274,U_3275)) = hAPP(U_3274,U_3275)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3270,tc_HOL_Obool)),U_3276),U_3275))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3270),U_3275)) ),
inference(clausify,[status(thm)],[f_773_4]) ).
fof(f_774_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__atLeastLessThan]) ).
fof(f_774_2,plain,
! [U_3278,U_3277] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3277),U_3278))),
inference(variable_rename,[status(thm)],[f_774_1]) ).
fof(f_774_3,plain,
! [U_3277,U_3278] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3277),U_3278))),
inference(definitional_conversion,[status(esa)],[f_774_2]) ).
cnf(f_774_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3277),U_3278))),
inference(clausify,[status(thm)],[f_774_3]) ).
fof(f_775_1,plain,
! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl]) ).
fof(f_775_2,plain,
! [U_3283,U_3282,U_3281,U_3280,U_3279] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3279),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3280),U_3281))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3281),U_3282))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3280),U_3282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3281),U_3282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3280),U_3281))
| ~ class_Groups_Ocomm__monoid__add(U_3279) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
fof(f_775_3,plain,
! [U_3279,U_3280,U_3281,U_3282,U_3283] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3279),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3280),U_3281))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3281),U_3282))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3280),U_3282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3281),U_3282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3280),U_3281))
| ~ class_Groups_Ocomm__monoid__add(U_3279) ),
inference(definitional_conversion,[status(esa)],[f_775_2]) ).
cnf(f_775_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3279),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3280),U_3281))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3281),U_3282))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3279),U_3283),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3280),U_3282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3281),U_3282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3280),U_3281))
| ~ class_Groups_Ocomm__monoid__add(U_3279) ),
inference(clausify,[status(thm)],[f_775_3]) ).
fof(f_776_1,plain,
! [V_N_2] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
| ! [B_m] :
? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) )
& ( ? [B_m] :
! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded__le]) ).
fof(f_776_2,plain,
! [U_3288] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3288))
| ! [U_3287] :
? [U_3286] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3286),U_3287))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3286),U_3288)) ) )
& ( ? [U_3285] :
! [U_3284] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3284),U_3285))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3284),U_3288)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3288)) ) ),
inference(variable_rename,[status(thm)],[f_776_1]) ).
fof(f_776_3,plain,
( ! [U_3290] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3290))
| ! [U_3287] :
? [U_3286] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3286),U_3287))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3286),U_3290)) ) )
& ! [U_3289] :
( ? [U_3285] :
! [U_3284] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3284),U_3285))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3284),U_3289)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3289)) ) ),
inference(miniscope,[status(thm)],[f_776_2]) ).
fof(f_776_4,plain,
( ! [U_3290] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3290))
| ! [U_3287] :
? [U_3286] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3286),U_3287))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3286),U_3290)) ) )
& ! [U_3289] :
( ! [U_3284] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3284),sK91(U_3289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3284),U_3289)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3289)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_3285,sK91(U_3289))],[f_776_3]) ).
fof(f_776_5,plain,
( ! [U_3290] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3290))
| ! [U_3287] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK92(U_3290,U_3287)),U_3287))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK92(U_3290,U_3287)),U_3290)) ) )
& ! [U_3289] :
( ! [U_3284] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3284),sK91(U_3289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3284),U_3289)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3289)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_3286,sK92(U_3290,U_3287))],[f_776_4]) ).
fof(f_776_6,plain,
( ! [U_3287,U_3290] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK92(U_3290,U_3287)),U_3287))
| ~ sP195(U_3287,U_3290) )
& ! [U_3287,U_3290] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK92(U_3290,U_3287)),U_3290))
| ~ sP195(U_3287,U_3290) )
& ! [U_3287,U_3290] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3290))
| sP195(U_3287,U_3290) )
& ! [U_3284,U_3289] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3284),sK91(U_3289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3284),U_3289))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3289)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195])],[f_776_5]) ).
cnf(f_776_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3284),sK91(U_3289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3284),U_3289))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3289)) ),
inference(clausify,[status(thm)],[f_776_6]) ).
cnf(f_776_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3290))
| sP195(U_3287,U_3290) ),
inference(clausify,[status(thm)],[f_776_6]) ).
cnf(f_776_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK92(U_3290,U_3287)),U_3290))
| ~ sP195(U_3287,U_3290) ),
inference(clausify,[status(thm)],[f_776_6]) ).
cnf(f_776_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK92(U_3290,U_3287)),U_3287))
| ~ sP195(U_3287,U_3290) ),
inference(clausify,[status(thm)],[f_776_6]) ).
fof(f_777_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Oab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J]) ).
fof(f_777_2,plain,
! [U_3294,U_3293,U_3292,U_3291] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3292),U_3293)),U_3294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3293),U_3294))
| ~ class_Groups_Oab__semigroup__add(U_3291) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
fof(f_777_3,plain,
! [U_3292,U_3293,U_3291,U_3294] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3292),U_3293)),U_3294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3293),U_3294))
| ~ class_Groups_Oab__semigroup__add(U_3291) ),
inference(definitional_conversion,[status(esa)],[f_777_2]) ).
cnf(f_777_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3292),U_3293)),U_3294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3291),U_3293),U_3294))
| ~ class_Groups_Oab__semigroup__add(U_3291) ),
inference(clausify,[status(thm)],[f_777_3]) ).
fof(f_778_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( 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_ca_2)
| V_b_2 != V_ca_2 )
& ( V_b_2 = V_ca_2
| 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_ca_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_778_2,plain,
! [U_3298,U_3297,U_3296,U_3295] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3297) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3298)
| U_3297 != U_3298 )
& ( U_3297 = U_3298
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3297) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3298) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_3295) ),
inference(variable_rename,[status(thm)],[f_778_1]) ).
fof(f_778_3,plain,
( ! [U_3296,U_3295,U_3297,U_3298] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3297) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3298)
| U_3297 != U_3298
| ~ sP196(U_3296,U_3295,U_3297,U_3298) )
& ! [U_3296,U_3295,U_3297,U_3298] :
( U_3297 = U_3298
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3297) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3298)
| ~ sP196(U_3296,U_3295,U_3297,U_3298) )
& ! [U_3296,U_3295,U_3297,U_3298] :
( sP196(U_3296,U_3295,U_3297,U_3298)
| ~ class_Groups_Ocancel__semigroup__add(U_3295) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196])],[f_778_2]) ).
cnf(f_778_4,plain,
( sP196(U_3296,U_3295,U_3297,U_3298)
| ~ class_Groups_Ocancel__semigroup__add(U_3295) ),
inference(clausify,[status(thm)],[f_778_3]) ).
cnf(f_778_5,plain,
( U_3297 = U_3298
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3297) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3298)
| ~ sP196(U_3296,U_3295,U_3297,U_3298) ),
inference(clausify,[status(thm)],[f_778_3]) ).
cnf(f_778_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3297) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3295),U_3296),U_3298)
| U_3297 != U_3298
| ~ sP196(U_3296,U_3295,U_3297,U_3298) ),
inference(clausify,[status(thm)],[f_778_3]) ).
fof(f_779_1,plain,
! [V_ca_2,V_a_2,V_b_2,T_b] :
( ( ( 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_ca_2),V_a_2)
| V_b_2 != V_ca_2 )
& ( V_b_2 = V_ca_2
| 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_ca_2),V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_779_2,plain,
! [U_3302,U_3301,U_3300,U_3299] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3302),U_3301)
| U_3300 != U_3302 )
& ( U_3300 = U_3302
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3302),U_3301) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_3299) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
fof(f_779_3,plain,
( ! [U_3302,U_3299,U_3300,U_3301] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3302),U_3301)
| U_3300 != U_3302
| ~ sP197(U_3302,U_3299,U_3300,U_3301) )
& ! [U_3302,U_3299,U_3300,U_3301] :
( U_3300 = U_3302
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3302),U_3301)
| ~ sP197(U_3302,U_3299,U_3300,U_3301) )
& ! [U_3302,U_3299,U_3300,U_3301] :
( sP197(U_3302,U_3299,U_3300,U_3301)
| ~ class_Groups_Ocancel__semigroup__add(U_3299) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_779_2]) ).
cnf(f_779_4,plain,
( sP197(U_3302,U_3299,U_3300,U_3301)
| ~ class_Groups_Ocancel__semigroup__add(U_3299) ),
inference(clausify,[status(thm)],[f_779_3]) ).
cnf(f_779_5,plain,
( U_3300 = U_3302
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3302),U_3301)
| ~ sP197(U_3302,U_3299,U_3300,U_3301) ),
inference(clausify,[status(thm)],[f_779_3]) ).
cnf(f_779_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3302),U_3301)
| U_3300 != U_3302
| ~ sP197(U_3302,U_3299,U_3300,U_3301) ),
inference(clausify,[status(thm)],[f_779_3]) ).
fof(f_780_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| 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)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq]) ).
fof(f_780_2,plain,
! [U_3306,U_3305,U_3304,U_3303] :
( U_3305 = U_3306
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3303),U_3304),U_3305) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3303),U_3304),U_3306)
| ~ class_Groups_Ocancel__semigroup__add(U_3303) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
fof(f_780_3,plain,
! [U_3305,U_3304,U_3306,U_3303] :
( U_3305 = U_3306
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3303),U_3304),U_3305) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3303),U_3304),U_3306)
| ~ class_Groups_Ocancel__semigroup__add(U_3303) ),
inference(definitional_conversion,[status(esa)],[f_780_2]) ).
cnf(f_780_4,plain,
( U_3305 = U_3306
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3303),U_3304),U_3305) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3303),U_3304),U_3306)
| ~ class_Groups_Ocancel__semigroup__add(U_3303) ),
inference(clausify,[status(thm)],[f_780_3]) ).
fof(f_781_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| 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)
| ~ class_Groups_Ocancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__imp__eq]) ).
fof(f_781_2,plain,
! [U_3310,U_3309,U_3308,U_3307] :
( U_3309 = U_3310
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3307),U_3308),U_3309) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3307),U_3308),U_3310)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_3307) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
fof(f_781_3,plain,
! [U_3307,U_3308,U_3309,U_3310] :
( U_3309 = U_3310
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3307),U_3308),U_3309) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3307),U_3308),U_3310)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_3307) ),
inference(definitional_conversion,[status(esa)],[f_781_2]) ).
cnf(f_781_4,plain,
( U_3309 = U_3310
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3307),U_3308),U_3309) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3307),U_3308),U_3310)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_3307) ),
inference(clausify,[status(thm)],[f_781_3]) ).
fof(f_782_1,plain,
! [V_c,V_a,V_b,T_a] :
( V_b = V_c
| 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)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq]) ).
fof(f_782_2,plain,
! [U_3314,U_3313,U_3312,U_3311] :
( U_3312 = U_3314
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3312),U_3313) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3314),U_3313)
| ~ class_Groups_Ocancel__semigroup__add(U_3311) ),
inference(variable_rename,[status(thm)],[f_782_1]) ).
fof(f_782_3,plain,
! [U_3311,U_3312,U_3313,U_3314] :
( U_3312 = U_3314
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3312),U_3313) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3314),U_3313)
| ~ class_Groups_Ocancel__semigroup__add(U_3311) ),
inference(definitional_conversion,[status(esa)],[f_782_2]) ).
cnf(f_782_4,plain,
( U_3312 = U_3314
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3312),U_3313) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3314),U_3313)
| ~ class_Groups_Ocancel__semigroup__add(U_3311) ),
inference(clausify,[status(thm)],[f_782_3]) ).
fof(f_783_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un]) ).
fof(f_783_2,plain,
! [U_3317,U_3316,U_3315] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3317)) = 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,U_3315),U_3316)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3315),U_3316)) ),
inference(variable_rename,[status(thm)],[f_783_1]) ).
fof(f_783_3,plain,
! [U_3315,U_3316,U_3317] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3317)) = 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,U_3315),U_3316)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3315),U_3316)) ),
inference(definitional_conversion,[status(esa)],[f_783_2]) ).
cnf(f_783_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3317)) = 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,U_3315),U_3316)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3315),U_3316)) ),
inference(clausify,[status(thm)],[f_783_3]) ).
fof(f_784_1,plain,
! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem]) ).
fof(f_784_2,plain,
! [U_3324,U_3323,U_3322,U_3321,U_3320,U_3319,U_3318] :
( hAPP(hAPP(U_3320,U_3324),U_3324) = U_3324
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_3318,U_3319,U_3320,U_3321,U_3322,U_3323) ),
inference(variable_rename,[status(thm)],[f_784_1]) ).
fof(f_784_3,plain,
! [U_3324,U_3323,U_3322,U_3321,U_3320] :
( ! [U_3319,U_3318] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_3318,U_3319,U_3320,U_3321,U_3322,U_3323)
| hAPP(hAPP(U_3320,U_3324),U_3324) = U_3324 ),
inference(miniscope,[status(thm)],[f_784_2]) ).
fof(f_784_4,plain,
! [U_3318,U_3320,U_3319,U_3321,U_3322,U_3323,U_3324] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3318,U_3319,U_3320,U_3321,U_3322,U_3323)
| hAPP(hAPP(U_3320,U_3324),U_3324) = U_3324 ),
inference(definitional_conversion,[status(esa)],[f_784_3]) ).
cnf(f_784_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3318,U_3319,U_3320,U_3321,U_3322,U_3323)
| hAPP(hAPP(U_3320,U_3324),U_3324) = U_3324 ),
inference(clausify,[status(thm)],[f_784_4]) ).
fof(f_785_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ 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)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left]) ).
fof(f_785_2,plain,
! [U_3328,U_3327,U_3326,U_3325] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3325),U_3327),U_3328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3325),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3325),U_3326),U_3327)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3325),U_3326),U_3328)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3325) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
fof(f_785_3,plain,
! [U_3326,U_3325,U_3327,U_3328] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3325),U_3327),U_3328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3325),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3325),U_3326),U_3327)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3325),U_3326),U_3328)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3325) ),
inference(definitional_conversion,[status(esa)],[f_785_2]) ).
cnf(f_785_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3325),U_3327),U_3328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3325),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3325),U_3326),U_3327)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3325),U_3326),U_3328)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3325) ),
inference(clausify,[status(thm)],[f_785_3]) ).
fof(f_786_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ 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)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right]) ).
fof(f_786_2,plain,
! [U_3332,U_3331,U_3330,U_3329] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3330),U_3332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3329),U_3330),U_3331)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3329),U_3332),U_3331)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3329) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
fof(f_786_3,plain,
! [U_3329,U_3330,U_3331,U_3332] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3330),U_3332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3329),U_3330),U_3331)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3329),U_3332),U_3331)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3329) ),
inference(definitional_conversion,[status(esa)],[f_786_2]) ).
cnf(f_786_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3330),U_3332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3329),U_3330),U_3331)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3329),U_3332),U_3331)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3329) ),
inference(clausify,[status(thm)],[f_786_3]) ).
fof(f_787_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__mono]) ).
fof(f_787_2,plain,
! [U_3337,U_3336,U_3335,U_3334,U_3333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3333),U_3334),U_3336)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3333),U_3335),U_3337)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3336),U_3337))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3334),U_3335))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3333) ),
inference(variable_rename,[status(thm)],[f_787_1]) ).
fof(f_787_3,plain,
! [U_3333,U_3334,U_3335,U_3336,U_3337] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3333),U_3334),U_3336)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3333),U_3335),U_3337)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3336),U_3337))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3334),U_3335))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3333) ),
inference(definitional_conversion,[status(esa)],[f_787_2]) ).
cnf(f_787_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3333),U_3334),U_3336)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3333),U_3335),U_3337)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3336),U_3337))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3334),U_3335))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3333) ),
inference(clausify,[status(thm)],[f_787_3]) ).
fof(f_788_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__mono]) ).
fof(f_788_2,plain,
! [U_3341,U_3340,U_3339,U_3338] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3338),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3338),U_3341),U_3339)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3338),U_3341),U_3340)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3338),U_3339),U_3340))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3338) ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
fof(f_788_3,plain,
! [U_3339,U_3338,U_3340,U_3341] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3338),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3338),U_3341),U_3339)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3338),U_3341),U_3340)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3338),U_3339),U_3340))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3338) ),
inference(definitional_conversion,[status(esa)],[f_788_2]) ).
cnf(f_788_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3338),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3338),U_3341),U_3339)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3338),U_3341),U_3340)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3338),U_3339),U_3340))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3338) ),
inference(clausify,[status(thm)],[f_788_3]) ).
fof(f_789_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__mono]) ).
fof(f_789_2,plain,
! [U_3345,U_3344,U_3343,U_3342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3343),U_3345)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3344),U_3345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3342),U_3343),U_3344))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3342) ),
inference(variable_rename,[status(thm)],[f_789_1]) ).
fof(f_789_3,plain,
! [U_3342,U_3343,U_3344,U_3345] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3343),U_3345)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3344),U_3345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3342),U_3343),U_3344))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3342) ),
inference(definitional_conversion,[status(esa)],[f_789_2]) ).
cnf(f_789_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3343),U_3345)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3344),U_3345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3342),U_3343),U_3344))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3342) ),
inference(clausify,[status(thm)],[f_789_3]) ).
fof(f_790_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).
fof(f_790_2,plain,
! [U_3349,U_3348,U_3347,U_3346] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3349)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),U_3348),U_3349)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),U_3348),U_3349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3349))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3346) ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
fof(f_790_3,plain,
( ! [U_3347,U_3346,U_3348,U_3349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3349)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),U_3348),U_3349))
| ~ sP198(U_3347,U_3346,U_3348,U_3349) )
& ! [U_3347,U_3346,U_3348,U_3349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),U_3348),U_3349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3349)))
| ~ sP198(U_3347,U_3346,U_3348,U_3349) )
& ! [U_3347,U_3346,U_3348,U_3349] :
( sP198(U_3347,U_3346,U_3348,U_3349)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3346) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_790_2]) ).
cnf(f_790_4,plain,
( sP198(U_3347,U_3346,U_3348,U_3349)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3346) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),U_3348),U_3349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3349)))
| ~ sP198(U_3347,U_3346,U_3348,U_3349) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3347),U_3349)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3346),U_3348),U_3349))
| ~ sP198(U_3347,U_3346,U_3348,U_3349) ),
inference(clausify,[status(thm)],[f_790_3]) ).
fof(f_791_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).
fof(f_791_2,plain,
! [U_3353,U_3352,U_3351,U_3350] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3353),U_3352)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),U_3351),U_3353)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),U_3351),U_3353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3353),U_3352))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3350) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
fof(f_791_3,plain,
( ! [U_3353,U_3351,U_3352,U_3350] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3353),U_3352)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),U_3351),U_3353))
| ~ sP199(U_3353,U_3351,U_3352,U_3350) )
& ! [U_3353,U_3351,U_3352,U_3350] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),U_3351),U_3353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3353),U_3352)))
| ~ sP199(U_3353,U_3351,U_3352,U_3350) )
& ! [U_3353,U_3351,U_3352,U_3350] :
( sP199(U_3353,U_3351,U_3352,U_3350)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3350) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_791_2]) ).
cnf(f_791_4,plain,
( sP199(U_3353,U_3351,U_3352,U_3350)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3350) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),U_3351),U_3353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3353),U_3352)))
| ~ sP199(U_3353,U_3351,U_3352,U_3350) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3353),U_3352)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3350),U_3351),U_3353))
| ~ sP199(U_3353,U_3351,U_3352,U_3350) ),
inference(clausify,[status(thm)],[f_791_3]) ).
fof(f_792_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ 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)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left]) ).
fof(f_792_2,plain,
! [U_3357,U_3356,U_3355,U_3354] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3354),U_3356),U_3357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3354),U_3355),U_3356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3354),U_3355),U_3357)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3354) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
fof(f_792_3,plain,
! [U_3356,U_3355,U_3354,U_3357] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3354),U_3356),U_3357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3354),U_3355),U_3356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3354),U_3355),U_3357)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3354) ),
inference(definitional_conversion,[status(esa)],[f_792_2]) ).
cnf(f_792_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3354),U_3356),U_3357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3354),U_3355),U_3356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3354),U_3355),U_3357)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3354) ),
inference(clausify,[status(thm)],[f_792_3]) ).
fof(f_793_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ 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)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right]) ).
fof(f_793_2,plain,
! [U_3361,U_3360,U_3359,U_3358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3358),U_3359),U_3361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3358),U_3359),U_3360)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3358),U_3361),U_3360)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3358) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
fof(f_793_3,plain,
! [U_3358,U_3359,U_3360,U_3361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3358),U_3359),U_3361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3358),U_3359),U_3360)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3358),U_3361),U_3360)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3358) ),
inference(definitional_conversion,[status(esa)],[f_793_2]) ).
cnf(f_793_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3358),U_3359),U_3361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3358),U_3359),U_3360)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3358),U_3361),U_3360)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3358) ),
inference(clausify,[status(thm)],[f_793_3]) ).
fof(f_794_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__mono]) ).
fof(f_794_2,plain,
! [U_3366,U_3365,U_3364,U_3363,U_3362] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3363),U_3365)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3364),U_3366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),U_3365),U_3366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),U_3363),U_3364))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3362) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
fof(f_794_3,plain,
! [U_3362,U_3363,U_3364,U_3365,U_3366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3363),U_3365)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3364),U_3366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),U_3365),U_3366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),U_3363),U_3364))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3362) ),
inference(definitional_conversion,[status(esa)],[f_794_2]) ).
cnf(f_794_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3363),U_3365)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3364),U_3366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),U_3365),U_3366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3362),U_3363),U_3364))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3362) ),
inference(clausify,[status(thm)],[f_794_3]) ).
fof(f_795_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono]) ).
fof(f_795_2,plain,
! [U_3370,U_3369,U_3368,U_3367] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3367),U_3370),U_3368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3367),U_3370),U_3369)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3367),U_3368),U_3369))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3367) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
fof(f_795_3,plain,
! [U_3367,U_3368,U_3369,U_3370] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3367),U_3370),U_3368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3367),U_3370),U_3369)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3367),U_3368),U_3369))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3367) ),
inference(definitional_conversion,[status(esa)],[f_795_2]) ).
cnf(f_795_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3367),U_3370),U_3368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3367),U_3370),U_3369)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3367),U_3368),U_3369))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3367) ),
inference(clausify,[status(thm)],[f_795_3]) ).
fof(f_796_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono]) ).
fof(f_796_2,plain,
! [U_3374,U_3373,U_3372,U_3371] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3371),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3371),U_3372),U_3374)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3371),U_3373),U_3374)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3371),U_3372),U_3373))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3371) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
fof(f_796_3,plain,
! [U_3371,U_3372,U_3373,U_3374] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3371),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3371),U_3372),U_3374)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3371),U_3373),U_3374)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3371),U_3372),U_3373))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3371) ),
inference(definitional_conversion,[status(esa)],[f_796_2]) ).
cnf(f_796_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3371),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3371),U_3372),U_3374)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3371),U_3373),U_3374)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3371),U_3372),U_3373))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3371) ),
inference(clausify,[status(thm)],[f_796_3]) ).
fof(f_797_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).
fof(f_797_2,plain,
! [U_3378,U_3377,U_3376,U_3375] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3378)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),U_3377),U_3378)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),U_3377),U_3378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3378))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3375) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
fof(f_797_3,plain,
( ! [U_3376,U_3375,U_3377,U_3378] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3378)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),U_3377),U_3378))
| ~ sP200(U_3376,U_3375,U_3377,U_3378) )
& ! [U_3376,U_3375,U_3377,U_3378] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),U_3377),U_3378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3378)))
| ~ sP200(U_3376,U_3375,U_3377,U_3378) )
& ! [U_3376,U_3375,U_3377,U_3378] :
( sP200(U_3376,U_3375,U_3377,U_3378)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3375) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200])],[f_797_2]) ).
cnf(f_797_4,plain,
( sP200(U_3376,U_3375,U_3377,U_3378)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3375) ),
inference(clausify,[status(thm)],[f_797_3]) ).
cnf(f_797_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),U_3377),U_3378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3378)))
| ~ sP200(U_3376,U_3375,U_3377,U_3378) ),
inference(clausify,[status(thm)],[f_797_3]) ).
cnf(f_797_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3375),U_3376),U_3378)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3375),U_3377),U_3378))
| ~ sP200(U_3376,U_3375,U_3377,U_3378) ),
inference(clausify,[status(thm)],[f_797_3]) ).
fof(f_798_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).
fof(f_798_2,plain,
! [U_3382,U_3381,U_3380,U_3379] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3380),U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3382),U_3381)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3380),U_3382)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3380),U_3382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3380),U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3382),U_3381))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3379) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
fof(f_798_3,plain,
( ! [U_3381,U_3382,U_3380,U_3379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3380),U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3382),U_3381)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3380),U_3382))
| ~ sP201(U_3381,U_3382,U_3380,U_3379) )
& ! [U_3381,U_3382,U_3380,U_3379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3380),U_3382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3380),U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3382),U_3381)))
| ~ sP201(U_3381,U_3382,U_3380,U_3379) )
& ! [U_3381,U_3382,U_3380,U_3379] :
( sP201(U_3381,U_3382,U_3380,U_3379)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3379) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201])],[f_798_2]) ).
cnf(f_798_4,plain,
( sP201(U_3381,U_3382,U_3380,U_3379)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3379) ),
inference(clausify,[status(thm)],[f_798_3]) ).
cnf(f_798_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3380),U_3382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3380),U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3382),U_3381)))
| ~ sP201(U_3381,U_3382,U_3380,U_3379) ),
inference(clausify,[status(thm)],[f_798_3]) ).
cnf(f_798_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3380),U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3382),U_3381)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3380),U_3382))
| ~ sP201(U_3381,U_3382,U_3380,U_3379) ),
inference(clausify,[status(thm)],[f_798_3]) ).
fof(f_799_1,plain,
! [V_c,V_b,V_e,V_a,T_a] :
( 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)
| ~ class_Rings_Osemiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_combine__common__factor]) ).
fof(f_799_2,plain,
! [U_3387,U_3386,U_3385,U_3384,U_3383] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),U_3384),U_3385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),U_3386),U_3385)),U_3387)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3386)),U_3385)),U_3387)
| ~ class_Rings_Osemiring(U_3383) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
fof(f_799_3,plain,
! [U_3383,U_3384,U_3385,U_3386,U_3387] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),U_3384),U_3385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),U_3386),U_3385)),U_3387)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3386)),U_3385)),U_3387)
| ~ class_Rings_Osemiring(U_3383) ),
inference(definitional_conversion,[status(esa)],[f_799_2]) ).
cnf(f_799_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),U_3384),U_3385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),U_3386),U_3385)),U_3387)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3386)),U_3385)),U_3387)
| ~ class_Rings_Osemiring(U_3383) ),
inference(clausify,[status(thm)],[f_799_3]) ).
fof(f_800_1,plain,
! [V_c,V_b,V_a,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_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))
| ~ class_Rings_Ocomm__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib]) ).
fof(f_800_2,plain,
! [U_3391,U_3390,U_3389,U_3388] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),U_3389),U_3390)),U_3391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3390),U_3391))
| ~ class_Rings_Ocomm__semiring(U_3388) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
fof(f_800_3,plain,
! [U_3388,U_3389,U_3390,U_3391] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),U_3389),U_3390)),U_3391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3390),U_3391))
| ~ class_Rings_Ocomm__semiring(U_3388) ),
inference(definitional_conversion,[status(esa)],[f_800_2]) ).
cnf(f_800_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),U_3389),U_3390)),U_3391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3390),U_3391))
| ~ class_Rings_Ocomm__semiring(U_3388) ),
inference(clausify,[status(thm)],[f_800_3]) ).
fof(f_801_1,plain,
! [V_b,V_a,T_a] :
( 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
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__cancel]) ).
fof(f_801_2,plain,
! [U_3394,U_3393,U_3392] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3392),U_3393),U_3394)),U_3394) = U_3393
| ~ class_Groups_Ogroup__add(U_3392) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
fof(f_801_3,plain,
! [U_3392,U_3393,U_3394] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3392),U_3393),U_3394)),U_3394) = U_3393
| ~ class_Groups_Ogroup__add(U_3392) ),
inference(definitional_conversion,[status(esa)],[f_801_2]) ).
cnf(f_801_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3392),U_3393),U_3394)),U_3394) = U_3393
| ~ class_Groups_Ogroup__add(U_3392) ),
inference(clausify,[status(thm)],[f_801_3]) ).
fof(f_802_1,plain,
! [V_b,V_a,T_a] :
( 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
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__cancel]) ).
fof(f_802_2,plain,
! [U_3397,U_3396,U_3395] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3395),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3395),U_3396),U_3397)),U_3397) = U_3396
| ~ class_Groups_Ogroup__add(U_3395) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
fof(f_802_3,plain,
! [U_3395,U_3396,U_3397] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3395),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3395),U_3396),U_3397)),U_3397) = U_3396
| ~ class_Groups_Ogroup__add(U_3395) ),
inference(definitional_conversion,[status(esa)],[f_802_2]) ).
cnf(f_802_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3395),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3395),U_3396),U_3397)),U_3397) = U_3396
| ~ class_Groups_Ogroup__add(U_3395) ),
inference(clausify,[status(thm)],[f_802_3]) ).
fof(f_803_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add__distrib]) ).
fof(f_803_2,plain,
! [U_3400,U_3399,U_3398] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3398),U_3399),U_3400)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3398),hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),U_3399)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),U_3400))
| ~ class_Groups_Oab__group__add(U_3398) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
fof(f_803_3,plain,
! [U_3398,U_3399,U_3400] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3398),U_3399),U_3400)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3398),hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),U_3399)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),U_3400))
| ~ class_Groups_Oab__group__add(U_3398) ),
inference(definitional_conversion,[status(esa)],[f_803_2]) ).
cnf(f_803_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3398),U_3399),U_3400)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3398),hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),U_3399)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3398),U_3400))
| ~ class_Groups_Oab__group__add(U_3398) ),
inference(clausify,[status(thm)],[f_803_3]) ).
fof(f_804_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add]) ).
fof(f_804_2,plain,
! [U_3403,U_3402,U_3401] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3401),U_3402),U_3403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3401),hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),U_3403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),U_3402))
| ~ class_Groups_Ogroup__add(U_3401) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
fof(f_804_3,plain,
! [U_3401,U_3402,U_3403] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3401),U_3402),U_3403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3401),hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),U_3403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),U_3402))
| ~ class_Groups_Ogroup__add(U_3401) ),
inference(definitional_conversion,[status(esa)],[f_804_2]) ).
cnf(f_804_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3401),U_3402),U_3403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3401),hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),U_3403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3401),U_3402))
| ~ class_Groups_Ogroup__add(U_3401) ),
inference(clausify,[status(thm)],[f_804_3]) ).
fof(f_805_1,plain,
! [V_b,V_a,T_a] :
( 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
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__minus__cancel]) ).
fof(f_805_2,plain,
! [U_3406,U_3405,U_3404] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3404),U_3405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3404),hAPP(c_Groups_Ouminus__class_Ouminus(U_3404),U_3405)),U_3406)) = U_3406
| ~ class_Groups_Ogroup__add(U_3404) ),
inference(variable_rename,[status(thm)],[f_805_1]) ).
fof(f_805_3,plain,
! [U_3404,U_3405,U_3406] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3404),U_3405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3404),hAPP(c_Groups_Ouminus__class_Ouminus(U_3404),U_3405)),U_3406)) = U_3406
| ~ class_Groups_Ogroup__add(U_3404) ),
inference(definitional_conversion,[status(esa)],[f_805_2]) ).
cnf(f_805_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3404),U_3405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3404),hAPP(c_Groups_Ouminus__class_Ouminus(U_3404),U_3405)),U_3406)) = U_3406
| ~ class_Groups_Ogroup__add(U_3404) ),
inference(clausify,[status(thm)],[f_805_3]) ).
fof(f_806_1,plain,
! [V_b,V_a,T_a] :
( 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
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add__cancel]) ).
fof(f_806_2,plain,
! [U_3409,U_3408,U_3407] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),hAPP(c_Groups_Ouminus__class_Ouminus(U_3407),U_3408)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3408),U_3409)) = U_3409
| ~ class_Groups_Ogroup__add(U_3407) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
fof(f_806_3,plain,
! [U_3407,U_3408,U_3409] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),hAPP(c_Groups_Ouminus__class_Ouminus(U_3407),U_3408)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3408),U_3409)) = U_3409
| ~ class_Groups_Ogroup__add(U_3407) ),
inference(definitional_conversion,[status(esa)],[f_806_2]) ).
cnf(f_806_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),hAPP(c_Groups_Ouminus__class_Ouminus(U_3407),U_3408)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3408),U_3409)) = U_3409
| ~ class_Groups_Ogroup__add(U_3407) ),
inference(clausify,[status(thm)],[f_806_3]) ).
fof(f_807_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__less__mono]) ).
fof(f_807_2,plain,
! [U_3414,U_3413,U_3412,U_3411,U_3410] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3410),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3410),U_3411),U_3413)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3410),U_3412),U_3414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3410),U_3413),U_3414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3410),U_3411),U_3412))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3410) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
fof(f_807_3,plain,
! [U_3410,U_3411,U_3412,U_3413,U_3414] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3410),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3410),U_3411),U_3413)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3410),U_3412),U_3414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3410),U_3413),U_3414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3410),U_3411),U_3412))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3410) ),
inference(definitional_conversion,[status(esa)],[f_807_2]) ).
cnf(f_807_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3410),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3410),U_3411),U_3413)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3410),U_3412),U_3414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3410),U_3413),U_3414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3410),U_3411),U_3412))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3410) ),
inference(clausify,[status(thm)],[f_807_3]) ).
fof(f_808_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__le__mono]) ).
fof(f_808_2,plain,
! [U_3419,U_3418,U_3417,U_3416,U_3415] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3415),U_3416),U_3418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3415),U_3417),U_3419)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3415),U_3418),U_3419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3416),U_3417))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3415) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
fof(f_808_3,plain,
! [U_3415,U_3416,U_3417,U_3418,U_3419] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3415),U_3416),U_3418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3415),U_3417),U_3419)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3415),U_3418),U_3419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3416),U_3417))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3415) ),
inference(definitional_conversion,[status(esa)],[f_808_2]) ).
cnf(f_808_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3415),U_3416),U_3418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3415),U_3417),U_3419)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3415),U_3418),U_3419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3416),U_3417))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3415) ),
inference(clausify,[status(thm)],[f_808_3]) ).
fof(f_809_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,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_ca_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)
| 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_ca_2) != V_d_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_a_2),V_b_2)),V_e_2)),V_ca_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_e_2)),V_ca_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) ) )
| ~ class_Rings_Oring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).
fof(f_809_2,plain,
! [U_3425,U_3424,U_3423,U_3422,U_3421,U_3420] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3421),U_3422)),U_3423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3424),U_3422)),U_3425)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3420),U_3421),U_3424)),U_3422)),U_3423) != U_3425 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3420),U_3421),U_3424)),U_3422)),U_3423) = U_3425
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3421),U_3422)),U_3423) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3424),U_3422)),U_3425) ) )
| ~ class_Rings_Oring(U_3420) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
fof(f_809_3,plain,
( ! [U_3420,U_3421,U_3422,U_3423,U_3424,U_3425] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3421),U_3422)),U_3423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3424),U_3422)),U_3425)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3420),U_3421),U_3424)),U_3422)),U_3423) != U_3425
| ~ sP202(U_3420,U_3421,U_3422,U_3423,U_3424,U_3425) )
& ! [U_3420,U_3421,U_3422,U_3423,U_3424,U_3425] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3420),U_3421),U_3424)),U_3422)),U_3423) = U_3425
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3421),U_3422)),U_3423) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3424),U_3422)),U_3425)
| ~ sP202(U_3420,U_3421,U_3422,U_3423,U_3424,U_3425) )
& ! [U_3420,U_3421,U_3422,U_3423,U_3424,U_3425] :
( sP202(U_3420,U_3421,U_3422,U_3423,U_3424,U_3425)
| ~ class_Rings_Oring(U_3420) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_809_2]) ).
cnf(f_809_4,plain,
( sP202(U_3420,U_3421,U_3422,U_3423,U_3424,U_3425)
| ~ class_Rings_Oring(U_3420) ),
inference(clausify,[status(thm)],[f_809_3]) ).
cnf(f_809_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3420),U_3421),U_3424)),U_3422)),U_3423) = U_3425
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3421),U_3422)),U_3423) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3424),U_3422)),U_3425)
| ~ sP202(U_3420,U_3421,U_3422,U_3423,U_3424,U_3425) ),
inference(clausify,[status(thm)],[f_809_3]) ).
cnf(f_809_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3421),U_3422)),U_3423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),U_3424),U_3422)),U_3425)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3420),U_3421),U_3424)),U_3422)),U_3423) != U_3425
| ~ sP202(U_3420,U_3421,U_3422,U_3423,U_3424,U_3425) ),
inference(clausify,[status(thm)],[f_809_3]) ).
fof(f_810_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,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_ca_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)
| V_ca_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) )
& ( V_ca_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)
| 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_ca_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) ) )
| ~ class_Rings_Oring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).
fof(f_810_2,plain,
! [U_3431,U_3430,U_3429,U_3428,U_3427,U_3426] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3427),U_3428)),U_3429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3430),U_3428)),U_3431)
| U_3429 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3426),U_3430),U_3427)),U_3428)),U_3431) )
& ( U_3429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3426),U_3430),U_3427)),U_3428)),U_3431)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3427),U_3428)),U_3429) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3430),U_3428)),U_3431) ) )
| ~ class_Rings_Oring(U_3426) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
fof(f_810_3,plain,
( ! [U_3427,U_3426,U_3428,U_3429,U_3430,U_3431] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3427),U_3428)),U_3429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3430),U_3428)),U_3431)
| U_3429 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3426),U_3430),U_3427)),U_3428)),U_3431)
| ~ sP203(U_3427,U_3426,U_3428,U_3429,U_3430,U_3431) )
& ! [U_3427,U_3426,U_3428,U_3429,U_3430,U_3431] :
( U_3429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3426),U_3430),U_3427)),U_3428)),U_3431)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3427),U_3428)),U_3429) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3430),U_3428)),U_3431)
| ~ sP203(U_3427,U_3426,U_3428,U_3429,U_3430,U_3431) )
& ! [U_3427,U_3426,U_3428,U_3429,U_3430,U_3431] :
( sP203(U_3427,U_3426,U_3428,U_3429,U_3430,U_3431)
| ~ class_Rings_Oring(U_3426) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_810_2]) ).
cnf(f_810_4,plain,
( sP203(U_3427,U_3426,U_3428,U_3429,U_3430,U_3431)
| ~ class_Rings_Oring(U_3426) ),
inference(clausify,[status(thm)],[f_810_3]) ).
cnf(f_810_5,plain,
( U_3429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3426),U_3430),U_3427)),U_3428)),U_3431)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3427),U_3428)),U_3429) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3430),U_3428)),U_3431)
| ~ sP203(U_3427,U_3426,U_3428,U_3429,U_3430,U_3431) ),
inference(clausify,[status(thm)],[f_810_3]) ).
cnf(f_810_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3427),U_3428)),U_3429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),U_3430),U_3428)),U_3431)
| U_3429 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3426),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3426),U_3430),U_3427)),U_3428)),U_3431)
| ~ sP203(U_3427,U_3426,U_3428,U_3429,U_3430,U_3431) ),
inference(clausify,[status(thm)],[f_810_3]) ).
fof(f_811_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__def]) ).
fof(f_811_2,plain,
! [U_3434,U_3433,U_3432] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3432),U_3433),U_3434) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3432),U_3433),hAPP(c_Groups_Ouminus__class_Ouminus(U_3432),U_3434))
| ~ class_Groups_Ogroup__add(U_3432) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
fof(f_811_3,plain,
! [U_3433,U_3434,U_3432] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3432),U_3433),U_3434) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3432),U_3433),hAPP(c_Groups_Ouminus__class_Ouminus(U_3432),U_3434))
| ~ class_Groups_Ogroup__add(U_3432) ),
inference(definitional_conversion,[status(esa)],[f_811_2]) ).
cnf(f_811_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3432),U_3433),U_3434) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3432),U_3433),hAPP(c_Groups_Ouminus__class_Ouminus(U_3432),U_3434))
| ~ class_Groups_Ogroup__add(U_3432) ),
inference(clausify,[status(thm)],[f_811_3]) ).
fof(f_812_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__diff__minus]) ).
fof(f_812_2,plain,
! [U_3437,U_3436,U_3435] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3435),U_3436),U_3437) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3435),U_3436),hAPP(c_Groups_Ouminus__class_Ouminus(U_3435),U_3437))
| ~ class_Groups_Oab__group__add(U_3435) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
fof(f_812_3,plain,
! [U_3435,U_3436,U_3437] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3435),U_3436),U_3437) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3435),U_3436),hAPP(c_Groups_Ouminus__class_Ouminus(U_3435),U_3437))
| ~ class_Groups_Oab__group__add(U_3435) ),
inference(definitional_conversion,[status(esa)],[f_812_2]) ).
cnf(f_812_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3435),U_3436),U_3437) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3435),U_3436),hAPP(c_Groups_Ouminus__class_Ouminus(U_3435),U_3437))
| ~ class_Groups_Oab__group__add(U_3435) ),
inference(clausify,[status(thm)],[f_812_3]) ).
fof(f_813_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add]) ).
fof(f_813_2,plain,
! [U_3440,U_3439,U_3438] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3438),U_3439),hAPP(c_Groups_Ouminus__class_Ouminus(U_3438),U_3440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3438),U_3439),U_3440)
| ~ class_Groups_Ogroup__add(U_3438) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
fof(f_813_3,plain,
! [U_3438,U_3439,U_3440] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3438),U_3439),hAPP(c_Groups_Ouminus__class_Ouminus(U_3438),U_3440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3438),U_3439),U_3440)
| ~ class_Groups_Ogroup__add(U_3438) ),
inference(definitional_conversion,[status(esa)],[f_813_2]) ).
cnf(f_813_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3438),U_3439),hAPP(c_Groups_Ouminus__class_Ouminus(U_3438),U_3440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3438),U_3439),U_3440)
| ~ class_Groups_Ogroup__add(U_3438) ),
inference(clausify,[status(thm)],[f_813_3]) ).
fof(f_814_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( ( ( 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_ca_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)))
| ~ 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_ca_2)),V_d_2)) )
& ( 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_ca_2)),V_d_2))
| ~ 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_ca_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))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).
fof(f_814_2,plain,
! [U_3446,U_3445,U_3444,U_3443,U_3442,U_3441] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3442),U_3443)),U_3444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3445),U_3443)),U_3446)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),U_3442),U_3445)),U_3443)),U_3444)),U_3446)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),U_3442),U_3445)),U_3443)),U_3444)),U_3446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3442),U_3443)),U_3444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3445),U_3443)),U_3446))) ) )
| ~ class_Rings_Oordered__ring(U_3441) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
fof(f_814_3,plain,
( ! [U_3441,U_3442,U_3443,U_3444,U_3445,U_3446] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3442),U_3443)),U_3444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3445),U_3443)),U_3446)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),U_3442),U_3445)),U_3443)),U_3444)),U_3446))
| ~ sP204(U_3441,U_3442,U_3443,U_3444,U_3445,U_3446) )
& ! [U_3441,U_3442,U_3443,U_3444,U_3445,U_3446] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),U_3442),U_3445)),U_3443)),U_3444)),U_3446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3442),U_3443)),U_3444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3445),U_3443)),U_3446)))
| ~ sP204(U_3441,U_3442,U_3443,U_3444,U_3445,U_3446) )
& ! [U_3441,U_3442,U_3443,U_3444,U_3445,U_3446] :
( sP204(U_3441,U_3442,U_3443,U_3444,U_3445,U_3446)
| ~ class_Rings_Oordered__ring(U_3441) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_814_2]) ).
cnf(f_814_4,plain,
( sP204(U_3441,U_3442,U_3443,U_3444,U_3445,U_3446)
| ~ class_Rings_Oordered__ring(U_3441) ),
inference(clausify,[status(thm)],[f_814_3]) ).
cnf(f_814_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),U_3442),U_3445)),U_3443)),U_3444)),U_3446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3442),U_3443)),U_3444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3445),U_3443)),U_3446)))
| ~ sP204(U_3441,U_3442,U_3443,U_3444,U_3445,U_3446) ),
inference(clausify,[status(thm)],[f_814_3]) ).
cnf(f_814_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3442),U_3443)),U_3444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3445),U_3443)),U_3446)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),U_3442),U_3445)),U_3443)),U_3444)),U_3446))
| ~ sP204(U_3441,U_3442,U_3443,U_3444,U_3445,U_3446) ),
inference(clausify,[status(thm)],[f_814_3]) ).
fof(f_815_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( ( ( 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_ca_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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_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)))
| ~ 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_ca_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))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).
fof(f_815_2,plain,
! [U_3452,U_3451,U_3450,U_3449,U_3448,U_3447] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3448),U_3449)),U_3450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3451),U_3449)),U_3452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3451),U_3448)),U_3449)),U_3452))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3451),U_3448)),U_3449)),U_3452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3448),U_3449)),U_3450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3451),U_3449)),U_3452))) ) )
| ~ class_Rings_Oordered__ring(U_3447) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
fof(f_815_3,plain,
( ! [U_3447,U_3448,U_3449,U_3450,U_3451,U_3452] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3448),U_3449)),U_3450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3451),U_3449)),U_3452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3451),U_3448)),U_3449)),U_3452)))
| ~ sP205(U_3447,U_3448,U_3449,U_3450,U_3451,U_3452) )
& ! [U_3447,U_3448,U_3449,U_3450,U_3451,U_3452] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3451),U_3448)),U_3449)),U_3452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3448),U_3449)),U_3450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3451),U_3449)),U_3452)))
| ~ sP205(U_3447,U_3448,U_3449,U_3450,U_3451,U_3452) )
& ! [U_3447,U_3448,U_3449,U_3450,U_3451,U_3452] :
( sP205(U_3447,U_3448,U_3449,U_3450,U_3451,U_3452)
| ~ class_Rings_Oordered__ring(U_3447) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_815_2]) ).
cnf(f_815_4,plain,
( sP205(U_3447,U_3448,U_3449,U_3450,U_3451,U_3452)
| ~ class_Rings_Oordered__ring(U_3447) ),
inference(clausify,[status(thm)],[f_815_3]) ).
cnf(f_815_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3451),U_3448)),U_3449)),U_3452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3448),U_3449)),U_3450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3451),U_3449)),U_3452)))
| ~ sP205(U_3447,U_3448,U_3449,U_3450,U_3451,U_3452) ),
inference(clausify,[status(thm)],[f_815_3]) ).
cnf(f_815_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3448),U_3449)),U_3450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),U_3451),U_3449)),U_3452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3451),U_3448)),U_3449)),U_3452)))
| ~ sP205(U_3447,U_3448,U_3449,U_3450,U_3451,U_3452) ),
inference(clausify,[status(thm)],[f_815_3]) ).
fof(f_816_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( ( ( 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_ca_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)))
| ~ 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_ca_2)),V_d_2)) )
& ( 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_ca_2)),V_d_2))
| ~ 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_ca_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))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).
fof(f_816_2,plain,
! [U_3458,U_3457,U_3456,U_3455,U_3454,U_3453] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3454),U_3455)),U_3456)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3457),U_3455)),U_3458)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3453),U_3454),U_3457)),U_3455)),U_3456)),U_3458)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3453),U_3454),U_3457)),U_3455)),U_3456)),U_3458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3454),U_3455)),U_3456)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3457),U_3455)),U_3458))) ) )
| ~ class_Rings_Oordered__ring(U_3453) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
fof(f_816_3,plain,
( ! [U_3453,U_3455,U_3454,U_3456,U_3457,U_3458] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3454),U_3455)),U_3456)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3457),U_3455)),U_3458)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3453),U_3454),U_3457)),U_3455)),U_3456)),U_3458))
| ~ sP206(U_3453,U_3455,U_3454,U_3456,U_3457,U_3458) )
& ! [U_3453,U_3455,U_3454,U_3456,U_3457,U_3458] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3453),U_3454),U_3457)),U_3455)),U_3456)),U_3458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3454),U_3455)),U_3456)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3457),U_3455)),U_3458)))
| ~ sP206(U_3453,U_3455,U_3454,U_3456,U_3457,U_3458) )
& ! [U_3453,U_3455,U_3454,U_3456,U_3457,U_3458] :
( sP206(U_3453,U_3455,U_3454,U_3456,U_3457,U_3458)
| ~ class_Rings_Oordered__ring(U_3453) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_816_2]) ).
cnf(f_816_4,plain,
( sP206(U_3453,U_3455,U_3454,U_3456,U_3457,U_3458)
| ~ class_Rings_Oordered__ring(U_3453) ),
inference(clausify,[status(thm)],[f_816_3]) ).
cnf(f_816_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3453),U_3454),U_3457)),U_3455)),U_3456)),U_3458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3454),U_3455)),U_3456)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3457),U_3455)),U_3458)))
| ~ sP206(U_3453,U_3455,U_3454,U_3456,U_3457,U_3458) ),
inference(clausify,[status(thm)],[f_816_3]) ).
cnf(f_816_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3454),U_3455)),U_3456)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),U_3457),U_3455)),U_3458)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3453),U_3454),U_3457)),U_3455)),U_3456)),U_3458))
| ~ sP206(U_3453,U_3455,U_3454,U_3456,U_3457,U_3458) ),
inference(clausify,[status(thm)],[f_816_3]) ).
fof(f_817_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
( ( ( 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_ca_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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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)))
| ~ 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_ca_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))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).
fof(f_817_2,plain,
! [U_3464,U_3463,U_3462,U_3461,U_3460,U_3459] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3460),U_3461)),U_3462)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3463),U_3461)),U_3464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),U_3462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3459),U_3463),U_3460)),U_3461)),U_3464))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),U_3462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3459),U_3463),U_3460)),U_3461)),U_3464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3460),U_3461)),U_3462)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3463),U_3461)),U_3464))) ) )
| ~ class_Rings_Oordered__ring(U_3459) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
fof(f_817_3,plain,
( ! [U_3460,U_3459,U_3461,U_3462,U_3463,U_3464] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3460),U_3461)),U_3462)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3463),U_3461)),U_3464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),U_3462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3459),U_3463),U_3460)),U_3461)),U_3464)))
| ~ sP207(U_3460,U_3459,U_3461,U_3462,U_3463,U_3464) )
& ! [U_3460,U_3459,U_3461,U_3462,U_3463,U_3464] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),U_3462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3459),U_3463),U_3460)),U_3461)),U_3464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3460),U_3461)),U_3462)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3463),U_3461)),U_3464)))
| ~ sP207(U_3460,U_3459,U_3461,U_3462,U_3463,U_3464) )
& ! [U_3460,U_3459,U_3461,U_3462,U_3463,U_3464] :
( sP207(U_3460,U_3459,U_3461,U_3462,U_3463,U_3464)
| ~ class_Rings_Oordered__ring(U_3459) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_817_2]) ).
cnf(f_817_4,plain,
( sP207(U_3460,U_3459,U_3461,U_3462,U_3463,U_3464)
| ~ class_Rings_Oordered__ring(U_3459) ),
inference(clausify,[status(thm)],[f_817_3]) ).
cnf(f_817_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),U_3462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3459),U_3463),U_3460)),U_3461)),U_3464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3460),U_3461)),U_3462)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3463),U_3461)),U_3464)))
| ~ sP207(U_3460,U_3459,U_3461,U_3462,U_3463,U_3464) ),
inference(clausify,[status(thm)],[f_817_3]) ).
cnf(f_817_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3460),U_3461)),U_3462)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3463),U_3461)),U_3464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3459),U_3462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3459),U_3463),U_3460)),U_3461)),U_3464)))
| ~ sP207(U_3460,U_3459,U_3461,U_3462,U_3463,U_3464) ),
inference(clausify,[status(thm)],[f_817_3]) ).
fof(f_818_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat]) ).
fof(f_818_2,plain,
! [U_3468,U_3467,U_3466,U_3465] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3465,tc_HOL_Obool)),U_3466),U_3467)) = 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(U_3465,tc_Nat_Onat),U_3468),U_3466)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),U_3467))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3465,tc_HOL_Obool)),U_3466),U_3467)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3465),U_3467))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3465),U_3466)) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
fof(f_818_3,plain,
! [U_3466,U_3465,U_3467,U_3468] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3465,tc_HOL_Obool)),U_3466),U_3467)) = 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(U_3465,tc_Nat_Onat),U_3468),U_3466)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),U_3467))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3465,tc_HOL_Obool)),U_3466),U_3467)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3465),U_3467))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3465),U_3466)) ),
inference(definitional_conversion,[status(esa)],[f_818_2]) ).
cnf(f_818_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3465,tc_HOL_Obool)),U_3466),U_3467)) = 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(U_3465,tc_Nat_Onat),U_3468),U_3466)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),U_3467))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,tc_Nat_Onat),U_3468),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3465,tc_HOL_Obool)),U_3466),U_3467)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3465),U_3467))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3465),U_3466)) ),
inference(clausify,[status(thm)],[f_818_3]) ).
fof(f_819_1,plain,
! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__insert]) ).
fof(f_819_2,plain,
! [U_3473,U_3472,U_3471,U_3470,U_3469] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3470,U_3469),U_3473),hAPP(hAPP(c_Set_Oinsert(U_3470),U_3472),U_3471)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3469),hAPP(U_3473,U_3472)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3470,U_3469),U_3473),U_3471))
| hBOOL(hAPP(hAPP(c_member(U_3470),U_3472),U_3471))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3470),U_3471))
| ~ class_Groups_Ocomm__monoid__add(U_3469) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
fof(f_819_3,plain,
! [U_3470,U_3469,U_3471,U_3472,U_3473] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3470,U_3469),U_3473),hAPP(hAPP(c_Set_Oinsert(U_3470),U_3472),U_3471)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3469),hAPP(U_3473,U_3472)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3470,U_3469),U_3473),U_3471))
| hBOOL(hAPP(hAPP(c_member(U_3470),U_3472),U_3471))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3470),U_3471))
| ~ class_Groups_Ocomm__monoid__add(U_3469) ),
inference(definitional_conversion,[status(esa)],[f_819_2]) ).
cnf(f_819_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3470,U_3469),U_3473),hAPP(hAPP(c_Set_Oinsert(U_3470),U_3472),U_3471)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3469),hAPP(U_3473,U_3472)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3470,U_3469),U_3473),U_3471))
| hBOOL(hAPP(hAPP(c_member(U_3470),U_3472),U_3471))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3470),U_3471))
| ~ class_Groups_Ocomm__monoid__add(U_3469) ),
inference(clausify,[status(thm)],[f_819_3]) ).
fof(f_820_1,plain,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert]) ).
fof(f_820_2,plain,
! [U_3478,U_3477,U_3476,U_3475,U_3474] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3475,U_3474),U_3478),hAPP(hAPP(c_Set_Oinsert(U_3475),U_3477),U_3476)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3474),hAPP(U_3478,U_3477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3475,U_3474),U_3478),U_3476))
| hBOOL(hAPP(hAPP(c_member(U_3475),U_3477),U_3476))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3475),U_3476))
| ~ class_Groups_Ocomm__monoid__add(U_3474) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
fof(f_820_3,plain,
! [U_3474,U_3475,U_3476,U_3477,U_3478] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3475,U_3474),U_3478),hAPP(hAPP(c_Set_Oinsert(U_3475),U_3477),U_3476)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3474),hAPP(U_3478,U_3477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3475,U_3474),U_3478),U_3476))
| hBOOL(hAPP(hAPP(c_member(U_3475),U_3477),U_3476))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3475),U_3476))
| ~ class_Groups_Ocomm__monoid__add(U_3474) ),
inference(definitional_conversion,[status(esa)],[f_820_2]) ).
cnf(f_820_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3475,U_3474),U_3478),hAPP(hAPP(c_Set_Oinsert(U_3475),U_3477),U_3476)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3474),hAPP(U_3478,U_3477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3475,U_3474),U_3478),U_3476))
| hBOOL(hAPP(hAPP(c_member(U_3475),U_3477),U_3476))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3475),U_3476))
| ~ class_Groups_Ocomm__monoid__add(U_3474) ),
inference(clausify,[status(thm)],[f_820_3]) ).
fof(f_821_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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_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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int]) ).
fof(f_821_2,plain,
! [U_3483,U_3482,U_3481,U_3480,U_3479] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3479),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3480,tc_HOL_Obool)),U_3481),U_3482))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3480,tc_HOL_Obool)),U_3481),U_3482))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3479),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),U_3481)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),U_3482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3480),U_3482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3480),U_3481))
| ~ class_Groups_Ocomm__monoid__add(U_3479) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
fof(f_821_3,plain,
! [U_3479,U_3480,U_3481,U_3482,U_3483] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3479),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3480,tc_HOL_Obool)),U_3481),U_3482))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3480,tc_HOL_Obool)),U_3481),U_3482))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3479),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),U_3481)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),U_3482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3480),U_3482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3480),U_3481))
| ~ class_Groups_Ocomm__monoid__add(U_3479) ),
inference(definitional_conversion,[status(esa)],[f_821_2]) ).
cnf(f_821_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3479),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3480,tc_HOL_Obool)),U_3481),U_3482))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3480,tc_HOL_Obool)),U_3481),U_3482))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3479),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),U_3481)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3480,U_3479),U_3483),U_3482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3480),U_3482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3480),U_3481))
| ~ class_Groups_Ocomm__monoid__add(U_3479) ),
inference(clausify,[status(thm)],[f_821_3]) ).
fof(f_822_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem]) ).
fof(f_822_2,plain,
! [U_3491,U_3490,U_3489,U_3488,U_3487,U_3486,U_3485,U_3484] :
( hAPP(hAPP(U_3486,hAPP(U_3488,U_3491)),hAPP(U_3489,U_3490)) = hAPP(U_3489,U_3490)
| ~ hBOOL(hAPP(hAPP(c_member(U_3485),U_3491),U_3490))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3485),U_3490))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_3484,U_3485,U_3486,U_3487,U_3488,U_3489) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
fof(f_822_3,plain,
! [U_3491,U_3490,U_3489,U_3488,U_3487,U_3486,U_3485] :
( ! [U_3484] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_3484,U_3485,U_3486,U_3487,U_3488,U_3489)
| hAPP(hAPP(U_3486,hAPP(U_3488,U_3491)),hAPP(U_3489,U_3490)) = hAPP(U_3489,U_3490)
| ~ hBOOL(hAPP(hAPP(c_member(U_3485),U_3491),U_3490))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3485),U_3490)) ),
inference(miniscope,[status(thm)],[f_822_2]) ).
fof(f_822_4,plain,
! [U_3487,U_3488,U_3486,U_3484,U_3489,U_3485,U_3490,U_3491] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3484,U_3485,U_3486,U_3487,U_3488,U_3489)
| hAPP(hAPP(U_3486,hAPP(U_3488,U_3491)),hAPP(U_3489,U_3490)) = hAPP(U_3489,U_3490)
| ~ hBOOL(hAPP(hAPP(c_member(U_3485),U_3491),U_3490))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3485),U_3490)) ),
inference(definitional_conversion,[status(esa)],[f_822_3]) ).
cnf(f_822_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3484,U_3485,U_3486,U_3487,U_3488,U_3489)
| hAPP(hAPP(U_3486,hAPP(U_3488,U_3491)),hAPP(U_3489,U_3490)) = hAPP(U_3489,U_3490)
| ~ hBOOL(hAPP(hAPP(c_member(U_3485),U_3491),U_3490))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3485),U_3490)) ),
inference(clausify,[status(thm)],[f_822_4]) ).
fof(f_823_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem]) ).
fof(f_823_2,plain,
! [U_3499,U_3498,U_3497,U_3496,U_3495,U_3494,U_3493,U_3492] :
( hAPP(U_3497,hAPP(hAPP(c_Set_Oinsert(U_3493),U_3499),U_3498)) = hAPP(hAPP(U_3494,hAPP(U_3496,U_3499)),hAPP(U_3497,U_3498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3493),U_3498))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_3492,U_3493,U_3494,U_3495,U_3496,U_3497) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
fof(f_823_3,plain,
! [U_3499,U_3498,U_3497,U_3496,U_3495,U_3494,U_3493] :
( ! [U_3492] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_3492,U_3493,U_3494,U_3495,U_3496,U_3497)
| hAPP(U_3497,hAPP(hAPP(c_Set_Oinsert(U_3493),U_3499),U_3498)) = hAPP(hAPP(U_3494,hAPP(U_3496,U_3499)),hAPP(U_3497,U_3498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3493),U_3498)) ),
inference(miniscope,[status(thm)],[f_823_2]) ).
fof(f_823_4,plain,
! [U_3492,U_3499,U_3493,U_3494,U_3495,U_3496,U_3497,U_3498] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3492,U_3493,U_3494,U_3495,U_3496,U_3497)
| hAPP(U_3497,hAPP(hAPP(c_Set_Oinsert(U_3493),U_3499),U_3498)) = hAPP(hAPP(U_3494,hAPP(U_3496,U_3499)),hAPP(U_3497,U_3498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3493),U_3498)) ),
inference(definitional_conversion,[status(esa)],[f_823_3]) ).
cnf(f_823_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3492,U_3493,U_3494,U_3495,U_3496,U_3497)
| hAPP(U_3497,hAPP(hAPP(c_Set_Oinsert(U_3493),U_3499),U_3498)) = hAPP(hAPP(U_3494,hAPP(U_3496,U_3499)),hAPP(U_3497,U_3498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3493),U_3498)) ),
inference(clausify,[status(thm)],[f_823_4]) ).
fof(f_824_1,plain,
! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
( 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))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove]) ).
fof(f_824_2,plain,
! [U_3504,U_3503,U_3502,U_3501,U_3500] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3501,U_3500),U_3503),hAPP(hAPP(c_Set_Oinsert(U_3501),U_3504),U_3502)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3500),hAPP(U_3503,U_3504)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3501,U_3500),U_3503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3501,tc_HOL_Obool)),U_3502),hAPP(hAPP(c_Set_Oinsert(U_3501),U_3504),c_Orderings_Obot__class_Obot(tc_fun(U_3501,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3501),U_3502))
| ~ class_Groups_Ocomm__monoid__add(U_3500) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
fof(f_824_3,plain,
! [U_3501,U_3500,U_3502,U_3503,U_3504] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3501,U_3500),U_3503),hAPP(hAPP(c_Set_Oinsert(U_3501),U_3504),U_3502)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3500),hAPP(U_3503,U_3504)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3501,U_3500),U_3503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3501,tc_HOL_Obool)),U_3502),hAPP(hAPP(c_Set_Oinsert(U_3501),U_3504),c_Orderings_Obot__class_Obot(tc_fun(U_3501,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3501),U_3502))
| ~ class_Groups_Ocomm__monoid__add(U_3500) ),
inference(definitional_conversion,[status(esa)],[f_824_2]) ).
cnf(f_824_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3501,U_3500),U_3503),hAPP(hAPP(c_Set_Oinsert(U_3501),U_3504),U_3502)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3500),hAPP(U_3503,U_3504)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3501,U_3500),U_3503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3501,tc_HOL_Obool)),U_3502),hAPP(hAPP(c_Set_Oinsert(U_3501),U_3504),c_Orderings_Obot__class_Obot(tc_fun(U_3501,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3501),U_3502))
| ~ class_Groups_Ocomm__monoid__add(U_3500) ),
inference(clausify,[status(thm)],[f_824_3]) ).
fof(f_825_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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_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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint]) ).
fof(f_825_2,plain,
! [U_3509,U_3508,U_3507,U_3506,U_3505] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3506,tc_HOL_Obool)),U_3507),U_3508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3505),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),U_3507)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),U_3508))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3506,tc_HOL_Obool)),U_3507),U_3508) != c_Orderings_Obot__class_Obot(tc_fun(U_3506,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3506),U_3508))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3506),U_3507))
| ~ class_Groups_Ocomm__monoid__add(U_3505) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
fof(f_825_3,plain,
! [U_3505,U_3506,U_3507,U_3508,U_3509] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3506,tc_HOL_Obool)),U_3507),U_3508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3505),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),U_3507)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),U_3508))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3506,tc_HOL_Obool)),U_3507),U_3508) != c_Orderings_Obot__class_Obot(tc_fun(U_3506,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3506),U_3508))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3506),U_3507))
| ~ class_Groups_Ocomm__monoid__add(U_3505) ),
inference(definitional_conversion,[status(esa)],[f_825_2]) ).
cnf(f_825_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3506,tc_HOL_Obool)),U_3507),U_3508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3505),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),U_3507)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3506,U_3505),U_3509),U_3508))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3506,tc_HOL_Obool)),U_3507),U_3508) != c_Orderings_Obot__class_Obot(tc_fun(U_3506,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3506),U_3508))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3506),U_3507))
| ~ class_Groups_Ocomm__monoid__add(U_3505) ),
inference(clausify,[status(thm)],[f_825_3]) ).
fof(f_826_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un]) ).
fof(f_826_2,plain,
! [U_3514,U_3513,U_3512,U_3511,U_3510] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3511,tc_HOL_Obool)),U_3512),U_3513)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3510),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),U_3512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),U_3513))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3511,tc_HOL_Obool)),U_3512),U_3513)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3512))
| ~ class_Groups_Oab__group__add(U_3510) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
fof(f_826_3,plain,
! [U_3511,U_3510,U_3512,U_3513,U_3514] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3511,tc_HOL_Obool)),U_3512),U_3513)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3510),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),U_3512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),U_3513))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3511,tc_HOL_Obool)),U_3512),U_3513)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3512))
| ~ class_Groups_Oab__group__add(U_3510) ),
inference(definitional_conversion,[status(esa)],[f_826_2]) ).
cnf(f_826_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3511,tc_HOL_Obool)),U_3512),U_3513)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3510),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),U_3512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),U_3513))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3514),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3511,tc_HOL_Obool)),U_3512),U_3513)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3512))
| ~ class_Groups_Oab__group__add(U_3510) ),
inference(clausify,[status(thm)],[f_826_3]) ).
fof(f_827_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J]) ).
fof(f_827_2,plain,
! [U_3517,U_3516,U_3515] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3515),U_3516),U_3517) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3515),U_3516),hAPP(c_Groups_Ouminus__class_Ouminus(U_3515),U_3517))
| ~ class_Rings_Ocomm__ring__1(U_3515) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
fof(f_827_3,plain,
! [U_3516,U_3515,U_3517] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3515),U_3516),U_3517) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3515),U_3516),hAPP(c_Groups_Ouminus__class_Ouminus(U_3515),U_3517))
| ~ class_Rings_Ocomm__ring__1(U_3515) ),
inference(definitional_conversion,[status(esa)],[f_827_2]) ).
cnf(f_827_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3515),U_3516),U_3517) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3515),U_3516),hAPP(c_Groups_Ouminus__class_Ouminus(U_3515),U_3517))
| ~ class_Rings_Ocomm__ring__1(U_3515) ),
inference(clausify,[status(thm)],[f_827_3]) ).
fof(f_828_1,plain,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( 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)))
| ~ 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))) )
& ( 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)))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2]) ).
fof(f_828_2,plain,
! [U_3522,U_3521,U_3520,U_3519,U_3518] :
( ( ( 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),U_3518),U_3520)),U_3521)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3519),U_3520)),U_3522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),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),U_3519),U_3518)),U_3520)),U_3522))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),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),U_3519),U_3518)),U_3520)),U_3522)))
| ~ 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),U_3518),U_3520)),U_3521)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3519),U_3520)),U_3522))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3518),U_3519)) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
fof(f_828_3,plain,
( ! [U_3518,U_3519,U_3520,U_3521,U_3522] :
( 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),U_3518),U_3520)),U_3521)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3519),U_3520)),U_3522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),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),U_3519),U_3518)),U_3520)),U_3522)))
| ~ sP208(U_3518,U_3519,U_3520,U_3521,U_3522) )
& ! [U_3518,U_3519,U_3520,U_3521,U_3522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),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),U_3519),U_3518)),U_3520)),U_3522)))
| ~ 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),U_3518),U_3520)),U_3521)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3519),U_3520)),U_3522)))
| ~ sP208(U_3518,U_3519,U_3520,U_3521,U_3522) )
& ! [U_3518,U_3519,U_3520,U_3521,U_3522] :
( sP208(U_3518,U_3519,U_3520,U_3521,U_3522)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3518),U_3519)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_828_2]) ).
cnf(f_828_4,plain,
( sP208(U_3518,U_3519,U_3520,U_3521,U_3522)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3518),U_3519)) ),
inference(clausify,[status(thm)],[f_828_3]) ).
cnf(f_828_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),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),U_3519),U_3518)),U_3520)),U_3522)))
| ~ 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),U_3518),U_3520)),U_3521)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3519),U_3520)),U_3522)))
| ~ sP208(U_3518,U_3519,U_3520,U_3521,U_3522) ),
inference(clausify,[status(thm)],[f_828_3]) ).
cnf(f_828_6,plain,
( 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),U_3518),U_3520)),U_3521)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3519),U_3520)),U_3522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),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),U_3519),U_3518)),U_3520)),U_3522)))
| ~ sP208(U_3518,U_3519,U_3520,U_3521,U_3522) ),
inference(clausify,[status(thm)],[f_828_3]) ).
fof(f_829_1,plain,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( 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)))
| ~ 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)) )
& ( 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))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1]) ).
fof(f_829_2,plain,
! [U_3527,U_3526,U_3525,U_3524,U_3523] :
( ( ( 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),U_3524),U_3525)),U_3526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3523),U_3525)),U_3527)))
| ~ 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),U_3524),U_3523)),U_3525)),U_3526)),U_3527)) )
& ( 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),U_3524),U_3523)),U_3525)),U_3526)),U_3527))
| ~ 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),U_3524),U_3525)),U_3526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3523),U_3525)),U_3527))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3523),U_3524)) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
fof(f_829_3,plain,
( ! [U_3524,U_3523,U_3526,U_3525,U_3527] :
( 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),U_3524),U_3525)),U_3526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3523),U_3525)),U_3527)))
| ~ 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),U_3524),U_3523)),U_3525)),U_3526)),U_3527))
| ~ sP209(U_3524,U_3523,U_3526,U_3525,U_3527) )
& ! [U_3524,U_3523,U_3526,U_3525,U_3527] :
( 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),U_3524),U_3523)),U_3525)),U_3526)),U_3527))
| ~ 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),U_3524),U_3525)),U_3526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3523),U_3525)),U_3527)))
| ~ sP209(U_3524,U_3523,U_3526,U_3525,U_3527) )
& ! [U_3524,U_3523,U_3526,U_3525,U_3527] :
( sP209(U_3524,U_3523,U_3526,U_3525,U_3527)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3523),U_3524)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_829_2]) ).
cnf(f_829_4,plain,
( sP209(U_3524,U_3523,U_3526,U_3525,U_3527)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3523),U_3524)) ),
inference(clausify,[status(thm)],[f_829_3]) ).
cnf(f_829_5,plain,
( 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),U_3524),U_3523)),U_3525)),U_3526)),U_3527))
| ~ 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),U_3524),U_3525)),U_3526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3523),U_3525)),U_3527)))
| ~ sP209(U_3524,U_3523,U_3526,U_3525,U_3527) ),
inference(clausify,[status(thm)],[f_829_3]) ).
cnf(f_829_6,plain,
( 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),U_3524),U_3525)),U_3526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3523),U_3525)),U_3527)))
| ~ 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),U_3524),U_3523)),U_3525)),U_3526)),U_3527))
| ~ sP209(U_3524,U_3523,U_3526,U_3525,U_3527) ),
inference(clausify,[status(thm)],[f_829_3]) ).
fof(f_830_1,plain,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( 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)
| 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) )
& ( 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)
| 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) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2]) ).
fof(f_830_2,plain,
! [U_3532,U_3531,U_3530,U_3529,U_3528] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530)),U_3531) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3529),U_3530)),U_3532)
| U_3531 != 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),U_3529),U_3528)),U_3530)),U_3532) )
& ( U_3531 = 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),U_3529),U_3528)),U_3530)),U_3532)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530)),U_3531) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3529),U_3530)),U_3532) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3528),U_3529)) ),
inference(variable_rename,[status(thm)],[f_830_1]) ).
fof(f_830_3,plain,
( ! [U_3530,U_3529,U_3528,U_3531,U_3532] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530)),U_3531) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3529),U_3530)),U_3532)
| U_3531 != 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),U_3529),U_3528)),U_3530)),U_3532)
| ~ sP210(U_3530,U_3529,U_3528,U_3531,U_3532) )
& ! [U_3530,U_3529,U_3528,U_3531,U_3532] :
( U_3531 = 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),U_3529),U_3528)),U_3530)),U_3532)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530)),U_3531) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3529),U_3530)),U_3532)
| ~ sP210(U_3530,U_3529,U_3528,U_3531,U_3532) )
& ! [U_3530,U_3529,U_3528,U_3531,U_3532] :
( sP210(U_3530,U_3529,U_3528,U_3531,U_3532)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3528),U_3529)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_830_2]) ).
cnf(f_830_4,plain,
( sP210(U_3530,U_3529,U_3528,U_3531,U_3532)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3528),U_3529)) ),
inference(clausify,[status(thm)],[f_830_3]) ).
cnf(f_830_5,plain,
( U_3531 = 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),U_3529),U_3528)),U_3530)),U_3532)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530)),U_3531) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3529),U_3530)),U_3532)
| ~ sP210(U_3530,U_3529,U_3528,U_3531,U_3532) ),
inference(clausify,[status(thm)],[f_830_3]) ).
cnf(f_830_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530)),U_3531) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3529),U_3530)),U_3532)
| U_3531 != 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),U_3529),U_3528)),U_3530)),U_3532)
| ~ sP210(U_3530,U_3529,U_3528,U_3531,U_3532) ),
inference(clausify,[status(thm)],[f_830_3]) ).
fof(f_831_1,plain,
! [V_n,V_m,V_u,V_j,V_i] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2]) ).
fof(f_831_2,plain,
! [U_3537,U_3536,U_3535,U_3534,U_3533] :
( 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),U_3533),U_3535)),U_3536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3534),U_3535)),U_3537)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3536),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),U_3534),U_3533)),U_3535)),U_3537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3533),U_3534)) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
fof(f_831_3,plain,
! [U_3533,U_3535,U_3534,U_3536,U_3537] :
( 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),U_3533),U_3535)),U_3536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3534),U_3535)),U_3537)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3536),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),U_3534),U_3533)),U_3535)),U_3537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3533),U_3534)) ),
inference(definitional_conversion,[status(esa)],[f_831_2]) ).
cnf(f_831_4,plain,
( 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),U_3533),U_3535)),U_3536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3534),U_3535)),U_3537)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3536),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),U_3534),U_3533)),U_3535)),U_3537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3533),U_3534)) ),
inference(clausify,[status(thm)],[f_831_3]) ).
fof(f_832_1,plain,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( 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)))
| ~ 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))) )
& ( 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)))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2]) ).
fof(f_832_2,plain,
! [U_3542,U_3541,U_3540,U_3539,U_3538] :
( ( ( 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),U_3538),U_3540)),U_3541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3539),U_3540)),U_3542)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3541),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),U_3539),U_3538)),U_3540)),U_3542))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3541),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),U_3539),U_3538)),U_3540)),U_3542)))
| ~ 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),U_3538),U_3540)),U_3541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3539),U_3540)),U_3542))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3538),U_3539)) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
fof(f_832_3,plain,
( ! [U_3538,U_3539,U_3540,U_3541,U_3542] :
( 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),U_3538),U_3540)),U_3541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3539),U_3540)),U_3542)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3541),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),U_3539),U_3538)),U_3540)),U_3542)))
| ~ sP211(U_3538,U_3539,U_3540,U_3541,U_3542) )
& ! [U_3538,U_3539,U_3540,U_3541,U_3542] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3541),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),U_3539),U_3538)),U_3540)),U_3542)))
| ~ 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),U_3538),U_3540)),U_3541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3539),U_3540)),U_3542)))
| ~ sP211(U_3538,U_3539,U_3540,U_3541,U_3542) )
& ! [U_3538,U_3539,U_3540,U_3541,U_3542] :
( sP211(U_3538,U_3539,U_3540,U_3541,U_3542)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3538),U_3539)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_832_2]) ).
cnf(f_832_4,plain,
( sP211(U_3538,U_3539,U_3540,U_3541,U_3542)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3538),U_3539)) ),
inference(clausify,[status(thm)],[f_832_3]) ).
cnf(f_832_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3541),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),U_3539),U_3538)),U_3540)),U_3542)))
| ~ 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),U_3538),U_3540)),U_3541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3539),U_3540)),U_3542)))
| ~ sP211(U_3538,U_3539,U_3540,U_3541,U_3542) ),
inference(clausify,[status(thm)],[f_832_3]) ).
cnf(f_832_6,plain,
( 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),U_3538),U_3540)),U_3541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3539),U_3540)),U_3542)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3541),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),U_3539),U_3538)),U_3540)),U_3542)))
| ~ sP211(U_3538,U_3539,U_3540,U_3541,U_3542) ),
inference(clausify,[status(thm)],[f_832_3]) ).
fof(f_833_1,plain,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( 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)
| 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 )
& ( 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
| 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) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1]) ).
fof(f_833_2,plain,
! [U_3547,U_3546,U_3545,U_3544,U_3543] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3544),U_3545)),U_3546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3543),U_3545)),U_3547)
| 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),U_3544),U_3543)),U_3545)),U_3546) != U_3547 )
& ( 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),U_3544),U_3543)),U_3545)),U_3546) = U_3547
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3544),U_3545)),U_3546) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3543),U_3545)),U_3547) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3543),U_3544)) ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
fof(f_833_3,plain,
( ! [U_3544,U_3545,U_3543,U_3547,U_3546] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3544),U_3545)),U_3546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3543),U_3545)),U_3547)
| 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),U_3544),U_3543)),U_3545)),U_3546) != U_3547
| ~ sP212(U_3544,U_3545,U_3543,U_3547,U_3546) )
& ! [U_3544,U_3545,U_3543,U_3547,U_3546] :
( 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),U_3544),U_3543)),U_3545)),U_3546) = U_3547
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3544),U_3545)),U_3546) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3543),U_3545)),U_3547)
| ~ sP212(U_3544,U_3545,U_3543,U_3547,U_3546) )
& ! [U_3544,U_3545,U_3543,U_3547,U_3546] :
( sP212(U_3544,U_3545,U_3543,U_3547,U_3546)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3543),U_3544)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_833_2]) ).
cnf(f_833_4,plain,
( sP212(U_3544,U_3545,U_3543,U_3547,U_3546)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3543),U_3544)) ),
inference(clausify,[status(thm)],[f_833_3]) ).
cnf(f_833_5,plain,
( 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),U_3544),U_3543)),U_3545)),U_3546) = U_3547
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3544),U_3545)),U_3546) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3543),U_3545)),U_3547)
| ~ sP212(U_3544,U_3545,U_3543,U_3547,U_3546) ),
inference(clausify,[status(thm)],[f_833_3]) ).
cnf(f_833_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3544),U_3545)),U_3546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3543),U_3545)),U_3547)
| 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),U_3544),U_3543)),U_3545)),U_3546) != U_3547
| ~ sP212(U_3544,U_3545,U_3543,U_3547,U_3546) ),
inference(clausify,[status(thm)],[f_833_3]) ).
fof(f_834_1,plain,
! [V_n,V_m,V_u,V_i,V_j] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1]) ).
fof(f_834_2,plain,
! [U_3552,U_3551,U_3550,U_3549,U_3548] :
( 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),U_3549),U_3550)),U_3551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3548),U_3550)),U_3552)) = 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),U_3549),U_3548)),U_3550)),U_3551)),U_3552)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3548),U_3549)) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
fof(f_834_3,plain,
! [U_3550,U_3548,U_3549,U_3551,U_3552] :
( 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),U_3549),U_3550)),U_3551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3548),U_3550)),U_3552)) = 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),U_3549),U_3548)),U_3550)),U_3551)),U_3552)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3548),U_3549)) ),
inference(definitional_conversion,[status(esa)],[f_834_2]) ).
cnf(f_834_4,plain,
( 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),U_3549),U_3550)),U_3551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3548),U_3550)),U_3552)) = 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),U_3549),U_3548)),U_3550)),U_3551)),U_3552)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3548),U_3549)) ),
inference(clausify,[status(thm)],[f_834_3]) ).
fof(f_835_1,plain,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))),
inference(fof_nnf,[status(thm)],[fact_finite__lessThan]) ).
fof(f_835_2,plain,
! [U_3553] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3553))),
inference(variable_rename,[status(thm)],[f_835_1]) ).
fof(f_835_3,plain,
! [U_3553] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3553))),
inference(definitional_conversion,[status(esa)],[f_835_2]) ).
cnf(f_835_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3553))),
inference(clausify,[status(thm)],[f_835_3]) ).
fof(f_836_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__greaterThanAtMost]) ).
fof(f_836_2,plain,
! [U_3555,U_3554] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_3554,U_3555))),
inference(variable_rename,[status(thm)],[f_836_1]) ).
fof(f_836_3,plain,
! [U_3554,U_3555] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_3554,U_3555))),
inference(definitional_conversion,[status(esa)],[f_836_2]) ).
cnf(f_836_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_3554,U_3555))),
inference(clausify,[status(thm)],[f_836_3]) ).
fof(f_837_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__greaterThanLessThan]) ).
fof(f_837_2,plain,
! [U_3557,U_3556] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_3556,U_3557))),
inference(variable_rename,[status(thm)],[f_837_1]) ).
fof(f_837_3,plain,
! [U_3556,U_3557] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_3556,U_3557))),
inference(definitional_conversion,[status(esa)],[f_837_2]) ).
cnf(f_837_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_3556,U_3557))),
inference(clausify,[status(thm)],[f_837_3]) ).
fof(f_838_1,plain,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))),
inference(fof_nnf,[status(thm)],[fact_finite__atMost]) ).
fof(f_838_2,plain,
! [U_3558] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_3558))),
inference(variable_rename,[status(thm)],[f_838_1]) ).
fof(f_838_3,plain,
! [U_3558] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_3558))),
inference(definitional_conversion,[status(esa)],[f_838_2]) ).
cnf(f_838_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_3558))),
inference(clausify,[status(thm)],[f_838_3]) ).
fof(f_839_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__atLeastAtMost]) ).
fof(f_839_2,plain,
! [U_3560,U_3559] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3559,U_3560))),
inference(variable_rename,[status(thm)],[f_839_1]) ).
fof(f_839_3,plain,
! [U_3559,U_3560] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3559,U_3560))),
inference(definitional_conversion,[status(esa)],[f_839_2]) ).
cnf(f_839_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3559,U_3560))),
inference(clausify,[status(thm)],[f_839_3]) ).
fof(f_840_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(f_840_2,plain,
! [U_3564,U_3563,U_3562,U_3561] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3561),U_3562)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3563),U_3562)),U_3564)) = 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),U_3561),U_3563)),U_3562)),U_3564),
inference(variable_rename,[status(thm)],[f_840_1]) ).
fof(f_840_3,plain,
! [U_3561,U_3562,U_3563,U_3564] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3561),U_3562)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3563),U_3562)),U_3564)) = 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),U_3561),U_3563)),U_3562)),U_3564),
inference(definitional_conversion,[status(esa)],[f_840_2]) ).
cnf(f_840_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3561),U_3562)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3563),U_3562)),U_3564)) = 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),U_3561),U_3563)),U_3562)),U_3564),
inference(clausify,[status(thm)],[f_840_3]) ).
fof(f_841_1,plain,
! [V_N_2] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
| ! [B_m] :
? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) )
& ( ? [B_m] :
! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded]) ).
fof(f_841_2,plain,
! [U_3569] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3569))
| ! [U_3568] :
? [U_3567] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3567),U_3568))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3567),U_3569)) ) )
& ( ? [U_3566] :
! [U_3565] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),U_3566))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3565),U_3569)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3569)) ) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
fof(f_841_3,plain,
( ! [U_3571] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3571))
| ! [U_3568] :
? [U_3567] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3567),U_3568))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3567),U_3571)) ) )
& ! [U_3570] :
( ? [U_3566] :
! [U_3565] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),U_3566))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3565),U_3570)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3570)) ) ),
inference(miniscope,[status(thm)],[f_841_2]) ).
fof(f_841_4,plain,
( ! [U_3571] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3571))
| ! [U_3568] :
? [U_3567] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3567),U_3568))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3567),U_3571)) ) )
& ! [U_3570] :
( ! [U_3565] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),sK93(U_3570)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3565),U_3570)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3570)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_3566,sK93(U_3570))],[f_841_3]) ).
fof(f_841_5,plain,
( ! [U_3571] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3571))
| ! [U_3568] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK94(U_3571,U_3568)),U_3568))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(U_3571,U_3568)),U_3571)) ) )
& ! [U_3570] :
( ! [U_3565] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),sK93(U_3570)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3565),U_3570)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3570)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_3567,sK94(U_3571,U_3568))],[f_841_4]) ).
fof(f_841_6,plain,
( ! [U_3568,U_3571] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK94(U_3571,U_3568)),U_3568))
| ~ sP213(U_3568,U_3571) )
& ! [U_3568,U_3571] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(U_3571,U_3568)),U_3571))
| ~ sP213(U_3568,U_3571) )
& ! [U_3568,U_3571] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3571))
| sP213(U_3568,U_3571) )
& ! [U_3565,U_3570] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),sK93(U_3570)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3565),U_3570))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3570)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_841_5]) ).
cnf(f_841_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),sK93(U_3570)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3565),U_3570))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3570)) ),
inference(clausify,[status(thm)],[f_841_6]) ).
cnf(f_841_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3571))
| sP213(U_3568,U_3571) ),
inference(clausify,[status(thm)],[f_841_6]) ).
cnf(f_841_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(U_3571,U_3568)),U_3571))
| ~ sP213(U_3568,U_3571) ),
inference(clausify,[status(thm)],[f_841_6]) ).
cnf(f_841_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK94(U_3571,U_3568)),U_3568))
| ~ sP213(U_3568,U_3571) ),
inference(clausify,[status(thm)],[f_841_6]) ).
fof(f_842_1,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__nat]) ).
fof(f_842_2,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_842_1]) ).
cnf(f_842_3,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_842_2]) ).
fof(f_843_1,plain,
! [V_c,V_a,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_c),V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_843_2,plain,
! [U_3574,U_3573,U_3572] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3572),U_3573),U_3574) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3572),U_3574),U_3573)
| ~ class_Rings_Ocomm__semiring__1(U_3572) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
fof(f_843_3,plain,
! [U_3573,U_3574,U_3572] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3572),U_3573),U_3574) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3572),U_3574),U_3573)
| ~ class_Rings_Ocomm__semiring__1(U_3572) ),
inference(definitional_conversion,[status(esa)],[f_843_2]) ).
cnf(f_843_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3572),U_3573),U_3574) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3572),U_3574),U_3573)
| ~ class_Rings_Ocomm__semiring__1(U_3572) ),
inference(clausify,[status(thm)],[f_843_3]) ).
fof(f_844_1,plain,
! [V_d,V_c,V_a,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_844_2,plain,
! [U_3578,U_3577,U_3576,U_3575] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3576),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3577),U_3578)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3577),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3576),U_3578))
| ~ class_Rings_Ocomm__semiring__1(U_3575) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
fof(f_844_3,plain,
! [U_3575,U_3576,U_3577,U_3578] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3576),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3577),U_3578)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3577),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3576),U_3578))
| ~ class_Rings_Ocomm__semiring__1(U_3575) ),
inference(definitional_conversion,[status(esa)],[f_844_2]) ).
cnf(f_844_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3576),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3577),U_3578)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3577),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3575),U_3576),U_3578))
| ~ class_Rings_Ocomm__semiring__1(U_3575) ),
inference(clausify,[status(thm)],[f_844_3]) ).
fof(f_845_1,plain,
! [V_d,V_c,V_a,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_845_2,plain,
! [U_3582,U_3581,U_3580,U_3579] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3581),U_3582)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3580),U_3581)),U_3582)
| ~ class_Rings_Ocomm__semiring__1(U_3579) ),
inference(variable_rename,[status(thm)],[f_845_1]) ).
fof(f_845_3,plain,
! [U_3579,U_3580,U_3581,U_3582] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3581),U_3582)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3580),U_3581)),U_3582)
| ~ class_Rings_Ocomm__semiring__1(U_3579) ),
inference(definitional_conversion,[status(esa)],[f_845_2]) ).
cnf(f_845_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3581),U_3582)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3580),U_3581)),U_3582)
| ~ class_Rings_Ocomm__semiring__1(U_3579) ),
inference(clausify,[status(thm)],[f_845_3]) ).
fof(f_846_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_846_2,plain,
! [U_3586,U_3585,U_3584,U_3583] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3584),U_3585)),U_3586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3585),U_3586))
| ~ class_Rings_Ocomm__semiring__1(U_3583) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
fof(f_846_3,plain,
! [U_3583,U_3584,U_3585,U_3586] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3584),U_3585)),U_3586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3585),U_3586))
| ~ class_Rings_Ocomm__semiring__1(U_3583) ),
inference(definitional_conversion,[status(esa)],[f_846_2]) ).
cnf(f_846_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3584),U_3585)),U_3586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),U_3585),U_3586))
| ~ class_Rings_Ocomm__semiring__1(U_3583) ),
inference(clausify,[status(thm)],[f_846_3]) ).
fof(f_847_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_847_2,plain,
! [U_3590,U_3589,U_3588,U_3587] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),U_3588),U_3589)),U_3590) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),U_3588),U_3590)),U_3589)
| ~ class_Rings_Ocomm__semiring__1(U_3587) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
fof(f_847_3,plain,
! [U_3587,U_3588,U_3589,U_3590] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),U_3588),U_3589)),U_3590) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),U_3588),U_3590)),U_3589)
| ~ class_Rings_Ocomm__semiring__1(U_3587) ),
inference(definitional_conversion,[status(esa)],[f_847_2]) ).
cnf(f_847_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),U_3588),U_3589)),U_3590) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3587),U_3588),U_3590)),U_3589)
| ~ class_Rings_Ocomm__semiring__1(U_3587) ),
inference(clausify,[status(thm)],[f_847_3]) ).
fof(f_848_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_848_2,plain,
! [U_3595,U_3594,U_3593,U_3592,U_3591] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3592),U_3593)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3594),U_3595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3592),U_3594)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3593),U_3595))
| ~ class_Rings_Ocomm__semiring__1(U_3591) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
! [U_3591,U_3592,U_3593,U_3594,U_3595] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3592),U_3593)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3594),U_3595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3592),U_3594)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3593),U_3595))
| ~ class_Rings_Ocomm__semiring__1(U_3591) ),
inference(definitional_conversion,[status(esa)],[f_848_2]) ).
cnf(f_848_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3592),U_3593)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3594),U_3595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3592),U_3594)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3591),U_3593),U_3595))
| ~ class_Rings_Ocomm__semiring__1(U_3591) ),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_1,plain,
! [V_b,V_a,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_b),V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(f_849_2,plain,
! [U_3598,U_3597,U_3596] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3596),U_3597),U_3598) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3596),U_3598),U_3597)
| ~ class_Rings_Ocomm__semiring__1(U_3596) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
fof(f_849_3,plain,
! [U_3597,U_3596,U_3598] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3596),U_3597),U_3598) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3596),U_3598),U_3597)
| ~ class_Rings_Ocomm__semiring__1(U_3596) ),
inference(definitional_conversion,[status(esa)],[f_849_2]) ).
cnf(f_849_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3596),U_3597),U_3598) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3596),U_3598),U_3597)
| ~ class_Rings_Ocomm__semiring__1(U_3596) ),
inference(clausify,[status(thm)],[f_849_3]) ).
fof(f_850_1,plain,
! [V_ry,V_rx,V_lx,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(f_850_2,plain,
! [U_3602,U_3601,U_3600,U_3599] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3601),U_3602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3600),U_3602))
| ~ class_Rings_Ocomm__semiring__1(U_3599) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
fof(f_850_3,plain,
! [U_3599,U_3600,U_3601,U_3602] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3601),U_3602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3600),U_3602))
| ~ class_Rings_Ocomm__semiring__1(U_3599) ),
inference(definitional_conversion,[status(esa)],[f_850_2]) ).
cnf(f_850_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3601),U_3602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3599),U_3600),U_3602))
| ~ class_Rings_Ocomm__semiring__1(U_3599) ),
inference(clausify,[status(thm)],[f_850_3]) ).
fof(f_851_1,plain,
! [V_ry,V_rx,V_lx,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(f_851_2,plain,
! [U_3606,U_3605,U_3604,U_3603] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3605),U_3606)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3604),U_3605)),U_3606)
| ~ class_Rings_Ocomm__semiring__1(U_3603) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
fof(f_851_3,plain,
! [U_3603,U_3604,U_3605,U_3606] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3605),U_3606)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3604),U_3605)),U_3606)
| ~ class_Rings_Ocomm__semiring__1(U_3603) ),
inference(definitional_conversion,[status(esa)],[f_851_2]) ).
cnf(f_851_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3605),U_3606)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3603),U_3604),U_3605)),U_3606)
| ~ class_Rings_Ocomm__semiring__1(U_3603) ),
inference(clausify,[status(thm)],[f_851_3]) ).
fof(f_852_1,plain,
! [V_rx,V_ly,V_lx,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(f_852_2,plain,
! [U_3610,U_3609,U_3608,U_3607] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3608),U_3609)),U_3610) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3609),U_3610))
| ~ class_Rings_Ocomm__semiring__1(U_3607) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
fof(f_852_3,plain,
! [U_3607,U_3608,U_3609,U_3610] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3608),U_3609)),U_3610) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3609),U_3610))
| ~ class_Rings_Ocomm__semiring__1(U_3607) ),
inference(definitional_conversion,[status(esa)],[f_852_2]) ).
cnf(f_852_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3608),U_3609)),U_3610) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3607),U_3609),U_3610))
| ~ class_Rings_Ocomm__semiring__1(U_3607) ),
inference(clausify,[status(thm)],[f_852_3]) ).
fof(f_853_1,plain,
! [V_rx,V_ly,V_lx,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(f_853_2,plain,
! [U_3614,U_3613,U_3612,U_3611] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3614)),U_3613)
| ~ class_Rings_Ocomm__semiring__1(U_3611) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
fof(f_853_3,plain,
! [U_3614,U_3611,U_3612,U_3613] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3614)),U_3613)
| ~ class_Rings_Ocomm__semiring__1(U_3611) ),
inference(definitional_conversion,[status(esa)],[f_853_2]) ).
cnf(f_853_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3614)),U_3613)
| ~ class_Rings_Ocomm__semiring__1(U_3611) ),
inference(clausify,[status(thm)],[f_853_3]) ).
fof(f_854_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( 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)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(f_854_2,plain,
! [U_3619,U_3618,U_3617,U_3616,U_3615] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3616),U_3617)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3618),U_3619)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3618),U_3619)))
| ~ class_Rings_Ocomm__semiring__1(U_3615) ),
inference(variable_rename,[status(thm)],[f_854_1]) ).
fof(f_854_3,plain,
! [U_3615,U_3616,U_3617,U_3618,U_3619] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3616),U_3617)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3618),U_3619)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3618),U_3619)))
| ~ class_Rings_Ocomm__semiring__1(U_3615) ),
inference(definitional_conversion,[status(esa)],[f_854_2]) ).
cnf(f_854_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3616),U_3617)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3618),U_3619)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3615),U_3618),U_3619)))
| ~ class_Rings_Ocomm__semiring__1(U_3615) ),
inference(clausify,[status(thm)],[f_854_3]) ).
fof(f_855_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(f_855_2,plain,
! [U_3624,U_3623,U_3622,U_3621,U_3620] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3623),U_3624)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3624))
| ~ class_Rings_Ocomm__semiring__1(U_3620) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
fof(f_855_3,plain,
! [U_3620,U_3621,U_3622,U_3623,U_3624] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3623),U_3624)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3624))
| ~ class_Rings_Ocomm__semiring__1(U_3620) ),
inference(definitional_conversion,[status(esa)],[f_855_2]) ).
cnf(f_855_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3623),U_3624)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3624))
| ~ class_Rings_Ocomm__semiring__1(U_3620) ),
inference(clausify,[status(thm)],[f_855_3]) ).
fof(f_856_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(f_856_2,plain,
! [U_3629,U_3628,U_3627,U_3626,U_3625] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3626),U_3627)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3628),U_3629)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3626),U_3628)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3627),U_3629))
| ~ class_Rings_Ocomm__semiring__1(U_3625) ),
inference(variable_rename,[status(thm)],[f_856_1]) ).
fof(f_856_3,plain,
! [U_3625,U_3626,U_3627,U_3628,U_3629] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3626),U_3627)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3628),U_3629)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3626),U_3628)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3627),U_3629))
| ~ class_Rings_Ocomm__semiring__1(U_3625) ),
inference(definitional_conversion,[status(esa)],[f_856_2]) ).
cnf(f_856_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3626),U_3627)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3628),U_3629)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3626),U_3628)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3625),U_3627),U_3629))
| ~ class_Rings_Ocomm__semiring__1(U_3625) ),
inference(clausify,[status(thm)],[f_856_3]) ).
fof(f_857_1,plain,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
( ( ( 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))
| ( V_y_2 != V_z_2
& V_w_2 != V_x_2 ) )
& ( V_y_2 = V_z_2
| V_w_2 = V_x_2
| 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)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).
fof(f_857_2,plain,
! [U_3634,U_3633,U_3632,U_3631,U_3630] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3632))
| ( U_3632 != U_3634
& U_3631 != U_3633 ) )
& ( U_3632 = U_3634
| U_3631 = U_3633
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3634)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3632)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3630) ),
inference(variable_rename,[status(thm)],[f_857_1]) ).
fof(f_857_3,plain,
( ! [U_3631,U_3632,U_3633,U_3634] :
( U_3632 != U_3634
| ~ sP214(U_3631,U_3632,U_3633,U_3634) )
& ! [U_3631,U_3632,U_3633,U_3634] :
( U_3631 != U_3633
| ~ sP214(U_3631,U_3632,U_3633,U_3634) )
& ! [U_3630,U_3631,U_3632,U_3633,U_3634] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3632))
| sP214(U_3631,U_3632,U_3633,U_3634)
| ~ sP215(U_3630,U_3631,U_3632,U_3633,U_3634) )
& ! [U_3630,U_3631,U_3632,U_3633,U_3634] :
( U_3632 = U_3634
| U_3631 = U_3633
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3634)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3632))
| ~ sP215(U_3630,U_3631,U_3632,U_3633,U_3634) )
& ! [U_3630,U_3631,U_3632,U_3633,U_3634] :
( sP215(U_3630,U_3631,U_3632,U_3633,U_3634)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3630) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214,sP215])],[f_857_2]) ).
cnf(f_857_4,plain,
( sP215(U_3630,U_3631,U_3632,U_3633,U_3634)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3630) ),
inference(clausify,[status(thm)],[f_857_3]) ).
cnf(f_857_5,plain,
( U_3632 = U_3634
| U_3631 = U_3633
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3634)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3632))
| ~ sP215(U_3630,U_3631,U_3632,U_3633,U_3634) ),
inference(clausify,[status(thm)],[f_857_3]) ).
cnf(f_857_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3631),U_3634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3630),U_3633),U_3632))
| sP214(U_3631,U_3632,U_3633,U_3634)
| ~ sP215(U_3630,U_3631,U_3632,U_3633,U_3634) ),
inference(clausify,[status(thm)],[f_857_3]) ).
cnf(f_857_7,plain,
( U_3631 != U_3633
| ~ sP214(U_3631,U_3632,U_3633,U_3634) ),
inference(clausify,[status(thm)],[f_857_3]) ).
cnf(f_857_8,plain,
( U_3632 != U_3634
| ~ sP214(U_3631,U_3632,U_3633,U_3634) ),
inference(clausify,[status(thm)],[f_857_3]) ).
fof(f_858_1,plain,
! [V_b,V_m,V_a,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_858_2,plain,
! [U_3638,U_3637,U_3636,U_3635] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),U_3636),U_3637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),U_3638),U_3637)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3635),U_3636),U_3638)),U_3637)
| ~ class_Rings_Ocomm__semiring__1(U_3635) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
fof(f_858_3,plain,
! [U_3636,U_3638,U_3637,U_3635] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),U_3636),U_3637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),U_3638),U_3637)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3635),U_3636),U_3638)),U_3637)
| ~ class_Rings_Ocomm__semiring__1(U_3635) ),
inference(definitional_conversion,[status(esa)],[f_858_2]) ).
cnf(f_858_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),U_3636),U_3637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),U_3638),U_3637)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3635),U_3636),U_3638)),U_3637)
| ~ class_Rings_Ocomm__semiring__1(U_3635) ),
inference(clausify,[status(thm)],[f_858_3]) ).
fof(f_859_1,plain,
! [V_c,V_b,V_a,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_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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_859_2,plain,
! [U_3642,U_3641,U_3640,U_3639] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3639),U_3640),U_3641)),U_3642) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),U_3640),U_3642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),U_3641),U_3642))
| ~ class_Rings_Ocomm__semiring__1(U_3639) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
fof(f_859_3,plain,
! [U_3639,U_3640,U_3641,U_3642] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3639),U_3640),U_3641)),U_3642) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),U_3640),U_3642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),U_3641),U_3642))
| ~ class_Rings_Ocomm__semiring__1(U_3639) ),
inference(definitional_conversion,[status(esa)],[f_859_2]) ).
cnf(f_859_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3639),U_3640),U_3641)),U_3642) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),U_3640),U_3642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3639),U_3641),U_3642))
| ~ class_Rings_Ocomm__semiring__1(U_3639) ),
inference(clausify,[status(thm)],[f_859_3]) ).
fof(f_860_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( ( V_ca_2 != V_d_2
& V_a_2 != V_b_2 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_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_ca_2)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_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_ca_2))
| V_ca_2 = V_d_2
| V_a_2 = V_b_2 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).
fof(f_860_2,plain,
! [U_3647,U_3646,U_3645,U_3644,U_3643] :
( ( ( ( U_3646 != U_3647
& U_3644 != U_3645 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3647)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3646)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3647)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3646))
| U_3646 = U_3647
| U_3644 = U_3645 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3643) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
fof(f_860_3,plain,
( ! [U_3644,U_3645,U_3646,U_3647] :
( U_3646 != U_3647
| ~ sP216(U_3644,U_3645,U_3646,U_3647) )
& ! [U_3644,U_3645,U_3646,U_3647] :
( U_3644 != U_3645
| ~ sP216(U_3644,U_3645,U_3646,U_3647) )
& ! [U_3643,U_3644,U_3645,U_3646,U_3647] :
( sP216(U_3644,U_3645,U_3646,U_3647)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3647)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3646))
| ~ sP217(U_3643,U_3644,U_3645,U_3646,U_3647) )
& ! [U_3643,U_3644,U_3645,U_3646,U_3647] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3647)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3646))
| U_3646 = U_3647
| U_3644 = U_3645
| ~ sP217(U_3643,U_3644,U_3645,U_3646,U_3647) )
& ! [U_3643,U_3644,U_3645,U_3646,U_3647] :
( sP217(U_3643,U_3644,U_3645,U_3646,U_3647)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3643) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216,sP217])],[f_860_2]) ).
cnf(f_860_4,plain,
( sP217(U_3643,U_3644,U_3645,U_3646,U_3647)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3643) ),
inference(clausify,[status(thm)],[f_860_3]) ).
cnf(f_860_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3647)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3646))
| U_3646 = U_3647
| U_3644 = U_3645
| ~ sP217(U_3643,U_3644,U_3645,U_3646,U_3647) ),
inference(clausify,[status(thm)],[f_860_3]) ).
cnf(f_860_6,plain,
( sP216(U_3644,U_3645,U_3646,U_3647)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3647)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3644),U_3647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3643),U_3645),U_3646))
| ~ sP217(U_3643,U_3644,U_3645,U_3646,U_3647) ),
inference(clausify,[status(thm)],[f_860_3]) ).
cnf(f_860_7,plain,
( U_3644 != U_3645
| ~ sP216(U_3644,U_3645,U_3646,U_3647) ),
inference(clausify,[status(thm)],[f_860_3]) ).
cnf(f_860_8,plain,
( U_3646 != U_3647
| ~ sP216(U_3644,U_3645,U_3646,U_3647) ),
inference(clausify,[status(thm)],[f_860_3]) ).
fof(f_861_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_861_2,plain,
! [U_3651,U_3650,U_3649,U_3648] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3648),U_3650),U_3651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),U_3650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),U_3651))
| ~ class_Rings_Ocomm__semiring__1(U_3648) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
fof(f_861_3,plain,
! [U_3650,U_3651,U_3649,U_3648] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3648),U_3650),U_3651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),U_3650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),U_3651))
| ~ class_Rings_Ocomm__semiring__1(U_3648) ),
inference(definitional_conversion,[status(esa)],[f_861_2]) ).
cnf(f_861_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3648),U_3650),U_3651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),U_3650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3648),U_3649),U_3651))
| ~ class_Rings_Ocomm__semiring__1(U_3648) ),
inference(clausify,[status(thm)],[f_861_3]) ).
fof(f_862_1,plain,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( 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)))
| ~ 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)) )
& ( 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))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1]) ).
fof(f_862_2,plain,
! [U_3656,U_3655,U_3654,U_3653,U_3652] :
( ( ( 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),U_3653),U_3654)),U_3655)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3654)),U_3656)))
| ~ 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),U_3653),U_3652)),U_3654)),U_3655)),U_3656)) )
& ( 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),U_3653),U_3652)),U_3654)),U_3655)),U_3656))
| ~ 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),U_3653),U_3654)),U_3655)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3654)),U_3656))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3652),U_3653)) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
fof(f_862_3,plain,
( ! [U_3652,U_3653,U_3654,U_3655,U_3656] :
( 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),U_3653),U_3654)),U_3655)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3654)),U_3656)))
| ~ 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),U_3653),U_3652)),U_3654)),U_3655)),U_3656))
| ~ sP218(U_3652,U_3653,U_3654,U_3655,U_3656) )
& ! [U_3652,U_3653,U_3654,U_3655,U_3656] :
( 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),U_3653),U_3652)),U_3654)),U_3655)),U_3656))
| ~ 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),U_3653),U_3654)),U_3655)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3654)),U_3656)))
| ~ sP218(U_3652,U_3653,U_3654,U_3655,U_3656) )
& ! [U_3652,U_3653,U_3654,U_3655,U_3656] :
( sP218(U_3652,U_3653,U_3654,U_3655,U_3656)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3652),U_3653)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_862_2]) ).
cnf(f_862_4,plain,
( sP218(U_3652,U_3653,U_3654,U_3655,U_3656)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3652),U_3653)) ),
inference(clausify,[status(thm)],[f_862_3]) ).
cnf(f_862_5,plain,
( 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),U_3653),U_3652)),U_3654)),U_3655)),U_3656))
| ~ 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),U_3653),U_3654)),U_3655)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3654)),U_3656)))
| ~ sP218(U_3652,U_3653,U_3654,U_3655,U_3656) ),
inference(clausify,[status(thm)],[f_862_3]) ).
cnf(f_862_6,plain,
( 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),U_3653),U_3654)),U_3655)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3654)),U_3656)))
| ~ 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),U_3653),U_3652)),U_3654)),U_3655)),U_3656))
| ~ sP218(U_3652,U_3653,U_3654,U_3655,U_3656) ),
inference(clausify,[status(thm)],[f_862_3]) ).
fof(f_863_1,plain,
! [V_i,V_j,V_k] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__right]) ).
fof(f_863_2,plain,
! [U_3659,U_3658,U_3657] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3658),U_3657)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3659),U_3657)),U_3658)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3657),U_3658)) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
fof(f_863_3,plain,
! [U_3659,U_3658,U_3657] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3658),U_3657)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3659),U_3657)),U_3658)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3657),U_3658)) ),
inference(definitional_conversion,[status(esa)],[f_863_2]) ).
cnf(f_863_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3658),U_3657)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3659),U_3657)),U_3658)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3657),U_3658)) ),
inference(clausify,[status(thm)],[f_863_3]) ).
fof(f_864_1,plain,
! [V_i_2,V_k_2,V_j_2] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__conv]) ).
fof(f_864_2,plain,
! [U_3662,U_3661,U_3660] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3660),U_3661)),U_3662))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3660),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3662),U_3661))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3660),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3662),U_3661)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3660),U_3661)),U_3662)) ) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
fof(f_864_3,plain,
( ! [U_3668,U_3666,U_3664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3664),U_3666)),U_3668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3668),U_3666))) )
& ! [U_3667,U_3665,U_3663] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3667),U_3665)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3663),U_3665)),U_3667)) ) ),
inference(miniscope,[status(thm)],[f_864_2]) ).
fof(f_864_4,plain,
( ! [U_3664,U_3666,U_3668] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3664),U_3666)),U_3668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3668),U_3666))) )
& ! [U_3665,U_3663,U_3667] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3667),U_3665)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3663),U_3665)),U_3667)) ) ),
inference(definitional_conversion,[status(esa)],[f_864_3]) ).
cnf(f_864_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3667),U_3665)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3663),U_3665)),U_3667)) ),
inference(clausify,[status(thm)],[f_864_4]) ).
cnf(f_864_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3664),U_3666)),U_3668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3668),U_3666))) ),
inference(clausify,[status(thm)],[f_864_4]) ).
fof(f_865_1,plain,
! [V_m,V_n,V_k] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff]) ).
fof(f_865_2,plain,
! [U_3671,U_3670,U_3669] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3671),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3670),U_3671)),U_3669)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3669),U_3670)) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
fof(f_865_3,plain,
! [U_3669,U_3670,U_3671] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3671),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3670),U_3671)),U_3669)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3669),U_3670)) ),
inference(definitional_conversion,[status(esa)],[f_865_2]) ).
cnf(f_865_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3671),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3670),U_3671)),U_3669)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3669),U_3670)) ),
inference(clausify,[status(thm)],[f_865_3]) ).
fof(f_866_1,plain,
! [V_m,V_n] :
( 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
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse]) ).
fof(f_866_2,plain,
! [U_3673,U_3672] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3672),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3672)) = U_3673
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3672),U_3673)) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
fof(f_866_3,plain,
! [U_3672,U_3673] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3672),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3672)) = U_3673
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3672),U_3673)) ),
inference(definitional_conversion,[status(esa)],[f_866_2]) ).
cnf(f_866_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3672),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3672)) = U_3673
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3672),U_3673)) ),
inference(clausify,[status(thm)],[f_866_3]) ).
fof(f_867_1,plain,
! [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)) = 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc]) ).
fof(f_867_2,plain,
! [U_3676,U_3675,U_3674] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3675),U_3674)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),U_3675)),U_3674)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3674),U_3675)) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
fof(f_867_3,plain,
! [U_3674,U_3675,U_3676] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3675),U_3674)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),U_3675)),U_3674)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3674),U_3675)) ),
inference(definitional_conversion,[status(esa)],[f_867_2]) ).
cnf(f_867_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3675),U_3674)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),U_3675)),U_3674)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3674),U_3675)) ),
inference(clausify,[status(thm)],[f_867_3]) ).
fof(f_868_1,plain,
! [V_i_2,V_j_2,V_k_2] :
( ( ( 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)))
| ~ 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)) )
& ( 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))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__conv2]) ).
fof(f_868_2,plain,
! [U_3679,U_3678,U_3677] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),U_3677)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),U_3677)),U_3678)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),U_3677)),U_3678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),U_3677))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3677),U_3678)) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
fof(f_868_3,plain,
( ! [U_3677,U_3678,U_3679] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),U_3677)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),U_3677)),U_3678))
| ~ sP219(U_3677,U_3678,U_3679) )
& ! [U_3677,U_3678,U_3679] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),U_3677)),U_3678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),U_3677)))
| ~ sP219(U_3677,U_3678,U_3679) )
& ! [U_3677,U_3678,U_3679] :
( sP219(U_3677,U_3678,U_3679)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3677),U_3678)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219])],[f_868_2]) ).
cnf(f_868_4,plain,
( sP219(U_3677,U_3678,U_3679)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3677),U_3678)) ),
inference(clausify,[status(thm)],[f_868_3]) ).
cnf(f_868_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),U_3677)),U_3678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),U_3677)))
| ~ sP219(U_3677,U_3678,U_3679) ),
inference(clausify,[status(thm)],[f_868_3]) ).
cnf(f_868_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),U_3677)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),U_3677)),U_3678))
| ~ sP219(U_3677,U_3678,U_3679) ),
inference(clausify,[status(thm)],[f_868_3]) ).
fof(f_869_1,plain,
! [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_m),V_n)),V_n) = V_m
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2]) ).
fof(f_869_2,plain,
! [U_3681,U_3680] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3681),U_3680)),U_3680) = U_3681
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3680),U_3681)) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
fof(f_869_3,plain,
! [U_3681,U_3680] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3681),U_3680)),U_3680) = U_3681
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3680),U_3681)) ),
inference(definitional_conversion,[status(esa)],[f_869_2]) ).
cnf(f_869_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3681),U_3680)),U_3680) = U_3681
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3680),U_3681)) ),
inference(clausify,[status(thm)],[f_869_3]) ).
fof(f_870_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
| V_j_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) )
& ( V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) != V_k_2 ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add]) ).
fof(f_870_2,plain,
! [U_3684,U_3683,U_3682] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682) = U_3684
| U_3683 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3682) )
& ( U_3683 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3682)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682) != U_3684 ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3682),U_3683)) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
fof(f_870_3,plain,
( ! [U_3682,U_3683,U_3684] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682) = U_3684
| U_3683 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3682)
| ~ sP220(U_3682,U_3683,U_3684) )
& ! [U_3682,U_3683,U_3684] :
( U_3683 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3682)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682) != U_3684
| ~ sP220(U_3682,U_3683,U_3684) )
& ! [U_3682,U_3683,U_3684] :
( sP220(U_3682,U_3683,U_3684)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3682),U_3683)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_870_2]) ).
cnf(f_870_4,plain,
( sP220(U_3682,U_3683,U_3684)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3682),U_3683)) ),
inference(clausify,[status(thm)],[f_870_3]) ).
cnf(f_870_5,plain,
( U_3683 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3682)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682) != U_3684
| ~ sP220(U_3682,U_3683,U_3684) ),
inference(clausify,[status(thm)],[f_870_3]) ).
cnf(f_870_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682) = U_3684
| U_3683 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3682)
| ~ sP220(U_3682,U_3683,U_3684) ),
inference(clausify,[status(thm)],[f_870_3]) ).
fof(f_871_1,plain,
! [V_Pa_2,V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
| ( ~ hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
| ( ~ hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
& V_m_2 = V_n_2 )
| ( ~ hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).
fof(f_871_2,plain,
! [U_3687,U_3686,U_3685] :
( hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| ( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3686),U_3685)) )
| ( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
& U_3685 = U_3686 )
| ( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3685),U_3686)) ) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
fof(f_871_3,plain,
( ! [U_3687,U_3686,U_3685] :
( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| ~ sP223(U_3687,U_3686,U_3685) )
& ! [U_3687,U_3686,U_3685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3686),U_3685))
| ~ sP223(U_3687,U_3686,U_3685) )
& ! [U_3687,U_3686,U_3685] :
( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| ~ sP222(U_3687,U_3686,U_3685) )
& ! [U_3687,U_3686,U_3685] :
( U_3685 = U_3686
| ~ sP222(U_3687,U_3686,U_3685) )
& ! [U_3687,U_3686,U_3685] :
( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| ~ sP221(U_3687,U_3686,U_3685) )
& ! [U_3687,U_3686,U_3685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3685),U_3686))
| ~ sP221(U_3687,U_3686,U_3685) )
& ! [U_3687,U_3686,U_3685] :
( hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| sP223(U_3687,U_3686,U_3685)
| sP222(U_3687,U_3686,U_3685)
| sP221(U_3687,U_3686,U_3685) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221,sP222,sP223])],[f_871_2]) ).
cnf(f_871_4,plain,
( hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| sP223(U_3687,U_3686,U_3685)
| sP222(U_3687,U_3686,U_3685)
| sP221(U_3687,U_3686,U_3685) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3685),U_3686))
| ~ sP221(U_3687,U_3686,U_3685) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_6,plain,
( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| ~ sP221(U_3687,U_3686,U_3685) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_7,plain,
( U_3685 = U_3686
| ~ sP222(U_3687,U_3686,U_3685) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_8,plain,
( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| ~ sP222(U_3687,U_3686,U_3685) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3686),U_3685))
| ~ sP223(U_3687,U_3686,U_3685) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_10,plain,
( ~ hBOOL(hAPP(hAPP(U_3687,U_3686),U_3685))
| ~ sP223(U_3687,U_3686,U_3685) ),
inference(clausify,[status(thm)],[f_871_3]) ).
fof(f_872_1,plain,
! [V_t,V_s] :
( V_s != V_t
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).
fof(f_872_2,plain,
! [U_3689,U_3688] :
( U_3688 != U_3689
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3688),U_3689)) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
fof(f_872_3,plain,
! [U_3688,U_3689] :
( U_3688 != U_3689
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3688),U_3689)) ),
inference(definitional_conversion,[status(esa)],[f_872_2]) ).
cnf(f_872_4,plain,
( U_3688 != U_3689
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3688),U_3689)) ),
inference(clausify,[status(thm)],[f_872_3]) ).
fof(f_873_1,plain,
! [V_m,V_n] :
( V_m != V_n
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).
fof(f_873_2,plain,
! [U_3691,U_3690] :
( U_3691 != U_3690
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3690),U_3691)) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
fof(f_873_3,plain,
! [U_3690,U_3691] :
( U_3691 != U_3690
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3690),U_3691)) ),
inference(definitional_conversion,[status(esa)],[f_873_2]) ).
cnf(f_873_4,plain,
( U_3691 != U_3690
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3690),U_3691)) ),
inference(clausify,[status(thm)],[f_873_3]) ).
fof(f_874_1,plain,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).
fof(f_874_2,plain,
! [U_3692] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3692),U_3692)),
inference(variable_rename,[status(thm)],[f_874_1]) ).
fof(f_874_3,plain,
! [U_3692] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3692),U_3692)),
inference(definitional_conversion,[status(esa)],[f_874_2]) ).
cnf(f_874_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3692),U_3692)),
inference(clausify,[status(thm)],[f_874_3]) ).
fof(f_875_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
| V_x = V_y ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(f_875_2,plain,
! [U_3694,U_3693] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3694),U_3693))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3693),U_3694))
| U_3693 = U_3694 ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
fof(f_875_3,plain,
! [U_3694,U_3693] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3694),U_3693))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3693),U_3694))
| U_3693 = U_3694 ),
inference(definitional_conversion,[status(esa)],[f_875_2]) ).
cnf(f_875_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3694),U_3693))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3693),U_3694))
| U_3693 = U_3694 ),
inference(clausify,[status(thm)],[f_875_3]) ).
fof(f_876_1,plain,
! [V_n_2,V_m_2] :
( ( V_m_2 != V_n_2
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| V_m_2 = V_n_2 ) ),
inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).
fof(f_876_2,plain,
! [U_3696,U_3695] :
( ( U_3695 != U_3696
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3696),U_3695))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3695),U_3696)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3696),U_3695))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3695),U_3696))
| U_3695 = U_3696 ) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
fof(f_876_3,plain,
( ! [U_3700,U_3698] :
( U_3698 != U_3700
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3700),U_3698))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3698),U_3700)) ) )
& ! [U_3699,U_3697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3699),U_3697))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3697),U_3699))
| U_3697 = U_3699 ) ),
inference(miniscope,[status(thm)],[f_876_2]) ).
fof(f_876_4,plain,
( ! [U_3700,U_3698] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3700),U_3698))
| ~ sP224(U_3700,U_3698) )
& ! [U_3700,U_3698] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3698),U_3700))
| ~ sP224(U_3700,U_3698) )
& ! [U_3700,U_3698] :
( U_3698 != U_3700
| sP224(U_3700,U_3698) )
& ! [U_3699,U_3697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3699),U_3697))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3697),U_3699))
| U_3697 = U_3699 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_876_3]) ).
cnf(f_876_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3699),U_3697))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3697),U_3699))
| U_3697 = U_3699 ),
inference(clausify,[status(thm)],[f_876_4]) ).
cnf(f_876_6,plain,
( U_3698 != U_3700
| sP224(U_3700,U_3698) ),
inference(clausify,[status(thm)],[f_876_4]) ).
cnf(f_876_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3698),U_3700))
| ~ sP224(U_3700,U_3698) ),
inference(clausify,[status(thm)],[f_876_4]) ).
cnf(f_876_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3700),U_3698))
| ~ sP224(U_3700,U_3698) ),
inference(clausify,[status(thm)],[f_876_4]) ).
fof(f_877_1,plain,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).
fof(f_877_2,plain,
! [U_3701] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3701),U_3701)),
inference(variable_rename,[status(thm)],[f_877_1]) ).
fof(f_877_3,plain,
! [U_3701] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3701),U_3701)),
inference(definitional_conversion,[status(esa)],[f_877_2]) ).
cnf(f_877_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3701),U_3701)),
inference(clausify,[status(thm)],[f_877_3]) ).
fof(f_878_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__add__commute]) ).
fof(f_878_2,plain,
! [U_3703,U_3702] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3702),U_3703) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3703),U_3702),
inference(variable_rename,[status(thm)],[f_878_1]) ).
fof(f_878_3,plain,
! [U_3703,U_3702] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3702),U_3703) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3703),U_3702),
inference(definitional_conversion,[status(esa)],[f_878_2]) ).
cnf(f_878_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3702),U_3703) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3703),U_3702),
inference(clausify,[status(thm)],[f_878_3]) ).
fof(f_879_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__commute]) ).
fof(f_879_2,plain,
! [U_3706,U_3705,U_3704] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3705),U_3706)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3704),U_3706)),
inference(variable_rename,[status(thm)],[f_879_1]) ).
fof(f_879_3,plain,
! [U_3704,U_3705,U_3706] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3705),U_3706)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3704),U_3706)),
inference(definitional_conversion,[status(esa)],[f_879_2]) ).
cnf(f_879_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3705),U_3706)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3704),U_3706)),
inference(clausify,[status(thm)],[f_879_3]) ).
fof(f_880_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_nat__add__assoc]) ).
fof(f_880_2,plain,
! [U_3709,U_3708,U_3707] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3707),U_3708)),U_3709) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3709)),
inference(variable_rename,[status(thm)],[f_880_1]) ).
fof(f_880_3,plain,
! [U_3707,U_3708,U_3709] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3707),U_3708)),U_3709) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3709)),
inference(definitional_conversion,[status(esa)],[f_880_2]) ).
cnf(f_880_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3707),U_3708)),U_3709) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3709)),
inference(clausify,[status(thm)],[f_880_3]) ).
fof(f_881_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).
fof(f_881_2,plain,
! [U_3712,U_3711,U_3710] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3710),U_3711) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3710),U_3712)
| U_3711 != U_3712 )
& ( U_3711 = U_3712
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3710),U_3711) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3710),U_3712) ) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
fof(f_881_3,plain,
( ! [U_3718,U_3716] :
( ! [U_3714] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3714),U_3716) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3714),U_3718)
| U_3716 != U_3718 )
& ! [U_3717,U_3715] :
( ! [U_3713] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3713),U_3715) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3713),U_3717)
| U_3715 = U_3717 ) ),
inference(miniscope,[status(thm)],[f_881_2]) ).
fof(f_881_4,plain,
( ! [U_3718,U_3714,U_3716] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3714),U_3716) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3714),U_3718)
| U_3716 != U_3718 )
& ! [U_3715,U_3717,U_3713] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3713),U_3715) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3713),U_3717)
| U_3715 = U_3717 ) ),
inference(definitional_conversion,[status(esa)],[f_881_3]) ).
cnf(f_881_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3713),U_3715) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3713),U_3717)
| U_3715 = U_3717 ),
inference(clausify,[status(thm)],[f_881_4]) ).
cnf(f_881_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3714),U_3716) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3714),U_3718)
| U_3716 != U_3718 ),
inference(clausify,[status(thm)],[f_881_4]) ).
fof(f_882_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( 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)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).
fof(f_882_2,plain,
! [U_3721,U_3720,U_3719] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3719),U_3720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3721),U_3720)
| U_3719 != U_3721 )
& ( U_3719 = U_3721
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3719),U_3720) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3721),U_3720) ) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
fof(f_882_3,plain,
( ! [U_3727,U_3725,U_3723] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3723),U_3725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3727),U_3725)
| U_3723 != U_3727 )
& ! [U_3726,U_3724,U_3722] :
( U_3722 = U_3726
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3722),U_3724) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),U_3724) ) ),
inference(miniscope,[status(thm)],[f_882_2]) ).
fof(f_882_4,plain,
( ! [U_3723,U_3725,U_3727] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3723),U_3725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3727),U_3725)
| U_3723 != U_3727 )
& ! [U_3724,U_3726,U_3722] :
( U_3722 = U_3726
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3722),U_3724) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),U_3724) ) ),
inference(definitional_conversion,[status(esa)],[f_882_3]) ).
cnf(f_882_5,plain,
( U_3722 = U_3726
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3722),U_3724) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),U_3724) ),
inference(clausify,[status(thm)],[f_882_4]) ).
cnf(f_882_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3723),U_3725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3727),U_3725)
| U_3723 != U_3727 ),
inference(clausify,[status(thm)],[f_882_4]) ).
fof(f_883_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).
fof(f_883_2,plain,
! [U_3729,U_3728] :
( U_3728 = U_3729
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3729),U_3728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3728),U_3729)) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
fof(f_883_3,plain,
! [U_3729,U_3728] :
( U_3728 = U_3729
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3729),U_3728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3728),U_3729)) ),
inference(definitional_conversion,[status(esa)],[f_883_2]) ).
cnf(f_883_4,plain,
( U_3728 = U_3729
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3729),U_3728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3728),U_3729)) ),
inference(clausify,[status(thm)],[f_883_3]) ).
fof(f_884_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_le__trans]) ).
fof(f_884_2,plain,
! [U_3732,U_3731,U_3730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3730),U_3732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),U_3732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3730),U_3731)) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
fof(f_884_3,plain,
! [U_3730,U_3731,U_3732] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3730),U_3732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),U_3732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3730),U_3731)) ),
inference(definitional_conversion,[status(esa)],[f_884_2]) ).
cnf(f_884_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3730),U_3732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),U_3732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3730),U_3731)) ),
inference(clausify,[status(thm)],[f_884_3]) ).
fof(f_885_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| V_m != V_n ),
inference(fof_nnf,[status(thm)],[fact_eq__imp__le]) ).
fof(f_885_2,plain,
! [U_3734,U_3733] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3733),U_3734))
| U_3733 != U_3734 ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
fof(f_885_3,plain,
! [U_3733,U_3734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3733),U_3734))
| U_3733 != U_3734 ),
inference(definitional_conversion,[status(esa)],[f_885_2]) ).
cnf(f_885_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3733),U_3734))
| U_3733 != U_3734 ),
inference(clausify,[status(thm)],[f_885_3]) ).
fof(f_886_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).
fof(f_886_2,plain,
! [U_3736,U_3735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3736),U_3735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3735),U_3736)) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
fof(f_886_3,plain,
! [U_3735,U_3736] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3736),U_3735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3735),U_3736)) ),
inference(definitional_conversion,[status(esa)],[f_886_2]) ).
cnf(f_886_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3736),U_3735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3735),U_3736)) ),
inference(clausify,[status(thm)],[f_886_3]) ).
fof(f_887_1,plain,
! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)),
inference(fof_nnf,[status(thm)],[fact_le__refl]) ).
fof(f_887_2,plain,
! [U_3737] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3737),U_3737)),
inference(variable_rename,[status(thm)],[f_887_1]) ).
fof(f_887_3,plain,
! [U_3737] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3737),U_3737)),
inference(definitional_conversion,[status(esa)],[f_887_2]) ).
cnf(f_887_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3737),U_3737)),
inference(clausify,[status(thm)],[f_887_3]) ).
fof(f_888_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_diff__commute]) ).
fof(f_888_2,plain,
! [U_3740,U_3739,U_3738] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3738),U_3739)),U_3740) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3738),U_3740)),U_3739),
inference(variable_rename,[status(thm)],[f_888_1]) ).
fof(f_888_3,plain,
! [U_3738,U_3739,U_3740] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3738),U_3739)),U_3740) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3738),U_3740)),U_3739),
inference(definitional_conversion,[status(esa)],[f_888_2]) ).
cnf(f_888_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3738),U_3739)),U_3740) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3738),U_3740)),U_3739),
inference(clausify,[status(thm)],[f_888_3]) ).
fof(f_889_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__mult__commute]) ).
fof(f_889_2,plain,
! [U_3742,U_3741] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3741),U_3742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3741),
inference(variable_rename,[status(thm)],[f_889_1]) ).
fof(f_889_3,plain,
! [U_3741,U_3742] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3741),U_3742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3741),
inference(definitional_conversion,[status(esa)],[f_889_2]) ).
cnf(f_889_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3741),U_3742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3741),
inference(clausify,[status(thm)],[f_889_3]) ).
fof(f_890_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_nat__mult__assoc]) ).
fof(f_890_2,plain,
! [U_3745,U_3744,U_3743] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3743),U_3744)),U_3745) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3744),U_3745)),
inference(variable_rename,[status(thm)],[f_890_1]) ).
fof(f_890_3,plain,
! [U_3743,U_3744,U_3745] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3743),U_3744)),U_3745) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3744),U_3745)),
inference(definitional_conversion,[status(esa)],[f_890_2]) ).
cnf(f_890_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3743),U_3744)),U_3745) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3744),U_3745)),
inference(clausify,[status(thm)],[f_890_3]) ).
fof(f_891_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_not__add__less1]) ).
fof(f_891_2,plain,
! [U_3747,U_3746] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3746),U_3747)),U_3746)),
inference(variable_rename,[status(thm)],[f_891_1]) ).
fof(f_891_3,plain,
! [U_3746,U_3747] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3746),U_3747)),U_3746)),
inference(definitional_conversion,[status(esa)],[f_891_2]) ).
cnf(f_891_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3746),U_3747)),U_3746)),
inference(clausify,[status(thm)],[f_891_3]) ).
fof(f_892_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_not__add__less2]) ).
fof(f_892_2,plain,
! [U_3749,U_3748] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3748),U_3749)),U_3749)),
inference(variable_rename,[status(thm)],[f_892_1]) ).
fof(f_892_3,plain,
! [U_3748,U_3749] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3748),U_3749)),U_3749)),
inference(definitional_conversion,[status(esa)],[f_892_2]) ).
cnf(f_892_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3748),U_3749)),U_3749)),
inference(clausify,[status(thm)],[f_892_3]) ).
fof(f_893_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).
fof(f_893_2,plain,
! [U_3752,U_3751,U_3750] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3750),U_3751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3750),U_3752)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3751),U_3752)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3751),U_3752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3750),U_3751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3750),U_3752))) ) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
fof(f_893_3,plain,
( ! [U_3758,U_3756] :
( ! [U_3754] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3754),U_3756)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3754),U_3758)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3756),U_3758)) )
& ! [U_3757,U_3755] :
( ! [U_3753] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3753),U_3755)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3753),U_3757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3755),U_3757)) ) ),
inference(miniscope,[status(thm)],[f_893_2]) ).
fof(f_893_4,plain,
( ! [U_3754,U_3756,U_3758] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3754),U_3756)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3754),U_3758)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3756),U_3758)) )
& ! [U_3753,U_3755,U_3757] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3753),U_3755)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3753),U_3757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3755),U_3757)) ) ),
inference(definitional_conversion,[status(esa)],[f_893_3]) ).
cnf(f_893_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3753),U_3755)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3753),U_3757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3755),U_3757)) ),
inference(clausify,[status(thm)],[f_893_4]) ).
cnf(f_893_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3754),U_3756)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3754),U_3758)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3756),U_3758)) ),
inference(clausify,[status(thm)],[f_893_4]) ).
fof(f_894_1,plain,
! [V_m,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add1]) ).
fof(f_894_2,plain,
! [U_3761,U_3760,U_3759] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3760),U_3761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3760)) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
fof(f_894_3,plain,
! [U_3760,U_3759,U_3761] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3760),U_3761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3760)) ),
inference(definitional_conversion,[status(esa)],[f_894_2]) ).
cnf(f_894_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3760),U_3761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3760)) ),
inference(clausify,[status(thm)],[f_894_3]) ).
fof(f_895_1,plain,
! [V_m,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add2]) ).
fof(f_895_2,plain,
! [U_3764,U_3763,U_3762] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3764),U_3763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3762),U_3763)) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
fof(f_895_3,plain,
! [U_3762,U_3763,U_3764] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3764),U_3763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3762),U_3763)) ),
inference(definitional_conversion,[status(esa)],[f_895_2]) ).
cnf(f_895_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3764),U_3763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3762),U_3763)) ),
inference(clausify,[status(thm)],[f_895_3]) ).
fof(f_896_1,plain,
! [V_k,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_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono1]) ).
fof(f_896_2,plain,
! [U_3767,U_3766,U_3765] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3765),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3766),U_3767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3765),U_3766)) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
fof(f_896_3,plain,
! [U_3765,U_3766,U_3767] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3765),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3766),U_3767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3765),U_3766)) ),
inference(definitional_conversion,[status(esa)],[f_896_2]) ).
cnf(f_896_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3765),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3766),U_3767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3765),U_3766)) ),
inference(clausify,[status(thm)],[f_896_3]) ).
fof(f_897_1,plain,
! [V_l,V_k,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_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono]) ).
fof(f_897_2,plain,
! [U_3771,U_3770,U_3769,U_3768] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3768),U_3770)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3769),U_3771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3770),U_3771))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3768),U_3769)) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
fof(f_897_3,plain,
! [U_3768,U_3769,U_3770,U_3771] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3768),U_3770)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3769),U_3771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3770),U_3771))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3768),U_3769)) ),
inference(definitional_conversion,[status(esa)],[f_897_2]) ).
cnf(f_897_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3768),U_3770)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3769),U_3771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3770),U_3771))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3768),U_3769)) ),
inference(clausify,[status(thm)],[f_897_3]) ).
fof(f_898_1,plain,
! [V_n,V_m,V_l,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) ),
inference(fof_nnf,[status(thm)],[fact_less__add__eq__less]) ).
fof(f_898_2,plain,
! [U_3775,U_3774,U_3773,U_3772] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3774),U_3775))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3774),U_3773) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3772),U_3775)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3772),U_3773)) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
fof(f_898_3,plain,
! [U_3773,U_3772,U_3774,U_3775] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3774),U_3775))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3774),U_3773) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3772),U_3775)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3772),U_3773)) ),
inference(definitional_conversion,[status(esa)],[f_898_2]) ).
cnf(f_898_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3774),U_3775))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3774),U_3773) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3772),U_3775)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3772),U_3773)) ),
inference(clausify,[status(thm)],[f_898_3]) ).
fof(f_899_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_add__lessD1]) ).
fof(f_899_2,plain,
! [U_3778,U_3777,U_3776] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3776),U_3777)),U_3778)) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
fof(f_899_3,plain,
! [U_3776,U_3777,U_3778] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3776),U_3777)),U_3778)) ),
inference(definitional_conversion,[status(esa)],[f_899_2]) ).
cnf(f_899_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3776),U_3777)),U_3778)) ),
inference(clausify,[status(thm)],[f_899_3]) ).
fof(f_900_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ( V_m != V_n
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le]) ).
fof(f_900_2,plain,
! [U_3780,U_3779] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3779),U_3780))
| ( U_3779 != U_3780
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3779),U_3780)) ) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
fof(f_900_3,plain,
( ! [U_3779,U_3780] :
( U_3779 != U_3780
| ~ sP225(U_3779,U_3780) )
& ! [U_3779,U_3780] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3779),U_3780))
| ~ sP225(U_3779,U_3780) )
& ! [U_3779,U_3780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3779),U_3780))
| sP225(U_3779,U_3780) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_900_2]) ).
cnf(f_900_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3779),U_3780))
| sP225(U_3779,U_3780) ),
inference(clausify,[status(thm)],[f_900_3]) ).
cnf(f_900_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3779),U_3780))
| ~ sP225(U_3779,U_3780) ),
inference(clausify,[status(thm)],[f_900_3]) ).
cnf(f_900_6,plain,
( U_3779 != U_3780
| ~ sP225(U_3779,U_3780) ),
inference(clausify,[status(thm)],[f_900_3]) ).
fof(f_901_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less]) ).
fof(f_901_2,plain,
! [U_3782,U_3781] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3781),U_3782))
| U_3781 = U_3782
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3781),U_3782)) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
fof(f_901_3,plain,
! [U_3782,U_3781] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3781),U_3782))
| U_3781 = U_3782
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3781),U_3782)) ),
inference(definitional_conversion,[status(esa)],[f_901_2]) ).
cnf(f_901_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3781),U_3782))
| U_3781 = U_3782
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3781),U_3782)) ),
inference(clausify,[status(thm)],[f_901_3]) ).
fof(f_902_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).
fof(f_902_2,plain,
! [U_3784,U_3783] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3783),U_3784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3783),U_3784)) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
fof(f_902_3,plain,
! [U_3783,U_3784] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3783),U_3784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3783),U_3784)) ),
inference(definitional_conversion,[status(esa)],[f_902_2]) ).
cnf(f_902_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3783),U_3784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3783),U_3784)) ),
inference(clausify,[status(thm)],[f_902_3]) ).
fof(f_903_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ( V_m_2 != V_n_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
& ( V_m_2 = V_n_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).
fof(f_903_2,plain,
! [U_3786,U_3785] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3785),U_3786))
| ( U_3785 != U_3786
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3785),U_3786)) ) )
& ( U_3785 = U_3786
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3785),U_3786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3785),U_3786)) ) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
fof(f_903_3,plain,
( ! [U_3790,U_3788] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3788),U_3790))
| ( U_3788 != U_3790
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3788),U_3790)) ) )
& ! [U_3789,U_3787] :
( U_3787 = U_3789
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3787),U_3789))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3787),U_3789)) ) ),
inference(miniscope,[status(thm)],[f_903_2]) ).
fof(f_903_4,plain,
( ! [U_3788,U_3790] :
( U_3788 != U_3790
| ~ sP226(U_3788,U_3790) )
& ! [U_3788,U_3790] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3788),U_3790))
| ~ sP226(U_3788,U_3790) )
& ! [U_3788,U_3790] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3788),U_3790))
| sP226(U_3788,U_3790) )
& ! [U_3789,U_3787] :
( U_3787 = U_3789
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3787),U_3789))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3787),U_3789)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_903_3]) ).
cnf(f_903_5,plain,
( U_3787 = U_3789
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3787),U_3789))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3787),U_3789)) ),
inference(clausify,[status(thm)],[f_903_4]) ).
cnf(f_903_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3788),U_3790))
| sP226(U_3788,U_3790) ),
inference(clausify,[status(thm)],[f_903_4]) ).
cnf(f_903_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3788),U_3790))
| ~ sP226(U_3788,U_3790) ),
inference(clausify,[status(thm)],[f_903_4]) ).
cnf(f_903_8,plain,
( U_3788 != U_3790
| ~ sP226(U_3788,U_3790) ),
inference(clausify,[status(thm)],[f_903_4]) ).
fof(f_904_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| V_m_2 = V_n_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( ( V_m_2 != V_n_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).
fof(f_904_2,plain,
! [U_3792,U_3791] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3791),U_3792))
| U_3791 = U_3792
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3791),U_3792)) )
& ( ( U_3791 != U_3792
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3791),U_3792)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3791),U_3792)) ) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
fof(f_904_3,plain,
( ! [U_3796,U_3794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3794),U_3796))
| U_3794 = U_3796
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3794),U_3796)) )
& ! [U_3795,U_3793] :
( ( U_3793 != U_3795
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3793),U_3795)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3793),U_3795)) ) ),
inference(miniscope,[status(thm)],[f_904_2]) ).
fof(f_904_4,plain,
( ! [U_3793,U_3795] :
( U_3793 != U_3795
| ~ sP227(U_3793,U_3795) )
& ! [U_3793,U_3795] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3793),U_3795))
| ~ sP227(U_3793,U_3795) )
& ! [U_3794,U_3796] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3794),U_3796))
| U_3794 = U_3796
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3794),U_3796)) )
& ! [U_3793,U_3795] :
( sP227(U_3793,U_3795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3793),U_3795)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_904_3]) ).
cnf(f_904_5,plain,
( sP227(U_3793,U_3795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3793),U_3795)) ),
inference(clausify,[status(thm)],[f_904_4]) ).
cnf(f_904_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3794),U_3796))
| U_3794 = U_3796
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3794),U_3796)) ),
inference(clausify,[status(thm)],[f_904_4]) ).
cnf(f_904_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3793),U_3795))
| ~ sP227(U_3793,U_3795) ),
inference(clausify,[status(thm)],[f_904_4]) ).
cnf(f_904_8,plain,
( U_3793 != U_3795
| ~ sP227(U_3793,U_3795) ),
inference(clausify,[status(thm)],[f_904_4]) ).
fof(f_905_1,plain,
! [V_n,V_k,V_m] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) )
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_add__leE]) ).
fof(f_905_2,plain,
! [U_3799,U_3798,U_3797] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3798),U_3799))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3797),U_3799)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3797),U_3798)),U_3799)) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
fof(f_905_3,plain,
( ! [U_3799,U_3798,U_3797] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3798),U_3799))
| ~ sP228(U_3799,U_3798,U_3797) )
& ! [U_3799,U_3798,U_3797] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3797),U_3799))
| ~ sP228(U_3799,U_3798,U_3797) )
& ! [U_3799,U_3798,U_3797] :
( sP228(U_3799,U_3798,U_3797)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3797),U_3798)),U_3799)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_905_2]) ).
cnf(f_905_4,plain,
( sP228(U_3799,U_3798,U_3797)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3797),U_3798)),U_3799)) ),
inference(clausify,[status(thm)],[f_905_3]) ).
cnf(f_905_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3797),U_3799))
| ~ sP228(U_3799,U_3798,U_3797) ),
inference(clausify,[status(thm)],[f_905_3]) ).
cnf(f_905_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3798),U_3799))
| ~ sP228(U_3799,U_3798,U_3797) ),
inference(clausify,[status(thm)],[f_905_3]) ).
fof(f_906_1,plain,
! [V_n,V_k,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_add__leD1]) ).
fof(f_906_2,plain,
! [U_3802,U_3801,U_3800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3800),U_3802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3800),U_3801)),U_3802)) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
fof(f_906_3,plain,
! [U_3801,U_3800,U_3802] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3800),U_3802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3800),U_3801)),U_3802)) ),
inference(definitional_conversion,[status(esa)],[f_906_2]) ).
cnf(f_906_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3800),U_3802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3800),U_3801)),U_3802)) ),
inference(clausify,[status(thm)],[f_906_3]) ).
fof(f_907_1,plain,
! [V_n,V_k,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_add__leD2]) ).
fof(f_907_2,plain,
! [U_3805,U_3804,U_3803] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3804),U_3805))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3803),U_3804)),U_3805)) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
fof(f_907_3,plain,
! [U_3805,U_3804] :
( ! [U_3803] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3803),U_3804)),U_3805))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3804),U_3805)) ),
inference(miniscope,[status(thm)],[f_907_2]) ).
fof(f_907_4,plain,
! [U_3803,U_3804,U_3805] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3803),U_3804)),U_3805))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3804),U_3805)) ),
inference(definitional_conversion,[status(esa)],[f_907_3]) ).
cnf(f_907_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3803),U_3804)),U_3805))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3804),U_3805)) ),
inference(clausify,[status(thm)],[f_907_4]) ).
fof(f_908_1,plain,
! [V_l,V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono]) ).
fof(f_908_2,plain,
! [U_3809,U_3808,U_3807,U_3806] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3808)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3807),U_3809)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3808),U_3809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3806),U_3807)) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
fof(f_908_3,plain,
! [U_3806,U_3807,U_3808,U_3809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3808)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3807),U_3809)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3808),U_3809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3806),U_3807)) ),
inference(definitional_conversion,[status(esa)],[f_908_2]) ).
cnf(f_908_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3808)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3807),U_3809)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3808),U_3809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3806),U_3807)) ),
inference(clausify,[status(thm)],[f_908_3]) ).
fof(f_909_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono1]) ).
fof(f_909_2,plain,
! [U_3812,U_3811,U_3810] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3810),U_3812)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3811),U_3812)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3810),U_3811)) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
fof(f_909_3,plain,
! [U_3812,U_3810,U_3811] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3810),U_3812)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3811),U_3812)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3810),U_3811)) ),
inference(definitional_conversion,[status(esa)],[f_909_2]) ).
cnf(f_909_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3810),U_3812)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3811),U_3812)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3810),U_3811)) ),
inference(clausify,[status(thm)],[f_909_3]) ).
fof(f_910_1,plain,
! [V_m,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add2]) ).
fof(f_910_2,plain,
! [U_3815,U_3814,U_3813] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3813),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3815),U_3814)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3813),U_3814)) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
fof(f_910_3,plain,
! [U_3813,U_3814,U_3815] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3813),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3815),U_3814)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3813),U_3814)) ),
inference(definitional_conversion,[status(esa)],[f_910_2]) ).
cnf(f_910_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3813),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3815),U_3814)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3813),U_3814)) ),
inference(clausify,[status(thm)],[f_910_3]) ).
fof(f_911_1,plain,
! [V_m,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add1]) ).
fof(f_911_2,plain,
! [U_3818,U_3817,U_3816] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3817),U_3818)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),U_3817)) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
fof(f_911_3,plain,
! [U_3816,U_3817,U_3818] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3817),U_3818)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),U_3817)) ),
inference(definitional_conversion,[status(esa)],[f_911_2]) ).
cnf(f_911_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3817),U_3818)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),U_3817)) ),
inference(clausify,[status(thm)],[f_911_3]) ).
fof(f_912_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).
fof(f_912_2,plain,
! [U_3821,U_3820,U_3819] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3819),U_3820)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3819),U_3821)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3820),U_3821)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3820),U_3821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3819),U_3820)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3819),U_3821))) ) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
fof(f_912_3,plain,
( ! [U_3827,U_3825] :
( ! [U_3823] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3823),U_3825)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3823),U_3827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3825),U_3827)) )
& ! [U_3826,U_3824] :
( ! [U_3822] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3822),U_3824)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3822),U_3826)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3824),U_3826)) ) ),
inference(miniscope,[status(thm)],[f_912_2]) ).
fof(f_912_4,plain,
( ! [U_3827,U_3823,U_3825] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3823),U_3825)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3823),U_3827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3825),U_3827)) )
& ! [U_3822,U_3826,U_3824] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3822),U_3824)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3822),U_3826)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3824),U_3826)) ) ),
inference(definitional_conversion,[status(esa)],[f_912_3]) ).
cnf(f_912_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3822),U_3824)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3822),U_3826)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3824),U_3826)) ),
inference(clausify,[status(thm)],[f_912_4]) ).
cnf(f_912_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3823),U_3825)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3823),U_3827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3825),U_3827)) ),
inference(clausify,[status(thm)],[f_912_4]) ).
fof(f_913_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ! [B_k] : V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) )
& ( ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).
fof(f_913_2,plain,
! [U_3831,U_3830] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3830),U_3831))
| ! [U_3829] : U_3831 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3830),U_3829) )
& ( ? [U_3828] : U_3831 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3830),U_3828)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3830),U_3831)) ) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
fof(f_913_3,plain,
( ! [U_3835,U_3833] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3833),U_3835))
| ! [U_3829] : U_3835 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3833),U_3829) )
& ! [U_3834,U_3832] :
( ? [U_3828] : U_3834 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3832),U_3828)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3832),U_3834)) ) ),
inference(miniscope,[status(thm)],[f_913_2]) ).
fof(f_913_4,plain,
( ! [U_3835,U_3833] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3833),U_3835))
| ! [U_3829] : U_3835 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3833),U_3829) )
& ! [U_3834,U_3832] :
( U_3834 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3832),sK95(U_3834,U_3832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3832),U_3834)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_3828,sK95(U_3834,U_3832))],[f_913_3]) ).
fof(f_913_5,plain,
( ! [U_3829,U_3833,U_3835] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3833),U_3835))
| U_3835 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3833),U_3829) )
& ! [U_3834,U_3832] :
( U_3834 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3832),sK95(U_3834,U_3832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3832),U_3834)) ) ),
inference(definitional_conversion,[status(esa)],[f_913_4]) ).
cnf(f_913_6,plain,
( U_3834 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3832),sK95(U_3834,U_3832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3832),U_3834)) ),
inference(clausify,[status(thm)],[f_913_5]) ).
cnf(f_913_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3833),U_3835))
| U_3835 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3833),U_3829) ),
inference(clausify,[status(thm)],[f_913_5]) ).
fof(f_914_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_le__add1]) ).
fof(f_914_2,plain,
! [U_3837,U_3836] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3836),U_3837))),
inference(variable_rename,[status(thm)],[f_914_1]) ).
fof(f_914_3,plain,
! [U_3837,U_3836] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3836),U_3837))),
inference(definitional_conversion,[status(esa)],[f_914_2]) ).
cnf(f_914_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3836),U_3837))),
inference(clausify,[status(thm)],[f_914_3]) ).
fof(f_915_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_le__add2]) ).
fof(f_915_2,plain,
! [U_3839,U_3838] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3839),U_3838))),
inference(variable_rename,[status(thm)],[f_915_1]) ).
fof(f_915_3,plain,
! [U_3838,U_3839] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3839),U_3838))),
inference(definitional_conversion,[status(esa)],[f_915_2]) ).
cnf(f_915_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3839),U_3838))),
inference(clausify,[status(thm)],[f_915_3]) ).
fof(f_916_1,plain,
! [V_l,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_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono2]) ).
fof(f_916_2,plain,
! [U_3842,U_3841,U_3840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3841)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3840)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3840),U_3842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3840),U_3841)) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
fof(f_916_3,plain,
! [U_3840,U_3841,U_3842] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3841)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3840)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3840),U_3842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3840),U_3841)) ),
inference(definitional_conversion,[status(esa)],[f_916_2]) ).
cnf(f_916_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3841)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3840)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3840),U_3842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3840),U_3841)) ),
inference(clausify,[status(thm)],[f_916_3]) ).
fof(f_917_1,plain,
! [V_n,V_k,V_j] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less]) ).
fof(f_917_2,plain,
! [U_3845,U_3844,U_3843] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3843),U_3845)),U_3844))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3843),U_3844)) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
fof(f_917_3,plain,
! [U_3843,U_3844,U_3845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3843),U_3845)),U_3844))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3843),U_3844)) ),
inference(definitional_conversion,[status(esa)],[f_917_2]) ).
cnf(f_917_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3843),U_3845)),U_3844))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3843),U_3844)) ),
inference(clausify,[status(thm)],[f_917_3]) ).
fof(f_918_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_diff__cancel2]) ).
fof(f_918_2,plain,
! [U_3848,U_3847,U_3846] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3846),U_3847)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3848),U_3847)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3848),
inference(variable_rename,[status(thm)],[f_918_1]) ).
fof(f_918_3,plain,
! [U_3846,U_3847,U_3848] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3846),U_3847)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3848),U_3847)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3848),
inference(definitional_conversion,[status(esa)],[f_918_2]) ).
cnf(f_918_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3846),U_3847)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3848),U_3847)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3848),
inference(clausify,[status(thm)],[f_918_3]) ).
fof(f_919_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_diff__cancel]) ).
fof(f_919_2,plain,
! [U_3851,U_3850,U_3849] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3849),U_3850)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3849),U_3851)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3850),U_3851),
inference(variable_rename,[status(thm)],[f_919_1]) ).
fof(f_919_3,plain,
! [U_3849,U_3850,U_3851] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3849),U_3850)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3849),U_3851)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3850),U_3851),
inference(definitional_conversion,[status(esa)],[f_919_2]) ).
cnf(f_919_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3849),U_3850)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3849),U_3851)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3850),U_3851),
inference(clausify,[status(thm)],[f_919_3]) ).
fof(f_920_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__diff__left]) ).
fof(f_920_2,plain,
! [U_3854,U_3853,U_3852] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3852),U_3853)),U_3854) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3853),U_3854)),
inference(variable_rename,[status(thm)],[f_920_1]) ).
fof(f_920_3,plain,
! [U_3852,U_3853,U_3854] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3852),U_3853)),U_3854) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3853),U_3854)),
inference(definitional_conversion,[status(esa)],[f_920_2]) ).
cnf(f_920_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3852),U_3853)),U_3854) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3853),U_3854)),
inference(clausify,[status(thm)],[f_920_3]) ).
fof(f_921_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_diff__add__inverse]) ).
fof(f_921_2,plain,
! [U_3856,U_3855] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3855),U_3856)),U_3855) = U_3856,
inference(variable_rename,[status(thm)],[f_921_1]) ).
fof(f_921_3,plain,
! [U_3855,U_3856] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3855),U_3856)),U_3855) = U_3856,
inference(definitional_conversion,[status(esa)],[f_921_2]) ).
cnf(f_921_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3855),U_3856)),U_3855) = U_3856,
inference(clausify,[status(thm)],[f_921_3]) ).
fof(f_922_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_diff__add__inverse2]) ).
fof(f_922_2,plain,
! [U_3858,U_3857] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3857),U_3858)),U_3858) = U_3857,
inference(variable_rename,[status(thm)],[f_922_1]) ).
fof(f_922_3,plain,
! [U_3857,U_3858] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3857),U_3858)),U_3858) = U_3857,
inference(definitional_conversion,[status(esa)],[f_922_2]) ).
cnf(f_922_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3857),U_3858)),U_3858) = U_3857,
inference(clausify,[status(thm)],[f_922_3]) ).
fof(f_923_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib]) ).
fof(f_923_2,plain,
! [U_3861,U_3860,U_3859] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3859),U_3860)),U_3861) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3859),U_3861)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3860),U_3861)),
inference(variable_rename,[status(thm)],[f_923_1]) ).
fof(f_923_3,plain,
! [U_3859,U_3860,U_3861] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3859),U_3860)),U_3861) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3859),U_3861)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3860),U_3861)),
inference(definitional_conversion,[status(esa)],[f_923_2]) ).
cnf(f_923_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3859),U_3860)),U_3861) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3859),U_3861)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3860),U_3861)),
inference(clausify,[status(thm)],[f_923_3]) ).
fof(f_924_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib2]) ).
fof(f_924_2,plain,
! [U_3864,U_3863,U_3862] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3863),U_3864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),U_3863)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),U_3864)),
inference(variable_rename,[status(thm)],[f_924_1]) ).
fof(f_924_3,plain,
! [U_3862,U_3863,U_3864] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3863),U_3864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),U_3863)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),U_3864)),
inference(definitional_conversion,[status(esa)],[f_924_2]) ).
cnf(f_924_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3863),U_3864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),U_3863)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3862),U_3864)),
inference(clausify,[status(thm)],[f_924_3]) ).
fof(f_925_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__iff]) ).
fof(f_925_2,plain,
! [U_3867,U_3866,U_3865] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3866),U_3865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3867),U_3865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3866),U_3867)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3866),U_3867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3866),U_3865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3867),U_3865))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3865),U_3867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3865),U_3866)) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
fof(f_925_3,plain,
( ! [U_3865,U_3866,U_3867] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3866),U_3865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3867),U_3865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3866),U_3867))
| ~ sP229(U_3865,U_3866,U_3867) )
& ! [U_3865,U_3866,U_3867] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3866),U_3867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3866),U_3865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3867),U_3865)))
| ~ sP229(U_3865,U_3866,U_3867) )
& ! [U_3865,U_3866,U_3867] :
( sP229(U_3865,U_3866,U_3867)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3865),U_3867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3865),U_3866)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_925_2]) ).
cnf(f_925_4,plain,
( sP229(U_3865,U_3866,U_3867)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3865),U_3867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3865),U_3866)) ),
inference(clausify,[status(thm)],[f_925_3]) ).
cnf(f_925_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3866),U_3867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3866),U_3865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3867),U_3865)))
| ~ sP229(U_3865,U_3866,U_3867) ),
inference(clausify,[status(thm)],[f_925_3]) ).
cnf(f_925_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3866),U_3865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3867),U_3865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3866),U_3867))
| ~ sP229(U_3865,U_3866,U_3867) ),
inference(clausify,[status(thm)],[f_925_3]) ).
fof(f_926_1,plain,
! [V_n,V_m,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_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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq]) ).
fof(f_926_2,plain,
! [U_3870,U_3869,U_3868] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3869),U_3868)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3870),U_3868)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3869),U_3870)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3868),U_3870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3868),U_3869)) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
fof(f_926_3,plain,
! [U_3870,U_3868,U_3869] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3869),U_3868)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3870),U_3868)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3869),U_3870)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3868),U_3870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3868),U_3869)) ),
inference(definitional_conversion,[status(esa)],[f_926_2]) ).
cnf(f_926_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3869),U_3868)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3870),U_3868)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3869),U_3870)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3868),U_3870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3868),U_3869)) ),
inference(clausify,[status(thm)],[f_926_3]) ).
fof(f_927_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( 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)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| 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) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_eq__diff__iff]) ).
fof(f_927_2,plain,
! [U_3873,U_3872,U_3871] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3872),U_3871) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3873),U_3871)
| U_3872 != U_3873 )
& ( U_3872 = U_3873
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3872),U_3871) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3873),U_3871) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3871),U_3873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3871),U_3872)) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
fof(f_927_3,plain,
( ! [U_3871,U_3872,U_3873] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3872),U_3871) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3873),U_3871)
| U_3872 != U_3873
| ~ sP230(U_3871,U_3872,U_3873) )
& ! [U_3871,U_3872,U_3873] :
( U_3872 = U_3873
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3872),U_3871) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3873),U_3871)
| ~ sP230(U_3871,U_3872,U_3873) )
& ! [U_3871,U_3872,U_3873] :
( sP230(U_3871,U_3872,U_3873)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3871),U_3873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3871),U_3872)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_927_2]) ).
cnf(f_927_4,plain,
( sP230(U_3871,U_3872,U_3873)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3871),U_3873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3871),U_3872)) ),
inference(clausify,[status(thm)],[f_927_3]) ).
cnf(f_927_5,plain,
( U_3872 = U_3873
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3872),U_3871) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3873),U_3871)
| ~ sP230(U_3871,U_3872,U_3873) ),
inference(clausify,[status(thm)],[f_927_3]) ).
cnf(f_927_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3872),U_3871) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3873),U_3871)
| U_3872 != U_3873
| ~ sP230(U_3871,U_3872,U_3873) ),
inference(clausify,[status(thm)],[f_927_3]) ).
fof(f_928_1,plain,
! [V_n,V_i] :
( 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
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel]) ).
fof(f_928_2,plain,
! [U_3875,U_3874] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3875),U_3874)) = U_3874
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3874),U_3875)) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
fof(f_928_3,plain,
! [U_3875,U_3874] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3875),U_3874)) = U_3874
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3874),U_3875)) ),
inference(definitional_conversion,[status(esa)],[f_928_2]) ).
cnf(f_928_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3875),U_3874)) = U_3874
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3874),U_3875)) ),
inference(clausify,[status(thm)],[f_928_3]) ).
fof(f_929_1,plain,
! [V_l,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_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono]) ).
fof(f_929_2,plain,
! [U_3878,U_3877,U_3876] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3876),U_3878)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3877),U_3878)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3876),U_3877)) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
fof(f_929_3,plain,
! [U_3876,U_3877,U_3878] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3876),U_3878)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3877),U_3878)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3876),U_3877)) ),
inference(definitional_conversion,[status(esa)],[f_929_2]) ).
cnf(f_929_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3876),U_3878)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3877),U_3878)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3876),U_3877)) ),
inference(clausify,[status(thm)],[f_929_3]) ).
fof(f_930_1,plain,
! [V_l,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_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono2]) ).
fof(f_930_2,plain,
! [U_3881,U_3880,U_3879] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3881),U_3880)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3881),U_3879)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3879),U_3880)) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
fof(f_930_3,plain,
! [U_3879,U_3880,U_3881] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3881),U_3880)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3881),U_3879)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3879),U_3880)) ),
inference(definitional_conversion,[status(esa)],[f_930_2]) ).
cnf(f_930_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3881),U_3880)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3881),U_3879)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3879),U_3880)) ),
inference(clausify,[status(thm)],[f_930_3]) ).
fof(f_931_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__le__self]) ).
fof(f_931_2,plain,
! [U_3883,U_3882] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3882),U_3883)),U_3882)),
inference(variable_rename,[status(thm)],[f_931_1]) ).
fof(f_931_3,plain,
! [U_3882,U_3883] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3882),U_3883)),U_3882)),
inference(definitional_conversion,[status(esa)],[f_931_2]) ).
cnf(f_931_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3882),U_3883)),U_3882)),
inference(clausify,[status(thm)],[f_931_3]) ).
fof(f_932_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_le__square]) ).
fof(f_932_2,plain,
! [U_3884] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3884),U_3884))),
inference(variable_rename,[status(thm)],[f_932_1]) ).
fof(f_932_3,plain,
! [U_3884] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3884),U_3884))),
inference(definitional_conversion,[status(esa)],[f_932_2]) ).
cnf(f_932_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3884),U_3884))),
inference(clausify,[status(thm)],[f_932_3]) ).
fof(f_933_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_le__cube]) ).
fof(f_933_2,plain,
! [U_3885] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3885),U_3885)))),
inference(variable_rename,[status(thm)],[f_933_1]) ).
fof(f_933_3,plain,
! [U_3885] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3885),U_3885)))),
inference(definitional_conversion,[status(esa)],[f_933_2]) ).
cnf(f_933_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3885),U_3885)))),
inference(clausify,[status(thm)],[f_933_3]) ).
fof(f_934_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono1]) ).
fof(f_934_2,plain,
! [U_3888,U_3887,U_3886] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3886),U_3888)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3887),U_3888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3886),U_3887)) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
fof(f_934_3,plain,
! [U_3886,U_3887,U_3888] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3886),U_3888)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3887),U_3888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3886),U_3887)) ),
inference(definitional_conversion,[status(esa)],[f_934_2]) ).
cnf(f_934_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3886),U_3888)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3887),U_3888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3886),U_3887)) ),
inference(clausify,[status(thm)],[f_934_3]) ).
fof(f_935_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono2]) ).
fof(f_935_2,plain,
! [U_3891,U_3890,U_3889] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3891),U_3889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3891),U_3890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3889),U_3890)) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
fof(f_935_3,plain,
! [U_3889,U_3890,U_3891] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3891),U_3889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3891),U_3890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3889),U_3890)) ),
inference(definitional_conversion,[status(esa)],[f_935_2]) ).
cnf(f_935_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3891),U_3889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3891),U_3890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3889),U_3890)) ),
inference(clausify,[status(thm)],[f_935_3]) ).
fof(f_936_1,plain,
! [V_l,V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono]) ).
fof(f_936_2,plain,
! [U_3895,U_3894,U_3893,U_3892] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3892),U_3894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3893),U_3895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3894),U_3895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3892),U_3893)) ),
inference(variable_rename,[status(thm)],[f_936_1]) ).
fof(f_936_3,plain,
! [U_3892,U_3893,U_3894,U_3895] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3892),U_3894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3893),U_3895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3894),U_3895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3892),U_3893)) ),
inference(definitional_conversion,[status(esa)],[f_936_2]) ).
cnf(f_936_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3892),U_3894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3893),U_3895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3894),U_3895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3892),U_3893)) ),
inference(clausify,[status(thm)],[f_936_3]) ).
fof(f_937_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(f_937_2,plain,
! [U_3898,U_3897,U_3896] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3897),U_3898)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),U_3897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),U_3898)),
inference(variable_rename,[status(thm)],[f_937_1]) ).
fof(f_937_3,plain,
! [U_3896,U_3897,U_3898] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3897),U_3898)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),U_3897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),U_3898)),
inference(definitional_conversion,[status(esa)],[f_937_2]) ).
cnf(f_937_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3897),U_3898)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),U_3897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3896),U_3898)),
inference(clausify,[status(thm)],[f_937_3]) ).
fof(f_938_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib]) ).
fof(f_938_2,plain,
! [U_3901,U_3900,U_3899] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3899),U_3900)),U_3901) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3899),U_3901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3900),U_3901)),
inference(variable_rename,[status(thm)],[f_938_1]) ).
fof(f_938_3,plain,
! [U_3899,U_3900,U_3901] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3899),U_3900)),U_3901) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3899),U_3901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3900),U_3901)),
inference(definitional_conversion,[status(esa)],[f_938_2]) ).
cnf(f_938_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3899),U_3900)),U_3901) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3899),U_3901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3900),U_3901)),
inference(clausify,[status(thm)],[f_938_3]) ).
fof(f_939_1,plain,
! [V_n,V_m] :
( 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
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).
fof(f_939_2,plain,
! [U_3903,U_3902] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3903),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3902),U_3903)) = U_3902
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3902),U_3903)) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
fof(f_939_3,plain,
! [U_3903,U_3902] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3903),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3902),U_3903)) = U_3902
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3902),U_3903)) ),
inference(definitional_conversion,[status(esa)],[f_939_2]) ).
cnf(f_939_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3903),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3902),U_3903)) = U_3902
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3902),U_3903)) ),
inference(clausify,[status(thm)],[f_939_3]) ).
fof(f_940_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( 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)))
| ~ 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)) )
& ( 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))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__conv]) ).
fof(f_940_2,plain,
! [U_3906,U_3905,U_3904] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3904),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3905),U_3906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3904),U_3906)),U_3905)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3904),U_3906)),U_3905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3904),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3905),U_3906))) ) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
fof(f_940_3,plain,
( ! [U_3912,U_3910,U_3908] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3908),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3910),U_3912)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3908),U_3912)),U_3910)) )
& ! [U_3911,U_3909,U_3907] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3907),U_3911)),U_3909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3907),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3909),U_3911))) ) ),
inference(miniscope,[status(thm)],[f_940_2]) ).
fof(f_940_4,plain,
( ! [U_3908,U_3910,U_3912] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3908),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3910),U_3912)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3908),U_3912)),U_3910)) )
& ! [U_3909,U_3907,U_3911] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3907),U_3911)),U_3909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3907),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3909),U_3911))) ) ),
inference(definitional_conversion,[status(esa)],[f_940_3]) ).
cnf(f_940_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3907),U_3911)),U_3909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3907),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3909),U_3911))) ),
inference(clausify,[status(thm)],[f_940_4]) ).
cnf(f_940_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3908),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3910),U_3912)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3908),U_3912)),U_3910)) ),
inference(clausify,[status(thm)],[f_940_4]) ).
fof(f_941_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__iff]) ).
fof(f_941_2,plain,
! [U_3915,U_3914,U_3913] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3913)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3915),U_3913)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3913)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3915),U_3913))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3913),U_3915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3913),U_3914)) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
fof(f_941_3,plain,
( ! [U_3913,U_3914,U_3915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3913)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3915),U_3913)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915))
| ~ sP231(U_3913,U_3914,U_3915) )
& ! [U_3913,U_3914,U_3915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3913)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3915),U_3913)))
| ~ sP231(U_3913,U_3914,U_3915) )
& ! [U_3913,U_3914,U_3915] :
( sP231(U_3913,U_3914,U_3915)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3913),U_3915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3913),U_3914)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_941_2]) ).
cnf(f_941_4,plain,
( sP231(U_3913,U_3914,U_3915)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3913),U_3915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3913),U_3914)) ),
inference(clausify,[status(thm)],[f_941_3]) ).
cnf(f_941_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3913)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3915),U_3913)))
| ~ sP231(U_3913,U_3914,U_3915) ),
inference(clausify,[status(thm)],[f_941_3]) ).
cnf(f_941_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3913)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3915),U_3913)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915))
| ~ sP231(U_3913,U_3914,U_3915) ),
inference(clausify,[status(thm)],[f_941_3]) ).
fof(f_942_1,plain,
! [V_c,V_b,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).
fof(f_942_2,plain,
! [U_3918,U_3917,U_3916] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3916),U_3918)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3917),U_3918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3918),U_3916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3916),U_3917)) ),
inference(variable_rename,[status(thm)],[f_942_1]) ).
fof(f_942_3,plain,
! [U_3918,U_3917,U_3916] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3916),U_3918)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3917),U_3918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3918),U_3916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3916),U_3917)) ),
inference(definitional_conversion,[status(esa)],[f_942_2]) ).
cnf(f_942_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3916),U_3918)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3917),U_3918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3918),U_3916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3916),U_3917)) ),
inference(clausify,[status(thm)],[f_942_3]) ).
fof(f_943_1,plain,
! [V_i,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_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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2]) ).
fof(f_943_2,plain,
! [U_3921,U_3920,U_3919] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3920),U_3921)),U_3919) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),U_3919)),U_3921)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3919),U_3920)) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
fof(f_943_3,plain,
! [U_3919,U_3920,U_3921] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3920),U_3921)),U_3919) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),U_3919)),U_3921)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3919),U_3920)) ),
inference(definitional_conversion,[status(esa)],[f_943_2]) ).
cnf(f_943_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3920),U_3921)),U_3919) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),U_3919)),U_3921)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3919),U_3920)) ),
inference(clausify,[status(thm)],[f_943_3]) ).
fof(f_944_1,plain,
! [V_i,V_j,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) = 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2]) ).
fof(f_944_2,plain,
! [U_3924,U_3923,U_3922] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3923),U_3922)),U_3924) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3924)),U_3922)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3922),U_3923)) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
fof(f_944_3,plain,
! [U_3922,U_3923,U_3924] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3923),U_3922)),U_3924) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3924)),U_3922)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3922),U_3923)) ),
inference(definitional_conversion,[status(esa)],[f_944_2]) ).
cnf(f_944_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3923),U_3922)),U_3924) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3924)),U_3922)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3922),U_3923)) ),
inference(clausify,[status(thm)],[f_944_3]) ).
fof(f_945_1,plain,
! [V_i,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) = 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc]) ).
fof(f_945_2,plain,
! [U_3927,U_3926,U_3925] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3927),U_3926)),U_3925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3926),U_3925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3925),U_3926)) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
fof(f_945_3,plain,
! [U_3925,U_3926,U_3927] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3927),U_3926)),U_3925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3926),U_3925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3925),U_3926)) ),
inference(definitional_conversion,[status(esa)],[f_945_2]) ).
cnf(f_945_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3927),U_3926)),U_3925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3926),U_3925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3925),U_3926)) ),
inference(clausify,[status(thm)],[f_945_3]) ).
fof(f_946_1,plain,
! [V_y,V_z,V_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J]) ).
fof(f_946_2,plain,
! [U_3930,U_3929,U_3928] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3930),U_3929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3928),U_3929)) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
fof(f_946_3,plain,
! [U_3928,U_3929,U_3930] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3930),U_3929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3928),U_3929)) ),
inference(definitional_conversion,[status(esa)],[f_946_2]) ).
cnf(f_946_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3930),U_3929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3928),U_3929)) ),
inference(clausify,[status(thm)],[f_946_3]) ).
fof(f_947_1,plain,
! [V_z,V_y,V_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J]) ).
fof(f_947_2,plain,
! [U_3933,U_3932,U_3931] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3932),U_3933)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3931),U_3932)) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
fof(f_947_3,plain,
! [U_3931,U_3932,U_3933] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3932),U_3933)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3931),U_3932)) ),
inference(definitional_conversion,[status(esa)],[f_947_2]) ).
cnf(f_947_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3932),U_3933)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3931),U_3932)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
fof(f_948_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J]) ).
fof(f_948_2,plain,
! [U_3935,U_3934] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3934),U_3935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3934),U_3935)) ),
inference(variable_rename,[status(thm)],[f_948_1]) ).
fof(f_948_3,plain,
! [U_3934,U_3935] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3934),U_3935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3934),U_3935)) ),
inference(definitional_conversion,[status(esa)],[f_948_2]) ).
cnf(f_948_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3934),U_3935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3934),U_3935)) ),
inference(clausify,[status(thm)],[f_948_3]) ).
fof(f_949_1,plain,
! [V_z,V_y,V_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J]) ).
fof(f_949_2,plain,
! [U_3938,U_3937,U_3936] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3937),U_3938)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3936),U_3937)) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
fof(f_949_3,plain,
! [U_3936,U_3937,U_3938] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3937),U_3938)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3936),U_3937)) ),
inference(definitional_conversion,[status(esa)],[f_949_2]) ).
cnf(f_949_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3937),U_3938)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3936),U_3937)) ),
inference(clausify,[status(thm)],[f_949_3]) ).
fof(f_950_1,plain,
! [V_y,V_z,V_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J]) ).
fof(f_950_2,plain,
! [U_3941,U_3940,U_3939] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3941),U_3940)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),U_3940)) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
fof(f_950_3,plain,
! [U_3939,U_3940,U_3941] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3941),U_3940)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),U_3940)) ),
inference(definitional_conversion,[status(esa)],[f_950_2]) ).
cnf(f_950_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3941),U_3940)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),U_3940)) ),
inference(clausify,[status(thm)],[f_950_3]) ).
fof(f_951_1,plain,
! [V_y_2,V_x_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff2__less]) ).
fof(f_951_2,plain,
! [U_3945,U_3944,U_3943,U_3942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3942),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3942,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3942,tc_HOL_Obool)),U_3943),hAPP(hAPP(c_Set_Oinsert(U_3942),U_3944),c_Orderings_Obot__class_Obot(tc_fun(U_3942,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_3942),U_3945),c_Orderings_Obot__class_Obot(tc_fun(U_3942,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3942),U_3943)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3945),U_3943))
| ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3944),U_3943))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3942),U_3943)) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
fof(f_951_3,plain,
! [U_3942,U_3943,U_3944,U_3945] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3942),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3942,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3942,tc_HOL_Obool)),U_3943),hAPP(hAPP(c_Set_Oinsert(U_3942),U_3944),c_Orderings_Obot__class_Obot(tc_fun(U_3942,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_3942),U_3945),c_Orderings_Obot__class_Obot(tc_fun(U_3942,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3942),U_3943)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3945),U_3943))
| ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3944),U_3943))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3942),U_3943)) ),
inference(definitional_conversion,[status(esa)],[f_951_2]) ).
cnf(f_951_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3942),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3942,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3942,tc_HOL_Obool)),U_3943),hAPP(hAPP(c_Set_Oinsert(U_3942),U_3944),c_Orderings_Obot__class_Obot(tc_fun(U_3942,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_3942),U_3945),c_Orderings_Obot__class_Obot(tc_fun(U_3942,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3942),U_3943)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3945),U_3943))
| ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3944),U_3943))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3942),U_3943)) ),
inference(clausify,[status(thm)],[f_951_3]) ).
fof(f_952_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff1__less]) ).
fof(f_952_2,plain,
! [U_3948,U_3947,U_3946] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3946),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3946,tc_HOL_Obool)),U_3947),hAPP(hAPP(c_Set_Oinsert(U_3946),U_3948),c_Orderings_Obot__class_Obot(tc_fun(U_3946,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3946),U_3947)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3946),U_3948),U_3947))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3946),U_3947)) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
fof(f_952_3,plain,
! [U_3946,U_3947,U_3948] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3946),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3946,tc_HOL_Obool)),U_3947),hAPP(hAPP(c_Set_Oinsert(U_3946),U_3948),c_Orderings_Obot__class_Obot(tc_fun(U_3946,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3946),U_3947)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3946),U_3948),U_3947))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3946),U_3947)) ),
inference(definitional_conversion,[status(esa)],[f_952_2]) ).
cnf(f_952_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3946),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3946,tc_HOL_Obool)),U_3947),hAPP(hAPP(c_Set_Oinsert(U_3946),U_3948),c_Orderings_Obot__class_Obot(tc_fun(U_3946,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3946),U_3947)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3946),U_3948),U_3947))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3946),U_3947)) ),
inference(clausify,[status(thm)],[f_952_3]) ).
fof(f_953_1,plain,
! [V_p_2,V_f_2,V_n_2,V_m_2,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,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))))
| ~ 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))))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat]) ).
fof(f_953_2,plain,
! [U_3953,U_3952,U_3951,U_3950,U_3949] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3950,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),U_3953))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3949),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3950,U_3951))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),U_3953))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_3949) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
fof(f_953_3,plain,
! [U_3949,U_3950,U_3951,U_3952,U_3953] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3950,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),U_3953))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3949),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3950,U_3951))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),U_3953))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_3949) ),
inference(definitional_conversion,[status(esa)],[f_953_2]) ).
cnf(f_953_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3950,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),U_3953))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3949),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3950,U_3951))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3949),U_3952),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),U_3953))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3951),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_3949) ),
inference(clausify,[status(thm)],[f_953_3]) ).
fof(f_954_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_card__UNIV__unit]) ).
fof(f_954_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_954_1]) ).
cnf(f_954_3,plain,
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),
inference(clausify,[status(thm)],[f_954_2]) ).
fof(f_955_1,plain,
! [V_x_2,T_b] :
( ( ( c_Groups_Oone__class_Oone(T_b) = V_x_2
| V_x_2 != c_Groups_Oone__class_Oone(T_b) )
& ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
| c_Groups_Oone__class_Oone(T_b) != V_x_2 ) )
| ~ class_Groups_Oone(T_b) ),
inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).
fof(f_955_2,plain,
! [U_3955,U_3954] :
( ( ( c_Groups_Oone__class_Oone(U_3954) = U_3955
| U_3955 != c_Groups_Oone__class_Oone(U_3954) )
& ( U_3955 = c_Groups_Oone__class_Oone(U_3954)
| c_Groups_Oone__class_Oone(U_3954) != U_3955 ) )
| ~ class_Groups_Oone(U_3954) ),
inference(variable_rename,[status(thm)],[f_955_1]) ).
fof(f_955_3,plain,
( ! [U_3955,U_3954] :
( c_Groups_Oone__class_Oone(U_3954) = U_3955
| U_3955 != c_Groups_Oone__class_Oone(U_3954)
| ~ sP232(U_3955,U_3954) )
& ! [U_3955,U_3954] :
( U_3955 = c_Groups_Oone__class_Oone(U_3954)
| c_Groups_Oone__class_Oone(U_3954) != U_3955
| ~ sP232(U_3955,U_3954) )
& ! [U_3955,U_3954] :
( sP232(U_3955,U_3954)
| ~ class_Groups_Oone(U_3954) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_955_2]) ).
cnf(f_955_4,plain,
( sP232(U_3955,U_3954)
| ~ class_Groups_Oone(U_3954) ),
inference(clausify,[status(thm)],[f_955_3]) ).
cnf(f_955_5,plain,
( U_3955 = c_Groups_Oone__class_Oone(U_3954)
| c_Groups_Oone__class_Oone(U_3954) != U_3955
| ~ sP232(U_3955,U_3954) ),
inference(clausify,[status(thm)],[f_955_3]) ).
cnf(f_955_6,plain,
( c_Groups_Oone__class_Oone(U_3954) = U_3955
| U_3955 != c_Groups_Oone__class_Oone(U_3954)
| ~ sP232(U_3955,U_3954) ),
inference(clausify,[status(thm)],[f_955_3]) ).
fof(f_956_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
fof(f_956_2,plain,
! [U_3957,U_3956] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3956),U_3957),c_Groups_Oone__class_Oone(U_3956)) = U_3957
| ~ class_Rings_Ocomm__semiring__1(U_3956) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
fof(f_956_3,plain,
! [U_3957,U_3956] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3956),U_3957),c_Groups_Oone__class_Oone(U_3956)) = U_3957
| ~ class_Rings_Ocomm__semiring__1(U_3956) ),
inference(definitional_conversion,[status(esa)],[f_956_2]) ).
cnf(f_956_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3956),U_3957),c_Groups_Oone__class_Oone(U_3956)) = U_3957
| ~ class_Rings_Ocomm__semiring__1(U_3956) ),
inference(clausify,[status(thm)],[f_956_3]) ).
fof(f_957_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
fof(f_957_2,plain,
! [U_3959,U_3958] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3958),c_Groups_Oone__class_Oone(U_3958)),U_3959) = U_3959
| ~ class_Rings_Ocomm__semiring__1(U_3958) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
fof(f_957_3,plain,
! [U_3958,U_3959] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3958),c_Groups_Oone__class_Oone(U_3958)),U_3959) = U_3959
| ~ class_Rings_Ocomm__semiring__1(U_3958) ),
inference(definitional_conversion,[status(esa)],[f_957_2]) ).
cnf(f_957_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3958),c_Groups_Oone__class_Oone(U_3958)),U_3959) = U_3959
| ~ class_Rings_Ocomm__semiring__1(U_3958) ),
inference(clausify,[status(thm)],[f_957_3]) ).
fof(f_958_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Groups_Ocomm__monoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral]) ).
fof(f_958_2,plain,
! [U_3961,U_3960] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3960),U_3961),c_Groups_Oone__class_Oone(U_3960)) = U_3961
| ~ class_Groups_Ocomm__monoid__mult(U_3960) ),
inference(variable_rename,[status(thm)],[f_958_1]) ).
fof(f_958_3,plain,
! [U_3960,U_3961] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3960),U_3961),c_Groups_Oone__class_Oone(U_3960)) = U_3961
| ~ class_Groups_Ocomm__monoid__mult(U_3960) ),
inference(definitional_conversion,[status(esa)],[f_958_2]) ).
cnf(f_958_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3960),U_3961),c_Groups_Oone__class_Oone(U_3960)) = U_3961
| ~ class_Groups_Ocomm__monoid__mult(U_3960) ),
inference(clausify,[status(thm)],[f_958_3]) ).
fof(f_959_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__1__right]) ).
fof(f_959_2,plain,
! [U_3963,U_3962] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3962),U_3963),c_Groups_Oone__class_Oone(U_3962)) = U_3963
| ~ class_Groups_Omonoid__mult(U_3962) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
fof(f_959_3,plain,
! [U_3962,U_3963] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3962),U_3963),c_Groups_Oone__class_Oone(U_3962)) = U_3963
| ~ class_Groups_Omonoid__mult(U_3962) ),
inference(definitional_conversion,[status(esa)],[f_959_2]) ).
cnf(f_959_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3962),U_3963),c_Groups_Oone__class_Oone(U_3962)) = U_3963
| ~ class_Groups_Omonoid__mult(U_3962) ),
inference(clausify,[status(thm)],[f_959_3]) ).
fof(f_960_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
| ~ class_Groups_Ocomm__monoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__1]) ).
fof(f_960_2,plain,
! [U_3965,U_3964] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3964),c_Groups_Oone__class_Oone(U_3964)),U_3965) = U_3965
| ~ class_Groups_Ocomm__monoid__mult(U_3964) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
fof(f_960_3,plain,
! [U_3964,U_3965] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3964),c_Groups_Oone__class_Oone(U_3964)),U_3965) = U_3965
| ~ class_Groups_Ocomm__monoid__mult(U_3964) ),
inference(definitional_conversion,[status(esa)],[f_960_2]) ).
cnf(f_960_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3964),c_Groups_Oone__class_Oone(U_3964)),U_3965) = U_3965
| ~ class_Groups_Ocomm__monoid__mult(U_3964) ),
inference(clausify,[status(thm)],[f_960_3]) ).
fof(f_961_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__1__left]) ).
fof(f_961_2,plain,
! [U_3967,U_3966] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3966),c_Groups_Oone__class_Oone(U_3966)),U_3967) = U_3967
| ~ class_Groups_Omonoid__mult(U_3966) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
fof(f_961_3,plain,
! [U_3966,U_3967] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3966),c_Groups_Oone__class_Oone(U_3966)),U_3967) = U_3967
| ~ class_Groups_Omonoid__mult(U_3966) ),
inference(definitional_conversion,[status(esa)],[f_961_2]) ).
cnf(f_961_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3966),c_Groups_Oone__class_Oone(U_3966)),U_3967) = U_3967
| ~ class_Groups_Omonoid__mult(U_3966) ),
inference(clausify,[status(thm)],[f_961_3]) ).
fof(f_962_1,plain,
! [V_f_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_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) ) )
& ( ! [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) )
| 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) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff]) ).
fof(f_962_2,plain,
! [U_3972,U_3971,U_3970] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3970,tc_Nat_Onat),U_3972),U_3971) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ? [U_3969] :
( hAPP(U_3972,U_3969) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_3970),U_3969),U_3971)) ) )
& ( ! [U_3968] :
( hAPP(U_3972,U_3968) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3970),U_3968),U_3971)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3970,tc_Nat_Onat),U_3972),U_3971) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3970),U_3971)) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
fof(f_962_3,plain,
! [U_3972,U_3971,U_3970] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3970,tc_Nat_Onat),U_3972),U_3971) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ( hAPP(U_3972,sK96(U_3972,U_3971,U_3970)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_3970),sK96(U_3972,U_3971,U_3970)),U_3971)) ) )
& ( ! [U_3968] :
( hAPP(U_3972,U_3968) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3970),U_3968),U_3971)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3970,tc_Nat_Onat),U_3972),U_3971) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3970),U_3971)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_3969,sK96(U_3972,U_3971,U_3970))],[f_962_2]) ).
fof(f_962_4,plain,
( ! [U_3970,U_3971,U_3972] :
( hAPP(U_3972,sK96(U_3972,U_3971,U_3970)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP233(U_3970,U_3971,U_3972) )
& ! [U_3970,U_3971,U_3972] :
( hBOOL(hAPP(hAPP(c_member(U_3970),sK96(U_3972,U_3971,U_3970)),U_3971))
| ~ sP233(U_3970,U_3971,U_3972) )
& ! [U_3968,U_3970,U_3971,U_3972] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3970,tc_Nat_Onat),U_3972),U_3971) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| sP233(U_3970,U_3971,U_3972)
| ~ sP234(U_3968,U_3970,U_3971,U_3972) )
& ! [U_3968,U_3970,U_3971,U_3972] :
( hAPP(U_3972,U_3968) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3970),U_3968),U_3971))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3970,tc_Nat_Onat),U_3972),U_3971) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP234(U_3968,U_3970,U_3971,U_3972) )
& ! [U_3968,U_3970,U_3971,U_3972] :
( sP234(U_3968,U_3970,U_3971,U_3972)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3970),U_3971)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233,sP234])],[f_962_3]) ).
cnf(f_962_5,plain,
( sP234(U_3968,U_3970,U_3971,U_3972)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3970),U_3971)) ),
inference(clausify,[status(thm)],[f_962_4]) ).
cnf(f_962_6,plain,
( hAPP(U_3972,U_3968) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3970),U_3968),U_3971))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3970,tc_Nat_Onat),U_3972),U_3971) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP234(U_3968,U_3970,U_3971,U_3972) ),
inference(clausify,[status(thm)],[f_962_4]) ).
cnf(f_962_7,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3970,tc_Nat_Onat),U_3972),U_3971) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| sP233(U_3970,U_3971,U_3972)
| ~ sP234(U_3968,U_3970,U_3971,U_3972) ),
inference(clausify,[status(thm)],[f_962_4]) ).
cnf(f_962_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_3970),sK96(U_3972,U_3971,U_3970)),U_3971))
| ~ sP233(U_3970,U_3971,U_3972) ),
inference(clausify,[status(thm)],[f_962_4]) ).
cnf(f_962_9,plain,
( hAPP(U_3972,sK96(U_3972,U_3971,U_3970)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP233(U_3970,U_3971,U_3972) ),
inference(clausify,[status(thm)],[f_962_4]) ).
fof(f_963_1,plain,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_nat__mult__1]) ).
fof(f_963_2,plain,
! [U_3973] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3973) = U_3973,
inference(variable_rename,[status(thm)],[f_963_1]) ).
fof(f_963_3,plain,
! [U_3973] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3973) = U_3973,
inference(definitional_conversion,[status(esa)],[f_963_2]) ).
cnf(f_963_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3973) = U_3973,
inference(clausify,[status(thm)],[f_963_3]) ).
fof(f_964_1,plain,
! [V_n_2,V_m_2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).
fof(f_964_2,plain,
! [U_3975,U_3974] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3974),U_3975)
| U_3975 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3974 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_3975 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_3974 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3974),U_3975) ) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
fof(f_964_3,plain,
( ! [U_3979,U_3977] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3977),U_3979)
| U_3979 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3977 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_3978,U_3976] :
( ( U_3978 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_3976 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3976),U_3978) ) ),
inference(miniscope,[status(thm)],[f_964_2]) ).
fof(f_964_4,plain,
( ! [U_3978,U_3976] :
( U_3978 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP235(U_3978,U_3976) )
& ! [U_3978,U_3976] :
( U_3976 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP235(U_3978,U_3976) )
& ! [U_3979,U_3977] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3977),U_3979)
| U_3979 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3977 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_3978,U_3976] :
( sP235(U_3978,U_3976)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3976),U_3978) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_964_3]) ).
cnf(f_964_5,plain,
( sP235(U_3978,U_3976)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3976),U_3978) ),
inference(clausify,[status(thm)],[f_964_4]) ).
cnf(f_964_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3977),U_3979)
| U_3979 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3977 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_964_4]) ).
cnf(f_964_7,plain,
( U_3976 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP235(U_3978,U_3976) ),
inference(clausify,[status(thm)],[f_964_4]) ).
cnf(f_964_8,plain,
( U_3978 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP235(U_3978,U_3976) ),
inference(clausify,[status(thm)],[f_964_4]) ).
fof(f_965_1,plain,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
inference(fof_nnf,[status(thm)],[fact_nat__mult__1__right]) ).
fof(f_965_2,plain,
! [U_3980] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3980),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3980,
inference(variable_rename,[status(thm)],[f_965_1]) ).
fof(f_965_3,plain,
! [U_3980] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3980),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3980,
inference(definitional_conversion,[status(esa)],[f_965_2]) ).
cnf(f_965_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3980),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3980,
inference(clausify,[status(thm)],[f_965_3]) ).
fof(f_966_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).
fof(f_966_2,plain,
! [U_3982,U_3981] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3981),U_3982) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3982 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3981 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_3982 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_3981 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3981),U_3982) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
fof(f_966_3,plain,
( ! [U_3986,U_3984] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3984),U_3986) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3986 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3984 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_3985,U_3983] :
( ( U_3985 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_3983 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3983),U_3985) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_966_2]) ).
fof(f_966_4,plain,
( ! [U_3985,U_3983] :
( U_3985 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP236(U_3985,U_3983) )
& ! [U_3985,U_3983] :
( U_3983 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP236(U_3985,U_3983) )
& ! [U_3986,U_3984] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3984),U_3986) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3986 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3984 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_3985,U_3983] :
( sP236(U_3985,U_3983)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3983),U_3985) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236])],[f_966_3]) ).
cnf(f_966_5,plain,
( sP236(U_3985,U_3983)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3983),U_3985) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_966_4]) ).
cnf(f_966_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3984),U_3986) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3986 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3984 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_966_4]) ).
cnf(f_966_7,plain,
( U_3983 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP236(U_3985,U_3983) ),
inference(clausify,[status(thm)],[f_966_4]) ).
cnf(f_966_8,plain,
( U_3985 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP236(U_3985,U_3983) ),
inference(clausify,[status(thm)],[f_966_4]) ).
fof(f_967_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_card__lessThan]) ).
fof(f_967_2,plain,
! [U_3987] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3987)) = U_3987,
inference(variable_rename,[status(thm)],[f_967_1]) ).
fof(f_967_3,plain,
! [U_3987] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3987)) = U_3987,
inference(definitional_conversion,[status(esa)],[f_967_2]) ).
cnf(f_967_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3987)) = U_3987,
inference(clausify,[status(thm)],[f_967_3]) ).
fof(f_968_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oinsert]) ).
fof(f_968_2,plain,
! [U_3990,U_3989,U_3988] :
( hAPP(c_Finite__Set_Ocard(U_3988),hAPP(hAPP(c_Set_Oinsert(U_3988),U_3990),U_3989)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3988),U_3989))
| hBOOL(hAPP(hAPP(c_member(U_3988),U_3990),U_3989))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3988),U_3989)) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
fof(f_968_3,plain,
! [U_3988,U_3989,U_3990] :
( hAPP(c_Finite__Set_Ocard(U_3988),hAPP(hAPP(c_Set_Oinsert(U_3988),U_3990),U_3989)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3988),U_3989))
| hBOOL(hAPP(hAPP(c_member(U_3988),U_3990),U_3989))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3988),U_3989)) ),
inference(definitional_conversion,[status(esa)],[f_968_2]) ).
cnf(f_968_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3988),hAPP(hAPP(c_Set_Oinsert(U_3988),U_3990),U_3989)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3988),U_3989))
| hBOOL(hAPP(hAPP(c_member(U_3988),U_3990),U_3989))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3988),U_3989)) ),
inference(clausify,[status(thm)],[f_968_3]) ).
fof(f_969_1,plain,
! [V_A_2,T_b] :
( V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV]) ).
fof(f_969_2,plain,
! [U_3992,U_3991] :
( U_3992 = c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_3991),U_3992) != hAPP(c_Finite__Set_Ocard(U_3991),c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3991),c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
fof(f_969_3,plain,
! [U_3991,U_3992] :
( U_3992 = c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_3991),U_3992) != hAPP(c_Finite__Set_Ocard(U_3991),c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3991),c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_969_2]) ).
cnf(f_969_4,plain,
( U_3992 = c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_3991),U_3992) != hAPP(c_Finite__Set_Ocard(U_3991),c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3991),c_Orderings_Otop__class_Otop(tc_fun(U_3991,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_969_3]) ).
fof(f_970_1,plain,
! [V_a,T_a] :
( 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))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__one]) ).
fof(f_970_2,plain,
! [U_3994,U_3993] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),U_3994),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3993),U_3994),c_Groups_Oone__class_Oone(U_3993))))
| ~ class_Rings_Olinordered__semidom(U_3993) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
fof(f_970_3,plain,
! [U_3993,U_3994] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),U_3994),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3993),U_3994),c_Groups_Oone__class_Oone(U_3993))))
| ~ class_Rings_Olinordered__semidom(U_3993) ),
inference(definitional_conversion,[status(esa)],[f_970_2]) ).
cnf(f_970_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),U_3994),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3993),U_3994),c_Groups_Oone__class_Oone(U_3993))))
| ~ class_Rings_Olinordered__semidom(U_3993) ),
inference(clausify,[status(thm)],[f_970_3]) ).
fof(f_971_1,plain,
! [V_n,V_m,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__1__mult]) ).
fof(f_971_2,plain,
! [U_3997,U_3996,U_3995] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3995),U_3996),U_3997)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),U_3997))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),U_3996))
| ~ class_Rings_Olinordered__semidom(U_3995) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
fof(f_971_3,plain,
! [U_3995,U_3996,U_3997] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3995),U_3996),U_3997)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),U_3997))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),U_3996))
| ~ class_Rings_Olinordered__semidom(U_3995) ),
inference(definitional_conversion,[status(esa)],[f_971_2]) ).
cnf(f_971_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3995),U_3996),U_3997)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),U_3997))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3995),c_Groups_Oone__class_Oone(U_3995)),U_3996))
| ~ class_Rings_Olinordered__semidom(U_3995) ),
inference(clausify,[status(thm)],[f_971_3]) ).
fof(f_972_1,plain,
! [V_m,V_a,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_972_2,plain,
! [U_4000,U_3999,U_3998] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3998),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3998),U_3999),U_4000)),U_4000) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3998),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3998),U_3999),c_Groups_Oone__class_Oone(U_3998))),U_4000)
| ~ class_Rings_Ocomm__semiring__1(U_3998) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
fof(f_972_3,plain,
! [U_3998,U_3999,U_4000] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3998),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3998),U_3999),U_4000)),U_4000) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3998),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3998),U_3999),c_Groups_Oone__class_Oone(U_3998))),U_4000)
| ~ class_Rings_Ocomm__semiring__1(U_3998) ),
inference(definitional_conversion,[status(esa)],[f_972_2]) ).
cnf(f_972_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3998),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3998),U_3999),U_4000)),U_4000) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3998),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3998),U_3999),c_Groups_Oone__class_Oone(U_3998))),U_4000)
| ~ class_Rings_Ocomm__semiring__1(U_3998) ),
inference(clausify,[status(thm)],[f_972_3]) ).
fof(f_973_1,plain,
! [V_a,V_m,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_973_2,plain,
! [U_4003,U_4002,U_4001] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4001),U_4002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4001),U_4003),U_4002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4001),U_4003),c_Groups_Oone__class_Oone(U_4001))),U_4002)
| ~ class_Rings_Ocomm__semiring__1(U_4001) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
fof(f_973_3,plain,
! [U_4001,U_4002,U_4003] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4001),U_4002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4001),U_4003),U_4002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4001),U_4003),c_Groups_Oone__class_Oone(U_4001))),U_4002)
| ~ class_Rings_Ocomm__semiring__1(U_4001) ),
inference(definitional_conversion,[status(esa)],[f_973_2]) ).
cnf(f_973_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4001),U_4002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4001),U_4003),U_4002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4001),U_4003),c_Groups_Oone__class_Oone(U_4001))),U_4002)
| ~ class_Rings_Ocomm__semiring__1(U_4001) ),
inference(clausify,[status(thm)],[f_973_3]) ).
fof(f_974_1,plain,
! [V_m,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_974_2,plain,
! [U_4005,U_4004] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4004),U_4005),U_4005) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4004),c_Groups_Oone__class_Oone(U_4004)),c_Groups_Oone__class_Oone(U_4004))),U_4005)
| ~ class_Rings_Ocomm__semiring__1(U_4004) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
fof(f_974_3,plain,
! [U_4004,U_4005] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4004),U_4005),U_4005) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4004),c_Groups_Oone__class_Oone(U_4004)),c_Groups_Oone__class_Oone(U_4004))),U_4005)
| ~ class_Rings_Ocomm__semiring__1(U_4004) ),
inference(definitional_conversion,[status(esa)],[f_974_2]) ).
cnf(f_974_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4004),U_4005),U_4005) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4004),c_Groups_Oone__class_Oone(U_4004)),c_Groups_Oone__class_Oone(U_4004))),U_4005)
| ~ class_Rings_Ocomm__semiring__1(U_4004) ),
inference(clausify,[status(thm)],[f_974_3]) ).
fof(f_975_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J]) ).
fof(f_975_2,plain,
! [U_4007,U_4006] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4006),U_4007) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4006),hAPP(c_Groups_Ouminus__class_Ouminus(U_4006),c_Groups_Oone__class_Oone(U_4006))),U_4007)
| ~ class_Rings_Ocomm__ring__1(U_4006) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
fof(f_975_3,plain,
! [U_4006,U_4007] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4006),U_4007) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4006),hAPP(c_Groups_Ouminus__class_Ouminus(U_4006),c_Groups_Oone__class_Oone(U_4006))),U_4007)
| ~ class_Rings_Ocomm__ring__1(U_4006) ),
inference(definitional_conversion,[status(esa)],[f_975_2]) ).
cnf(f_975_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4006),U_4007) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4006),hAPP(c_Groups_Ouminus__class_Ouminus(U_4006),c_Groups_Oone__class_Oone(U_4006))),U_4007)
| ~ class_Rings_Ocomm__ring__1(U_4006) ),
inference(clausify,[status(thm)],[f_975_3]) ).
fof(f_976_1,plain,
! [V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
| ( V_x_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
& V_x_2 != c_Groups_Oone__class_Oone(T_b) ) )
& ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| V_x_2 = c_Groups_Oone__class_Oone(T_b)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_b) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).
fof(f_976_2,plain,
! [U_4009,U_4008] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4008),U_4009),U_4009) = c_Groups_Oone__class_Oone(U_4008)
| ( U_4009 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),c_Groups_Oone__class_Oone(U_4008))
& U_4009 != c_Groups_Oone__class_Oone(U_4008) ) )
& ( U_4009 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),c_Groups_Oone__class_Oone(U_4008))
| U_4009 = c_Groups_Oone__class_Oone(U_4008)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4008),U_4009),U_4009) != c_Groups_Oone__class_Oone(U_4008) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_4008) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
fof(f_976_3,plain,
( ! [U_4009,U_4008] :
( U_4009 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),c_Groups_Oone__class_Oone(U_4008))
| ~ sP237(U_4009,U_4008) )
& ! [U_4009,U_4008] :
( U_4009 != c_Groups_Oone__class_Oone(U_4008)
| ~ sP237(U_4009,U_4008) )
& ! [U_4009,U_4008] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4008),U_4009),U_4009) = c_Groups_Oone__class_Oone(U_4008)
| sP237(U_4009,U_4008)
| ~ sP238(U_4009,U_4008) )
& ! [U_4009,U_4008] :
( U_4009 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),c_Groups_Oone__class_Oone(U_4008))
| U_4009 = c_Groups_Oone__class_Oone(U_4008)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4008),U_4009),U_4009) != c_Groups_Oone__class_Oone(U_4008)
| ~ sP238(U_4009,U_4008) )
& ! [U_4009,U_4008] :
( sP238(U_4009,U_4008)
| ~ class_Rings_Oring__1__no__zero__divisors(U_4008) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237,sP238])],[f_976_2]) ).
cnf(f_976_4,plain,
( sP238(U_4009,U_4008)
| ~ class_Rings_Oring__1__no__zero__divisors(U_4008) ),
inference(clausify,[status(thm)],[f_976_3]) ).
cnf(f_976_5,plain,
( U_4009 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),c_Groups_Oone__class_Oone(U_4008))
| U_4009 = c_Groups_Oone__class_Oone(U_4008)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4008),U_4009),U_4009) != c_Groups_Oone__class_Oone(U_4008)
| ~ sP238(U_4009,U_4008) ),
inference(clausify,[status(thm)],[f_976_3]) ).
cnf(f_976_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4008),U_4009),U_4009) = c_Groups_Oone__class_Oone(U_4008)
| sP237(U_4009,U_4008)
| ~ sP238(U_4009,U_4008) ),
inference(clausify,[status(thm)],[f_976_3]) ).
cnf(f_976_7,plain,
( U_4009 != c_Groups_Oone__class_Oone(U_4008)
| ~ sP237(U_4009,U_4008) ),
inference(clausify,[status(thm)],[f_976_3]) ).
cnf(f_976_8,plain,
( U_4009 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),c_Groups_Oone__class_Oone(U_4008))
| ~ sP237(U_4009,U_4008) ),
inference(clausify,[status(thm)],[f_976_3]) ).
fof(f_977_1,plain,
! [V_k_2,V_A_2] :
( 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)))
| ~ 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))))) ),
inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl]) ).
fof(f_977_2,plain,
! [U_4011,U_4010] :
( U_4010 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4010)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_4010),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4010))))) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
fof(f_977_3,plain,
! [U_4010,U_4011] :
( U_4010 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4010)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_4010),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4010))))) ),
inference(definitional_conversion,[status(esa)],[f_977_2]) ).
cnf(f_977_4,plain,
( U_4010 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4010)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_4010),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4010))))) ),
inference(clausify,[status(thm)],[f_977_3]) ).
fof(f_978_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_card__atLeastLessThan]) ).
fof(f_978_2,plain,
! [U_4013,U_4012] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4012),U_4013)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4013),U_4012),
inference(variable_rename,[status(thm)],[f_978_1]) ).
fof(f_978_3,plain,
! [U_4012,U_4013] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4012),U_4013)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4013),U_4012),
inference(definitional_conversion,[status(esa)],[f_978_2]) ).
cnf(f_978_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4012),U_4013)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4013),U_4012),
inference(clausify,[status(thm)],[f_978_3]) ).
fof(f_979_1,plain,
! [V_g_2,T_c,T_b] :
( 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)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oempty]) ).
fof(f_979_2,plain,
! [U_4016,U_4015,U_4014] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4015,U_4014),U_4016),c_Orderings_Obot__class_Obot(tc_fun(U_4015,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4014)
| ~ class_Groups_Ocomm__monoid__mult(U_4014) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
fof(f_979_3,plain,
! [U_4014,U_4015,U_4016] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4015,U_4014),U_4016),c_Orderings_Obot__class_Obot(tc_fun(U_4015,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4014)
| ~ class_Groups_Ocomm__monoid__mult(U_4014) ),
inference(definitional_conversion,[status(esa)],[f_979_2]) ).
cnf(f_979_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4015,U_4014),U_4016),c_Orderings_Obot__class_Obot(tc_fun(U_4015,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4014)
| ~ class_Groups_Ocomm__monoid__mult(U_4014) ),
inference(clausify,[status(thm)],[f_979_3]) ).
fof(f_980_1,plain,
! [V_f_2,T_c,T_b] :
( 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)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod__empty]) ).
fof(f_980_2,plain,
! [U_4019,U_4018,U_4017] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4018,U_4017),U_4019),c_Orderings_Obot__class_Obot(tc_fun(U_4018,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4017)
| ~ class_Groups_Ocomm__monoid__mult(U_4017) ),
inference(variable_rename,[status(thm)],[f_980_1]) ).
fof(f_980_3,plain,
! [U_4017,U_4018,U_4019] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4018,U_4017),U_4019),c_Orderings_Obot__class_Obot(tc_fun(U_4018,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4017)
| ~ class_Groups_Ocomm__monoid__mult(U_4017) ),
inference(definitional_conversion,[status(esa)],[f_980_2]) ).
cnf(f_980_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4018,U_4017),U_4019),c_Orderings_Obot__class_Obot(tc_fun(U_4018,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4017)
| ~ class_Groups_Ocomm__monoid__mult(U_4017) ),
inference(clausify,[status(thm)],[f_980_3]) ).
fof(f_981_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( 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)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinfinite]) ).
fof(f_981_2,plain,
! [U_4023,U_4022,U_4021,U_4020] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4021,U_4020),U_4023),U_4022) = c_Groups_Oone__class_Oone(U_4020)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4021),U_4022))
| ~ class_Groups_Ocomm__monoid__mult(U_4020) ),
inference(variable_rename,[status(thm)],[f_981_1]) ).
fof(f_981_3,plain,
! [U_4020,U_4021,U_4022,U_4023] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4021,U_4020),U_4023),U_4022) = c_Groups_Oone__class_Oone(U_4020)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4021),U_4022))
| ~ class_Groups_Ocomm__monoid__mult(U_4020) ),
inference(definitional_conversion,[status(esa)],[f_981_2]) ).
cnf(f_981_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4021,U_4020),U_4023),U_4022) = c_Groups_Oone__class_Oone(U_4020)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4021),U_4022))
| ~ class_Groups_Ocomm__monoid__mult(U_4020) ),
inference(clausify,[status(thm)],[f_981_3]) ).
fof(f_982_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( 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)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__infinite]) ).
fof(f_982_2,plain,
! [U_4027,U_4026,U_4025,U_4024] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4025,U_4024),U_4027),U_4026) = c_Groups_Oone__class_Oone(U_4024)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4025),U_4026))
| ~ class_Groups_Ocomm__monoid__mult(U_4024) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
fof(f_982_3,plain,
! [U_4025,U_4024,U_4026,U_4027] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4025,U_4024),U_4027),U_4026) = c_Groups_Oone__class_Oone(U_4024)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4025),U_4026))
| ~ class_Groups_Ocomm__monoid__mult(U_4024) ),
inference(definitional_conversion,[status(esa)],[f_982_2]) ).
cnf(f_982_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4025,U_4024),U_4027),U_4026) = c_Groups_Oone__class_Oone(U_4024)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4025),U_4026))
| ~ class_Groups_Ocomm__monoid__mult(U_4024) ),
inference(clausify,[status(thm)],[f_982_3]) ).
fof(f_983_1,plain,
! [V_B_2,V_a_2,V_A_2,T_b] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__insert]) ).
fof(f_983_2,plain,
! [U_4031,U_4030,U_4029,U_4028] :
( hAPP(c_Finite__Set_Ocard(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4028,tc_HOL_Obool)),U_4029),hAPP(hAPP(c_Set_Oinsert(U_4028),U_4030),U_4031))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4028,tc_HOL_Obool)),U_4029),U_4031))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_4028),U_4030),U_4031))
| ~ hBOOL(hAPP(hAPP(c_member(U_4028),U_4030),U_4029))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4028),U_4029)) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
fof(f_983_3,plain,
! [U_4028,U_4029,U_4030,U_4031] :
( hAPP(c_Finite__Set_Ocard(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4028,tc_HOL_Obool)),U_4029),hAPP(hAPP(c_Set_Oinsert(U_4028),U_4030),U_4031))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4028,tc_HOL_Obool)),U_4029),U_4031))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_4028),U_4030),U_4031))
| ~ hBOOL(hAPP(hAPP(c_member(U_4028),U_4030),U_4029))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4028),U_4029)) ),
inference(definitional_conversion,[status(esa)],[f_983_2]) ).
cnf(f_983_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4028,tc_HOL_Obool)),U_4029),hAPP(hAPP(c_Set_Oinsert(U_4028),U_4030),U_4031))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4028,tc_HOL_Obool)),U_4029),U_4031))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_4028),U_4030),U_4031))
| ~ hBOOL(hAPP(hAPP(c_member(U_4028),U_4030),U_4029))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4028),U_4029)) ),
inference(clausify,[status(thm)],[f_983_3]) ).
fof(f_984_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove]) ).
fof(f_984_2,plain,
! [U_4034,U_4033,U_4032] :
( hAPP(c_Finite__Set_Ocard(U_4032),hAPP(hAPP(c_Set_Oinsert(U_4032),U_4034),U_4033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4032,tc_HOL_Obool)),U_4033),hAPP(hAPP(c_Set_Oinsert(U_4032),U_4034),c_Orderings_Obot__class_Obot(tc_fun(U_4032,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4032),U_4033)) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
fof(f_984_3,plain,
! [U_4032,U_4033,U_4034] :
( hAPP(c_Finite__Set_Ocard(U_4032),hAPP(hAPP(c_Set_Oinsert(U_4032),U_4034),U_4033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4032,tc_HOL_Obool)),U_4033),hAPP(hAPP(c_Set_Oinsert(U_4032),U_4034),c_Orderings_Obot__class_Obot(tc_fun(U_4032,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4032),U_4033)) ),
inference(definitional_conversion,[status(esa)],[f_984_2]) ).
cnf(f_984_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4032),hAPP(hAPP(c_Set_Oinsert(U_4032),U_4034),U_4033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4032,tc_HOL_Obool)),U_4033),hAPP(hAPP(c_Set_Oinsert(U_4032),U_4034),c_Orderings_Obot__class_Obot(tc_fun(U_4032,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4032),U_4033)) ),
inference(clausify,[status(thm)],[f_984_3]) ).
fof(f_985_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_card__greaterThanAtMost]) ).
fof(f_985_2,plain,
! [U_4036,U_4035] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4035,U_4036)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4036),U_4035),
inference(variable_rename,[status(thm)],[f_985_1]) ).
fof(f_985_3,plain,
! [U_4036,U_4035] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4035,U_4036)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4036),U_4035),
inference(definitional_conversion,[status(esa)],[f_985_2]) ).
cnf(f_985_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4035,U_4036)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4036),U_4035),
inference(clausify,[status(thm)],[f_985_3]) ).
fof(f_986_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oremove]) ).
fof(f_986_2,plain,
! [U_4039,U_4038,U_4037] :
( hAPP(c_Finite__Set_Ocard(U_4037),U_4038) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4037),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4037,tc_HOL_Obool)),U_4038),hAPP(hAPP(c_Set_Oinsert(U_4037),U_4039),c_Orderings_Obot__class_Obot(tc_fun(U_4037,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_4037),U_4039),U_4038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4037),U_4038)) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
fof(f_986_3,plain,
! [U_4037,U_4038,U_4039] :
( hAPP(c_Finite__Set_Ocard(U_4037),U_4038) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4037),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4037,tc_HOL_Obool)),U_4038),hAPP(hAPP(c_Set_Oinsert(U_4037),U_4039),c_Orderings_Obot__class_Obot(tc_fun(U_4037,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_4037),U_4039),U_4038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4037),U_4038)) ),
inference(definitional_conversion,[status(esa)],[f_986_2]) ).
cnf(f_986_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4037),U_4038) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4037),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4037,tc_HOL_Obool)),U_4038),hAPP(hAPP(c_Set_Oinsert(U_4037),U_4039),c_Orderings_Obot__class_Obot(tc_fun(U_4037,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_4037),U_4039),U_4038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4037),U_4038)) ),
inference(clausify,[status(thm)],[f_986_3]) ).
fof(f_987_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton]) ).
fof(f_987_2,plain,
! [U_4042,U_4041,U_4040] :
( hAPP(c_Finite__Set_Ocard(U_4040),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4040,tc_HOL_Obool)),U_4041),hAPP(hAPP(c_Set_Oinsert(U_4040),U_4042),c_Orderings_Obot__class_Obot(tc_fun(U_4040,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4040),U_4041)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4040),U_4042),U_4041))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4040),U_4041)) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
fof(f_987_3,plain,
! [U_4040,U_4041,U_4042] :
( hAPP(c_Finite__Set_Ocard(U_4040),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4040,tc_HOL_Obool)),U_4041),hAPP(hAPP(c_Set_Oinsert(U_4040),U_4042),c_Orderings_Obot__class_Obot(tc_fun(U_4040,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4040),U_4041)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4040),U_4042),U_4041))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4040),U_4041)) ),
inference(definitional_conversion,[status(esa)],[f_987_2]) ).
cnf(f_987_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4040),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4040,tc_HOL_Obool)),U_4041),hAPP(hAPP(c_Set_Oinsert(U_4040),U_4042),c_Orderings_Obot__class_Obot(tc_fun(U_4040,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4040),U_4041)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4040),U_4042),U_4041))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4040),U_4041)) ),
inference(clausify,[status(thm)],[f_987_3]) ).
fof(f_988_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_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),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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton__if]) ).
fof(f_988_2,plain,
! [U_4045,U_4044,U_4043] :
( ( ( hAPP(c_Finite__Set_Ocard(U_4043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4043,tc_HOL_Obool)),U_4044),hAPP(hAPP(c_Set_Oinsert(U_4043),U_4045),c_Orderings_Obot__class_Obot(tc_fun(U_4043,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_4043),U_4044)
| hBOOL(hAPP(hAPP(c_member(U_4043),U_4045),U_4044)) )
& ( hAPP(c_Finite__Set_Ocard(U_4043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4043,tc_HOL_Obool)),U_4044),hAPP(hAPP(c_Set_Oinsert(U_4043),U_4045),c_Orderings_Obot__class_Obot(tc_fun(U_4043,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4043),U_4044)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4043),U_4045),U_4044)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4043),U_4044)) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
fof(f_988_3,plain,
( ! [U_4043,U_4044,U_4045] :
( hAPP(c_Finite__Set_Ocard(U_4043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4043,tc_HOL_Obool)),U_4044),hAPP(hAPP(c_Set_Oinsert(U_4043),U_4045),c_Orderings_Obot__class_Obot(tc_fun(U_4043,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_4043),U_4044)
| hBOOL(hAPP(hAPP(c_member(U_4043),U_4045),U_4044))
| ~ sP239(U_4043,U_4044,U_4045) )
& ! [U_4043,U_4044,U_4045] :
( hAPP(c_Finite__Set_Ocard(U_4043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4043,tc_HOL_Obool)),U_4044),hAPP(hAPP(c_Set_Oinsert(U_4043),U_4045),c_Orderings_Obot__class_Obot(tc_fun(U_4043,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4043),U_4044)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4043),U_4045),U_4044))
| ~ sP239(U_4043,U_4044,U_4045) )
& ! [U_4043,U_4044,U_4045] :
( sP239(U_4043,U_4044,U_4045)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4043),U_4044)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239])],[f_988_2]) ).
cnf(f_988_4,plain,
( sP239(U_4043,U_4044,U_4045)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4043),U_4044)) ),
inference(clausify,[status(thm)],[f_988_3]) ).
cnf(f_988_5,plain,
( hAPP(c_Finite__Set_Ocard(U_4043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4043,tc_HOL_Obool)),U_4044),hAPP(hAPP(c_Set_Oinsert(U_4043),U_4045),c_Orderings_Obot__class_Obot(tc_fun(U_4043,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4043),U_4044)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4043),U_4045),U_4044))
| ~ sP239(U_4043,U_4044,U_4045) ),
inference(clausify,[status(thm)],[f_988_3]) ).
cnf(f_988_6,plain,
( hAPP(c_Finite__Set_Ocard(U_4043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4043,tc_HOL_Obool)),U_4044),hAPP(hAPP(c_Set_Oinsert(U_4043),U_4045),c_Orderings_Obot__class_Obot(tc_fun(U_4043,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_4043),U_4044)
| hBOOL(hAPP(hAPP(c_member(U_4043),U_4045),U_4044))
| ~ sP239(U_4043,U_4044,U_4045) ),
inference(clausify,[status(thm)],[f_988_3]) ).
fof(f_989_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__le]) ).
fof(f_989_2,plain,
! [U_4048,U_4047,U_4046] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4046),U_4047)),hAPP(c_Finite__Set_Ocard(U_4046),hAPP(hAPP(c_Set_Oinsert(U_4046),U_4048),U_4047))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4046),U_4047)) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
fof(f_989_3,plain,
! [U_4046,U_4047,U_4048] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4046),U_4047)),hAPP(c_Finite__Set_Ocard(U_4046),hAPP(hAPP(c_Set_Oinsert(U_4046),U_4048),U_4047))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4046),U_4047)) ),
inference(definitional_conversion,[status(esa)],[f_989_2]) ).
cnf(f_989_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4046),U_4047)),hAPP(c_Finite__Set_Ocard(U_4046),hAPP(hAPP(c_Set_Oinsert(U_4046),U_4048),U_4047))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4046),U_4047)) ),
inference(clausify,[status(thm)],[f_989_3]) ).
fof(f_990_1,plain,
! [V_A_2,V_B_2,T_b] :
( V_A_2 = V_B_2
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__seteq]) ).
fof(f_990_2,plain,
! [U_4051,U_4050,U_4049] :
( U_4051 = U_4050
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4049),U_4050)),hAPP(c_Finite__Set_Ocard(U_4049),U_4051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4049,tc_HOL_Obool)),U_4051),U_4050))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4049),U_4050)) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
fof(f_990_3,plain,
! [U_4049,U_4050,U_4051] :
( U_4051 = U_4050
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4049),U_4050)),hAPP(c_Finite__Set_Ocard(U_4049),U_4051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4049,tc_HOL_Obool)),U_4051),U_4050))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4049),U_4050)) ),
inference(definitional_conversion,[status(esa)],[f_990_2]) ).
cnf(f_990_4,plain,
( U_4051 = U_4050
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4049),U_4050)),hAPP(c_Finite__Set_Ocard(U_4049),U_4051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4049,tc_HOL_Obool)),U_4051),U_4050))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4049),U_4050)) ),
inference(clausify,[status(thm)],[f_990_3]) ).
fof(f_991_1,plain,
! [V_A_2,V_B_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__mono]) ).
fof(f_991_2,plain,
! [U_4054,U_4053,U_4052] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4052),U_4054)),hAPP(c_Finite__Set_Ocard(U_4052),U_4053)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4052,tc_HOL_Obool)),U_4054),U_4053))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4052),U_4053)) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
fof(f_991_3,plain,
! [U_4053,U_4052,U_4054] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4052),U_4054)),hAPP(c_Finite__Set_Ocard(U_4052),U_4053)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4052,tc_HOL_Obool)),U_4054),U_4053))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4052),U_4053)) ),
inference(definitional_conversion,[status(esa)],[f_991_2]) ).
cnf(f_991_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4052),U_4054)),hAPP(c_Finite__Set_Ocard(U_4052),U_4053)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4052,tc_HOL_Obool)),U_4054),U_4053))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4052),U_4053)) ),
inference(clausify,[status(thm)],[f_991_3]) ).
fof(f_992_1,plain,
! [V_f_2,T_c,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__image__le]) ).
fof(f_992_2,plain,
! [U_4058,U_4057,U_4056,U_4055] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4057),hAPP(c_Set_Oimage(U_4055,U_4057,U_4058),U_4056))),hAPP(c_Finite__Set_Ocard(U_4055),U_4056)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4055),U_4056)) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
fof(f_992_3,plain,
! [U_4055,U_4056,U_4057,U_4058] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4057),hAPP(c_Set_Oimage(U_4055,U_4057,U_4058),U_4056))),hAPP(c_Finite__Set_Ocard(U_4055),U_4056)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4055),U_4056)) ),
inference(definitional_conversion,[status(esa)],[f_992_2]) ).
cnf(f_992_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4057),hAPP(c_Set_Oimage(U_4055,U_4057,U_4058),U_4056))),hAPP(c_Finite__Set_Ocard(U_4055),U_4056)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4055),U_4056)) ),
inference(clausify,[status(thm)],[f_992_3]) ).
fof(f_993_1,plain,
! [V_A_2,V_B_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__card__mono]) ).
fof(f_993_2,plain,
! [U_4061,U_4060,U_4059] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4059),U_4061)),hAPP(c_Finite__Set_Ocard(U_4059),U_4060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4059,tc_HOL_Obool)),U_4061),U_4060))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4059),U_4060)) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
fof(f_993_3,plain,
! [U_4059,U_4060,U_4061] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4059),U_4061)),hAPP(c_Finite__Set_Ocard(U_4059),U_4060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4059,tc_HOL_Obool)),U_4061),U_4060))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4059),U_4060)) ),
inference(definitional_conversion,[status(esa)],[f_993_2]) ).
cnf(f_993_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4059),U_4061)),hAPP(c_Finite__Set_Ocard(U_4059),U_4060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4059,tc_HOL_Obool)),U_4061),U_4060))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4059),U_4060)) ),
inference(clausify,[status(thm)],[f_993_3]) ).
fof(f_994_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Un__Int]) ).
fof(f_994_2,plain,
! [U_4064,U_4063,U_4062] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4062),U_4063)),hAPP(c_Finite__Set_Ocard(U_4062),U_4064)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4062,tc_HOL_Obool)),U_4063),U_4064))),hAPP(c_Finite__Set_Ocard(U_4062),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4062,tc_HOL_Obool)),U_4063),U_4064)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4062),U_4064))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4062),U_4063)) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
fof(f_994_3,plain,
! [U_4062,U_4063,U_4064] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4062),U_4063)),hAPP(c_Finite__Set_Ocard(U_4062),U_4064)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4062,tc_HOL_Obool)),U_4063),U_4064))),hAPP(c_Finite__Set_Ocard(U_4062),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4062,tc_HOL_Obool)),U_4063),U_4064)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4062),U_4064))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4062),U_4063)) ),
inference(definitional_conversion,[status(esa)],[f_994_2]) ).
cnf(f_994_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4062),U_4063)),hAPP(c_Finite__Set_Ocard(U_4062),U_4064)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4062,tc_HOL_Obool)),U_4063),U_4064))),hAPP(c_Finite__Set_Ocard(U_4062),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4062,tc_HOL_Obool)),U_4063),U_4064)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4062),U_4064))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4062),U_4063)) ),
inference(clausify,[status(thm)],[f_994_3]) ).
fof(f_995_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter]) ).
fof(f_995_2,plain,
! [U_4067,U_4066,U_4065] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4065),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4065,tc_HOL_Obool)),U_4066),U_4067))),hAPP(c_Finite__Set_Ocard(U_4065),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4065,tc_HOL_Obool)),U_4066),U_4067))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4065),U_4066)),hAPP(c_Finite__Set_Ocard(U_4065),U_4067))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4065),U_4067))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4065),U_4066)) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
fof(f_995_3,plain,
! [U_4065,U_4066,U_4067] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4065),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4065,tc_HOL_Obool)),U_4066),U_4067))),hAPP(c_Finite__Set_Ocard(U_4065),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4065,tc_HOL_Obool)),U_4066),U_4067))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4065),U_4066)),hAPP(c_Finite__Set_Ocard(U_4065),U_4067))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4065),U_4067))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4065),U_4066)) ),
inference(definitional_conversion,[status(esa)],[f_995_2]) ).
cnf(f_995_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4065),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4065,tc_HOL_Obool)),U_4066),U_4067))),hAPP(c_Finite__Set_Ocard(U_4065),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4065,tc_HOL_Obool)),U_4066),U_4067))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4065),U_4066)),hAPP(c_Finite__Set_Ocard(U_4065),U_4067))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4065),U_4067))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4065),U_4066)) ),
inference(clausify,[status(thm)],[f_995_3]) ).
fof(f_996_1,plain,
! [V_A_2,V_B_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__subset]) ).
fof(f_996_2,plain,
! [U_4070,U_4069,U_4068] :
( hAPP(c_Finite__Set_Ocard(U_4068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4068,tc_HOL_Obool)),U_4070),U_4069)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4068),U_4070)),hAPP(c_Finite__Set_Ocard(U_4068),U_4069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4068,tc_HOL_Obool)),U_4069),U_4070))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4068),U_4069)) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
fof(f_996_3,plain,
! [U_4068,U_4069,U_4070] :
( hAPP(c_Finite__Set_Ocard(U_4068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4068,tc_HOL_Obool)),U_4070),U_4069)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4068),U_4070)),hAPP(c_Finite__Set_Ocard(U_4068),U_4069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4068,tc_HOL_Obool)),U_4069),U_4070))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4068),U_4069)) ),
inference(definitional_conversion,[status(esa)],[f_996_2]) ).
cnf(f_996_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4068,tc_HOL_Obool)),U_4070),U_4069)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4068),U_4070)),hAPP(c_Finite__Set_Ocard(U_4068),U_4069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4068,tc_HOL_Obool)),U_4069),U_4070))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4068),U_4069)) ),
inference(clausify,[status(thm)],[f_996_3]) ).
fof(f_997_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int]) ).
fof(f_997_2,plain,
! [U_4073,U_4072,U_4071] :
( hAPP(c_Finite__Set_Ocard(U_4071),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4071),U_4072)),hAPP(c_Finite__Set_Ocard(U_4071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073))) ),
inference(variable_rename,[status(thm)],[f_997_1]) ).
fof(f_997_3,plain,
! [U_4071,U_4072,U_4073] :
( hAPP(c_Finite__Set_Ocard(U_4071),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4071),U_4072)),hAPP(c_Finite__Set_Ocard(U_4071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073))) ),
inference(definitional_conversion,[status(esa)],[f_997_2]) ).
cnf(f_997_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4071),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4071),U_4072)),hAPP(c_Finite__Set_Ocard(U_4071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4071,tc_HOL_Obool)),U_4072),U_4073))) ),
inference(clausify,[status(thm)],[f_997_3]) ).
fof(f_998_1,plain,
! [V_A_2,V_B_2,T_b] :
( 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))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff]) ).
fof(f_998_2,plain,
! [U_4076,U_4075,U_4074] :
( 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(U_4074),U_4076)),hAPP(c_Finite__Set_Ocard(U_4074),U_4075))),hAPP(c_Finite__Set_Ocard(U_4074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4074,tc_HOL_Obool)),U_4076),U_4075))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4074),U_4075)) ),
inference(variable_rename,[status(thm)],[f_998_1]) ).
fof(f_998_3,plain,
! [U_4074,U_4075,U_4076] :
( 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(U_4074),U_4076)),hAPP(c_Finite__Set_Ocard(U_4074),U_4075))),hAPP(c_Finite__Set_Ocard(U_4074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4074,tc_HOL_Obool)),U_4076),U_4075))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4074),U_4075)) ),
inference(definitional_conversion,[status(esa)],[f_998_2]) ).
cnf(f_998_4,plain,
( 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(U_4074),U_4076)),hAPP(c_Finite__Set_Ocard(U_4074),U_4075))),hAPP(c_Finite__Set_Ocard(U_4074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4074,tc_HOL_Obool)),U_4076),U_4075))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4074),U_4075)) ),
inference(clausify,[status(thm)],[f_998_3]) ).
fof(f_999_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__psubset]) ).
fof(f_999_2,plain,
! [U_4079,U_4078,U_4077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4077,tc_HOL_Obool)),U_4079),U_4078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4077),U_4079)),hAPP(c_Finite__Set_Ocard(U_4077),U_4078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4077,tc_HOL_Obool)),U_4079),U_4078))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4077),U_4078)) ),
inference(variable_rename,[status(thm)],[f_999_1]) ).
fof(f_999_3,plain,
! [U_4077,U_4078,U_4079] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4077,tc_HOL_Obool)),U_4079),U_4078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4077),U_4079)),hAPP(c_Finite__Set_Ocard(U_4077),U_4078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4077,tc_HOL_Obool)),U_4079),U_4078))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4077),U_4078)) ),
inference(definitional_conversion,[status(esa)],[f_999_2]) ).
cnf(f_999_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4077,tc_HOL_Obool)),U_4079),U_4078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4077),U_4079)),hAPP(c_Finite__Set_Ocard(U_4077),U_4078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4077,tc_HOL_Obool)),U_4079),U_4078))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4077),U_4078)) ),
inference(clausify,[status(thm)],[f_999_3]) ).
fof(f_1000_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint]) ).
fof(f_1000_2,plain,
! [U_4082,U_4081,U_4080] :
( hAPP(c_Finite__Set_Ocard(U_4080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4080),U_4081)),hAPP(c_Finite__Set_Ocard(U_4080),U_4082))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082) != c_Orderings_Obot__class_Obot(tc_fun(U_4080,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4081)) ),
inference(variable_rename,[status(thm)],[f_1000_1]) ).
fof(f_1000_3,plain,
! [U_4080,U_4081,U_4082] :
( hAPP(c_Finite__Set_Ocard(U_4080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4080),U_4081)),hAPP(c_Finite__Set_Ocard(U_4080),U_4082))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082) != c_Orderings_Obot__class_Obot(tc_fun(U_4080,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4081)) ),
inference(definitional_conversion,[status(esa)],[f_1000_2]) ).
cnf(f_1000_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4080),U_4081)),hAPP(c_Finite__Set_Ocard(U_4080),U_4082))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082) != c_Orderings_Obot__class_Obot(tc_fun(U_4080,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4081)) ),
inference(clausify,[status(thm)],[f_1000_3]) ).
fof(f_1001_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff1__le]) ).
fof(f_1001_2,plain,
! [U_4085,U_4084,U_4083] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4083,tc_HOL_Obool)),U_4084),hAPP(hAPP(c_Set_Oinsert(U_4083),U_4085),c_Orderings_Obot__class_Obot(tc_fun(U_4083,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4083),U_4084)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4083),U_4084)) ),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
fof(f_1001_3,plain,
! [U_4084,U_4083,U_4085] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4083,tc_HOL_Obool)),U_4084),hAPP(hAPP(c_Set_Oinsert(U_4083),U_4085),c_Orderings_Obot__class_Obot(tc_fun(U_4083,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4083),U_4084)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4083),U_4084)) ),
inference(definitional_conversion,[status(esa)],[f_1001_2]) ).
cnf(f_1001_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4083,tc_HOL_Obool)),U_4084),hAPP(hAPP(c_Set_Oinsert(U_4083),U_4085),c_Orderings_Obot__class_Obot(tc_fun(U_4083,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4083),U_4084)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4083),U_4084)) ),
inference(clausify,[status(thm)],[f_1001_3]) ).
fof(f_1002_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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_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))
| ? [B_x] :
( hAPP(V_g_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& 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))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter__neutral]) ).
fof(f_1002_2,plain,
! [U_4091,U_4090,U_4089,U_4088,U_4087] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4088,tc_HOL_Obool)),U_4089),U_4090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4087),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),U_4089)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),U_4090))
| ? [U_4086] :
( hAPP(U_4091,U_4086) != c_Groups_Oone__class_Oone(U_4087)
& hBOOL(hAPP(hAPP(c_member(U_4088),U_4086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4088,tc_HOL_Obool)),U_4089),U_4090))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4088),U_4090))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4088),U_4089))
| ~ class_Groups_Ocomm__monoid__mult(U_4087) ),
inference(variable_rename,[status(thm)],[f_1002_1]) ).
fof(f_1002_3,plain,
! [U_4091,U_4090,U_4089,U_4088,U_4087] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4088,tc_HOL_Obool)),U_4089),U_4090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4087),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),U_4089)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),U_4090))
| ( hAPP(U_4091,sK97(U_4091,U_4090,U_4089,U_4088,U_4087)) != c_Groups_Oone__class_Oone(U_4087)
& hBOOL(hAPP(hAPP(c_member(U_4088),sK97(U_4091,U_4090,U_4089,U_4088,U_4087)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4088,tc_HOL_Obool)),U_4089),U_4090))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4088),U_4090))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4088),U_4089))
| ~ class_Groups_Ocomm__monoid__mult(U_4087) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_4086,sK97(U_4091,U_4090,U_4089,U_4088,U_4087))],[f_1002_2]) ).
fof(f_1002_4,plain,
( ! [U_4087,U_4088,U_4089,U_4090,U_4091] :
( hAPP(U_4091,sK97(U_4091,U_4090,U_4089,U_4088,U_4087)) != c_Groups_Oone__class_Oone(U_4087)
| ~ sP240(U_4087,U_4088,U_4089,U_4090,U_4091) )
& ! [U_4087,U_4088,U_4089,U_4090,U_4091] :
( hBOOL(hAPP(hAPP(c_member(U_4088),sK97(U_4091,U_4090,U_4089,U_4088,U_4087)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4088,tc_HOL_Obool)),U_4089),U_4090)))
| ~ sP240(U_4087,U_4088,U_4089,U_4090,U_4091) )
& ! [U_4087,U_4088,U_4089,U_4090,U_4091] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4088,tc_HOL_Obool)),U_4089),U_4090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4087),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),U_4089)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),U_4090))
| sP240(U_4087,U_4088,U_4089,U_4090,U_4091)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4088),U_4090))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4088),U_4089))
| ~ class_Groups_Ocomm__monoid__mult(U_4087) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_1002_3]) ).
cnf(f_1002_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4088,tc_HOL_Obool)),U_4089),U_4090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4087),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),U_4089)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4088,U_4087),U_4091),U_4090))
| sP240(U_4087,U_4088,U_4089,U_4090,U_4091)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4088),U_4090))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4088),U_4089))
| ~ class_Groups_Ocomm__monoid__mult(U_4087) ),
inference(clausify,[status(thm)],[f_1002_4]) ).
cnf(f_1002_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4088),sK97(U_4091,U_4090,U_4089,U_4088,U_4087)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4088,tc_HOL_Obool)),U_4089),U_4090)))
| ~ sP240(U_4087,U_4088,U_4089,U_4090,U_4091) ),
inference(clausify,[status(thm)],[f_1002_4]) ).
cnf(f_1002_7,plain,
( hAPP(U_4091,sK97(U_4091,U_4090,U_4089,U_4088,U_4087)) != c_Groups_Oone__class_Oone(U_4087)
| ~ sP240(U_4087,U_4088,U_4089,U_4090,U_4091) ),
inference(clausify,[status(thm)],[f_1002_4]) ).
fof(f_1003_1,plain,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( 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))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& 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))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__one]) ).
fof(f_1003_2,plain,
! [U_4097,U_4096,U_4095,U_4094,U_4093] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4094,tc_HOL_Obool)),U_4095),U_4096)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4093),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),U_4095)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),U_4096))
| ? [U_4092] :
( hAPP(U_4097,U_4092) != c_Groups_Oone__class_Oone(U_4093)
& hBOOL(hAPP(hAPP(c_member(U_4094),U_4092),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4094,tc_HOL_Obool)),U_4095),U_4096))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4094),U_4096))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4094),U_4095))
| ~ class_Groups_Ocomm__monoid__mult(U_4093) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
fof(f_1003_3,plain,
! [U_4097,U_4096,U_4095,U_4094,U_4093] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4094,tc_HOL_Obool)),U_4095),U_4096)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4093),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),U_4095)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),U_4096))
| ( hAPP(U_4097,sK98(U_4097,U_4096,U_4095,U_4094,U_4093)) != c_Groups_Oone__class_Oone(U_4093)
& hBOOL(hAPP(hAPP(c_member(U_4094),sK98(U_4097,U_4096,U_4095,U_4094,U_4093)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4094,tc_HOL_Obool)),U_4095),U_4096))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4094),U_4096))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4094),U_4095))
| ~ class_Groups_Ocomm__monoid__mult(U_4093) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_4092,sK98(U_4097,U_4096,U_4095,U_4094,U_4093))],[f_1003_2]) ).
fof(f_1003_4,plain,
( ! [U_4094,U_4095,U_4093,U_4096,U_4097] :
( hAPP(U_4097,sK98(U_4097,U_4096,U_4095,U_4094,U_4093)) != c_Groups_Oone__class_Oone(U_4093)
| ~ sP241(U_4094,U_4095,U_4093,U_4096,U_4097) )
& ! [U_4094,U_4095,U_4093,U_4096,U_4097] :
( hBOOL(hAPP(hAPP(c_member(U_4094),sK98(U_4097,U_4096,U_4095,U_4094,U_4093)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4094,tc_HOL_Obool)),U_4095),U_4096)))
| ~ sP241(U_4094,U_4095,U_4093,U_4096,U_4097) )
& ! [U_4094,U_4095,U_4093,U_4096,U_4097] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4094,tc_HOL_Obool)),U_4095),U_4096)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4093),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),U_4095)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),U_4096))
| sP241(U_4094,U_4095,U_4093,U_4096,U_4097)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4094),U_4096))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4094),U_4095))
| ~ class_Groups_Ocomm__monoid__mult(U_4093) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_1003_3]) ).
cnf(f_1003_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4094,tc_HOL_Obool)),U_4095),U_4096)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4093),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),U_4095)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4094,U_4093),U_4097),U_4096))
| sP241(U_4094,U_4095,U_4093,U_4096,U_4097)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4094),U_4096))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4094),U_4095))
| ~ class_Groups_Ocomm__monoid__mult(U_4093) ),
inference(clausify,[status(thm)],[f_1003_4]) ).
cnf(f_1003_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4094),sK98(U_4097,U_4096,U_4095,U_4094,U_4093)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4094,tc_HOL_Obool)),U_4095),U_4096)))
| ~ sP241(U_4094,U_4095,U_4093,U_4096,U_4097) ),
inference(clausify,[status(thm)],[f_1003_4]) ).
cnf(f_1003_7,plain,
( hAPP(U_4097,sK98(U_4097,U_4096,U_4095,U_4094,U_4093)) != c_Groups_Oone__class_Oone(U_4093)
| ~ sP241(U_4094,U_4095,U_4093,U_4096,U_4097) ),
inference(clausify,[status(thm)],[f_1003_4]) ).
fof(f_1004_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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(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_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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint]) ).
fof(f_1004_2,plain,
! [U_4102,U_4101,U_4100,U_4099,U_4098] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4099,tc_HOL_Obool)),U_4100),U_4101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4098),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),U_4100)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),U_4101))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4099,tc_HOL_Obool)),U_4100),U_4101) != c_Orderings_Obot__class_Obot(tc_fun(U_4099,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4099),U_4101))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4099),U_4100))
| ~ class_Groups_Ocomm__monoid__mult(U_4098) ),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
fof(f_1004_3,plain,
! [U_4101,U_4098,U_4100,U_4099,U_4102] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4099,tc_HOL_Obool)),U_4100),U_4101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4098),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),U_4100)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),U_4101))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4099,tc_HOL_Obool)),U_4100),U_4101) != c_Orderings_Obot__class_Obot(tc_fun(U_4099,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4099),U_4101))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4099),U_4100))
| ~ class_Groups_Ocomm__monoid__mult(U_4098) ),
inference(definitional_conversion,[status(esa)],[f_1004_2]) ).
cnf(f_1004_4,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4099,tc_HOL_Obool)),U_4100),U_4101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4098),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),U_4100)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4098,U_4099,c_Groups_Otimes__class_Otimes(U_4098)),U_4102),c_Groups_Oone__class_Oone(U_4098)),U_4101))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4099,tc_HOL_Obool)),U_4100),U_4101) != c_Orderings_Obot__class_Obot(tc_fun(U_4099,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4099),U_4101))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4099),U_4100))
| ~ class_Groups_Ocomm__monoid__mult(U_4098) ),
inference(clausify,[status(thm)],[f_1004_3]) ).
fof(f_1005_1,plain,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( 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)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right]) ).
fof(f_1005_2,plain,
! [U_4108,U_4107,U_4106,U_4105,U_4104] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4105,U_4104),U_4108),U_4106) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4105,U_4104),U_4108),U_4107)
| ? [U_4103] :
( hAPP(U_4108,U_4103) != c_Groups_Oone__class_Oone(U_4104)
& hBOOL(hAPP(hAPP(c_member(U_4105),U_4103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4105,tc_HOL_Obool)),U_4106),U_4107))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4105,tc_HOL_Obool)),U_4107),U_4106))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4105),U_4106))
| ~ class_Groups_Ocomm__monoid__mult(U_4104) ),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
fof(f_1005_3,plain,
! [U_4108,U_4107,U_4106,U_4105,U_4104] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4105,U_4104),U_4108),U_4106) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4105,U_4104),U_4108),U_4107)
| ( hAPP(U_4108,sK99(U_4108,U_4107,U_4106,U_4105,U_4104)) != c_Groups_Oone__class_Oone(U_4104)
& hBOOL(hAPP(hAPP(c_member(U_4105),sK99(U_4108,U_4107,U_4106,U_4105,U_4104)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4105,tc_HOL_Obool)),U_4106),U_4107))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4105,tc_HOL_Obool)),U_4107),U_4106))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4105),U_4106))
| ~ class_Groups_Ocomm__monoid__mult(U_4104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_4103,sK99(U_4108,U_4107,U_4106,U_4105,U_4104))],[f_1005_2]) ).
fof(f_1005_4,plain,
( ! [U_4104,U_4105,U_4106,U_4107,U_4108] :
( hAPP(U_4108,sK99(U_4108,U_4107,U_4106,U_4105,U_4104)) != c_Groups_Oone__class_Oone(U_4104)
| ~ sP242(U_4104,U_4105,U_4106,U_4107,U_4108) )
& ! [U_4104,U_4105,U_4106,U_4107,U_4108] :
( hBOOL(hAPP(hAPP(c_member(U_4105),sK99(U_4108,U_4107,U_4106,U_4105,U_4104)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4105,tc_HOL_Obool)),U_4106),U_4107)))
| ~ sP242(U_4104,U_4105,U_4106,U_4107,U_4108) )
& ! [U_4104,U_4105,U_4106,U_4107,U_4108] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4105,U_4104),U_4108),U_4106) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4105,U_4104),U_4108),U_4107)
| sP242(U_4104,U_4105,U_4106,U_4107,U_4108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4105,tc_HOL_Obool)),U_4107),U_4106))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4105),U_4106))
| ~ class_Groups_Ocomm__monoid__mult(U_4104) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242])],[f_1005_3]) ).
cnf(f_1005_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4105,U_4104),U_4108),U_4106) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4105,U_4104),U_4108),U_4107)
| sP242(U_4104,U_4105,U_4106,U_4107,U_4108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4105,tc_HOL_Obool)),U_4107),U_4106))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4105),U_4106))
| ~ class_Groups_Ocomm__monoid__mult(U_4104) ),
inference(clausify,[status(thm)],[f_1005_4]) ).
cnf(f_1005_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4105),sK99(U_4108,U_4107,U_4106,U_4105,U_4104)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4105,tc_HOL_Obool)),U_4106),U_4107)))
| ~ sP242(U_4104,U_4105,U_4106,U_4107,U_4108) ),
inference(clausify,[status(thm)],[f_1005_4]) ).
cnf(f_1005_7,plain,
( hAPP(U_4108,sK99(U_4108,U_4107,U_4106,U_4105,U_4104)) != c_Groups_Oone__class_Oone(U_4104)
| ~ sP242(U_4104,U_4105,U_4106,U_4107,U_4108) ),
inference(clausify,[status(thm)],[f_1005_4]) ).
fof(f_1006_1,plain,
! [V_f_2,V_S_2,V_T_2,T_b,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)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left]) ).
fof(f_1006_2,plain,
! [U_4114,U_4113,U_4112,U_4111,U_4110] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4111,U_4110),U_4114),U_4113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4111,U_4110),U_4114),U_4112)
| ? [U_4109] :
( hAPP(U_4114,U_4109) != c_Groups_Oone__class_Oone(U_4110)
& hBOOL(hAPP(hAPP(c_member(U_4111),U_4109),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4111,tc_HOL_Obool)),U_4112),U_4113))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4111,tc_HOL_Obool)),U_4113),U_4112))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4111),U_4112))
| ~ class_Groups_Ocomm__monoid__mult(U_4110) ),
inference(variable_rename,[status(thm)],[f_1006_1]) ).
fof(f_1006_3,plain,
! [U_4114,U_4113,U_4112,U_4111,U_4110] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4111,U_4110),U_4114),U_4113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4111,U_4110),U_4114),U_4112)
| ( hAPP(U_4114,sK100(U_4114,U_4113,U_4112,U_4111,U_4110)) != c_Groups_Oone__class_Oone(U_4110)
& hBOOL(hAPP(hAPP(c_member(U_4111),sK100(U_4114,U_4113,U_4112,U_4111,U_4110)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4111,tc_HOL_Obool)),U_4112),U_4113))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4111,tc_HOL_Obool)),U_4113),U_4112))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4111),U_4112))
| ~ class_Groups_Ocomm__monoid__mult(U_4110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_4109,sK100(U_4114,U_4113,U_4112,U_4111,U_4110))],[f_1006_2]) ).
fof(f_1006_4,plain,
( ! [U_4110,U_4111,U_4113,U_4114,U_4112] :
( hAPP(U_4114,sK100(U_4114,U_4113,U_4112,U_4111,U_4110)) != c_Groups_Oone__class_Oone(U_4110)
| ~ sP243(U_4110,U_4111,U_4113,U_4114,U_4112) )
& ! [U_4110,U_4111,U_4113,U_4114,U_4112] :
( hBOOL(hAPP(hAPP(c_member(U_4111),sK100(U_4114,U_4113,U_4112,U_4111,U_4110)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4111,tc_HOL_Obool)),U_4112),U_4113)))
| ~ sP243(U_4110,U_4111,U_4113,U_4114,U_4112) )
& ! [U_4110,U_4111,U_4113,U_4114,U_4112] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4111,U_4110),U_4114),U_4113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4111,U_4110),U_4114),U_4112)
| sP243(U_4110,U_4111,U_4113,U_4114,U_4112)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4111,tc_HOL_Obool)),U_4113),U_4112))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4111),U_4112))
| ~ class_Groups_Ocomm__monoid__mult(U_4110) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243])],[f_1006_3]) ).
cnf(f_1006_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4111,U_4110),U_4114),U_4113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4111,U_4110),U_4114),U_4112)
| sP243(U_4110,U_4111,U_4113,U_4114,U_4112)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4111,tc_HOL_Obool)),U_4113),U_4112))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4111),U_4112))
| ~ class_Groups_Ocomm__monoid__mult(U_4110) ),
inference(clausify,[status(thm)],[f_1006_4]) ).
cnf(f_1006_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4111),sK100(U_4114,U_4113,U_4112,U_4111,U_4110)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4111,tc_HOL_Obool)),U_4112),U_4113)))
| ~ sP243(U_4110,U_4111,U_4113,U_4114,U_4112) ),
inference(clausify,[status(thm)],[f_1006_4]) ).
cnf(f_1006_7,plain,
( hAPP(U_4114,sK100(U_4114,U_4113,U_4112,U_4111,U_4110)) != c_Groups_Oone__class_Oone(U_4110)
| ~ sP243(U_4110,U_4111,U_4113,U_4114,U_4112) ),
inference(clausify,[status(thm)],[f_1006_4]) ).
fof(f_1007_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1]) ).
fof(f_1007_2,plain,
! [U_4117,U_4116,U_4115] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4115,tc_HOL_Obool)),U_4116),hAPP(hAPP(c_Set_Oinsert(U_4115),U_4117),c_Orderings_Obot__class_Obot(tc_fun(U_4115,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_4115),U_4116)
| ~ hBOOL(hAPP(hAPP(c_member(U_4115),U_4117),U_4116))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4115),U_4116)) ),
inference(variable_rename,[status(thm)],[f_1007_1]) ).
fof(f_1007_3,plain,
! [U_4116,U_4115,U_4117] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4115,tc_HOL_Obool)),U_4116),hAPP(hAPP(c_Set_Oinsert(U_4115),U_4117),c_Orderings_Obot__class_Obot(tc_fun(U_4115,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_4115),U_4116)
| ~ hBOOL(hAPP(hAPP(c_member(U_4115),U_4117),U_4116))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4115),U_4116)) ),
inference(definitional_conversion,[status(esa)],[f_1007_2]) ).
cnf(f_1007_4,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4115,tc_HOL_Obool)),U_4116),hAPP(hAPP(c_Set_Oinsert(U_4115),U_4117),c_Orderings_Obot__class_Obot(tc_fun(U_4115,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_4115),U_4116)
| ~ hBOOL(hAPP(hAPP(c_member(U_4115),U_4117),U_4116))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4115),U_4116)) ),
inference(clausify,[status(thm)],[f_1007_3]) ).
fof(f_1008_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int]) ).
fof(f_1008_2,plain,
! [U_4122,U_4121,U_4120,U_4119,U_4118] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),U_4120)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),U_4121)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4119,tc_HOL_Obool)),U_4120),U_4121))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4119,tc_HOL_Obool)),U_4120),U_4121)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4121))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4120))
| ~ class_Groups_Ocomm__monoid__mult(U_4118) ),
inference(variable_rename,[status(thm)],[f_1008_1]) ).
fof(f_1008_3,plain,
! [U_4119,U_4118,U_4120,U_4121,U_4122] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),U_4120)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),U_4121)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4119,tc_HOL_Obool)),U_4120),U_4121))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4119,tc_HOL_Obool)),U_4120),U_4121)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4121))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4120))
| ~ class_Groups_Ocomm__monoid__mult(U_4118) ),
inference(definitional_conversion,[status(esa)],[f_1008_2]) ).
cnf(f_1008_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),U_4120)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),U_4121)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4119,tc_HOL_Obool)),U_4120),U_4121))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4118,U_4119,c_Groups_Otimes__class_Otimes(U_4118)),U_4122),c_Groups_Oone__class_Oone(U_4118)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4119,tc_HOL_Obool)),U_4120),U_4121)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4121))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4120))
| ~ class_Groups_Ocomm__monoid__mult(U_4118) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
fof(f_1009_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( 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))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
| ~ class_Rings_Olinordered__semiring__1__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convex__bound__lt]) ).
fof(f_1009_2,plain,
! [U_4128,U_4127,U_4126,U_4125,U_4124,U_4123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),U_4127),U_4124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),U_4128),U_4126))),U_4125))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4123),U_4127),U_4128) != c_Groups_Oone__class_Oone(U_4123)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4123),c_Groups_Ozero__class_Ozero(U_4123)),U_4128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4123),c_Groups_Ozero__class_Ozero(U_4123)),U_4127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4126),U_4125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4124),U_4125))
| ~ class_Rings_Olinordered__semiring__1__strict(U_4123) ),
inference(variable_rename,[status(thm)],[f_1009_1]) ).
fof(f_1009_3,plain,
! [U_4124,U_4123,U_4125,U_4126,U_4127,U_4128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),U_4127),U_4124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),U_4128),U_4126))),U_4125))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4123),U_4127),U_4128) != c_Groups_Oone__class_Oone(U_4123)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4123),c_Groups_Ozero__class_Ozero(U_4123)),U_4128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4123),c_Groups_Ozero__class_Ozero(U_4123)),U_4127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4126),U_4125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4124),U_4125))
| ~ class_Rings_Olinordered__semiring__1__strict(U_4123) ),
inference(definitional_conversion,[status(esa)],[f_1009_2]) ).
cnf(f_1009_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),U_4127),U_4124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),U_4128),U_4126))),U_4125))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4123),U_4127),U_4128) != c_Groups_Oone__class_Oone(U_4123)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4123),c_Groups_Ozero__class_Ozero(U_4123)),U_4128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4123),c_Groups_Ozero__class_Ozero(U_4123)),U_4127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4126),U_4125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4124),U_4125))
| ~ class_Rings_Olinordered__semiring__1__strict(U_4123) ),
inference(clausify,[status(thm)],[f_1009_3]) ).
fof(f_1010_1,plain,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_less__zeroE]) ).
fof(f_1010_2,plain,
! [U_4129] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4129),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1010_1]) ).
fof(f_1010_3,plain,
! [U_4129] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4129),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1010_2]) ).
cnf(f_1010_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4129),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1010_3]) ).
fof(f_1011_1,plain,
! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
inference(fof_nnf,[status(thm)],[fact_le0]) ).
fof(f_1011_2,plain,
! [U_4130] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4130)),
inference(variable_rename,[status(thm)],[f_1011_1]) ).
fof(f_1011_3,plain,
! [U_4130] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4130)),
inference(definitional_conversion,[status(esa)],[f_1011_2]) ).
cnf(f_1011_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4130)),
inference(clausify,[status(thm)],[f_1011_3]) ).
fof(f_1012_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_zero__less__Suc]) ).
fof(f_1012_2,plain,
! [U_4131] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_4131))),
inference(variable_rename,[status(thm)],[f_1012_1]) ).
fof(f_1012_3,plain,
! [U_4131] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_4131))),
inference(definitional_conversion,[status(esa)],[f_1012_2]) ).
cnf(f_1012_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_4131))),
inference(clausify,[status(thm)],[f_1012_3]) ).
fof(f_1013_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mono]) ).
fof(f_1013_2,plain,
! [U_4133,U_4132] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4132)),hAPP(c_Nat_OSuc,U_4133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4132),U_4133)) ),
inference(variable_rename,[status(thm)],[f_1013_1]) ).
fof(f_1013_3,plain,
! [U_4132,U_4133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4132)),hAPP(c_Nat_OSuc,U_4133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4132),U_4133)) ),
inference(definitional_conversion,[status(esa)],[f_1013_2]) ).
cnf(f_1013_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4132)),hAPP(c_Nat_OSuc,U_4133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4132),U_4133)) ),
inference(clausify,[status(thm)],[f_1013_3]) ).
fof(f_1014_1,plain,
! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))),
inference(fof_nnf,[status(thm)],[fact_lessI]) ).
fof(f_1014_2,plain,
! [U_4134] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4134),hAPP(c_Nat_OSuc,U_4134))),
inference(variable_rename,[status(thm)],[f_1014_1]) ).
fof(f_1014_3,plain,
! [U_4134] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4134),hAPP(c_Nat_OSuc,U_4134))),
inference(definitional_conversion,[status(esa)],[f_1014_2]) ).
cnf(f_1014_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4134),hAPP(c_Nat_OSuc,U_4134))),
inference(clausify,[status(thm)],[f_1014_3]) ).
fof(f_1015_1,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_One__nat__def]) ).
fof(f_1015_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_1015_1]) ).
cnf(f_1015_3,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1015_2]) ).
fof(f_1016_1,plain,
! [V_k_2,V_f_2,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,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))
| hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt]) ).
fof(f_1016_2,plain,
! [U_4137,U_4136,U_4135] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4135),U_4136),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4135),U_4136),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4137))
| hAPP(U_4136,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_4135)
| ~ class_Groups_Ocomm__monoid__add(U_4135) ),
inference(variable_rename,[status(thm)],[f_1016_1]) ).
fof(f_1016_3,plain,
! [U_4135,U_4136,U_4137] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4135),U_4136),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4135),U_4136),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4137))
| hAPP(U_4136,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_4135)
| ~ class_Groups_Ocomm__monoid__add(U_4135) ),
inference(definitional_conversion,[status(esa)],[f_1016_2]) ).
cnf(f_1016_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4135),U_4136),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4135),U_4136),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4137))
| hAPP(U_4136,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_4135)
| ~ class_Groups_Ocomm__monoid__add(U_4135) ),
inference(clausify,[status(thm)],[f_1016_3]) ).
fof(f_1017_1,plain,
! [V_x_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
| c_Groups_Ozero__class_Ozero(T_b) != V_x_2 ) )
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).
fof(f_1017_2,plain,
! [U_4139,U_4138] :
( ( ( c_Groups_Ozero__class_Ozero(U_4138) = U_4139
| U_4139 != c_Groups_Ozero__class_Ozero(U_4138) )
& ( U_4139 = c_Groups_Ozero__class_Ozero(U_4138)
| c_Groups_Ozero__class_Ozero(U_4138) != U_4139 ) )
| ~ class_Groups_Ozero(U_4138) ),
inference(variable_rename,[status(thm)],[f_1017_1]) ).
fof(f_1017_3,plain,
( ! [U_4138,U_4139] :
( c_Groups_Ozero__class_Ozero(U_4138) = U_4139
| U_4139 != c_Groups_Ozero__class_Ozero(U_4138)
| ~ sP244(U_4138,U_4139) )
& ! [U_4138,U_4139] :
( U_4139 = c_Groups_Ozero__class_Ozero(U_4138)
| c_Groups_Ozero__class_Ozero(U_4138) != U_4139
| ~ sP244(U_4138,U_4139) )
& ! [U_4138,U_4139] :
( sP244(U_4138,U_4139)
| ~ class_Groups_Ozero(U_4138) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244])],[f_1017_2]) ).
cnf(f_1017_4,plain,
( sP244(U_4138,U_4139)
| ~ class_Groups_Ozero(U_4138) ),
inference(clausify,[status(thm)],[f_1017_3]) ).
cnf(f_1017_5,plain,
( U_4139 = c_Groups_Ozero__class_Ozero(U_4138)
| c_Groups_Ozero__class_Ozero(U_4138) != U_4139
| ~ sP244(U_4138,U_4139) ),
inference(clausify,[status(thm)],[f_1017_3]) ).
cnf(f_1017_6,plain,
( c_Groups_Ozero__class_Ozero(U_4138) = U_4139
| U_4139 != c_Groups_Ozero__class_Ozero(U_4138)
| ~ sP244(U_4138,U_4139) ),
inference(clausify,[status(thm)],[f_1017_3]) ).
fof(f_1018_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).
fof(f_1018_2,plain,
! [U_4140] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4140)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4140),
inference(variable_rename,[status(thm)],[f_1018_1]) ).
fof(f_1018_3,plain,
! [U_4140] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4140)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4140),
inference(definitional_conversion,[status(esa)],[f_1018_2]) ).
cnf(f_1018_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4140)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4140),
inference(clausify,[status(thm)],[f_1018_3]) ).
fof(f_1019_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_greaterThan__Suc]) ).
fof(f_1019_2,plain,
! [U_4141] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4141)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4141)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4141)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_1019_1]) ).
fof(f_1019_3,plain,
! [U_4141] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4141)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4141)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4141)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_1019_2]) ).
cnf(f_1019_4,plain,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4141)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4141)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4141)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_1019_3]) ).
fof(f_1020_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_atLeast__Suc]) ).
fof(f_1020_2,plain,
! [U_4142] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4142)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),U_4142)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4142),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_1020_1]) ).
fof(f_1020_3,plain,
! [U_4142] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4142)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),U_4142)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4142),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_1020_2]) ).
cnf(f_1020_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4142)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),U_4142)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4142),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_1020_3]) ).
fof(f_1021_1,plain,
! [V_k_2,V_f_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,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))
| hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0]) ).
fof(f_1021_2,plain,
! [U_4144,U_4143] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_4143),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4144)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_4143),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_4144))
| hAPP(U_4143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_1021_1]) ).
fof(f_1021_3,plain,
! [U_4143,U_4144] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_4143),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4144)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_4143),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_4144))
| hAPP(U_4143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1021_2]) ).
cnf(f_1021_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_4143),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4144)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_4143),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_4144))
| hAPP(U_4143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1021_3]) ).
fof(f_1022_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).
fof(f_1022_2,plain,
! [U_4145] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4145)) = 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),U_4145))),
inference(variable_rename,[status(thm)],[f_1022_1]) ).
fof(f_1022_3,plain,
! [U_4145] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4145)) = 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),U_4145))),
inference(definitional_conversion,[status(esa)],[f_1022_2]) ).
cnf(f_1022_4,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4145)) = 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),U_4145))),
inference(clausify,[status(thm)],[f_1022_3]) ).
fof(f_1023_1,plain,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
inference(fof_nnf,[status(thm)],[fact_Zero__not__Suc]) ).
fof(f_1023_2,plain,
! [U_4146] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4146),
inference(variable_rename,[status(thm)],[f_1023_1]) ).
fof(f_1023_3,plain,
! [U_4146] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4146),
inference(definitional_conversion,[status(esa)],[f_1023_2]) ).
cnf(f_1023_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4146),
inference(clausify,[status(thm)],[f_1023_3]) ).
fof(f_1024_1,plain,
! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H),
inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(f_1024_2,plain,
! [U_4147] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4147),
inference(variable_rename,[status(thm)],[f_1024_1]) ).
fof(f_1024_3,plain,
! [U_4147] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4147),
inference(definitional_conversion,[status(esa)],[f_1024_2]) ).
cnf(f_1024_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4147),
inference(clausify,[status(thm)],[f_1024_3]) ).
fof(f_1025_1,plain,
! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_1025_2,plain,
! [U_4148] : U_4148 != hAPP(c_Nat_OSuc,U_4148),
inference(variable_rename,[status(thm)],[f_1025_1]) ).
fof(f_1025_3,plain,
! [U_4148] : U_4148 != hAPP(c_Nat_OSuc,U_4148),
inference(definitional_conversion,[status(esa)],[f_1025_2]) ).
cnf(f_1025_4,plain,
U_4148 != hAPP(c_Nat_OSuc,U_4148),
inference(clausify,[status(thm)],[f_1025_3]) ).
fof(f_1026_1,plain,
! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_Suc__not__Zero]) ).
fof(f_1026_2,plain,
! [U_4149] : hAPP(c_Nat_OSuc,U_4149) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1026_1]) ).
fof(f_1026_3,plain,
! [U_4149] : hAPP(c_Nat_OSuc,U_4149) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1026_2]) ).
cnf(f_1026_4,plain,
hAPP(c_Nat_OSuc,U_4149) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1026_3]) ).
fof(f_1027_1,plain,
! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(f_1027_2,plain,
! [U_4150] : hAPP(c_Nat_OSuc,U_4150) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1027_1]) ).
fof(f_1027_3,plain,
! [U_4150] : hAPP(c_Nat_OSuc,U_4150) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1027_2]) ).
cnf(f_1027_4,plain,
hAPP(c_Nat_OSuc,U_4150) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1027_3]) ).
fof(f_1028_1,plain,
! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_1028_2,plain,
! [U_4151] : hAPP(c_Nat_OSuc,U_4151) != U_4151,
inference(variable_rename,[status(thm)],[f_1028_1]) ).
fof(f_1028_3,plain,
! [U_4151] : hAPP(c_Nat_OSuc,U_4151) != U_4151,
inference(definitional_conversion,[status(esa)],[f_1028_2]) ).
cnf(f_1028_4,plain,
hAPP(c_Nat_OSuc,U_4151) != U_4151,
inference(clausify,[status(thm)],[f_1028_3]) ).
fof(f_1029_1,plain,
! [V_nat_H_2,V_nat_2] :
( ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
| V_nat_2 != V_nat_H_2 )
& ( V_nat_2 = V_nat_H_2
| hAPP(c_Nat_OSuc,V_nat_2) != hAPP(c_Nat_OSuc,V_nat_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat_Oinject]) ).
fof(f_1029_2,plain,
! [U_4153,U_4152] :
( ( hAPP(c_Nat_OSuc,U_4152) = hAPP(c_Nat_OSuc,U_4153)
| U_4152 != U_4153 )
& ( U_4152 = U_4153
| hAPP(c_Nat_OSuc,U_4152) != hAPP(c_Nat_OSuc,U_4153) ) ),
inference(variable_rename,[status(thm)],[f_1029_1]) ).
fof(f_1029_3,plain,
( ! [U_4157,U_4155] :
( hAPP(c_Nat_OSuc,U_4155) = hAPP(c_Nat_OSuc,U_4157)
| U_4155 != U_4157 )
& ! [U_4156,U_4154] :
( U_4154 = U_4156
| hAPP(c_Nat_OSuc,U_4154) != hAPP(c_Nat_OSuc,U_4156) ) ),
inference(miniscope,[status(thm)],[f_1029_2]) ).
fof(f_1029_4,plain,
( ! [U_4155,U_4157] :
( hAPP(c_Nat_OSuc,U_4155) = hAPP(c_Nat_OSuc,U_4157)
| U_4155 != U_4157 )
& ! [U_4156,U_4154] :
( U_4154 = U_4156
| hAPP(c_Nat_OSuc,U_4154) != hAPP(c_Nat_OSuc,U_4156) ) ),
inference(definitional_conversion,[status(esa)],[f_1029_3]) ).
cnf(f_1029_5,plain,
( U_4154 = U_4156
| hAPP(c_Nat_OSuc,U_4154) != hAPP(c_Nat_OSuc,U_4156) ),
inference(clausify,[status(thm)],[f_1029_4]) ).
cnf(f_1029_6,plain,
( hAPP(c_Nat_OSuc,U_4155) = hAPP(c_Nat_OSuc,U_4157)
| U_4155 != U_4157 ),
inference(clausify,[status(thm)],[f_1029_4]) ).
fof(f_1030_1,plain,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
inference(fof_nnf,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(f_1030_2,plain,
! [U_4158] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4158),
inference(variable_rename,[status(thm)],[f_1030_1]) ).
fof(f_1030_3,plain,
! [U_4158] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4158),
inference(definitional_conversion,[status(esa)],[f_1030_2]) ).
cnf(f_1030_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4158),
inference(clausify,[status(thm)],[f_1030_3]) ).
fof(f_1031_1,plain,
! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(f_1031_2,plain,
! [U_4159] : hAPP(c_Nat_OSuc,U_4159) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1031_1]) ).
fof(f_1031_3,plain,
! [U_4159] : hAPP(c_Nat_OSuc,U_4159) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1031_2]) ).
cnf(f_1031_4,plain,
hAPP(c_Nat_OSuc,U_4159) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1031_3]) ).
fof(f_1032_1,plain,
! [V_y,V_x] :
( V_x = V_y
| hAPP(c_Nat_OSuc,V_x) != hAPP(c_Nat_OSuc,V_y) ),
inference(fof_nnf,[status(thm)],[fact_Suc__inject]) ).
fof(f_1032_2,plain,
! [U_4161,U_4160] :
( U_4160 = U_4161
| hAPP(c_Nat_OSuc,U_4160) != hAPP(c_Nat_OSuc,U_4161) ),
inference(variable_rename,[status(thm)],[f_1032_1]) ).
fof(f_1032_3,plain,
! [U_4160,U_4161] :
( U_4160 = U_4161
| hAPP(c_Nat_OSuc,U_4160) != hAPP(c_Nat_OSuc,U_4161) ),
inference(definitional_conversion,[status(esa)],[f_1032_2]) ).
cnf(f_1032_4,plain,
( U_4160 = U_4161
| hAPP(c_Nat_OSuc,U_4160) != hAPP(c_Nat_OSuc,U_4161) ),
inference(clausify,[status(thm)],[f_1032_3]) ).
fof(f_1033_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_greaterThan__0]) ).
fof(f_1033_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1033_1]) ).
cnf(f_1033_3,plain,
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))),
inference(clausify,[status(thm)],[f_1033_2]) ).
fof(f_1034_1,plain,
! [V_n_2,V_m_2] :
( ( 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))
| V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = 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) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff]) ).
fof(f_1034_2,plain,
! [U_4163,U_4162] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4162),U_4163) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4163 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4162 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_4163 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_4162 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4162),U_4163) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1034_1]) ).
fof(f_1034_3,plain,
( ! [U_4167,U_4165] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4165),U_4167) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4167 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4165 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_4166,U_4164] :
( ( U_4166 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_4164 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4164),U_4166) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1034_2]) ).
fof(f_1034_4,plain,
( ! [U_4166,U_4164] :
( U_4166 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP245(U_4166,U_4164) )
& ! [U_4166,U_4164] :
( U_4164 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP245(U_4166,U_4164) )
& ! [U_4167,U_4165] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4165),U_4167) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4167 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4165 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_4166,U_4164] :
( sP245(U_4166,U_4164)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4164),U_4166) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245])],[f_1034_3]) ).
cnf(f_1034_5,plain,
( sP245(U_4166,U_4164)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4164),U_4166) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1034_4]) ).
cnf(f_1034_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4165),U_4167) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4167 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4165 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1034_4]) ).
cnf(f_1034_7,plain,
( U_4164 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP245(U_4166,U_4164) ),
inference(clausify,[status(thm)],[f_1034_4]) ).
cnf(f_1034_8,plain,
( U_4166 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP245(U_4166,U_4164) ),
inference(clausify,[status(thm)],[f_1034_4]) ).
fof(f_1035_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
| ( ! [B_j] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
| V_m_2 != hAPP(c_Nat_OSuc,B_j) )
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
& V_m_2 = hAPP(c_Nat_OSuc,B_j) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).
fof(f_1035_2,plain,
! [U_4171,U_4170] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4170),hAPP(c_Nat_OSuc,U_4171)))
| ( ! [U_4169] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4169),U_4171))
| U_4170 != hAPP(c_Nat_OSuc,U_4169) )
& U_4170 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_4168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4168),U_4171))
& U_4170 = hAPP(c_Nat_OSuc,U_4168) )
| U_4170 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4170),hAPP(c_Nat_OSuc,U_4171))) ) ),
inference(variable_rename,[status(thm)],[f_1035_1]) ).
fof(f_1035_3,plain,
( ! [U_4175,U_4173] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4173),hAPP(c_Nat_OSuc,U_4175)))
| ( ! [U_4169] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4169),U_4175))
| U_4173 != hAPP(c_Nat_OSuc,U_4169) )
& U_4173 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_4174,U_4172] :
( ? [U_4168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4168),U_4174))
& U_4172 = hAPP(c_Nat_OSuc,U_4168) )
| U_4172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4172),hAPP(c_Nat_OSuc,U_4174))) ) ),
inference(miniscope,[status(thm)],[f_1035_2]) ).
fof(f_1035_4,plain,
( ! [U_4175,U_4173] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4173),hAPP(c_Nat_OSuc,U_4175)))
| ( ! [U_4169] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4169),U_4175))
| U_4173 != hAPP(c_Nat_OSuc,U_4169) )
& U_4173 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_4174,U_4172] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK101(U_4174,U_4172)),U_4174))
& U_4172 = hAPP(c_Nat_OSuc,sK101(U_4174,U_4172)) )
| U_4172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4172),hAPP(c_Nat_OSuc,U_4174))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_4168,sK101(U_4174,U_4172))],[f_1035_3]) ).
fof(f_1035_5,plain,
( ! [U_4175,U_4173,U_4169] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4169),U_4175))
| U_4173 != hAPP(c_Nat_OSuc,U_4169)
| ~ sP247(U_4175,U_4173,U_4169) )
& ! [U_4175,U_4173,U_4169] :
( U_4173 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP247(U_4175,U_4173,U_4169) )
& ! [U_4172,U_4174] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK101(U_4174,U_4172)),U_4174))
| ~ sP246(U_4172,U_4174) )
& ! [U_4172,U_4174] :
( U_4172 = hAPP(c_Nat_OSuc,sK101(U_4174,U_4172))
| ~ sP246(U_4172,U_4174) )
& ! [U_4175,U_4173,U_4169] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4173),hAPP(c_Nat_OSuc,U_4175)))
| sP247(U_4175,U_4173,U_4169) )
& ! [U_4172,U_4174] :
( sP246(U_4172,U_4174)
| U_4172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4172),hAPP(c_Nat_OSuc,U_4174))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246,sP247])],[f_1035_4]) ).
cnf(f_1035_6,plain,
( sP246(U_4172,U_4174)
| U_4172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4172),hAPP(c_Nat_OSuc,U_4174))) ),
inference(clausify,[status(thm)],[f_1035_5]) ).
cnf(f_1035_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4173),hAPP(c_Nat_OSuc,U_4175)))
| sP247(U_4175,U_4173,U_4169) ),
inference(clausify,[status(thm)],[f_1035_5]) ).
cnf(f_1035_8,plain,
( U_4172 = hAPP(c_Nat_OSuc,sK101(U_4174,U_4172))
| ~ sP246(U_4172,U_4174) ),
inference(clausify,[status(thm)],[f_1035_5]) ).
cnf(f_1035_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK101(U_4174,U_4172)),U_4174))
| ~ sP246(U_4172,U_4174) ),
inference(clausify,[status(thm)],[f_1035_5]) ).
cnf(f_1035_10,plain,
( U_4173 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP247(U_4175,U_4173,U_4169) ),
inference(clausify,[status(thm)],[f_1035_5]) ).
cnf(f_1035_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4169),U_4175))
| U_4173 != hAPP(c_Nat_OSuc,U_4169)
| ~ sP247(U_4175,U_4173,U_4169) ),
inference(clausify,[status(thm)],[f_1035_5]) ).
fof(f_1036_1,plain,
! [V_n_2] :
( ( 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))))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc0]) ).
fof(f_1036_2,plain,
! [U_4176] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4176),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_4176 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_4176 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4176),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[f_1036_1]) ).
fof(f_1036_3,plain,
( ! [U_4178] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4178),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_4178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_4177] :
( U_4177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4177),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(miniscope,[status(thm)],[f_1036_2]) ).
fof(f_1036_4,plain,
( ! [U_4178] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4178),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_4178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_4177] :
( U_4177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4177),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(definitional_conversion,[status(esa)],[f_1036_3]) ).
cnf(f_1036_5,plain,
( U_4177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4177),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_1036_4]) ).
cnf(f_1036_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4178),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_4178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1036_4]) ).
fof(f_1037_1,plain,
! [V_n_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| ! [B_m] : V_n_2 != hAPP(c_Nat_OSuc,B_m) )
& ( ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).
fof(f_1037_2,plain,
! [U_4181] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4181))
| ! [U_4180] : U_4181 != hAPP(c_Nat_OSuc,U_4180) )
& ( ? [U_4179] : U_4181 = hAPP(c_Nat_OSuc,U_4179)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4181)) ) ),
inference(variable_rename,[status(thm)],[f_1037_1]) ).
fof(f_1037_3,plain,
( ! [U_4183] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4183))
| ! [U_4180] : U_4183 != hAPP(c_Nat_OSuc,U_4180) )
& ! [U_4182] :
( ? [U_4179] : U_4182 = hAPP(c_Nat_OSuc,U_4179)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4182)) ) ),
inference(miniscope,[status(thm)],[f_1037_2]) ).
fof(f_1037_4,plain,
( ! [U_4183] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4183))
| ! [U_4180] : U_4183 != hAPP(c_Nat_OSuc,U_4180) )
& ! [U_4182] :
( U_4182 = hAPP(c_Nat_OSuc,sK102(U_4182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4182)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_4179,sK102(U_4182))],[f_1037_3]) ).
fof(f_1037_5,plain,
( ! [U_4183,U_4180] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4183))
| U_4183 != hAPP(c_Nat_OSuc,U_4180) )
& ! [U_4182] :
( U_4182 = hAPP(c_Nat_OSuc,sK102(U_4182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4182)) ) ),
inference(definitional_conversion,[status(esa)],[f_1037_4]) ).
cnf(f_1037_6,plain,
( U_4182 = hAPP(c_Nat_OSuc,sK102(U_4182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4182)) ),
inference(clausify,[status(thm)],[f_1037_5]) ).
cnf(f_1037_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4183))
| U_4183 != hAPP(c_Nat_OSuc,U_4180) ),
inference(clausify,[status(thm)],[f_1037_5]) ).
fof(f_1038_1,plain,
! [V_n_2,V_m_2] :
( ( 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)
| ( ( V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).
fof(f_1038_2,plain,
! [U_4185,U_4184] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4184),U_4185)
| ( ( U_4185 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4184 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_4185 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4184 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_4185 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_4184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_4185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4184 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4184),U_4185) ) ),
inference(variable_rename,[status(thm)],[f_1038_1]) ).
fof(f_1038_3,plain,
( ! [U_4189,U_4187] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4187),U_4189)
| ( ( U_4189 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4187 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_4189 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4187 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_4188,U_4186] :
( ( U_4188 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_4186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_4188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4186 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4186),U_4188) ) ),
inference(miniscope,[status(thm)],[f_1038_2]) ).
fof(f_1038_4,plain,
( ! [U_4187,U_4189] :
( U_4189 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4187 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP250(U_4187,U_4189) )
& ! [U_4187,U_4189] :
( U_4189 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4187 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP250(U_4187,U_4189) )
& ! [U_4188,U_4186] :
( U_4188 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP249(U_4188,U_4186) )
& ! [U_4188,U_4186] :
( U_4186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP249(U_4188,U_4186) )
& ! [U_4188,U_4186] :
( U_4188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP248(U_4188,U_4186) )
& ! [U_4188,U_4186] :
( U_4186 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP248(U_4188,U_4186) )
& ! [U_4187,U_4189] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4187),U_4189)
| sP250(U_4187,U_4189) )
& ! [U_4188,U_4186] :
( sP249(U_4188,U_4186)
| sP248(U_4188,U_4186)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4186),U_4188) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248,sP249,sP250])],[f_1038_3]) ).
cnf(f_1038_5,plain,
( sP249(U_4188,U_4186)
| sP248(U_4188,U_4186)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4186),U_4188) ),
inference(clausify,[status(thm)],[f_1038_4]) ).
cnf(f_1038_6,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4187),U_4189)
| sP250(U_4187,U_4189) ),
inference(clausify,[status(thm)],[f_1038_4]) ).
cnf(f_1038_7,plain,
( U_4186 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP248(U_4188,U_4186) ),
inference(clausify,[status(thm)],[f_1038_4]) ).
cnf(f_1038_8,plain,
( U_4188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP248(U_4188,U_4186) ),
inference(clausify,[status(thm)],[f_1038_4]) ).
cnf(f_1038_9,plain,
( U_4186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP249(U_4188,U_4186) ),
inference(clausify,[status(thm)],[f_1038_4]) ).
cnf(f_1038_10,plain,
( U_4188 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP249(U_4188,U_4186) ),
inference(clausify,[status(thm)],[f_1038_4]) ).
cnf(f_1038_11,plain,
( U_4189 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4187 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP250(U_4187,U_4189) ),
inference(clausify,[status(thm)],[f_1038_4]) ).
cnf(f_1038_12,plain,
( U_4189 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4187 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP250(U_4187,U_4189) ),
inference(clausify,[status(thm)],[f_1038_4]) ).
fof(f_1039_1,plain,
! [V_n_2,V_m_2] :
( ( 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))
| ( ( V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = 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) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).
fof(f_1039_2,plain,
! [U_4191,U_4190] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4190),U_4191) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_4191 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4190 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_4191 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4190 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_4191 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_4190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_4191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4190 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4190),U_4191) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1039_1]) ).
fof(f_1039_3,plain,
( ! [U_4195,U_4193] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4193),U_4195) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_4195 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4193 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_4195 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4193 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_4194,U_4192] :
( ( U_4194 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_4192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_4194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4192 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4192),U_4194) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1039_2]) ).
fof(f_1039_4,plain,
( ! [U_4195,U_4193] :
( U_4195 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4193 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP253(U_4195,U_4193) )
& ! [U_4195,U_4193] :
( U_4195 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4193 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP253(U_4195,U_4193) )
& ! [U_4192,U_4194] :
( U_4194 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP252(U_4192,U_4194) )
& ! [U_4192,U_4194] :
( U_4192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP252(U_4192,U_4194) )
& ! [U_4192,U_4194] :
( U_4194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP251(U_4192,U_4194) )
& ! [U_4192,U_4194] :
( U_4192 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP251(U_4192,U_4194) )
& ! [U_4195,U_4193] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4193),U_4195) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP253(U_4195,U_4193) )
& ! [U_4192,U_4194] :
( sP252(U_4192,U_4194)
| sP251(U_4192,U_4194)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4192),U_4194) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251,sP252,sP253])],[f_1039_3]) ).
cnf(f_1039_5,plain,
( sP252(U_4192,U_4194)
| sP251(U_4192,U_4194)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4192),U_4194) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1039_4]) ).
cnf(f_1039_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4193),U_4195) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP253(U_4195,U_4193) ),
inference(clausify,[status(thm)],[f_1039_4]) ).
cnf(f_1039_7,plain,
( U_4192 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP251(U_4192,U_4194) ),
inference(clausify,[status(thm)],[f_1039_4]) ).
cnf(f_1039_8,plain,
( U_4194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP251(U_4192,U_4194) ),
inference(clausify,[status(thm)],[f_1039_4]) ).
cnf(f_1039_9,plain,
( U_4192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP252(U_4192,U_4194) ),
inference(clausify,[status(thm)],[f_1039_4]) ).
cnf(f_1039_10,plain,
( U_4194 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP252(U_4192,U_4194) ),
inference(clausify,[status(thm)],[f_1039_4]) ).
cnf(f_1039_11,plain,
( U_4195 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4193 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP253(U_4195,U_4193) ),
inference(clausify,[status(thm)],[f_1039_4]) ).
cnf(f_1039_12,plain,
( U_4195 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4193 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP253(U_4195,U_4193) ),
inference(clausify,[status(thm)],[f_1039_4]) ).
fof(f_1040_1,plain,
! [V_n] :
( 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
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred]) ).
fof(f_1040_2,plain,
! [U_4196] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4196),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_4196
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4196)) ),
inference(variable_rename,[status(thm)],[f_1040_1]) ).
fof(f_1040_3,plain,
! [U_4196] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4196),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_4196
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4196)) ),
inference(definitional_conversion,[status(esa)],[f_1040_2]) ).
cnf(f_1040_4,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4196),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_4196
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4196)) ),
inference(clausify,[status(thm)],[f_1040_3]) ).
fof(f_1041_1,plain,
! [V_i,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__less]) ).
fof(f_1041_2,plain,
! [U_4198,U_4197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4197),hAPP(c_Nat_OSuc,U_4198))),U_4197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4197)) ),
inference(variable_rename,[status(thm)],[f_1041_1]) ).
fof(f_1041_3,plain,
! [U_4197,U_4198] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4197),hAPP(c_Nat_OSuc,U_4198))),U_4197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4197)) ),
inference(definitional_conversion,[status(esa)],[f_1041_2]) ).
cnf(f_1041_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4197),hAPP(c_Nat_OSuc,U_4198))),U_4197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4197)) ),
inference(clausify,[status(thm)],[f_1041_3]) ).
fof(f_1042_1,plain,
! [V_m,V_n] :
( 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)))
| ~ 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))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n]) ).
fof(f_1042_2,plain,
! [U_4200,U_4199] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4200),U_4199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4199)) ),
inference(variable_rename,[status(thm)],[f_1042_1]) ).
fof(f_1042_3,plain,
! [U_4199,U_4200] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4200),U_4199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4199)) ),
inference(definitional_conversion,[status(esa)],[f_1042_2]) ).
cnf(f_1042_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4200),U_4199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4199)) ),
inference(clausify,[status(thm)],[f_1042_3]) ).
fof(f_1043_1,plain,
! [V_m,V_n] :
( 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)))
| ~ 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))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m]) ).
fof(f_1043_2,plain,
! [U_4202,U_4201] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4201),U_4202)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4201)) ),
inference(variable_rename,[status(thm)],[f_1043_1]) ).
fof(f_1043_3,plain,
! [U_4201,U_4202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4201),U_4202)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4201)) ),
inference(definitional_conversion,[status(esa)],[f_1043_2]) ).
cnf(f_1043_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4201),U_4202)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4201)) ),
inference(clausify,[status(thm)],[f_1043_3]) ).
fof(f_1044_1,plain,
! [V_m,V_n] :
( 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)))
| ~ 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))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_one__less__mult]) ).
fof(f_1044_2,plain,
! [U_4204,U_4203] :
( 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),U_4204),U_4203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4204))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4203)) ),
inference(variable_rename,[status(thm)],[f_1044_1]) ).
fof(f_1044_3,plain,
! [U_4203,U_4204] :
( 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),U_4204),U_4203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4204))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4203)) ),
inference(definitional_conversion,[status(esa)],[f_1044_2]) ).
cnf(f_1044_4,plain,
( 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),U_4204),U_4203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4204))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4203)) ),
inference(clausify,[status(thm)],[f_1044_3]) ).
fof(f_1045_1,plain,
! [V_n_2,V_m_2] :
( ( 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)))
| ~ 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))
| ~ 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)) )
& ( ( 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))
& 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)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).
fof(f_1045_2,plain,
! [U_4206,U_4205] :
( ( 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),U_4205),U_4206)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4206))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4205)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4206))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4205)) )
| ~ 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),U_4205),U_4206))) ) ),
inference(variable_rename,[status(thm)],[f_1045_1]) ).
fof(f_1045_3,plain,
( ! [U_4210,U_4208] :
( 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),U_4208),U_4210)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4208)) )
& ! [U_4209,U_4207] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4209))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4207)) )
| ~ 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),U_4207),U_4209))) ) ),
inference(miniscope,[status(thm)],[f_1045_2]) ).
fof(f_1045_4,plain,
( ! [U_4209,U_4207] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4209))
| ~ sP254(U_4209,U_4207) )
& ! [U_4209,U_4207] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4207))
| ~ sP254(U_4209,U_4207) )
& ! [U_4210,U_4208] :
( 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),U_4208),U_4210)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4208)) )
& ! [U_4209,U_4207] :
( sP254(U_4209,U_4207)
| ~ 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),U_4207),U_4209))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_1045_3]) ).
cnf(f_1045_5,plain,
( sP254(U_4209,U_4207)
| ~ 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),U_4207),U_4209))) ),
inference(clausify,[status(thm)],[f_1045_4]) ).
cnf(f_1045_6,plain,
( 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),U_4208),U_4210)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4208)) ),
inference(clausify,[status(thm)],[f_1045_4]) ).
cnf(f_1045_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4207))
| ~ sP254(U_4209,U_4207) ),
inference(clausify,[status(thm)],[f_1045_4]) ).
cnf(f_1045_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4209))
| ~ sP254(U_4209,U_4207) ),
inference(clausify,[status(thm)],[f_1045_4]) ).
fof(f_1046_1,plain,
! [V_f_2,V_A_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_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [B_x] :
( ? [B_xa] :
( hAPP(V_f_2,B_xa) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& B_x != B_xa
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
| hAPP(V_f_2,B_x) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( ! [B_xa] :
( hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| B_x = B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
& hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| 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)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__Suc0__iff]) ).
fof(f_1046_2,plain,
! [U_4217,U_4216,U_4215] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_4214] :
( ? [U_4213] :
( hAPP(U_4217,U_4213) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4214 != U_4213
& hBOOL(hAPP(hAPP(c_member(U_4215),U_4213),U_4216)) )
| hAPP(U_4217,U_4214) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4214),U_4216)) ) )
& ( ? [U_4212] :
( ! [U_4211] :
( hAPP(U_4217,U_4211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4212 = U_4211
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4211),U_4216)) )
& hAPP(U_4217,U_4212) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_4215),U_4212),U_4216)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4215),U_4216)) ),
inference(variable_rename,[status(thm)],[f_1046_1]) ).
fof(f_1046_3,plain,
! [U_4217,U_4216,U_4215] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_4214] :
( ? [U_4213] :
( hAPP(U_4217,U_4213) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4214 != U_4213
& hBOOL(hAPP(hAPP(c_member(U_4215),U_4213),U_4216)) )
| hAPP(U_4217,U_4214) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4214),U_4216)) ) )
& ( ( ! [U_4211] :
( hAPP(U_4217,U_4211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK103(U_4217,U_4216,U_4215) = U_4211
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4211),U_4216)) )
& hAPP(U_4217,sK103(U_4217,U_4216,U_4215)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_4215),sK103(U_4217,U_4216,U_4215)),U_4216)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4215),U_4216)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_4212,sK103(U_4217,U_4216,U_4215))],[f_1046_2]) ).
fof(f_1046_4,plain,
! [U_4217,U_4216,U_4215] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_4214] :
( ( hAPP(U_4217,sK104(U_4217,U_4216,U_4215,U_4214)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4214 != sK104(U_4217,U_4216,U_4215,U_4214)
& hBOOL(hAPP(hAPP(c_member(U_4215),sK104(U_4217,U_4216,U_4215,U_4214)),U_4216)) )
| hAPP(U_4217,U_4214) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4214),U_4216)) ) )
& ( ( ! [U_4211] :
( hAPP(U_4217,U_4211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK103(U_4217,U_4216,U_4215) = U_4211
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4211),U_4216)) )
& hAPP(U_4217,sK103(U_4217,U_4216,U_4215)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_4215),sK103(U_4217,U_4216,U_4215)),U_4216)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4215),U_4216)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_4213,sK104(U_4217,U_4216,U_4215,U_4214))],[f_1046_3]) ).
fof(f_1046_5,plain,
( ! [U_4214,U_4215,U_4216,U_4217] :
( hAPP(U_4217,sK104(U_4217,U_4216,U_4215,U_4214)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP256(U_4214,U_4215,U_4216,U_4217) )
& ! [U_4214,U_4215,U_4216,U_4217] :
( U_4214 != sK104(U_4217,U_4216,U_4215,U_4214)
| ~ sP256(U_4214,U_4215,U_4216,U_4217) )
& ! [U_4214,U_4215,U_4216,U_4217] :
( hBOOL(hAPP(hAPP(c_member(U_4215),sK104(U_4217,U_4216,U_4215,U_4214)),U_4216))
| ~ sP256(U_4214,U_4215,U_4216,U_4217) )
& ! [U_4211,U_4215,U_4216,U_4217] :
( hAPP(U_4217,U_4211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK103(U_4217,U_4216,U_4215) = U_4211
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4211),U_4216))
| ~ sP255(U_4211,U_4215,U_4216,U_4217) )
& ! [U_4211,U_4215,U_4216,U_4217] :
( hAPP(U_4217,sK103(U_4217,U_4216,U_4215)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP255(U_4211,U_4215,U_4216,U_4217) )
& ! [U_4211,U_4215,U_4216,U_4217] :
( hBOOL(hAPP(hAPP(c_member(U_4215),sK103(U_4217,U_4216,U_4215)),U_4216))
| ~ sP255(U_4211,U_4215,U_4216,U_4217) )
& ! [U_4211,U_4214,U_4215,U_4216,U_4217] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP256(U_4214,U_4215,U_4216,U_4217)
| hAPP(U_4217,U_4214) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4214),U_4216))
| ~ sP257(U_4211,U_4214,U_4215,U_4216,U_4217) )
& ! [U_4211,U_4214,U_4215,U_4216,U_4217] :
( sP255(U_4211,U_4215,U_4216,U_4217)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP257(U_4211,U_4214,U_4215,U_4216,U_4217) )
& ! [U_4211,U_4214,U_4215,U_4216,U_4217] :
( sP257(U_4211,U_4214,U_4215,U_4216,U_4217)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4215),U_4216)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255,sP256,sP257])],[f_1046_4]) ).
cnf(f_1046_6,plain,
( sP257(U_4211,U_4214,U_4215,U_4216,U_4217)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4215),U_4216)) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
cnf(f_1046_7,plain,
( sP255(U_4211,U_4215,U_4216,U_4217)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP257(U_4211,U_4214,U_4215,U_4216,U_4217) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
cnf(f_1046_8,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4215,tc_Nat_Onat),U_4217),U_4216) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP256(U_4214,U_4215,U_4216,U_4217)
| hAPP(U_4217,U_4214) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4214),U_4216))
| ~ sP257(U_4211,U_4214,U_4215,U_4216,U_4217) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
cnf(f_1046_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_4215),sK103(U_4217,U_4216,U_4215)),U_4216))
| ~ sP255(U_4211,U_4215,U_4216,U_4217) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
cnf(f_1046_10,plain,
( hAPP(U_4217,sK103(U_4217,U_4216,U_4215)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP255(U_4211,U_4215,U_4216,U_4217) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
cnf(f_1046_11,plain,
( hAPP(U_4217,U_4211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK103(U_4217,U_4216,U_4215) = U_4211
| ~ hBOOL(hAPP(hAPP(c_member(U_4215),U_4211),U_4216))
| ~ sP255(U_4211,U_4215,U_4216,U_4217) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
cnf(f_1046_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_4215),sK104(U_4217,U_4216,U_4215,U_4214)),U_4216))
| ~ sP256(U_4214,U_4215,U_4216,U_4217) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
cnf(f_1046_13,plain,
( U_4214 != sK104(U_4217,U_4216,U_4215,U_4214)
| ~ sP256(U_4214,U_4215,U_4216,U_4217) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
cnf(f_1046_14,plain,
( hAPP(U_4217,sK104(U_4217,U_4216,U_4215,U_4214)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP256(U_4214,U_4215,U_4216,U_4217) ),
inference(clausify,[status(thm)],[f_1046_5]) ).
fof(f_1047_1,plain,
! [V_n_2,V_m_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).
fof(f_1047_2,plain,
! [U_4219,U_4218] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4218),U_4219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4219),hAPP(c_Nat_OSuc,U_4218))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4219),hAPP(c_Nat_OSuc,U_4218)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4218),U_4219)) ) ),
inference(variable_rename,[status(thm)],[f_1047_1]) ).
fof(f_1047_3,plain,
( ! [U_4223,U_4221] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4221),U_4223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4223),hAPP(c_Nat_OSuc,U_4221))) )
& ! [U_4222,U_4220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4222),hAPP(c_Nat_OSuc,U_4220)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4220),U_4222)) ) ),
inference(miniscope,[status(thm)],[f_1047_2]) ).
fof(f_1047_4,plain,
( ! [U_4221,U_4223] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4221),U_4223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4223),hAPP(c_Nat_OSuc,U_4221))) )
& ! [U_4222,U_4220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4222),hAPP(c_Nat_OSuc,U_4220)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4220),U_4222)) ) ),
inference(definitional_conversion,[status(esa)],[f_1047_3]) ).
cnf(f_1047_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4222),hAPP(c_Nat_OSuc,U_4220)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4220),U_4222)) ),
inference(clausify,[status(thm)],[f_1047_4]) ).
cnf(f_1047_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4221),U_4223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4223),hAPP(c_Nat_OSuc,U_4221))) ),
inference(clausify,[status(thm)],[f_1047_4]) ).
fof(f_1048_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
| ( V_m_2 != V_n_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
& ( V_m_2 = V_n_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).
fof(f_1048_2,plain,
! [U_4225,U_4224] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4224),hAPP(c_Nat_OSuc,U_4225)))
| ( U_4224 != U_4225
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4224),U_4225)) ) )
& ( U_4224 = U_4225
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4224),U_4225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4224),hAPP(c_Nat_OSuc,U_4225))) ) ),
inference(variable_rename,[status(thm)],[f_1048_1]) ).
fof(f_1048_3,plain,
( ! [U_4229,U_4227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4227),hAPP(c_Nat_OSuc,U_4229)))
| ( U_4227 != U_4229
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4227),U_4229)) ) )
& ! [U_4228,U_4226] :
( U_4226 = U_4228
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4226),U_4228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4226),hAPP(c_Nat_OSuc,U_4228))) ) ),
inference(miniscope,[status(thm)],[f_1048_2]) ).
fof(f_1048_4,plain,
( ! [U_4227,U_4229] :
( U_4227 != U_4229
| ~ sP258(U_4227,U_4229) )
& ! [U_4227,U_4229] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4227),U_4229))
| ~ sP258(U_4227,U_4229) )
& ! [U_4227,U_4229] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4227),hAPP(c_Nat_OSuc,U_4229)))
| sP258(U_4227,U_4229) )
& ! [U_4226,U_4228] :
( U_4226 = U_4228
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4226),U_4228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4226),hAPP(c_Nat_OSuc,U_4228))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_1048_3]) ).
cnf(f_1048_5,plain,
( U_4226 = U_4228
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4226),U_4228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4226),hAPP(c_Nat_OSuc,U_4228))) ),
inference(clausify,[status(thm)],[f_1048_4]) ).
cnf(f_1048_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4227),hAPP(c_Nat_OSuc,U_4229)))
| sP258(U_4227,U_4229) ),
inference(clausify,[status(thm)],[f_1048_4]) ).
cnf(f_1048_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4227),U_4229))
| ~ sP258(U_4227,U_4229) ),
inference(clausify,[status(thm)],[f_1048_4]) ).
cnf(f_1048_8,plain,
( U_4227 != U_4229
| ~ sP258(U_4227,U_4229) ),
inference(clausify,[status(thm)],[f_1048_4]) ).
fof(f_1049_1,plain,
! [V_n_2,V_m_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).
fof(f_1049_2,plain,
! [U_4231,U_4230] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4230)),hAPP(c_Nat_OSuc,U_4231)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4230),U_4231)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4230),U_4231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4230)),hAPP(c_Nat_OSuc,U_4231))) ) ),
inference(variable_rename,[status(thm)],[f_1049_1]) ).
fof(f_1049_3,plain,
( ! [U_4235,U_4233] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4233)),hAPP(c_Nat_OSuc,U_4235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),U_4235)) )
& ! [U_4234,U_4232] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4232),U_4234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4232)),hAPP(c_Nat_OSuc,U_4234))) ) ),
inference(miniscope,[status(thm)],[f_1049_2]) ).
fof(f_1049_4,plain,
( ! [U_4235,U_4233] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4233)),hAPP(c_Nat_OSuc,U_4235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),U_4235)) )
& ! [U_4234,U_4232] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4232),U_4234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4232)),hAPP(c_Nat_OSuc,U_4234))) ) ),
inference(definitional_conversion,[status(esa)],[f_1049_3]) ).
cnf(f_1049_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4232),U_4234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4232)),hAPP(c_Nat_OSuc,U_4234))) ),
inference(clausify,[status(thm)],[f_1049_4]) ).
cnf(f_1049_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4233)),hAPP(c_Nat_OSuc,U_4235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),U_4235)) ),
inference(clausify,[status(thm)],[f_1049_4]) ).
fof(f_1050_1,plain,
! [V_m_2,V_n_2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
| V_n_2 != V_m_2 )
& ( V_n_2 = V_m_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(f_1050_2,plain,
! [U_4237,U_4236] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),hAPP(c_Nat_OSuc,U_4237)))
| U_4236 != U_4237 )
& ( U_4236 = U_4237
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),hAPP(c_Nat_OSuc,U_4237))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),U_4237)) ),
inference(variable_rename,[status(thm)],[f_1050_1]) ).
fof(f_1050_3,plain,
( ! [U_4237,U_4236] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),hAPP(c_Nat_OSuc,U_4237)))
| U_4236 != U_4237
| ~ sP259(U_4237,U_4236) )
& ! [U_4237,U_4236] :
( U_4236 = U_4237
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),hAPP(c_Nat_OSuc,U_4237)))
| ~ sP259(U_4237,U_4236) )
& ! [U_4237,U_4236] :
( sP259(U_4237,U_4236)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),U_4237)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259])],[f_1050_2]) ).
cnf(f_1050_4,plain,
( sP259(U_4237,U_4236)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),U_4237)) ),
inference(clausify,[status(thm)],[f_1050_3]) ).
cnf(f_1050_5,plain,
( U_4236 = U_4237
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),hAPP(c_Nat_OSuc,U_4237)))
| ~ sP259(U_4237,U_4236) ),
inference(clausify,[status(thm)],[f_1050_3]) ).
cnf(f_1050_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4236),hAPP(c_Nat_OSuc,U_4237)))
| U_4236 != U_4237
| ~ sP259(U_4237,U_4236) ),
inference(clausify,[status(thm)],[f_1050_3]) ).
fof(f_1051_1,plain,
! [V_m,V_n] :
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_less__antisym]) ).
fof(f_1051_2,plain,
! [U_4239,U_4238] :
( U_4239 = U_4238
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4238),hAPP(c_Nat_OSuc,U_4239)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4238),U_4239)) ),
inference(variable_rename,[status(thm)],[f_1051_1]) ).
fof(f_1051_3,plain,
! [U_4239,U_4238] :
( U_4239 = U_4238
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4238),hAPP(c_Nat_OSuc,U_4239)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4238),U_4239)) ),
inference(definitional_conversion,[status(esa)],[f_1051_2]) ).
cnf(f_1051_4,plain,
( U_4239 = U_4238
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4238),hAPP(c_Nat_OSuc,U_4239)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4238),U_4239)) ),
inference(clausify,[status(thm)],[f_1051_3]) ).
fof(f_1052_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_less__SucI]) ).
fof(f_1052_2,plain,
! [U_4241,U_4240] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4240),hAPP(c_Nat_OSuc,U_4241)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4240),U_4241)) ),
inference(variable_rename,[status(thm)],[f_1052_1]) ).
fof(f_1052_3,plain,
! [U_4240,U_4241] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4240),hAPP(c_Nat_OSuc,U_4241)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4240),U_4241)) ),
inference(definitional_conversion,[status(esa)],[f_1052_2]) ).
cnf(f_1052_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4240),hAPP(c_Nat_OSuc,U_4241)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4240),U_4241)) ),
inference(clausify,[status(thm)],[f_1052_3]) ).
fof(f_1053_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
| hAPP(c_Nat_OSuc,V_m) = V_n
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessI]) ).
fof(f_1053_2,plain,
! [U_4243,U_4242] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4242)),U_4243))
| hAPP(c_Nat_OSuc,U_4242) = U_4243
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4243)) ),
inference(variable_rename,[status(thm)],[f_1053_1]) ).
fof(f_1053_3,plain,
! [U_4242,U_4243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4242)),U_4243))
| hAPP(c_Nat_OSuc,U_4242) = U_4243
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4243)) ),
inference(definitional_conversion,[status(esa)],[f_1053_2]) ).
cnf(f_1053_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4242)),U_4243))
| hAPP(c_Nat_OSuc,U_4242) = U_4243
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4243)) ),
inference(clausify,[status(thm)],[f_1053_3]) ).
fof(f_1054_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_less__trans__Suc]) ).
fof(f_1054_2,plain,
! [U_4246,U_4245,U_4244] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4244)),U_4246))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4245),U_4246))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4244),U_4245)) ),
inference(variable_rename,[status(thm)],[f_1054_1]) ).
fof(f_1054_3,plain,
! [U_4244,U_4245,U_4246] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4244)),U_4246))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4245),U_4246))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4244),U_4245)) ),
inference(definitional_conversion,[status(esa)],[f_1054_2]) ).
cnf(f_1054_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4244)),U_4246))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4245),U_4246))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4244),U_4245)) ),
inference(clausify,[status(thm)],[f_1054_3]) ).
fof(f_1055_1,plain,
! [V_n,V_m] :
( V_m = V_n
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
inference(fof_nnf,[status(thm)],[fact_less__SucE]) ).
fof(f_1055_2,plain,
! [U_4248,U_4247] :
( U_4247 = U_4248
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4247),U_4248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4247),hAPP(c_Nat_OSuc,U_4248))) ),
inference(variable_rename,[status(thm)],[f_1055_1]) ).
fof(f_1055_3,plain,
! [U_4247,U_4248] :
( U_4247 = U_4248
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4247),U_4248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4247),hAPP(c_Nat_OSuc,U_4248))) ),
inference(definitional_conversion,[status(esa)],[f_1055_2]) ).
cnf(f_1055_4,plain,
( U_4247 = U_4248
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4247),U_4248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4247),hAPP(c_Nat_OSuc,U_4248))) ),
inference(clausify,[status(thm)],[f_1055_3]) ).
fof(f_1056_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessD]) ).
fof(f_1056_2,plain,
! [U_4250,U_4249] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4249),U_4250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4249)),U_4250)) ),
inference(variable_rename,[status(thm)],[f_1056_1]) ).
fof(f_1056_3,plain,
! [U_4249,U_4250] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4249),U_4250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4249)),U_4250)) ),
inference(definitional_conversion,[status(esa)],[f_1056_2]) ).
cnf(f_1056_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4249),U_4250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4249)),U_4250)) ),
inference(clausify,[status(thm)],[f_1056_3]) ).
fof(f_1057_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD]) ).
fof(f_1057_2,plain,
! [U_4252,U_4251] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4251),U_4252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4251)),hAPP(c_Nat_OSuc,U_4252))) ),
inference(variable_rename,[status(thm)],[f_1057_1]) ).
fof(f_1057_3,plain,
! [U_4251,U_4252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4251),U_4252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4251)),hAPP(c_Nat_OSuc,U_4252))) ),
inference(definitional_conversion,[status(esa)],[f_1057_2]) ).
cnf(f_1057_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4251),U_4252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4251)),hAPP(c_Nat_OSuc,U_4252))) ),
inference(clausify,[status(thm)],[f_1057_3]) ).
fof(f_1058_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__shift]) ).
fof(f_1058_2,plain,
! [U_4254,U_4253] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4253)),U_4254) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4253),hAPP(c_Nat_OSuc,U_4254)),
inference(variable_rename,[status(thm)],[f_1058_1]) ).
fof(f_1058_3,plain,
! [U_4253,U_4254] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4253)),U_4254) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4253),hAPP(c_Nat_OSuc,U_4254)),
inference(definitional_conversion,[status(esa)],[f_1058_2]) ).
cnf(f_1058_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4253)),U_4254) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4253),hAPP(c_Nat_OSuc,U_4254)),
inference(clausify,[status(thm)],[f_1058_3]) ).
fof(f_1059_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__Suc]) ).
fof(f_1059_2,plain,
! [U_4256,U_4255] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4255)),U_4256) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4255),U_4256)),
inference(variable_rename,[status(thm)],[f_1059_1]) ).
fof(f_1059_3,plain,
! [U_4255,U_4256] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4255)),U_4256) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4255),U_4256)),
inference(definitional_conversion,[status(esa)],[f_1059_2]) ).
cnf(f_1059_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4255)),U_4256) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4255),U_4256)),
inference(clausify,[status(thm)],[f_1059_3]) ).
fof(f_1060_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__right]) ).
fof(f_1060_2,plain,
! [U_4258,U_4257] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4257),hAPP(c_Nat_OSuc,U_4258)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4257),U_4258)),
inference(variable_rename,[status(thm)],[f_1060_1]) ).
fof(f_1060_3,plain,
! [U_4257,U_4258] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4257),hAPP(c_Nat_OSuc,U_4258)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4257),U_4258)),
inference(definitional_conversion,[status(esa)],[f_1060_2]) ).
cnf(f_1060_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4257),hAPP(c_Nat_OSuc,U_4258)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4257),U_4258)),
inference(clausify,[status(thm)],[f_1060_3]) ).
fof(f_1061_1,plain,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)),
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(f_1061_2,plain,
! [U_4259] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4259)),U_4259)),
inference(variable_rename,[status(thm)],[f_1061_1]) ).
fof(f_1061_3,plain,
! [U_4259] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4259)),U_4259)),
inference(definitional_conversion,[status(esa)],[f_1061_2]) ).
cnf(f_1061_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4259)),U_4259)),
inference(clausify,[status(thm)],[f_1061_3]) ).
fof(f_1062_1,plain,
! [V_n_2,V_m_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).
fof(f_1062_2,plain,
! [U_4261,U_4260] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4260),U_4261))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4261)),U_4260)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4261)),U_4260))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4260),U_4261)) ) ),
inference(variable_rename,[status(thm)],[f_1062_1]) ).
fof(f_1062_3,plain,
( ! [U_4265,U_4263] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4263),U_4265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4265)),U_4263)) )
& ! [U_4264,U_4262] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4264)),U_4262))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4262),U_4264)) ) ),
inference(miniscope,[status(thm)],[f_1062_2]) ).
fof(f_1062_4,plain,
( ! [U_4263,U_4265] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4263),U_4265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4265)),U_4263)) )
& ! [U_4264,U_4262] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4264)),U_4262))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4262),U_4264)) ) ),
inference(definitional_conversion,[status(esa)],[f_1062_3]) ).
cnf(f_1062_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4264)),U_4262))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4262),U_4264)) ),
inference(clausify,[status(thm)],[f_1062_4]) ).
cnf(f_1062_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4263),U_4265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4265)),U_4263)) ),
inference(clausify,[status(thm)],[f_1062_4]) ).
fof(f_1063_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
| ( V_m_2 != hAPP(c_Nat_OSuc,V_n_2)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) )
& ( V_m_2 = hAPP(c_Nat_OSuc,V_n_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).
fof(f_1063_2,plain,
! [U_4267,U_4266] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4266),hAPP(c_Nat_OSuc,U_4267)))
| ( U_4266 != hAPP(c_Nat_OSuc,U_4267)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4266),U_4267)) ) )
& ( U_4266 = hAPP(c_Nat_OSuc,U_4267)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4266),U_4267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4266),hAPP(c_Nat_OSuc,U_4267))) ) ),
inference(variable_rename,[status(thm)],[f_1063_1]) ).
fof(f_1063_3,plain,
( ! [U_4271,U_4269] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4269),hAPP(c_Nat_OSuc,U_4271)))
| ( U_4269 != hAPP(c_Nat_OSuc,U_4271)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4269),U_4271)) ) )
& ! [U_4270,U_4268] :
( U_4268 = hAPP(c_Nat_OSuc,U_4270)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4268),U_4270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4268),hAPP(c_Nat_OSuc,U_4270))) ) ),
inference(miniscope,[status(thm)],[f_1063_2]) ).
fof(f_1063_4,plain,
( ! [U_4271,U_4269] :
( U_4269 != hAPP(c_Nat_OSuc,U_4271)
| ~ sP260(U_4271,U_4269) )
& ! [U_4271,U_4269] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4269),U_4271))
| ~ sP260(U_4271,U_4269) )
& ! [U_4271,U_4269] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4269),hAPP(c_Nat_OSuc,U_4271)))
| sP260(U_4271,U_4269) )
& ! [U_4270,U_4268] :
( U_4268 = hAPP(c_Nat_OSuc,U_4270)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4268),U_4270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4268),hAPP(c_Nat_OSuc,U_4270))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260])],[f_1063_3]) ).
cnf(f_1063_5,plain,
( U_4268 = hAPP(c_Nat_OSuc,U_4270)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4268),U_4270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4268),hAPP(c_Nat_OSuc,U_4270))) ),
inference(clausify,[status(thm)],[f_1063_4]) ).
cnf(f_1063_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4269),hAPP(c_Nat_OSuc,U_4271)))
| sP260(U_4271,U_4269) ),
inference(clausify,[status(thm)],[f_1063_4]) ).
cnf(f_1063_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4269),U_4271))
| ~ sP260(U_4271,U_4269) ),
inference(clausify,[status(thm)],[f_1063_4]) ).
cnf(f_1063_8,plain,
( U_4269 != hAPP(c_Nat_OSuc,U_4271)
| ~ sP260(U_4271,U_4269) ),
inference(clausify,[status(thm)],[f_1063_4]) ).
fof(f_1064_1,plain,
! [V_m_2,V_n_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).
fof(f_1064_2,plain,
! [U_4273,U_4272] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4272)),hAPP(c_Nat_OSuc,U_4273)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4272),U_4273)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4272),U_4273))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4272)),hAPP(c_Nat_OSuc,U_4273))) ) ),
inference(variable_rename,[status(thm)],[f_1064_1]) ).
fof(f_1064_3,plain,
( ! [U_4277,U_4275] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4275)),hAPP(c_Nat_OSuc,U_4277)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4275),U_4277)) )
& ! [U_4276,U_4274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4274),U_4276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4274)),hAPP(c_Nat_OSuc,U_4276))) ) ),
inference(miniscope,[status(thm)],[f_1064_2]) ).
fof(f_1064_4,plain,
( ! [U_4275,U_4277] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4275)),hAPP(c_Nat_OSuc,U_4277)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4275),U_4277)) )
& ! [U_4276,U_4274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4274),U_4276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4274)),hAPP(c_Nat_OSuc,U_4276))) ) ),
inference(definitional_conversion,[status(esa)],[f_1064_3]) ).
cnf(f_1064_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4274),U_4276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4274)),hAPP(c_Nat_OSuc,U_4276))) ),
inference(clausify,[status(thm)],[f_1064_4]) ).
cnf(f_1064_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4275)),hAPP(c_Nat_OSuc,U_4277)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4275),U_4277)) ),
inference(clausify,[status(thm)],[f_1064_4]) ).
fof(f_1065_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__SucI]) ).
fof(f_1065_2,plain,
! [U_4279,U_4278] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4278),hAPP(c_Nat_OSuc,U_4279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4278),U_4279)) ),
inference(variable_rename,[status(thm)],[f_1065_1]) ).
fof(f_1065_3,plain,
! [U_4279,U_4278] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4278),hAPP(c_Nat_OSuc,U_4279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4278),U_4279)) ),
inference(definitional_conversion,[status(esa)],[f_1065_2]) ).
cnf(f_1065_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4278),hAPP(c_Nat_OSuc,U_4279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4278),U_4279)) ),
inference(clausify,[status(thm)],[f_1065_3]) ).
fof(f_1066_1,plain,
! [V_n,V_m] :
( V_m = hAPP(c_Nat_OSuc,V_n)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
inference(fof_nnf,[status(thm)],[fact_le__SucE]) ).
fof(f_1066_2,plain,
! [U_4281,U_4280] :
( U_4280 = hAPP(c_Nat_OSuc,U_4281)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4280),U_4281))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4280),hAPP(c_Nat_OSuc,U_4281))) ),
inference(variable_rename,[status(thm)],[f_1066_1]) ).
fof(f_1066_3,plain,
! [U_4280,U_4281] :
( U_4280 = hAPP(c_Nat_OSuc,U_4281)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4280),U_4281))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4280),hAPP(c_Nat_OSuc,U_4281))) ),
inference(definitional_conversion,[status(esa)],[f_1066_2]) ).
cnf(f_1066_4,plain,
( U_4280 = hAPP(c_Nat_OSuc,U_4281)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4280),U_4281))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4280),hAPP(c_Nat_OSuc,U_4281))) ),
inference(clausify,[status(thm)],[f_1066_3]) ).
fof(f_1067_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leD]) ).
fof(f_1067_2,plain,
! [U_4283,U_4282] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4282),U_4283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4282)),U_4283)) ),
inference(variable_rename,[status(thm)],[f_1067_1]) ).
fof(f_1067_3,plain,
! [U_4282,U_4283] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4282),U_4283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4282)),U_4283)) ),
inference(definitional_conversion,[status(esa)],[f_1067_2]) ).
cnf(f_1067_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4282),U_4283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4282)),U_4283)) ),
inference(clausify,[status(thm)],[f_1067_3]) ).
fof(f_1068_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(f_1068_2,plain,
! [U_4285,U_4284] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4284)),hAPP(c_Nat_OSuc,U_4285)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4284),U_4285),
inference(variable_rename,[status(thm)],[f_1068_1]) ).
fof(f_1068_3,plain,
! [U_4284,U_4285] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4284)),hAPP(c_Nat_OSuc,U_4285)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4284),U_4285),
inference(definitional_conversion,[status(esa)],[f_1068_2]) ).
cnf(f_1068_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4284)),hAPP(c_Nat_OSuc,U_4285)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4284),U_4285),
inference(clausify,[status(thm)],[f_1068_3]) ).
fof(f_1069_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__diff]) ).
fof(f_1069_2,plain,
! [U_4288,U_4287,U_4286] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4286)),U_4287)),hAPP(c_Nat_OSuc,U_4288)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4286),U_4287)),U_4288),
inference(variable_rename,[status(thm)],[f_1069_1]) ).
fof(f_1069_3,plain,
! [U_4286,U_4287,U_4288] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4286)),U_4287)),hAPP(c_Nat_OSuc,U_4288)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4286),U_4287)),U_4288),
inference(definitional_conversion,[status(esa)],[f_1069_2]) ).
cnf(f_1069_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4286)),U_4287)),hAPP(c_Nat_OSuc,U_4288)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4286),U_4287)),U_4288),
inference(clausify,[status(thm)],[f_1069_3]) ).
fof(f_1070_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1]) ).
fof(f_1070_2,plain,
! [U_4291,U_4290,U_4289] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4289)),U_4290) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4289)),U_4291)
| U_4290 != U_4291 )
& ( U_4290 = U_4291
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4289)),U_4290) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4289)),U_4291) ) ),
inference(variable_rename,[status(thm)],[f_1070_1]) ).
fof(f_1070_3,plain,
( ! [U_4297,U_4295] :
( ! [U_4293] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4293)),U_4295) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4293)),U_4297)
| U_4295 != U_4297 )
& ! [U_4296,U_4294] :
( ! [U_4292] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4292)),U_4294) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4292)),U_4296)
| U_4294 = U_4296 ) ),
inference(miniscope,[status(thm)],[f_1070_2]) ).
fof(f_1070_4,plain,
( ! [U_4297,U_4293,U_4295] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4293)),U_4295) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4293)),U_4297)
| U_4295 != U_4297 )
& ! [U_4296,U_4294,U_4292] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4292)),U_4294) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4292)),U_4296)
| U_4294 = U_4296 ) ),
inference(definitional_conversion,[status(esa)],[f_1070_3]) ).
cnf(f_1070_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4292)),U_4294) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4292)),U_4296)
| U_4294 = U_4296 ),
inference(clausify,[status(thm)],[f_1070_4]) ).
cnf(f_1070_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4293)),U_4295) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4293)),U_4297)
| U_4295 != U_4297 ),
inference(clausify,[status(thm)],[f_1070_4]) ).
fof(f_1071_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_Groups_Omonoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__left]) ).
fof(f_1071_2,plain,
! [U_4299,U_4298] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4298),c_Groups_Ozero__class_Ozero(U_4298)),U_4299) = U_4299
| ~ class_Groups_Omonoid__add(U_4298) ),
inference(variable_rename,[status(thm)],[f_1071_1]) ).
fof(f_1071_3,plain,
! [U_4298,U_4299] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4298),c_Groups_Ozero__class_Ozero(U_4298)),U_4299) = U_4299
| ~ class_Groups_Omonoid__add(U_4298) ),
inference(definitional_conversion,[status(esa)],[f_1071_2]) ).
cnf(f_1071_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4298),c_Groups_Ozero__class_Ozero(U_4298)),U_4299) = U_4299
| ~ class_Groups_Omonoid__add(U_4298) ),
inference(clausify,[status(thm)],[f_1071_3]) ).
fof(f_1072_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0]) ).
fof(f_1072_2,plain,
! [U_4301,U_4300] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4300),c_Groups_Ozero__class_Ozero(U_4300)),U_4301) = U_4301
| ~ class_Groups_Ocomm__monoid__add(U_4300) ),
inference(variable_rename,[status(thm)],[f_1072_1]) ).
fof(f_1072_3,plain,
! [U_4300,U_4301] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4300),c_Groups_Ozero__class_Ozero(U_4300)),U_4301) = U_4301
| ~ class_Groups_Ocomm__monoid__add(U_4300) ),
inference(definitional_conversion,[status(esa)],[f_1072_2]) ).
cnf(f_1072_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4300),c_Groups_Ozero__class_Ozero(U_4300)),U_4301) = U_4301
| ~ class_Groups_Ocomm__monoid__add(U_4300) ),
inference(clausify,[status(thm)],[f_1072_3]) ).
fof(f_1073_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| c_Groups_Ozero__class_Ozero(T_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).
fof(f_1073_2,plain,
! [U_4303,U_4302] :
( ( ( c_Groups_Ozero__class_Ozero(U_4302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4302),U_4303),U_4303)
| U_4303 != c_Groups_Ozero__class_Ozero(U_4302) )
& ( U_4303 = c_Groups_Ozero__class_Ozero(U_4302)
| c_Groups_Ozero__class_Ozero(U_4302) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4302),U_4303),U_4303) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4302) ),
inference(variable_rename,[status(thm)],[f_1073_1]) ).
fof(f_1073_3,plain,
( ! [U_4302,U_4303] :
( c_Groups_Ozero__class_Ozero(U_4302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4302),U_4303),U_4303)
| U_4303 != c_Groups_Ozero__class_Ozero(U_4302)
| ~ sP261(U_4302,U_4303) )
& ! [U_4302,U_4303] :
( U_4303 = c_Groups_Ozero__class_Ozero(U_4302)
| c_Groups_Ozero__class_Ozero(U_4302) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4302),U_4303),U_4303)
| ~ sP261(U_4302,U_4303) )
& ! [U_4302,U_4303] :
( sP261(U_4302,U_4303)
| ~ class_Groups_Olinordered__ab__group__add(U_4302) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP261])],[f_1073_2]) ).
cnf(f_1073_4,plain,
( sP261(U_4302,U_4303)
| ~ class_Groups_Olinordered__ab__group__add(U_4302) ),
inference(clausify,[status(thm)],[f_1073_3]) ).
cnf(f_1073_5,plain,
( U_4303 = c_Groups_Ozero__class_Ozero(U_4302)
| c_Groups_Ozero__class_Ozero(U_4302) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4302),U_4303),U_4303)
| ~ sP261(U_4302,U_4303) ),
inference(clausify,[status(thm)],[f_1073_3]) ).
cnf(f_1073_6,plain,
( c_Groups_Ozero__class_Ozero(U_4302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4302),U_4303),U_4303)
| U_4303 != c_Groups_Ozero__class_Ozero(U_4302)
| ~ sP261(U_4302,U_4303) ),
inference(clausify,[status(thm)],[f_1073_3]) ).
fof(f_1074_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Omonoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__right]) ).
fof(f_1074_2,plain,
! [U_4305,U_4304] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4304),U_4305),c_Groups_Ozero__class_Ozero(U_4304)) = U_4305
| ~ class_Groups_Omonoid__add(U_4304) ),
inference(variable_rename,[status(thm)],[f_1074_1]) ).
fof(f_1074_3,plain,
! [U_4304,U_4305] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4304),U_4305),c_Groups_Ozero__class_Ozero(U_4304)) = U_4305
| ~ class_Groups_Omonoid__add(U_4304) ),
inference(definitional_conversion,[status(esa)],[f_1074_2]) ).
cnf(f_1074_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4304),U_4305),c_Groups_Ozero__class_Ozero(U_4304)) = U_4305
| ~ class_Groups_Omonoid__add(U_4304) ),
inference(clausify,[status(thm)],[f_1074_3]) ).
fof(f_1075_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral]) ).
fof(f_1075_2,plain,
! [U_4307,U_4306] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4306),U_4307),c_Groups_Ozero__class_Ozero(U_4306)) = U_4307
| ~ class_Groups_Ocomm__monoid__add(U_4306) ),
inference(variable_rename,[status(thm)],[f_1075_1]) ).
fof(f_1075_3,plain,
! [U_4306,U_4307] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4306),U_4307),c_Groups_Ozero__class_Ozero(U_4306)) = U_4307
| ~ class_Groups_Ocomm__monoid__add(U_4306) ),
inference(definitional_conversion,[status(esa)],[f_1075_2]) ).
cnf(f_1075_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4306),U_4307),c_Groups_Ozero__class_Ozero(U_4306)) = U_4307
| ~ class_Groups_Ocomm__monoid__add(U_4306) ),
inference(clausify,[status(thm)],[f_1075_3]) ).
fof(f_1076_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_1076_2,plain,
! [U_4309,U_4308] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4308),c_Groups_Ozero__class_Ozero(U_4308)),U_4309) = U_4309
| ~ class_Rings_Ocomm__semiring__1(U_4308) ),
inference(variable_rename,[status(thm)],[f_1076_1]) ).
fof(f_1076_3,plain,
! [U_4308,U_4309] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4308),c_Groups_Ozero__class_Ozero(U_4308)),U_4309) = U_4309
| ~ class_Rings_Ocomm__semiring__1(U_4308) ),
inference(definitional_conversion,[status(esa)],[f_1076_2]) ).
cnf(f_1076_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4308),c_Groups_Ozero__class_Ozero(U_4308)),U_4309) = U_4309
| ~ class_Rings_Ocomm__semiring__1(U_4308) ),
inference(clausify,[status(thm)],[f_1076_3]) ).
fof(f_1077_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_1077_2,plain,
! [U_4311,U_4310] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),U_4311),c_Groups_Ozero__class_Ozero(U_4310)) = U_4311
| ~ class_Rings_Ocomm__semiring__1(U_4310) ),
inference(variable_rename,[status(thm)],[f_1077_1]) ).
fof(f_1077_3,plain,
! [U_4310,U_4311] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),U_4311),c_Groups_Ozero__class_Ozero(U_4310)) = U_4311
| ~ class_Rings_Ocomm__semiring__1(U_4310) ),
inference(definitional_conversion,[status(esa)],[f_1077_2]) ).
cnf(f_1077_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),U_4311),c_Groups_Ozero__class_Ozero(U_4310)) = U_4311
| ~ class_Rings_Ocomm__semiring__1(U_4310) ),
inference(clausify,[status(thm)],[f_1077_3]) ).
fof(f_1078_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_b_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).
fof(f_1078_2,plain,
! [U_4314,U_4313,U_4312] :
( ( ( U_4313 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4312),U_4313),U_4314)
| U_4314 != c_Groups_Ozero__class_Ozero(U_4312) )
& ( U_4314 = c_Groups_Ozero__class_Ozero(U_4312)
| U_4313 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4312),U_4313),U_4314) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4312) ),
inference(variable_rename,[status(thm)],[f_1078_1]) ).
fof(f_1078_3,plain,
( ! [U_4312,U_4313,U_4314] :
( U_4313 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4312),U_4313),U_4314)
| U_4314 != c_Groups_Ozero__class_Ozero(U_4312)
| ~ sP262(U_4312,U_4313,U_4314) )
& ! [U_4312,U_4313,U_4314] :
( U_4314 = c_Groups_Ozero__class_Ozero(U_4312)
| U_4313 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4312),U_4313),U_4314)
| ~ sP262(U_4312,U_4313,U_4314) )
& ! [U_4312,U_4313,U_4314] :
( sP262(U_4312,U_4313,U_4314)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4312) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262])],[f_1078_2]) ).
cnf(f_1078_4,plain,
( sP262(U_4312,U_4313,U_4314)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4312) ),
inference(clausify,[status(thm)],[f_1078_3]) ).
cnf(f_1078_5,plain,
( U_4314 = c_Groups_Ozero__class_Ozero(U_4312)
| U_4313 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4312),U_4313),U_4314)
| ~ sP262(U_4312,U_4313,U_4314) ),
inference(clausify,[status(thm)],[f_1078_3]) ).
cnf(f_1078_6,plain,
( U_4313 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4312),U_4313),U_4314)
| U_4314 != c_Groups_Ozero__class_Ozero(U_4312)
| ~ sP262(U_4312,U_4313,U_4314) ),
inference(clausify,[status(thm)],[f_1078_3]) ).
fof(f_1079_1,plain,
! [V_b,V_a,T_a] :
( V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divisors__zero]) ).
fof(f_1079_2,plain,
! [U_4317,U_4316,U_4315] :
( U_4317 = c_Groups_Ozero__class_Ozero(U_4315)
| U_4316 = c_Groups_Ozero__class_Ozero(U_4315)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4315),U_4316),U_4317) != c_Groups_Ozero__class_Ozero(U_4315)
| ~ class_Rings_Ono__zero__divisors(U_4315) ),
inference(variable_rename,[status(thm)],[f_1079_1]) ).
fof(f_1079_3,plain,
! [U_4317,U_4316,U_4315] :
( U_4317 = c_Groups_Ozero__class_Ozero(U_4315)
| U_4316 = c_Groups_Ozero__class_Ozero(U_4315)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4315),U_4316),U_4317) != c_Groups_Ozero__class_Ozero(U_4315)
| ~ class_Rings_Ono__zero__divisors(U_4315) ),
inference(definitional_conversion,[status(esa)],[f_1079_2]) ).
cnf(f_1079_4,plain,
( U_4317 = c_Groups_Ozero__class_Ozero(U_4315)
| U_4316 = c_Groups_Ozero__class_Ozero(U_4315)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4315),U_4316),U_4317) != c_Groups_Ozero__class_Ozero(U_4315)
| ~ class_Rings_Ono__zero__divisors(U_4315) ),
inference(clausify,[status(thm)],[f_1079_3]) ).
fof(f_1080_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_no__zero__divisors]) ).
fof(f_1080_2,plain,
! [U_4320,U_4319,U_4318] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4318),U_4319),U_4320) != c_Groups_Ozero__class_Ozero(U_4318)
| U_4320 = c_Groups_Ozero__class_Ozero(U_4318)
| U_4319 = c_Groups_Ozero__class_Ozero(U_4318)
| ~ class_Rings_Ono__zero__divisors(U_4318) ),
inference(variable_rename,[status(thm)],[f_1080_1]) ).
fof(f_1080_3,plain,
! [U_4319,U_4320,U_4318] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4318),U_4319),U_4320) != c_Groups_Ozero__class_Ozero(U_4318)
| U_4320 = c_Groups_Ozero__class_Ozero(U_4318)
| U_4319 = c_Groups_Ozero__class_Ozero(U_4318)
| ~ class_Rings_Ono__zero__divisors(U_4318) ),
inference(definitional_conversion,[status(esa)],[f_1080_2]) ).
cnf(f_1080_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4318),U_4319),U_4320) != c_Groups_Ozero__class_Ozero(U_4318)
| U_4320 = c_Groups_Ozero__class_Ozero(U_4318)
| U_4319 = c_Groups_Ozero__class_Ozero(U_4318)
| ~ class_Rings_Ono__zero__divisors(U_4318) ),
inference(clausify,[status(thm)],[f_1080_3]) ).
fof(f_1081_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
| ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
& V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Oring__no__zero__divisors(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).
fof(f_1081_2,plain,
! [U_4323,U_4322,U_4321] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4321),U_4322),U_4323) = c_Groups_Ozero__class_Ozero(U_4321)
| ( U_4323 != c_Groups_Ozero__class_Ozero(U_4321)
& U_4322 != c_Groups_Ozero__class_Ozero(U_4321) ) )
& ( U_4323 = c_Groups_Ozero__class_Ozero(U_4321)
| U_4322 = c_Groups_Ozero__class_Ozero(U_4321)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4321),U_4322),U_4323) != c_Groups_Ozero__class_Ozero(U_4321) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_4321) ),
inference(variable_rename,[status(thm)],[f_1081_1]) ).
fof(f_1081_3,plain,
( ! [U_4321,U_4322,U_4323] :
( U_4323 != c_Groups_Ozero__class_Ozero(U_4321)
| ~ sP263(U_4321,U_4322,U_4323) )
& ! [U_4321,U_4322,U_4323] :
( U_4322 != c_Groups_Ozero__class_Ozero(U_4321)
| ~ sP263(U_4321,U_4322,U_4323) )
& ! [U_4321,U_4322,U_4323] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4321),U_4322),U_4323) = c_Groups_Ozero__class_Ozero(U_4321)
| sP263(U_4321,U_4322,U_4323)
| ~ sP264(U_4321,U_4322,U_4323) )
& ! [U_4321,U_4322,U_4323] :
( U_4323 = c_Groups_Ozero__class_Ozero(U_4321)
| U_4322 = c_Groups_Ozero__class_Ozero(U_4321)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4321),U_4322),U_4323) != c_Groups_Ozero__class_Ozero(U_4321)
| ~ sP264(U_4321,U_4322,U_4323) )
& ! [U_4321,U_4322,U_4323] :
( sP264(U_4321,U_4322,U_4323)
| ~ class_Rings_Oring__no__zero__divisors(U_4321) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263,sP264])],[f_1081_2]) ).
cnf(f_1081_4,plain,
( sP264(U_4321,U_4322,U_4323)
| ~ class_Rings_Oring__no__zero__divisors(U_4321) ),
inference(clausify,[status(thm)],[f_1081_3]) ).
cnf(f_1081_5,plain,
( U_4323 = c_Groups_Ozero__class_Ozero(U_4321)
| U_4322 = c_Groups_Ozero__class_Ozero(U_4321)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4321),U_4322),U_4323) != c_Groups_Ozero__class_Ozero(U_4321)
| ~ sP264(U_4321,U_4322,U_4323) ),
inference(clausify,[status(thm)],[f_1081_3]) ).
cnf(f_1081_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4321),U_4322),U_4323) = c_Groups_Ozero__class_Ozero(U_4321)
| sP263(U_4321,U_4322,U_4323)
| ~ sP264(U_4321,U_4322,U_4323) ),
inference(clausify,[status(thm)],[f_1081_3]) ).
cnf(f_1081_7,plain,
( U_4322 != c_Groups_Ozero__class_Ozero(U_4321)
| ~ sP263(U_4321,U_4322,U_4323) ),
inference(clausify,[status(thm)],[f_1081_3]) ).
cnf(f_1081_8,plain,
( U_4323 != c_Groups_Ozero__class_Ozero(U_4321)
| ~ sP263(U_4321,U_4322,U_4323) ),
inference(clausify,[status(thm)],[f_1081_3]) ).
fof(f_1082_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Rings_Omult__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__zero__right]) ).
fof(f_1082_2,plain,
! [U_4325,U_4324] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4324),U_4325),c_Groups_Ozero__class_Ozero(U_4324)) = c_Groups_Ozero__class_Ozero(U_4324)
| ~ class_Rings_Omult__zero(U_4324) ),
inference(variable_rename,[status(thm)],[f_1082_1]) ).
fof(f_1082_3,plain,
! [U_4324,U_4325] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4324),U_4325),c_Groups_Ozero__class_Ozero(U_4324)) = c_Groups_Ozero__class_Ozero(U_4324)
| ~ class_Rings_Omult__zero(U_4324) ),
inference(definitional_conversion,[status(esa)],[f_1082_2]) ).
cnf(f_1082_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4324),U_4325),c_Groups_Ozero__class_Ozero(U_4324)) = c_Groups_Ozero__class_Ozero(U_4324)
| ~ class_Rings_Omult__zero(U_4324) ),
inference(clausify,[status(thm)],[f_1082_3]) ).
fof(f_1083_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Rings_Omult__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__zero__left]) ).
fof(f_1083_2,plain,
! [U_4327,U_4326] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4326),c_Groups_Ozero__class_Ozero(U_4326)),U_4327) = c_Groups_Ozero__class_Ozero(U_4326)
| ~ class_Rings_Omult__zero(U_4326) ),
inference(variable_rename,[status(thm)],[f_1083_1]) ).
fof(f_1083_3,plain,
! [U_4327,U_4326] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4326),c_Groups_Ozero__class_Ozero(U_4326)),U_4327) = c_Groups_Ozero__class_Ozero(U_4326)
| ~ class_Rings_Omult__zero(U_4326) ),
inference(definitional_conversion,[status(esa)],[f_1083_2]) ).
cnf(f_1083_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4326),c_Groups_Ozero__class_Ozero(U_4326)),U_4327) = c_Groups_Ozero__class_Ozero(U_4326)
| ~ class_Rings_Omult__zero(U_4326) ),
inference(clausify,[status(thm)],[f_1083_3]) ).
fof(f_1084_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
fof(f_1084_2,plain,
! [U_4329,U_4328] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4328),c_Groups_Ozero__class_Ozero(U_4328)),U_4329) = c_Groups_Ozero__class_Ozero(U_4328)
| ~ class_Rings_Ocomm__semiring__1(U_4328) ),
inference(variable_rename,[status(thm)],[f_1084_1]) ).
fof(f_1084_3,plain,
! [U_4329,U_4328] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4328),c_Groups_Ozero__class_Ozero(U_4328)),U_4329) = c_Groups_Ozero__class_Ozero(U_4328)
| ~ class_Rings_Ocomm__semiring__1(U_4328) ),
inference(definitional_conversion,[status(esa)],[f_1084_2]) ).
cnf(f_1084_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4328),c_Groups_Ozero__class_Ozero(U_4328)),U_4329) = c_Groups_Ozero__class_Ozero(U_4328)
| ~ class_Rings_Ocomm__semiring__1(U_4328) ),
inference(clausify,[status(thm)],[f_1084_3]) ).
fof(f_1085_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(f_1085_2,plain,
! [U_4331,U_4330] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4330),U_4331),c_Groups_Ozero__class_Ozero(U_4330)) = c_Groups_Ozero__class_Ozero(U_4330)
| ~ class_Rings_Ocomm__semiring__1(U_4330) ),
inference(variable_rename,[status(thm)],[f_1085_1]) ).
fof(f_1085_3,plain,
! [U_4330,U_4331] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4330),U_4331),c_Groups_Ozero__class_Ozero(U_4330)) = c_Groups_Ozero__class_Ozero(U_4330)
| ~ class_Rings_Ocomm__semiring__1(U_4330) ),
inference(definitional_conversion,[status(esa)],[f_1085_2]) ).
cnf(f_1085_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4330),U_4331),c_Groups_Ozero__class_Ozero(U_4330)) = c_Groups_Ozero__class_Ozero(U_4330)
| ~ class_Rings_Ocomm__semiring__1(U_4330) ),
inference(clausify,[status(thm)],[f_1085_3]) ).
fof(f_1086_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).
fof(f_1086_2,plain,
! [U_4334,U_4333,U_4332] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4332),U_4333),U_4334) = c_Groups_Ozero__class_Ozero(U_4332)
| U_4333 != U_4334 )
& ( U_4333 = U_4334
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4332),U_4333),U_4334) != c_Groups_Ozero__class_Ozero(U_4332) ) )
| ~ class_Groups_Ogroup__add(U_4332) ),
inference(variable_rename,[status(thm)],[f_1086_1]) ).
fof(f_1086_3,plain,
( ! [U_4332,U_4333,U_4334] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4332),U_4333),U_4334) = c_Groups_Ozero__class_Ozero(U_4332)
| U_4333 != U_4334
| ~ sP265(U_4332,U_4333,U_4334) )
& ! [U_4332,U_4333,U_4334] :
( U_4333 = U_4334
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4332),U_4333),U_4334) != c_Groups_Ozero__class_Ozero(U_4332)
| ~ sP265(U_4332,U_4333,U_4334) )
& ! [U_4332,U_4333,U_4334] :
( sP265(U_4332,U_4333,U_4334)
| ~ class_Groups_Ogroup__add(U_4332) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265])],[f_1086_2]) ).
cnf(f_1086_4,plain,
( sP265(U_4332,U_4333,U_4334)
| ~ class_Groups_Ogroup__add(U_4332) ),
inference(clausify,[status(thm)],[f_1086_3]) ).
cnf(f_1086_5,plain,
( U_4333 = U_4334
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4332),U_4333),U_4334) != c_Groups_Ozero__class_Ozero(U_4332)
| ~ sP265(U_4332,U_4333,U_4334) ),
inference(clausify,[status(thm)],[f_1086_3]) ).
cnf(f_1086_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4332),U_4333),U_4334) = c_Groups_Ozero__class_Ozero(U_4332)
| U_4333 != U_4334
| ~ sP265(U_4332,U_4333,U_4334) ),
inference(clausify,[status(thm)],[f_1086_3]) ).
fof(f_1087_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != V_b_2 ) )
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).
fof(f_1087_2,plain,
! [U_4337,U_4336,U_4335] :
( ( ( U_4336 = U_4337
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4335),U_4336),U_4337) != c_Groups_Ozero__class_Ozero(U_4335) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4335),U_4336),U_4337) = c_Groups_Ozero__class_Ozero(U_4335)
| U_4336 != U_4337 ) )
| ~ class_Groups_Oab__group__add(U_4335) ),
inference(variable_rename,[status(thm)],[f_1087_1]) ).
fof(f_1087_3,plain,
( ! [U_4336,U_4335,U_4337] :
( U_4336 = U_4337
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4335),U_4336),U_4337) != c_Groups_Ozero__class_Ozero(U_4335)
| ~ sP266(U_4336,U_4335,U_4337) )
& ! [U_4336,U_4335,U_4337] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4335),U_4336),U_4337) = c_Groups_Ozero__class_Ozero(U_4335)
| U_4336 != U_4337
| ~ sP266(U_4336,U_4335,U_4337) )
& ! [U_4336,U_4335,U_4337] :
( sP266(U_4336,U_4335,U_4337)
| ~ class_Groups_Oab__group__add(U_4335) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266])],[f_1087_2]) ).
cnf(f_1087_4,plain,
( sP266(U_4336,U_4335,U_4337)
| ~ class_Groups_Oab__group__add(U_4335) ),
inference(clausify,[status(thm)],[f_1087_3]) ).
cnf(f_1087_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4335),U_4336),U_4337) = c_Groups_Ozero__class_Ozero(U_4335)
| U_4336 != U_4337
| ~ sP266(U_4336,U_4335,U_4337) ),
inference(clausify,[status(thm)],[f_1087_3]) ).
cnf(f_1087_6,plain,
( U_4336 = U_4337
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4335),U_4336),U_4337) != c_Groups_Ozero__class_Ozero(U_4335)
| ~ sP266(U_4336,U_4335,U_4337) ),
inference(clausify,[status(thm)],[f_1087_3]) ).
fof(f_1088_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__self]) ).
fof(f_1088_2,plain,
! [U_4339,U_4338] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4338),U_4339),U_4339) = c_Groups_Ozero__class_Ozero(U_4338)
| ~ class_Groups_Ogroup__add(U_4338) ),
inference(variable_rename,[status(thm)],[f_1088_1]) ).
fof(f_1088_3,plain,
! [U_4339,U_4338] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4338),U_4339),U_4339) = c_Groups_Ozero__class_Ozero(U_4338)
| ~ class_Groups_Ogroup__add(U_4338) ),
inference(definitional_conversion,[status(esa)],[f_1088_2]) ).
cnf(f_1088_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4338),U_4339),U_4339) = c_Groups_Ozero__class_Ozero(U_4338)
| ~ class_Groups_Ogroup__add(U_4338) ),
inference(clausify,[status(thm)],[f_1088_3]) ).
fof(f_1089_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__0__right]) ).
fof(f_1089_2,plain,
! [U_4341,U_4340] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4340),U_4341),c_Groups_Ozero__class_Ozero(U_4340)) = U_4341
| ~ class_Groups_Ogroup__add(U_4340) ),
inference(variable_rename,[status(thm)],[f_1089_1]) ).
fof(f_1089_3,plain,
! [U_4340,U_4341] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4340),U_4341),c_Groups_Ozero__class_Ozero(U_4340)) = U_4341
| ~ class_Groups_Ogroup__add(U_4340) ),
inference(definitional_conversion,[status(esa)],[f_1089_2]) ).
cnf(f_1089_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4340),U_4341),c_Groups_Ozero__class_Ozero(U_4340)) = U_4341
| ~ class_Groups_Ogroup__add(U_4340) ),
inference(clausify,[status(thm)],[f_1089_3]) ).
fof(f_1090_1,plain,
! [T_a] :
( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__neq__zero]) ).
fof(f_1090_2,plain,
! [U_4342] :
( c_Groups_Oone__class_Oone(U_4342) != c_Groups_Ozero__class_Ozero(U_4342)
| ~ class_Rings_Ozero__neq__one(U_4342) ),
inference(variable_rename,[status(thm)],[f_1090_1]) ).
fof(f_1090_3,plain,
! [U_4342] :
( c_Groups_Oone__class_Oone(U_4342) != c_Groups_Ozero__class_Ozero(U_4342)
| ~ class_Rings_Ozero__neq__one(U_4342) ),
inference(definitional_conversion,[status(esa)],[f_1090_2]) ).
cnf(f_1090_4,plain,
( c_Groups_Oone__class_Oone(U_4342) != c_Groups_Ozero__class_Ozero(U_4342)
| ~ class_Rings_Ozero__neq__one(U_4342) ),
inference(clausify,[status(thm)],[f_1090_3]) ).
fof(f_1091_1,plain,
! [T_a] :
( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__neq__one]) ).
fof(f_1091_2,plain,
! [U_4343] :
( c_Groups_Ozero__class_Ozero(U_4343) != c_Groups_Oone__class_Oone(U_4343)
| ~ class_Rings_Ozero__neq__one(U_4343) ),
inference(variable_rename,[status(thm)],[f_1091_1]) ).
fof(f_1091_3,plain,
! [U_4343] :
( c_Groups_Ozero__class_Ozero(U_4343) != c_Groups_Oone__class_Oone(U_4343)
| ~ class_Rings_Ozero__neq__one(U_4343) ),
inference(definitional_conversion,[status(esa)],[f_1091_2]) ).
cnf(f_1091_4,plain,
( c_Groups_Ozero__class_Ozero(U_4343) != c_Groups_Oone__class_Oone(U_4343)
| ~ class_Rings_Ozero__neq__one(U_4343) ),
inference(clausify,[status(thm)],[f_1091_3]) ).
fof(f_1092_1,plain,
! [T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__zero]) ).
fof(f_1092_2,plain,
! [U_4344] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4344),c_Groups_Ozero__class_Ozero(U_4344)) = c_Groups_Ozero__class_Ozero(U_4344)
| ~ class_Groups_Ogroup__add(U_4344) ),
inference(variable_rename,[status(thm)],[f_1092_1]) ).
fof(f_1092_3,plain,
! [U_4344] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4344),c_Groups_Ozero__class_Ozero(U_4344)) = c_Groups_Ozero__class_Ozero(U_4344)
| ~ class_Groups_Ogroup__add(U_4344) ),
inference(definitional_conversion,[status(esa)],[f_1092_2]) ).
cnf(f_1092_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4344),c_Groups_Ozero__class_Ozero(U_4344)) = c_Groups_Ozero__class_Ozero(U_4344)
| ~ class_Groups_Ogroup__add(U_4344) ),
inference(clausify,[status(thm)],[f_1092_3]) ).
fof(f_1093_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
| c_Groups_Ozero__class_Ozero(T_b) != V_a_2 )
& ( c_Groups_Ozero__class_Ozero(T_b) = V_a_2
| c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).
fof(f_1093_2,plain,
! [U_4346,U_4345] :
( ( ( c_Groups_Ozero__class_Ozero(U_4345) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4345),U_4346)
| c_Groups_Ozero__class_Ozero(U_4345) != U_4346 )
& ( c_Groups_Ozero__class_Ozero(U_4345) = U_4346
| c_Groups_Ozero__class_Ozero(U_4345) != hAPP(c_Groups_Ouminus__class_Ouminus(U_4345),U_4346) ) )
| ~ class_Groups_Ogroup__add(U_4345) ),
inference(variable_rename,[status(thm)],[f_1093_1]) ).
fof(f_1093_3,plain,
( ! [U_4345,U_4346] :
( c_Groups_Ozero__class_Ozero(U_4345) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4345),U_4346)
| c_Groups_Ozero__class_Ozero(U_4345) != U_4346
| ~ sP267(U_4345,U_4346) )
& ! [U_4345,U_4346] :
( c_Groups_Ozero__class_Ozero(U_4345) = U_4346
| c_Groups_Ozero__class_Ozero(U_4345) != hAPP(c_Groups_Ouminus__class_Ouminus(U_4345),U_4346)
| ~ sP267(U_4345,U_4346) )
& ! [U_4345,U_4346] :
( sP267(U_4345,U_4346)
| ~ class_Groups_Ogroup__add(U_4345) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267])],[f_1093_2]) ).
cnf(f_1093_4,plain,
( sP267(U_4345,U_4346)
| ~ class_Groups_Ogroup__add(U_4345) ),
inference(clausify,[status(thm)],[f_1093_3]) ).
cnf(f_1093_5,plain,
( c_Groups_Ozero__class_Ozero(U_4345) = U_4346
| c_Groups_Ozero__class_Ozero(U_4345) != hAPP(c_Groups_Ouminus__class_Ouminus(U_4345),U_4346)
| ~ sP267(U_4345,U_4346) ),
inference(clausify,[status(thm)],[f_1093_3]) ).
cnf(f_1093_6,plain,
( c_Groups_Ozero__class_Ozero(U_4345) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4345),U_4346)
| c_Groups_Ozero__class_Ozero(U_4345) != U_4346
| ~ sP267(U_4345,U_4346) ),
inference(clausify,[status(thm)],[f_1093_3]) ).
fof(f_1094_1,plain,
! [V_a_2,T_b] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).
fof(f_1094_2,plain,
! [U_4348,U_4347] :
( ( ( U_4348 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4347),U_4348)
| U_4348 != c_Groups_Ozero__class_Ozero(U_4347) )
& ( U_4348 = c_Groups_Ozero__class_Ozero(U_4347)
| U_4348 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4347),U_4348) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4347) ),
inference(variable_rename,[status(thm)],[f_1094_1]) ).
fof(f_1094_3,plain,
( ! [U_4348,U_4347] :
( U_4348 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4347),U_4348)
| U_4348 != c_Groups_Ozero__class_Ozero(U_4347)
| ~ sP268(U_4348,U_4347) )
& ! [U_4348,U_4347] :
( U_4348 = c_Groups_Ozero__class_Ozero(U_4347)
| U_4348 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4347),U_4348)
| ~ sP268(U_4348,U_4347) )
& ! [U_4348,U_4347] :
( sP268(U_4348,U_4347)
| ~ class_Groups_Olinordered__ab__group__add(U_4347) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268])],[f_1094_2]) ).
cnf(f_1094_4,plain,
( sP268(U_4348,U_4347)
| ~ class_Groups_Olinordered__ab__group__add(U_4347) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
cnf(f_1094_5,plain,
( U_4348 = c_Groups_Ozero__class_Ozero(U_4347)
| U_4348 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4347),U_4348)
| ~ sP268(U_4348,U_4347) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
cnf(f_1094_6,plain,
( U_4348 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4347),U_4348)
| U_4348 != c_Groups_Ozero__class_Ozero(U_4347)
| ~ sP268(U_4348,U_4347) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
fof(f_1095_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).
fof(f_1095_2,plain,
! [U_4350,U_4349] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4349),U_4350) = c_Groups_Ozero__class_Ozero(U_4349)
| U_4350 != c_Groups_Ozero__class_Ozero(U_4349) )
& ( U_4350 = c_Groups_Ozero__class_Ozero(U_4349)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_4349),U_4350) != c_Groups_Ozero__class_Ozero(U_4349) ) )
| ~ class_Groups_Ogroup__add(U_4349) ),
inference(variable_rename,[status(thm)],[f_1095_1]) ).
fof(f_1095_3,plain,
( ! [U_4350,U_4349] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4349),U_4350) = c_Groups_Ozero__class_Ozero(U_4349)
| U_4350 != c_Groups_Ozero__class_Ozero(U_4349)
| ~ sP269(U_4350,U_4349) )
& ! [U_4350,U_4349] :
( U_4350 = c_Groups_Ozero__class_Ozero(U_4349)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_4349),U_4350) != c_Groups_Ozero__class_Ozero(U_4349)
| ~ sP269(U_4350,U_4349) )
& ! [U_4350,U_4349] :
( sP269(U_4350,U_4349)
| ~ class_Groups_Ogroup__add(U_4349) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP269])],[f_1095_2]) ).
cnf(f_1095_4,plain,
( sP269(U_4350,U_4349)
| ~ class_Groups_Ogroup__add(U_4349) ),
inference(clausify,[status(thm)],[f_1095_3]) ).
cnf(f_1095_5,plain,
( U_4350 = c_Groups_Ozero__class_Ozero(U_4349)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_4349),U_4350) != c_Groups_Ozero__class_Ozero(U_4349)
| ~ sP269(U_4350,U_4349) ),
inference(clausify,[status(thm)],[f_1095_3]) ).
cnf(f_1095_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4349),U_4350) = c_Groups_Ozero__class_Ozero(U_4349)
| U_4350 != c_Groups_Ozero__class_Ozero(U_4349)
| ~ sP269(U_4350,U_4349) ),
inference(clausify,[status(thm)],[f_1095_3]) ).
fof(f_1096_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != V_a_2 ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).
fof(f_1096_2,plain,
! [U_4352,U_4351] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4351),U_4352) = U_4352
| U_4352 != c_Groups_Ozero__class_Ozero(U_4351) )
& ( U_4352 = c_Groups_Ozero__class_Ozero(U_4351)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_4351),U_4352) != U_4352 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4351) ),
inference(variable_rename,[status(thm)],[f_1096_1]) ).
fof(f_1096_3,plain,
( ! [U_4352,U_4351] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4351),U_4352) = U_4352
| U_4352 != c_Groups_Ozero__class_Ozero(U_4351)
| ~ sP270(U_4352,U_4351) )
& ! [U_4352,U_4351] :
( U_4352 = c_Groups_Ozero__class_Ozero(U_4351)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_4351),U_4352) != U_4352
| ~ sP270(U_4352,U_4351) )
& ! [U_4352,U_4351] :
( sP270(U_4352,U_4351)
| ~ class_Groups_Olinordered__ab__group__add(U_4351) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP270])],[f_1096_2]) ).
cnf(f_1096_4,plain,
( sP270(U_4352,U_4351)
| ~ class_Groups_Olinordered__ab__group__add(U_4351) ),
inference(clausify,[status(thm)],[f_1096_3]) ).
cnf(f_1096_5,plain,
( U_4352 = c_Groups_Ozero__class_Ozero(U_4351)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_4351),U_4352) != U_4352
| ~ sP270(U_4352,U_4351) ),
inference(clausify,[status(thm)],[f_1096_3]) ).
cnf(f_1096_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4351),U_4352) = U_4352
| U_4352 != c_Groups_Ozero__class_Ozero(U_4351)
| ~ sP270(U_4352,U_4351) ),
inference(clausify,[status(thm)],[f_1096_3]) ).
fof(f_1097_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_fold__image__empty]) ).
fof(f_1097_2,plain,
! [U_4357,U_4356,U_4355,U_4354,U_4353] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4353,U_4354,U_4355),U_4356),U_4357),c_Orderings_Obot__class_Obot(tc_fun(U_4354,tc_HOL_Obool))) = U_4357,
inference(variable_rename,[status(thm)],[f_1097_1]) ).
fof(f_1097_3,plain,
! [U_4354,U_4355,U_4353,U_4356,U_4357] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4353,U_4354,U_4355),U_4356),U_4357),c_Orderings_Obot__class_Obot(tc_fun(U_4354,tc_HOL_Obool))) = U_4357,
inference(definitional_conversion,[status(esa)],[f_1097_2]) ).
cnf(f_1097_4,plain,
hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4353,U_4354,U_4355),U_4356),U_4357),c_Orderings_Obot__class_Obot(tc_fun(U_4354,tc_HOL_Obool))) = U_4357,
inference(clausify,[status(thm)],[f_1097_3]) ).
fof(f_1098_1,plain,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_not__less0]) ).
fof(f_1098_2,plain,
! [U_4358] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4358),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1098_1]) ).
fof(f_1098_3,plain,
! [U_4358] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4358),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1098_2]) ).
cnf(f_1098_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4358),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1098_3]) ).
fof(f_1099_1,plain,
! [V_n_2] :
( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).
fof(f_1099_2,plain,
! [U_4359] :
( ( U_4359 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4359)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4359))
| U_4359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1099_1]) ).
fof(f_1099_3,plain,
( ! [U_4361] :
( U_4361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4361)) )
& ! [U_4360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4360))
| U_4360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1099_2]) ).
fof(f_1099_4,plain,
( ! [U_4361] :
( U_4361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4361)) )
& ! [U_4360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4360))
| U_4360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1099_3]) ).
cnf(f_1099_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4360))
| U_4360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1099_4]) ).
cnf(f_1099_6,plain,
( U_4361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4361)) ),
inference(clausify,[status(thm)],[f_1099_4]) ).
fof(f_1100_1,plain,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_less__nat__zero__code]) ).
fof(f_1100_2,plain,
! [U_4362] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4362),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1100_1]) ).
fof(f_1100_3,plain,
! [U_4362] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4362),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1100_2]) ).
cnf(f_1100_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4362),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1100_3]) ).
fof(f_1101_1,plain,
! [V_n,V_m] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_gr__implies__not0]) ).
fof(f_1101_2,plain,
! [U_4364,U_4363] :
( U_4364 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4363),U_4364)) ),
inference(variable_rename,[status(thm)],[f_1101_1]) ).
fof(f_1101_3,plain,
! [U_4364] :
( ! [U_4363] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4363),U_4364))
| U_4364 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_1101_2]) ).
fof(f_1101_4,plain,
! [U_4363,U_4364] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4363),U_4364))
| U_4364 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1101_3]) ).
cnf(f_1101_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4363),U_4364))
| U_4364 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1101_4]) ).
fof(f_1102_1,plain,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_gr0I]) ).
fof(f_1102_2,plain,
! [U_4365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4365))
| U_4365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_1102_1]) ).
fof(f_1102_3,plain,
! [U_4365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4365))
| U_4365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1102_2]) ).
cnf(f_1102_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4365))
| U_4365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1102_3]) ).
fof(f_1103_1,plain,
! [V_n,V_m] :
( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) != V_m ),
inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero]) ).
fof(f_1103_2,plain,
! [U_4367,U_4366] :
( U_4367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4366),U_4367) != U_4366 ),
inference(variable_rename,[status(thm)],[f_1103_1]) ).
fof(f_1103_3,plain,
! [U_4367] :
( ! [U_4366] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4366),U_4367) != U_4366
| U_4367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_1103_2]) ).
fof(f_1103_4,plain,
! [U_4366,U_4367] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4366),U_4367) != U_4366
| U_4367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1103_3]) ).
cnf(f_1103_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4366),U_4367) != U_4366
| U_4367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1103_4]) ).
fof(f_1104_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).
fof(f_1104_2,plain,
! [U_4369,U_4368] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4368),U_4369) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4369 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4368 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_4369 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4368 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4368),U_4369) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1104_1]) ).
fof(f_1104_3,plain,
( ! [U_4373,U_4371] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4371),U_4373) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4373 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_4372,U_4370] :
( ( U_4372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4370),U_4372) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1104_2]) ).
fof(f_1104_4,plain,
( ! [U_4372,U_4370] :
( U_4372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP271(U_4372,U_4370) )
& ! [U_4372,U_4370] :
( U_4370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP271(U_4372,U_4370) )
& ! [U_4373,U_4371] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4371),U_4373) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4373 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_4372,U_4370] :
( sP271(U_4372,U_4370)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4370),U_4372) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271])],[f_1104_3]) ).
cnf(f_1104_5,plain,
( sP271(U_4372,U_4370)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4370),U_4372) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1104_4]) ).
cnf(f_1104_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4371),U_4373) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4373 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1104_4]) ).
cnf(f_1104_7,plain,
( U_4370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP271(U_4372,U_4370) ),
inference(clausify,[status(thm)],[f_1104_4]) ).
cnf(f_1104_8,plain,
( U_4372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP271(U_4372,U_4370) ),
inference(clausify,[status(thm)],[f_1104_4]) ).
fof(f_1105_1,plain,
! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
inference(fof_nnf,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(f_1105_2,plain,
! [U_4374] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4374),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4374,
inference(variable_rename,[status(thm)],[f_1105_1]) ).
fof(f_1105_3,plain,
! [U_4374] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4374),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4374,
inference(definitional_conversion,[status(esa)],[f_1105_2]) ).
cnf(f_1105_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4374),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4374,
inference(clausify,[status(thm)],[f_1105_3]) ).
fof(f_1106_1,plain,
! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(f_1106_2,plain,
! [U_4375] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4375) = U_4375,
inference(variable_rename,[status(thm)],[f_1106_1]) ).
fof(f_1106_3,plain,
! [U_4375] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4375) = U_4375,
inference(definitional_conversion,[status(esa)],[f_1106_2]) ).
cnf(f_1106_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4375) = U_4375,
inference(clausify,[status(thm)],[f_1106_3]) ).
fof(f_1107_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__singleton]) ).
fof(f_1107_2,plain,
! [U_4376] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4376),hAPP(c_Nat_OSuc,U_4376)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4376),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_1107_1]) ).
fof(f_1107_3,plain,
! [U_4376] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4376),hAPP(c_Nat_OSuc,U_4376)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4376),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_1107_2]) ).
cnf(f_1107_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4376),hAPP(c_Nat_OSuc,U_4376)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4376),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_1107_3]) ).
fof(f_1108_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).
fof(f_1108_2,plain,
! [U_4378,U_4377] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4377),U_4378)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4377)),hAPP(c_Nat_OSuc,U_4378)),
inference(variable_rename,[status(thm)],[f_1108_1]) ).
fof(f_1108_3,plain,
! [U_4377,U_4378] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4377),U_4378)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4377)),hAPP(c_Nat_OSuc,U_4378)),
inference(definitional_conversion,[status(esa)],[f_1108_2]) ).
cnf(f_1108_4,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4377),U_4378)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4377)),hAPP(c_Nat_OSuc,U_4378)),
inference(clausify,[status(thm)],[f_1108_3]) ).
fof(f_1109_1,plain,
! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(f_1109_2,plain,
! [U_4379] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4379)),
inference(variable_rename,[status(thm)],[f_1109_1]) ).
fof(f_1109_3,plain,
! [U_4379] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4379)),
inference(definitional_conversion,[status(esa)],[f_1109_2]) ).
cnf(f_1109_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4379)),
inference(clausify,[status(thm)],[f_1109_3]) ).
fof(f_1110_1,plain,
! [V_n_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__0__eq]) ).
fof(f_1110_2,plain,
! [U_4380] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4380),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_4380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_4380 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4380),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_1110_1]) ).
fof(f_1110_3,plain,
( ! [U_4382] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4382),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_4382 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_4381] :
( U_4381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4381),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_1110_2]) ).
fof(f_1110_4,plain,
( ! [U_4382] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4382),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_4382 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_4381] :
( U_4381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4381),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa)],[f_1110_3]) ).
cnf(f_1110_5,plain,
( U_4381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4381),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_1110_4]) ).
cnf(f_1110_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4382),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_4382 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1110_4]) ).
fof(f_1111_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_diff__0__eq__0]) ).
fof(f_1111_2,plain,
! [U_4383] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4383) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1111_1]) ).
fof(f_1111_3,plain,
! [U_4383] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4383) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1111_2]) ).
cnf(f_1111_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4383) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1111_3]) ).
fof(f_1112_1,plain,
! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
inference(fof_nnf,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(f_1112_2,plain,
! [U_4384] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4384),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4384,
inference(variable_rename,[status(thm)],[f_1112_1]) ).
fof(f_1112_3,plain,
! [U_4384] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4384),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4384,
inference(definitional_conversion,[status(esa)],[f_1112_2]) ).
cnf(f_1112_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4384),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4384,
inference(clausify,[status(thm)],[f_1112_3]) ).
fof(f_1113_1,plain,
! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_diff__self__eq__0]) ).
fof(f_1113_2,plain,
! [U_4385] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4385),U_4385) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1113_1]) ).
fof(f_1113_3,plain,
! [U_4385] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4385),U_4385) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1113_2]) ).
cnf(f_1113_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4385),U_4385) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1113_3]) ).
fof(f_1114_1,plain,
! [V_n,V_m] :
( V_m = V_n
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal]) ).
fof(f_1114_2,plain,
! [U_4387,U_4386] :
( U_4386 = U_4387
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4387),U_4386) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4386),U_4387) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_1114_1]) ).
fof(f_1114_3,plain,
! [U_4386,U_4387] :
( U_4386 = U_4387
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4387),U_4386) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4386),U_4387) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1114_2]) ).
cnf(f_1114_4,plain,
( U_4386 = U_4387
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4387),U_4386) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4386),U_4387) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1114_3]) ).
fof(f_1115_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( 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)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).
fof(f_1115_2,plain,
! [U_4390,U_4389,U_4388] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4388),U_4389) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4390),U_4389)
| ( U_4389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4388 != U_4390 ) )
& ( U_4389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4388 = U_4390
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4388),U_4389) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4390),U_4389) ) ),
inference(variable_rename,[status(thm)],[f_1115_1]) ).
fof(f_1115_3,plain,
( ! [U_4396,U_4394,U_4392] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4392),U_4394) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4396),U_4394)
| ( U_4394 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4392 != U_4396 ) )
& ! [U_4395,U_4393,U_4391] :
( U_4393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4391 = U_4395
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4391),U_4393) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4395),U_4393) ) ),
inference(miniscope,[status(thm)],[f_1115_2]) ).
fof(f_1115_4,plain,
( ! [U_4396,U_4394,U_4392] :
( U_4394 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP272(U_4396,U_4394,U_4392) )
& ! [U_4396,U_4394,U_4392] :
( U_4392 != U_4396
| ~ sP272(U_4396,U_4394,U_4392) )
& ! [U_4396,U_4394,U_4392] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4392),U_4394) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4396),U_4394)
| sP272(U_4396,U_4394,U_4392) )
& ! [U_4393,U_4391,U_4395] :
( U_4393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4391 = U_4395
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4391),U_4393) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4395),U_4393) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP272])],[f_1115_3]) ).
cnf(f_1115_5,plain,
( U_4393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4391 = U_4395
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4391),U_4393) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4395),U_4393) ),
inference(clausify,[status(thm)],[f_1115_4]) ).
cnf(f_1115_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4392),U_4394) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4396),U_4394)
| sP272(U_4396,U_4394,U_4392) ),
inference(clausify,[status(thm)],[f_1115_4]) ).
cnf(f_1115_7,plain,
( U_4392 != U_4396
| ~ sP272(U_4396,U_4394,U_4392) ),
inference(clausify,[status(thm)],[f_1115_4]) ).
cnf(f_1115_8,plain,
( U_4394 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP272(U_4396,U_4394,U_4392) ),
inference(clausify,[status(thm)],[f_1115_4]) ).
fof(f_1116_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).
fof(f_1116_2,plain,
! [U_4399,U_4398,U_4397] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4397),U_4398) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4397),U_4399)
| ( U_4397 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4398 != U_4399 ) )
& ( U_4397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4398 = U_4399
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4397),U_4398) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4397),U_4399) ) ),
inference(variable_rename,[status(thm)],[f_1116_1]) ).
fof(f_1116_3,plain,
( ! [U_4405,U_4403,U_4401] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4401),U_4403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4401),U_4405)
| ( U_4401 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4403 != U_4405 ) )
& ! [U_4404,U_4402,U_4400] :
( U_4400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4402 = U_4404
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4400),U_4402) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4400),U_4404) ) ),
inference(miniscope,[status(thm)],[f_1116_2]) ).
fof(f_1116_4,plain,
( ! [U_4405,U_4403,U_4401] :
( U_4401 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP273(U_4405,U_4403,U_4401) )
& ! [U_4405,U_4403,U_4401] :
( U_4403 != U_4405
| ~ sP273(U_4405,U_4403,U_4401) )
& ! [U_4405,U_4403,U_4401] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4401),U_4403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4401),U_4405)
| sP273(U_4405,U_4403,U_4401) )
& ! [U_4400,U_4402,U_4404] :
( U_4400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4402 = U_4404
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4400),U_4402) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4400),U_4404) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273])],[f_1116_3]) ).
cnf(f_1116_5,plain,
( U_4400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4402 = U_4404
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4400),U_4402) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4400),U_4404) ),
inference(clausify,[status(thm)],[f_1116_4]) ).
cnf(f_1116_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4401),U_4403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4401),U_4405)
| sP273(U_4405,U_4403,U_4401) ),
inference(clausify,[status(thm)],[f_1116_4]) ).
cnf(f_1116_7,plain,
( U_4403 != U_4405
| ~ sP273(U_4405,U_4403,U_4401) ),
inference(clausify,[status(thm)],[f_1116_4]) ).
cnf(f_1116_8,plain,
( U_4401 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP273(U_4405,U_4403,U_4401) ),
inference(clausify,[status(thm)],[f_1116_4]) ).
fof(f_1117_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).
fof(f_1117_2,plain,
! [U_4407,U_4406] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4406),U_4407) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_4407 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4406 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_4407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4406 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4406),U_4407) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1117_1]) ).
fof(f_1117_3,plain,
( ! [U_4411,U_4409] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4409),U_4411) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_4411 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4409 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_4410,U_4408] :
( U_4410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4408),U_4410) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1117_2]) ).
fof(f_1117_4,plain,
( ! [U_4411,U_4409] :
( U_4411 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP274(U_4411,U_4409) )
& ! [U_4411,U_4409] :
( U_4409 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP274(U_4411,U_4409) )
& ! [U_4411,U_4409] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4409),U_4411) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP274(U_4411,U_4409) )
& ! [U_4410,U_4408] :
( U_4410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4408),U_4410) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274])],[f_1117_3]) ).
cnf(f_1117_5,plain,
( U_4410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4408),U_4410) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1117_4]) ).
cnf(f_1117_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4409),U_4411) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP274(U_4411,U_4409) ),
inference(clausify,[status(thm)],[f_1117_4]) ).
cnf(f_1117_7,plain,
( U_4409 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP274(U_4411,U_4409) ),
inference(clausify,[status(thm)],[f_1117_4]) ).
cnf(f_1117_8,plain,
( U_4411 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP274(U_4411,U_4409) ),
inference(clausify,[status(thm)],[f_1117_4]) ).
fof(f_1118_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_mult__0__right]) ).
fof(f_1118_2,plain,
! [U_4412] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4412),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1118_1]) ).
fof(f_1118_3,plain,
! [U_4412] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4412),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1118_2]) ).
cnf(f_1118_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4412),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1118_3]) ).
fof(f_1119_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_mult__0]) ).
fof(f_1119_2,plain,
! [U_4413] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4413) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1119_1]) ).
fof(f_1119_3,plain,
! [U_4413] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4413) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1119_2]) ).
cnf(f_1119_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4413) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1119_3]) ).
fof(f_1120_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)
| ( V_m_2 != V_n_2
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_m_2 = V_n_2
| V_k_2 = c_Groups_Ozero__class_Ozero(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) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).
fof(f_1120_2,plain,
! [U_4416,U_4415,U_4414] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4414),U_4415) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4414),U_4416)
| ( U_4415 != U_4416
& U_4414 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_4415 = U_4416
| U_4414 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4414),U_4415) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4414),U_4416) ) ),
inference(variable_rename,[status(thm)],[f_1120_1]) ).
fof(f_1120_3,plain,
( ! [U_4422,U_4420,U_4418] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4418),U_4420) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4418),U_4422)
| ( U_4420 != U_4422
& U_4418 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_4421,U_4419,U_4417] :
( U_4419 = U_4421
| U_4417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4417),U_4419) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4417),U_4421) ) ),
inference(miniscope,[status(thm)],[f_1120_2]) ).
fof(f_1120_4,plain,
( ! [U_4422,U_4420,U_4418] :
( U_4420 != U_4422
| ~ sP275(U_4422,U_4420,U_4418) )
& ! [U_4422,U_4420,U_4418] :
( U_4418 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP275(U_4422,U_4420,U_4418) )
& ! [U_4422,U_4420,U_4418] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4418),U_4420) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4418),U_4422)
| sP275(U_4422,U_4420,U_4418) )
& ! [U_4419,U_4417,U_4421] :
( U_4419 = U_4421
| U_4417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4417),U_4419) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4417),U_4421) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275])],[f_1120_3]) ).
cnf(f_1120_5,plain,
( U_4419 = U_4421
| U_4417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4417),U_4419) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4417),U_4421) ),
inference(clausify,[status(thm)],[f_1120_4]) ).
cnf(f_1120_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4418),U_4420) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4418),U_4422)
| sP275(U_4422,U_4420,U_4418) ),
inference(clausify,[status(thm)],[f_1120_4]) ).
cnf(f_1120_7,plain,
( U_4418 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP275(U_4422,U_4420,U_4418) ),
inference(clausify,[status(thm)],[f_1120_4]) ).
cnf(f_1120_8,plain,
( U_4420 != U_4422
| ~ sP275(U_4422,U_4420,U_4418) ),
inference(clausify,[status(thm)],[f_1120_4]) ).
fof(f_1121_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).
fof(f_1121_2,plain,
! [U_4424,U_4423] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4423,U_4424)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4423),hAPP(c_Nat_OSuc,U_4424)),
inference(variable_rename,[status(thm)],[f_1121_1]) ).
fof(f_1121_3,plain,
! [U_4423,U_4424] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4423,U_4424)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4423),hAPP(c_Nat_OSuc,U_4424)),
inference(definitional_conversion,[status(esa)],[f_1121_2]) ).
cnf(f_1121_4,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4423,U_4424)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4423),hAPP(c_Nat_OSuc,U_4424)),
inference(clausify,[status(thm)],[f_1121_3]) ).
fof(f_1122_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_lessThan__Suc]) ).
fof(f_1122_2,plain,
! [U_4425] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4425)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4425),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4425)),
inference(variable_rename,[status(thm)],[f_1122_1]) ).
fof(f_1122_3,plain,
! [U_4425] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4425)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4425),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4425)),
inference(definitional_conversion,[status(esa)],[f_1122_2]) ).
cnf(f_1122_4,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4425)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4425),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4425)),
inference(clausify,[status(thm)],[f_1122_3]) ).
fof(f_1123_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan0]) ).
fof(f_1123_2,plain,
! [U_4426] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4426),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1123_1]) ).
fof(f_1123_3,plain,
! [U_4426] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4426),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1123_2]) ).
cnf(f_1123_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4426),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1123_3]) ).
fof(f_1124_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_atMost__Suc]) ).
fof(f_1124_2,plain,
! [U_4427] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4427)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4427)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4427)),
inference(variable_rename,[status(thm)],[f_1124_1]) ).
fof(f_1124_3,plain,
! [U_4427] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4427)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4427)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4427)),
inference(definitional_conversion,[status(esa)],[f_1124_2]) ).
cnf(f_1124_4,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4427)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4427)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4427)),
inference(clausify,[status(thm)],[f_1124_3]) ).
fof(f_1125_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_card__atMost]) ).
fof(f_1125_2,plain,
! [U_4428] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4428)) = hAPP(c_Nat_OSuc,U_4428),
inference(variable_rename,[status(thm)],[f_1125_1]) ).
fof(f_1125_3,plain,
! [U_4428] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4428)) = hAPP(c_Nat_OSuc,U_4428),
inference(definitional_conversion,[status(esa)],[f_1125_2]) ).
cnf(f_1125_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4428)) = hAPP(c_Nat_OSuc,U_4428),
inference(clausify,[status(thm)],[f_1125_3]) ).
fof(f_1126_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_atLeast__0]) ).
fof(f_1126_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_1126_1]) ).
cnf(f_1126_3,plain,
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)),
inference(clausify,[status(thm)],[f_1126_2]) ).
fof(f_1127_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_lessThan__0]) ).
fof(f_1127_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_1127_1]) ).
cnf(f_1127_3,plain,
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)),
inference(clausify,[status(thm)],[f_1127_2]) ).
fof(f_1128_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold]) ).
fof(f_1128_2,plain,
! [U_4432,U_4431,U_4430,U_4429] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4430,U_4429),U_4432),U_4431) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4429,U_4430,c_Groups_Oplus__class_Oplus(U_4429)),U_4432),c_Groups_Ozero__class_Ozero(U_4429)),U_4431)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4430),U_4431))
| ~ class_Groups_Ocomm__monoid__add(U_4429) ),
inference(variable_rename,[status(thm)],[f_1128_1]) ).
fof(f_1128_3,plain,
! [U_4429,U_4430,U_4431,U_4432] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4430,U_4429),U_4432),U_4431) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4429,U_4430,c_Groups_Oplus__class_Oplus(U_4429)),U_4432),c_Groups_Ozero__class_Ozero(U_4429)),U_4431)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4430),U_4431))
| ~ class_Groups_Ocomm__monoid__add(U_4429) ),
inference(definitional_conversion,[status(esa)],[f_1128_2]) ).
cnf(f_1128_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4430,U_4429),U_4432),U_4431) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4429,U_4430,c_Groups_Oplus__class_Oplus(U_4429)),U_4432),c_Groups_Ozero__class_Ozero(U_4429)),U_4431)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4430),U_4431))
| ~ class_Groups_Ocomm__monoid__add(U_4429) ),
inference(clausify,[status(thm)],[f_1128_3]) ).
fof(f_1129_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( ( ( 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)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_OF__eq]) ).
fof(f_1129_2,plain,
! [U_4436,U_4435,U_4434,U_4433] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4434,U_4433),U_4436),U_4435) = c_Groups_Ozero__class_Ozero(U_4433)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4434),U_4435)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4434,U_4433),U_4436),U_4435) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4433,U_4434,c_Groups_Oplus__class_Oplus(U_4433)),U_4436),c_Groups_Ozero__class_Ozero(U_4433)),U_4435)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4434),U_4435)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_4433) ),
inference(variable_rename,[status(thm)],[f_1129_1]) ).
fof(f_1129_3,plain,
( ! [U_4433,U_4434,U_4435,U_4436] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4434,U_4433),U_4436),U_4435) = c_Groups_Ozero__class_Ozero(U_4433)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4434),U_4435))
| ~ sP276(U_4433,U_4434,U_4435,U_4436) )
& ! [U_4433,U_4434,U_4435,U_4436] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4434,U_4433),U_4436),U_4435) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4433,U_4434,c_Groups_Oplus__class_Oplus(U_4433)),U_4436),c_Groups_Ozero__class_Ozero(U_4433)),U_4435)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4434),U_4435))
| ~ sP276(U_4433,U_4434,U_4435,U_4436) )
& ! [U_4433,U_4434,U_4435,U_4436] :
( sP276(U_4433,U_4434,U_4435,U_4436)
| ~ class_Groups_Ocomm__monoid__add(U_4433) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276])],[f_1129_2]) ).
cnf(f_1129_4,plain,
( sP276(U_4433,U_4434,U_4435,U_4436)
| ~ class_Groups_Ocomm__monoid__add(U_4433) ),
inference(clausify,[status(thm)],[f_1129_3]) ).
cnf(f_1129_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4434,U_4433),U_4436),U_4435) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4433,U_4434,c_Groups_Oplus__class_Oplus(U_4433)),U_4436),c_Groups_Ozero__class_Ozero(U_4433)),U_4435)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4434),U_4435))
| ~ sP276(U_4433,U_4434,U_4435,U_4436) ),
inference(clausify,[status(thm)],[f_1129_3]) ).
cnf(f_1129_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4434,U_4433),U_4436),U_4435) = c_Groups_Ozero__class_Ozero(U_4433)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4434),U_4435))
| ~ sP276(U_4433,U_4434,U_4435,U_4436) ),
inference(clausify,[status(thm)],[f_1129_3]) ).
fof(f_1130_1,plain,
! [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))) = V_n
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__1]) ).
fof(f_1130_2,plain,
! [U_4437] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4437),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4437
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4437)) ),
inference(variable_rename,[status(thm)],[f_1130_1]) ).
fof(f_1130_3,plain,
! [U_4437] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4437),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4437
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4437)) ),
inference(definitional_conversion,[status(esa)],[f_1130_2]) ).
cnf(f_1130_4,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4437),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4437
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4437)) ),
inference(clausify,[status(thm)],[f_1130_3]) ).
fof(f_1131_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_atMost__0]) ).
fof(f_1131_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1131_1]) ).
cnf(f_1131_3,plain,
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))),
inference(clausify,[status(thm)],[f_1131_2]) ).
fof(f_1132_1,plain,
! [V_f_2,V_m_2,V_n_2,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),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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_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,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) )
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__op__ivl__Suc]) ).
fof(f_1132_2,plain,
! [U_4441,U_4440,U_4439,U_4438] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),hAPP(c_Nat_OSuc,U_4439))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4438),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),U_4439))),hAPP(U_4441,U_4439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4439),U_4440)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),hAPP(c_Nat_OSuc,U_4439))) = c_Groups_Ozero__class_Ozero(U_4438)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4439),U_4440)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_4438) ),
inference(variable_rename,[status(thm)],[f_1132_1]) ).
fof(f_1132_3,plain,
( ! [U_4438,U_4439,U_4440,U_4441] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),hAPP(c_Nat_OSuc,U_4439))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4438),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),U_4439))),hAPP(U_4441,U_4439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4439),U_4440))
| ~ sP277(U_4438,U_4439,U_4440,U_4441) )
& ! [U_4438,U_4439,U_4440,U_4441] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),hAPP(c_Nat_OSuc,U_4439))) = c_Groups_Ozero__class_Ozero(U_4438)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4439),U_4440))
| ~ sP277(U_4438,U_4439,U_4440,U_4441) )
& ! [U_4438,U_4439,U_4440,U_4441] :
( sP277(U_4438,U_4439,U_4440,U_4441)
| ~ class_Groups_Ocomm__monoid__add(U_4438) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277])],[f_1132_2]) ).
cnf(f_1132_4,plain,
( sP277(U_4438,U_4439,U_4440,U_4441)
| ~ class_Groups_Ocomm__monoid__add(U_4438) ),
inference(clausify,[status(thm)],[f_1132_3]) ).
cnf(f_1132_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),hAPP(c_Nat_OSuc,U_4439))) = c_Groups_Ozero__class_Ozero(U_4438)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4439),U_4440))
| ~ sP277(U_4438,U_4439,U_4440,U_4441) ),
inference(clausify,[status(thm)],[f_1132_3]) ).
cnf(f_1132_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),hAPP(c_Nat_OSuc,U_4439))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4438),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4438),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4440),U_4439))),hAPP(U_4441,U_4439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4439),U_4440))
| ~ sP277(U_4438,U_4439,U_4440,U_4441) ),
inference(clausify,[status(thm)],[f_1132_3]) ).
fof(f_1133_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc1]) ).
fof(f_1133_2,plain,
! [U_4443,U_4442] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4442),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4442),U_4443)))),
inference(variable_rename,[status(thm)],[f_1133_1]) ).
fof(f_1133_3,plain,
! [U_4442,U_4443] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4442),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4442),U_4443)))),
inference(definitional_conversion,[status(esa)],[f_1133_2]) ).
cnf(f_1133_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4442),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4442),U_4443)))),
inference(clausify,[status(thm)],[f_1133_3]) ).
fof(f_1134_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc2]) ).
fof(f_1134_2,plain,
! [U_4445,U_4444] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4444),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4445),U_4444)))),
inference(variable_rename,[status(thm)],[f_1134_1]) ).
fof(f_1134_3,plain,
! [U_4445,U_4444] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4444),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4445),U_4444)))),
inference(definitional_conversion,[status(esa)],[f_1134_2]) ).
cnf(f_1134_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4444),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4445),U_4444)))),
inference(clausify,[status(thm)],[f_1134_3]) ).
fof(f_1135_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ! [B_k] : V_n_2 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) )
& ( ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).
fof(f_1135_2,plain,
! [U_4449,U_4448] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4448),U_4449))
| ! [U_4447] : U_4449 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4448),U_4447)) )
& ( ? [U_4446] : U_4449 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4448),U_4446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4448),U_4449)) ) ),
inference(variable_rename,[status(thm)],[f_1135_1]) ).
fof(f_1135_3,plain,
( ! [U_4453,U_4451] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4451),U_4453))
| ! [U_4447] : U_4453 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4451),U_4447)) )
& ! [U_4452,U_4450] :
( ? [U_4446] : U_4452 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4450),U_4446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4450),U_4452)) ) ),
inference(miniscope,[status(thm)],[f_1135_2]) ).
fof(f_1135_4,plain,
( ! [U_4453,U_4451] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4451),U_4453))
| ! [U_4447] : U_4453 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4451),U_4447)) )
& ! [U_4452,U_4450] :
( U_4452 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4450),sK105(U_4452,U_4450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4450),U_4452)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_4446,sK105(U_4452,U_4450))],[f_1135_3]) ).
fof(f_1135_5,plain,
( ! [U_4447,U_4451,U_4453] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4451),U_4453))
| U_4453 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4451),U_4447)) )
& ! [U_4452,U_4450] :
( U_4452 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4450),sK105(U_4452,U_4450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4450),U_4452)) ) ),
inference(definitional_conversion,[status(esa)],[f_1135_4]) ).
cnf(f_1135_6,plain,
( U_4452 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4450),sK105(U_4452,U_4450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4450),U_4452)) ),
inference(clausify,[status(thm)],[f_1135_5]) ).
cnf(f_1135_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4451),U_4453))
| U_4453 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4451),U_4447)) ),
inference(clausify,[status(thm)],[f_1135_5]) ).
fof(f_1136_1,plain,
! [V_m_2,V_n_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).
fof(f_1136_2,plain,
! [U_4455,U_4454] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4454),U_4455))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4454)),U_4455)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4454)),U_4455))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4454),U_4455)) ) ),
inference(variable_rename,[status(thm)],[f_1136_1]) ).
fof(f_1136_3,plain,
( ! [U_4459,U_4457] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4457),U_4459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4457)),U_4459)) )
& ! [U_4458,U_4456] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4456)),U_4458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4456),U_4458)) ) ),
inference(miniscope,[status(thm)],[f_1136_2]) ).
fof(f_1136_4,plain,
( ! [U_4457,U_4459] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4457),U_4459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4457)),U_4459)) )
& ! [U_4458,U_4456] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4456)),U_4458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4456),U_4458)) ) ),
inference(definitional_conversion,[status(esa)],[f_1136_3]) ).
cnf(f_1136_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4456)),U_4458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4456),U_4458)) ),
inference(clausify,[status(thm)],[f_1136_4]) ).
cnf(f_1136_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4457),U_4459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4457)),U_4459)) ),
inference(clausify,[status(thm)],[f_1136_4]) ).
fof(f_1137_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).
fof(f_1137_2,plain,
! [U_4461,U_4460] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4460),hAPP(c_Nat_OSuc,U_4461)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4460),U_4461)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4460),U_4461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4460),hAPP(c_Nat_OSuc,U_4461))) ) ),
inference(variable_rename,[status(thm)],[f_1137_1]) ).
fof(f_1137_3,plain,
( ! [U_4465,U_4463] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4463),hAPP(c_Nat_OSuc,U_4465)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4463),U_4465)) )
& ! [U_4464,U_4462] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4462),U_4464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4462),hAPP(c_Nat_OSuc,U_4464))) ) ),
inference(miniscope,[status(thm)],[f_1137_2]) ).
fof(f_1137_4,plain,
( ! [U_4463,U_4465] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4463),hAPP(c_Nat_OSuc,U_4465)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4463),U_4465)) )
& ! [U_4464,U_4462] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4462),U_4464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4462),hAPP(c_Nat_OSuc,U_4464))) ) ),
inference(definitional_conversion,[status(esa)],[f_1137_3]) ).
cnf(f_1137_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4462),U_4464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4462),hAPP(c_Nat_OSuc,U_4464))) ),
inference(clausify,[status(thm)],[f_1137_4]) ).
cnf(f_1137_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4463),hAPP(c_Nat_OSuc,U_4465)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4463),U_4465)) ),
inference(clausify,[status(thm)],[f_1137_4]) ).
fof(f_1138_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).
fof(f_1138_2,plain,
! [U_4467,U_4466] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4466)),U_4467))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4466),U_4467)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4466),U_4467))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4466)),U_4467)) ) ),
inference(variable_rename,[status(thm)],[f_1138_1]) ).
fof(f_1138_3,plain,
( ! [U_4471,U_4469] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4469)),U_4471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4469),U_4471)) )
& ! [U_4470,U_4468] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4468),U_4470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4468)),U_4470)) ) ),
inference(miniscope,[status(thm)],[f_1138_2]) ).
fof(f_1138_4,plain,
( ! [U_4469,U_4471] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4469)),U_4471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4469),U_4471)) )
& ! [U_4470,U_4468] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4468),U_4470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4468)),U_4470)) ) ),
inference(definitional_conversion,[status(esa)],[f_1138_3]) ).
cnf(f_1138_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4468),U_4470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4468)),U_4470)) ),
inference(clausify,[status(thm)],[f_1138_4]) ).
cnf(f_1138_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4469)),U_4471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4469),U_4471)) ),
inference(clausify,[status(thm)],[f_1138_4]) ).
fof(f_1139_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc]) ).
fof(f_1139_2,plain,
! [U_4473,U_4472] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4472),hAPP(c_Nat_OSuc,U_4473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4472),U_4473)) ),
inference(variable_rename,[status(thm)],[f_1139_1]) ).
fof(f_1139_3,plain,
! [U_4472,U_4473] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4472),hAPP(c_Nat_OSuc,U_4473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4472),U_4473)) ),
inference(definitional_conversion,[status(esa)],[f_1139_2]) ).
cnf(f_1139_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4472),hAPP(c_Nat_OSuc,U_4473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4472),U_4473)) ),
inference(clausify,[status(thm)],[f_1139_3]) ).
fof(f_1140_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leI]) ).
fof(f_1140_2,plain,
! [U_4475,U_4474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4474)),U_4475))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4474),U_4475)) ),
inference(variable_rename,[status(thm)],[f_1140_1]) ).
fof(f_1140_3,plain,
! [U_4474,U_4475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4474)),U_4475))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4474),U_4475)) ),
inference(definitional_conversion,[status(esa)],[f_1140_2]) ).
cnf(f_1140_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4474)),U_4475))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4474),U_4475)) ),
inference(clausify,[status(thm)],[f_1140_3]) ).
fof(f_1141_1,plain,
! [V_n_2,V_m_2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
| V_n_2 != V_m_2 )
& ( V_n_2 = V_m_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).
fof(f_1141_2,plain,
! [U_4477,U_4476] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4477),hAPP(c_Nat_OSuc,U_4476)))
| U_4477 != U_4476 )
& ( U_4477 = U_4476
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4477),hAPP(c_Nat_OSuc,U_4476))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4476),U_4477)) ),
inference(variable_rename,[status(thm)],[f_1141_1]) ).
fof(f_1141_3,plain,
( ! [U_4476,U_4477] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4477),hAPP(c_Nat_OSuc,U_4476)))
| U_4477 != U_4476
| ~ sP278(U_4476,U_4477) )
& ! [U_4476,U_4477] :
( U_4477 = U_4476
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4477),hAPP(c_Nat_OSuc,U_4476)))
| ~ sP278(U_4476,U_4477) )
& ! [U_4476,U_4477] :
( sP278(U_4476,U_4477)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4476),U_4477)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP278])],[f_1141_2]) ).
cnf(f_1141_4,plain,
( sP278(U_4476,U_4477)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4476),U_4477)) ),
inference(clausify,[status(thm)],[f_1141_3]) ).
cnf(f_1141_5,plain,
( U_4477 = U_4476
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4477),hAPP(c_Nat_OSuc,U_4476)))
| ~ sP278(U_4476,U_4477) ),
inference(clausify,[status(thm)],[f_1141_3]) ).
cnf(f_1141_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4477),hAPP(c_Nat_OSuc,U_4476)))
| U_4477 != U_4476
| ~ sP278(U_4476,U_4477) ),
inference(clausify,[status(thm)],[f_1141_3]) ).
fof(f_1142_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD]) ).
fof(f_1142_2,plain,
! [U_4479,U_4478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4478),U_4479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4478)),U_4479)) ),
inference(variable_rename,[status(thm)],[f_1142_1]) ).
fof(f_1142_3,plain,
! [U_4479,U_4478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4478),U_4479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4478)),U_4479)) ),
inference(definitional_conversion,[status(esa)],[f_1142_2]) ).
cnf(f_1142_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4478),U_4479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4478)),U_4479)) ),
inference(clausify,[status(thm)],[f_1142_3]) ).
fof(f_1143_1,plain,
! [V_f_2,V_m_2,V_n_2,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,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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_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,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) )
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).
fof(f_1143_2,plain,
! [U_4483,U_4482,U_4481,U_4480] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,hAPP(c_Nat_OSuc,U_4481))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4480),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,U_4481))),hAPP(U_4483,hAPP(c_Nat_OSuc,U_4481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4481)),U_4482)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,hAPP(c_Nat_OSuc,U_4481))) = c_Groups_Ozero__class_Ozero(U_4480)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4481)),U_4482)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_4480) ),
inference(variable_rename,[status(thm)],[f_1143_1]) ).
fof(f_1143_3,plain,
( ! [U_4480,U_4481,U_4482,U_4483] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,hAPP(c_Nat_OSuc,U_4481))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4480),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,U_4481))),hAPP(U_4483,hAPP(c_Nat_OSuc,U_4481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4481)),U_4482))
| ~ sP279(U_4480,U_4481,U_4482,U_4483) )
& ! [U_4480,U_4481,U_4482,U_4483] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,hAPP(c_Nat_OSuc,U_4481))) = c_Groups_Ozero__class_Ozero(U_4480)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4481)),U_4482))
| ~ sP279(U_4480,U_4481,U_4482,U_4483) )
& ! [U_4480,U_4481,U_4482,U_4483] :
( sP279(U_4480,U_4481,U_4482,U_4483)
| ~ class_Groups_Ocomm__monoid__add(U_4480) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279])],[f_1143_2]) ).
cnf(f_1143_4,plain,
( sP279(U_4480,U_4481,U_4482,U_4483)
| ~ class_Groups_Ocomm__monoid__add(U_4480) ),
inference(clausify,[status(thm)],[f_1143_3]) ).
cnf(f_1143_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,hAPP(c_Nat_OSuc,U_4481))) = c_Groups_Ozero__class_Ozero(U_4480)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4481)),U_4482))
| ~ sP279(U_4480,U_4481,U_4482,U_4483) ),
inference(clausify,[status(thm)],[f_1143_3]) ).
cnf(f_1143_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,hAPP(c_Nat_OSuc,U_4481))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4480),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4480),U_4483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4482,U_4481))),hAPP(U_4483,hAPP(c_Nat_OSuc,U_4481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4481)),U_4482))
| ~ sP279(U_4480,U_4481,U_4482,U_4483) ),
inference(clausify,[status(thm)],[f_1143_3]) ).
fof(f_1144_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_diff__less__Suc]) ).
fof(f_1144_2,plain,
! [U_4485,U_4484] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4484),U_4485)),hAPP(c_Nat_OSuc,U_4484))),
inference(variable_rename,[status(thm)],[f_1144_1]) ).
fof(f_1144_3,plain,
! [U_4485,U_4484] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4484),U_4485)),hAPP(c_Nat_OSuc,U_4484))),
inference(definitional_conversion,[status(esa)],[f_1144_2]) ).
cnf(f_1144_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4484),U_4485)),hAPP(c_Nat_OSuc,U_4484))),
inference(clausify,[status(thm)],[f_1144_3]) ).
fof(f_1145_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1]) ).
fof(f_1145_2,plain,
! [U_4488,U_4487,U_4486] :
( ( 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,U_4486)),U_4487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4486)),U_4488)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4487),U_4488)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4487),U_4488))
| ~ 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,U_4486)),U_4487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4486)),U_4488))) ) ),
inference(variable_rename,[status(thm)],[f_1145_1]) ).
fof(f_1145_3,plain,
( ! [U_4494,U_4492] :
( ! [U_4490] : 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,U_4490)),U_4492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4490)),U_4494)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4492),U_4494)) )
& ! [U_4493,U_4491] :
( ! [U_4489] : ~ 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,U_4489)),U_4491)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4489)),U_4493)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4491),U_4493)) ) ),
inference(miniscope,[status(thm)],[f_1145_2]) ).
fof(f_1145_4,plain,
( ! [U_4494,U_4490,U_4492] :
( 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,U_4490)),U_4492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4490)),U_4494)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4492),U_4494)) )
& ! [U_4489,U_4491,U_4493] :
( ~ 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,U_4489)),U_4491)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4489)),U_4493)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4491),U_4493)) ) ),
inference(definitional_conversion,[status(esa)],[f_1145_3]) ).
cnf(f_1145_5,plain,
( ~ 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,U_4489)),U_4491)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4489)),U_4493)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4491),U_4493)) ),
inference(clausify,[status(thm)],[f_1145_4]) ).
cnf(f_1145_6,plain,
( 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,U_4490)),U_4492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4490)),U_4494)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4492),U_4494)) ),
inference(clausify,[status(thm)],[f_1145_4]) ).
fof(f_1146_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mult__Suc]) ).
fof(f_1146_2,plain,
! [U_4496,U_4495] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4495)),U_4496) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4495),U_4496)),
inference(variable_rename,[status(thm)],[f_1146_1]) ).
fof(f_1146_3,plain,
! [U_4496,U_4495] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4495)),U_4496) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4495),U_4496)),
inference(definitional_conversion,[status(esa)],[f_1146_2]) ).
cnf(f_1146_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4495)),U_4496) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4495),U_4496)),
inference(clausify,[status(thm)],[f_1146_3]) ).
fof(f_1147_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mult__Suc__right]) ).
fof(f_1147_2,plain,
! [U_4498,U_4497] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4497),hAPP(c_Nat_OSuc,U_4498)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4497),U_4498)),
inference(variable_rename,[status(thm)],[f_1147_1]) ).
fof(f_1147_3,plain,
! [U_4497,U_4498] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4497),hAPP(c_Nat_OSuc,U_4498)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4497),U_4498)),
inference(definitional_conversion,[status(esa)],[f_1147_2]) ).
cnf(f_1147_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4497),hAPP(c_Nat_OSuc,U_4498)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4497),U_4498)),
inference(clausify,[status(thm)],[f_1147_3]) ).
fof(f_1148_1,plain,
! [V_m,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__le]) ).
fof(f_1148_2,plain,
! [U_4500,U_4499] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4500)),U_4499) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4499),U_4500)) ),
inference(variable_rename,[status(thm)],[f_1148_1]) ).
fof(f_1148_3,plain,
! [U_4499,U_4500] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4500)),U_4499) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4499),U_4500)) ),
inference(definitional_conversion,[status(esa)],[f_1148_2]) ).
cnf(f_1148_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4500)),U_4499) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4499),U_4500)) ),
inference(clausify,[status(thm)],[f_1148_3]) ).
fof(f_1149_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1]) ).
fof(f_1149_2,plain,
! [U_4503,U_4502,U_4501] :
( ( 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,U_4501)),U_4502)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4501)),U_4503)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4502),U_4503)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4502),U_4503))
| ~ 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,U_4501)),U_4502)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4501)),U_4503))) ) ),
inference(variable_rename,[status(thm)],[f_1149_1]) ).
fof(f_1149_3,plain,
( ! [U_4509,U_4507] :
( ! [U_4505] : 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,U_4505)),U_4507)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4505)),U_4509)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4507),U_4509)) )
& ! [U_4508,U_4506] :
( ! [U_4504] : ~ 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,U_4504)),U_4506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4504)),U_4508)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4506),U_4508)) ) ),
inference(miniscope,[status(thm)],[f_1149_2]) ).
fof(f_1149_4,plain,
( ! [U_4509,U_4505,U_4507] :
( 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,U_4505)),U_4507)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4505)),U_4509)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4507),U_4509)) )
& ! [U_4506,U_4504,U_4508] :
( ~ 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,U_4504)),U_4506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4504)),U_4508)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4506),U_4508)) ) ),
inference(definitional_conversion,[status(esa)],[f_1149_3]) ).
cnf(f_1149_5,plain,
( ~ 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,U_4504)),U_4506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4504)),U_4508)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4506),U_4508)) ),
inference(clausify,[status(thm)],[f_1149_4]) ).
cnf(f_1149_6,plain,
( 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,U_4505)),U_4507)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4505)),U_4509)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4507),U_4509)) ),
inference(clausify,[status(thm)],[f_1149_4]) ).
fof(f_1150_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ 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))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).
fof(f_1150_2,plain,
! [U_4511,U_4510] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4510),U_4511),U_4511)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),U_4511)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),U_4511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4510),U_4511),U_4511))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4510) ),
inference(variable_rename,[status(thm)],[f_1150_1]) ).
fof(f_1150_3,plain,
( ! [U_4510,U_4511] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4510),U_4511),U_4511)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),U_4511))
| ~ sP280(U_4510,U_4511) )
& ! [U_4510,U_4511] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),U_4511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4510),U_4511),U_4511)))
| ~ sP280(U_4510,U_4511) )
& ! [U_4510,U_4511] :
( sP280(U_4510,U_4511)
| ~ class_Groups_Olinordered__ab__group__add(U_4510) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP280])],[f_1150_2]) ).
cnf(f_1150_4,plain,
( sP280(U_4510,U_4511)
| ~ class_Groups_Olinordered__ab__group__add(U_4510) ),
inference(clausify,[status(thm)],[f_1150_3]) ).
cnf(f_1150_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),U_4511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4510),U_4511),U_4511)))
| ~ sP280(U_4510,U_4511) ),
inference(clausify,[status(thm)],[f_1150_3]) ).
cnf(f_1150_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4510),U_4511),U_4511)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4510),c_Groups_Ozero__class_Ozero(U_4510)),U_4511))
| ~ sP280(U_4510,U_4511) ),
inference(clausify,[status(thm)],[f_1150_3]) ).
fof(f_1151_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ 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))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).
fof(f_1151_2,plain,
! [U_4513,U_4512] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4512),U_4513),U_4513)),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),U_4513),c_Groups_Ozero__class_Ozero(U_4512))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),U_4513),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4512),U_4513),U_4513)),c_Groups_Ozero__class_Ozero(U_4512))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4512) ),
inference(variable_rename,[status(thm)],[f_1151_1]) ).
fof(f_1151_3,plain,
( ! [U_4513,U_4512] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4512),U_4513),U_4513)),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),U_4513),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ sP281(U_4513,U_4512) )
& ! [U_4513,U_4512] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),U_4513),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4512),U_4513),U_4513)),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ sP281(U_4513,U_4512) )
& ! [U_4513,U_4512] :
( sP281(U_4513,U_4512)
| ~ class_Groups_Olinordered__ab__group__add(U_4512) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281])],[f_1151_2]) ).
cnf(f_1151_4,plain,
( sP281(U_4513,U_4512)
| ~ class_Groups_Olinordered__ab__group__add(U_4512) ),
inference(clausify,[status(thm)],[f_1151_3]) ).
cnf(f_1151_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),U_4513),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4512),U_4513),U_4513)),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ sP281(U_4513,U_4512) ),
inference(clausify,[status(thm)],[f_1151_3]) ).
cnf(f_1151_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4512),U_4513),U_4513)),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4512),U_4513),c_Groups_Ozero__class_Ozero(U_4512)))
| ~ sP281(U_4513,U_4512) ),
inference(clausify,[status(thm)],[f_1151_3]) ).
fof(f_1152_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg]) ).
fof(f_1152_2,plain,
! [U_4516,U_4515,U_4514] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4514),U_4515),U_4516)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),U_4516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),U_4515))
| ~ class_Groups_Oordered__comm__monoid__add(U_4514) ),
inference(variable_rename,[status(thm)],[f_1152_1]) ).
fof(f_1152_3,plain,
! [U_4515,U_4514,U_4516] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4514),U_4515),U_4516)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),U_4516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),U_4515))
| ~ class_Groups_Oordered__comm__monoid__add(U_4514) ),
inference(definitional_conversion,[status(esa)],[f_1152_2]) ).
cnf(f_1152_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4514),U_4515),U_4516)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),U_4516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4514),c_Groups_Ozero__class_Ozero(U_4514)),U_4515))
| ~ class_Groups_Oordered__comm__monoid__add(U_4514) ),
inference(clausify,[status(thm)],[f_1152_3]) ).
fof(f_1153_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
| ~ class_Groups_Oordered__comm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).
fof(f_1153_2,plain,
! [U_4519,U_4518,U_4517] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4517),U_4518),U_4519) = c_Groups_Ozero__class_Ozero(U_4517)
| U_4519 != c_Groups_Ozero__class_Ozero(U_4517)
| U_4518 != c_Groups_Ozero__class_Ozero(U_4517) )
& ( ( U_4519 = c_Groups_Ozero__class_Ozero(U_4517)
& U_4518 = c_Groups_Ozero__class_Ozero(U_4517) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4517),U_4518),U_4519) != c_Groups_Ozero__class_Ozero(U_4517) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),c_Groups_Ozero__class_Ozero(U_4517)),U_4519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),c_Groups_Ozero__class_Ozero(U_4517)),U_4518))
| ~ class_Groups_Oordered__comm__monoid__add(U_4517) ),
inference(variable_rename,[status(thm)],[f_1153_1]) ).
fof(f_1153_3,plain,
( ! [U_4517,U_4518,U_4519] :
( U_4519 = c_Groups_Ozero__class_Ozero(U_4517)
| ~ sP282(U_4517,U_4518,U_4519) )
& ! [U_4517,U_4518,U_4519] :
( U_4518 = c_Groups_Ozero__class_Ozero(U_4517)
| ~ sP282(U_4517,U_4518,U_4519) )
& ! [U_4517,U_4518,U_4519] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4517),U_4518),U_4519) = c_Groups_Ozero__class_Ozero(U_4517)
| U_4519 != c_Groups_Ozero__class_Ozero(U_4517)
| U_4518 != c_Groups_Ozero__class_Ozero(U_4517)
| ~ sP283(U_4517,U_4518,U_4519) )
& ! [U_4517,U_4518,U_4519] :
( sP282(U_4517,U_4518,U_4519)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4517),U_4518),U_4519) != c_Groups_Ozero__class_Ozero(U_4517)
| ~ sP283(U_4517,U_4518,U_4519) )
& ! [U_4517,U_4518,U_4519] :
( sP283(U_4517,U_4518,U_4519)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),c_Groups_Ozero__class_Ozero(U_4517)),U_4519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),c_Groups_Ozero__class_Ozero(U_4517)),U_4518))
| ~ class_Groups_Oordered__comm__monoid__add(U_4517) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282,sP283])],[f_1153_2]) ).
cnf(f_1153_4,plain,
( sP283(U_4517,U_4518,U_4519)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),c_Groups_Ozero__class_Ozero(U_4517)),U_4519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),c_Groups_Ozero__class_Ozero(U_4517)),U_4518))
| ~ class_Groups_Oordered__comm__monoid__add(U_4517) ),
inference(clausify,[status(thm)],[f_1153_3]) ).
cnf(f_1153_5,plain,
( sP282(U_4517,U_4518,U_4519)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4517),U_4518),U_4519) != c_Groups_Ozero__class_Ozero(U_4517)
| ~ sP283(U_4517,U_4518,U_4519) ),
inference(clausify,[status(thm)],[f_1153_3]) ).
cnf(f_1153_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4517),U_4518),U_4519) = c_Groups_Ozero__class_Ozero(U_4517)
| U_4519 != c_Groups_Ozero__class_Ozero(U_4517)
| U_4518 != c_Groups_Ozero__class_Ozero(U_4517)
| ~ sP283(U_4517,U_4518,U_4519) ),
inference(clausify,[status(thm)],[f_1153_3]) ).
cnf(f_1153_7,plain,
( U_4518 = c_Groups_Ozero__class_Ozero(U_4517)
| ~ sP282(U_4517,U_4518,U_4519) ),
inference(clausify,[status(thm)],[f_1153_3]) ).
cnf(f_1153_8,plain,
( U_4519 = c_Groups_Ozero__class_Ozero(U_4517)
| ~ sP282(U_4517,U_4518,U_4519) ),
inference(clausify,[status(thm)],[f_1153_3]) ).
fof(f_1154_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__increasing]) ).
fof(f_1154_2,plain,
! [U_4523,U_4522,U_4521,U_4520] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),U_4522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4520),U_4521),U_4523)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),U_4522),U_4523))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),c_Groups_Ozero__class_Ozero(U_4520)),U_4521))
| ~ class_Groups_Oordered__comm__monoid__add(U_4520) ),
inference(variable_rename,[status(thm)],[f_1154_1]) ).
fof(f_1154_3,plain,
! [U_4523,U_4522,U_4521,U_4520] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),U_4522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4520),U_4521),U_4523)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),U_4522),U_4523))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),c_Groups_Ozero__class_Ozero(U_4520)),U_4521))
| ~ class_Groups_Oordered__comm__monoid__add(U_4520) ),
inference(definitional_conversion,[status(esa)],[f_1154_2]) ).
cnf(f_1154_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),U_4522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4520),U_4521),U_4523)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),U_4522),U_4523))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4520),c_Groups_Ozero__class_Ozero(U_4520)),U_4521))
| ~ class_Groups_Oordered__comm__monoid__add(U_4520) ),
inference(clausify,[status(thm)],[f_1154_3]) ).
fof(f_1155_1,plain,
! [V_a,V_b,V_c,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__increasing2]) ).
fof(f_1155_2,plain,
! [U_4527,U_4526,U_4525,U_4524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),U_4526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4524),U_4527),U_4525)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),U_4526),U_4527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),c_Groups_Ozero__class_Ozero(U_4524)),U_4525))
| ~ class_Groups_Oordered__comm__monoid__add(U_4524) ),
inference(variable_rename,[status(thm)],[f_1155_1]) ).
fof(f_1155_3,plain,
! [U_4526,U_4527,U_4524,U_4525] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),U_4526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4524),U_4527),U_4525)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),U_4526),U_4527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),c_Groups_Ozero__class_Ozero(U_4524)),U_4525))
| ~ class_Groups_Oordered__comm__monoid__add(U_4524) ),
inference(definitional_conversion,[status(esa)],[f_1155_2]) ).
cnf(f_1155_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),U_4526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4524),U_4527),U_4525)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),U_4526),U_4527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4524),c_Groups_Ozero__class_Ozero(U_4524)),U_4525))
| ~ class_Groups_Oordered__comm__monoid__add(U_4524) ),
inference(clausify,[status(thm)],[f_1155_3]) ).
fof(f_1156_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos]) ).
fof(f_1156_2,plain,
! [U_4530,U_4529,U_4528] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4528),U_4529),U_4530)),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),U_4530),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),U_4529),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4528) ),
inference(variable_rename,[status(thm)],[f_1156_1]) ).
fof(f_1156_3,plain,
! [U_4528,U_4529,U_4530] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4528),U_4529),U_4530)),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),U_4530),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),U_4529),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4528) ),
inference(definitional_conversion,[status(esa)],[f_1156_2]) ).
cnf(f_1156_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4528),U_4529),U_4530)),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),U_4530),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4528),U_4529),c_Groups_Ozero__class_Ozero(U_4528)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4528) ),
inference(clausify,[status(thm)],[f_1156_3]) ).
fof(f_1157_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le]) ).
fof(f_1157_2,plain,
! [U_4533,U_4532,U_4531] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4531),U_4532),U_4533)),c_Groups_Ozero__class_Ozero(U_4531)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),c_Groups_Ozero__class_Ozero(U_4531)),U_4533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),U_4532),c_Groups_Ozero__class_Ozero(U_4531))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),U_4533),c_Groups_Ozero__class_Ozero(U_4531)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),c_Groups_Ozero__class_Ozero(U_4531)),U_4532)) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_4531) ),
inference(variable_rename,[status(thm)],[f_1157_1]) ).
fof(f_1157_3,plain,
( ! [U_4531,U_4532,U_4533] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),c_Groups_Ozero__class_Ozero(U_4531)),U_4533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),U_4532),c_Groups_Ozero__class_Ozero(U_4531)))
| ~ sP284(U_4531,U_4532,U_4533) )
& ! [U_4531,U_4532,U_4533] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),U_4533),c_Groups_Ozero__class_Ozero(U_4531)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),c_Groups_Ozero__class_Ozero(U_4531)),U_4532))
| ~ sP284(U_4531,U_4532,U_4533) )
& ! [U_4531,U_4532,U_4533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4531),U_4532),U_4533)),c_Groups_Ozero__class_Ozero(U_4531)))
| sP284(U_4531,U_4532,U_4533)
| ~ class_Rings_Oordered__cancel__semiring(U_4531) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284])],[f_1157_2]) ).
cnf(f_1157_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4531),U_4532),U_4533)),c_Groups_Ozero__class_Ozero(U_4531)))
| sP284(U_4531,U_4532,U_4533)
| ~ class_Rings_Oordered__cancel__semiring(U_4531) ),
inference(clausify,[status(thm)],[f_1157_3]) ).
cnf(f_1157_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),U_4533),c_Groups_Ozero__class_Ozero(U_4531)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),c_Groups_Ozero__class_Ozero(U_4531)),U_4532))
| ~ sP284(U_4531,U_4532,U_4533) ),
inference(clausify,[status(thm)],[f_1157_3]) ).
cnf(f_1157_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),c_Groups_Ozero__class_Ozero(U_4531)),U_4533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4531),U_4532),c_Groups_Ozero__class_Ozero(U_4531)))
| ~ sP284(U_4531,U_4532,U_4533) ),
inference(clausify,[status(thm)],[f_1157_3]) ).
fof(f_1158_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le]) ).
fof(f_1158_2,plain,
! [U_4536,U_4535,U_4534] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4534),U_4535),U_4536)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),U_4536),c_Groups_Ozero__class_Ozero(U_4534)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),U_4535),c_Groups_Ozero__class_Ozero(U_4534))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),U_4536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),U_4535)) ) )
| ~ class_Rings_Oordered__ring(U_4534) ),
inference(variable_rename,[status(thm)],[f_1158_1]) ).
fof(f_1158_3,plain,
( ! [U_4536,U_4534,U_4535] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),U_4536),c_Groups_Ozero__class_Ozero(U_4534)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),U_4535),c_Groups_Ozero__class_Ozero(U_4534)))
| ~ sP285(U_4536,U_4534,U_4535) )
& ! [U_4536,U_4534,U_4535] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),U_4536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),U_4535))
| ~ sP285(U_4536,U_4534,U_4535) )
& ! [U_4536,U_4534,U_4535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4534),U_4535),U_4536)))
| sP285(U_4536,U_4534,U_4535)
| ~ class_Rings_Oordered__ring(U_4534) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP285])],[f_1158_2]) ).
cnf(f_1158_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4534),U_4535),U_4536)))
| sP285(U_4536,U_4534,U_4535)
| ~ class_Rings_Oordered__ring(U_4534) ),
inference(clausify,[status(thm)],[f_1158_3]) ).
cnf(f_1158_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),U_4536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),c_Groups_Ozero__class_Ozero(U_4534)),U_4535))
| ~ sP285(U_4536,U_4534,U_4535) ),
inference(clausify,[status(thm)],[f_1158_3]) ).
cnf(f_1158_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),U_4536),c_Groups_Ozero__class_Ozero(U_4534)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4534),U_4535),c_Groups_Ozero__class_Ozero(U_4534)))
| ~ sP285(U_4536,U_4534,U_4535) ),
inference(clausify,[status(thm)],[f_1158_3]) ).
fof(f_1159_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__mono]) ).
fof(f_1159_2,plain,
! [U_4541,U_4540,U_4539,U_4538,U_4537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4537),U_4538),U_4540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4537),U_4539),U_4541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),c_Groups_Ozero__class_Ozero(U_4537)),U_4540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),c_Groups_Ozero__class_Ozero(U_4537)),U_4539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),U_4540),U_4541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),U_4538),U_4539))
| ~ class_Rings_Oordered__semiring(U_4537) ),
inference(variable_rename,[status(thm)],[f_1159_1]) ).
fof(f_1159_3,plain,
! [U_4538,U_4539,U_4541,U_4540,U_4537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4537),U_4538),U_4540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4537),U_4539),U_4541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),c_Groups_Ozero__class_Ozero(U_4537)),U_4540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),c_Groups_Ozero__class_Ozero(U_4537)),U_4539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),U_4540),U_4541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),U_4538),U_4539))
| ~ class_Rings_Oordered__semiring(U_4537) ),
inference(definitional_conversion,[status(esa)],[f_1159_2]) ).
cnf(f_1159_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4537),U_4538),U_4540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4537),U_4539),U_4541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),c_Groups_Ozero__class_Ozero(U_4537)),U_4540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),c_Groups_Ozero__class_Ozero(U_4537)),U_4539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),U_4540),U_4541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4537),U_4538),U_4539))
| ~ class_Rings_Oordered__semiring(U_4537) ),
inference(clausify,[status(thm)],[f_1159_3]) ).
fof(f_1160_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__mono_H]) ).
fof(f_1160_2,plain,
! [U_4546,U_4545,U_4544,U_4543,U_4542] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4542),U_4543),U_4545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4542),U_4544),U_4546)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),c_Groups_Ozero__class_Ozero(U_4542)),U_4545))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),c_Groups_Ozero__class_Ozero(U_4542)),U_4543))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),U_4545),U_4546))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),U_4543),U_4544))
| ~ class_Rings_Oordered__semiring(U_4542) ),
inference(variable_rename,[status(thm)],[f_1160_1]) ).
fof(f_1160_3,plain,
! [U_4543,U_4544,U_4545,U_4542,U_4546] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4542),U_4543),U_4545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4542),U_4544),U_4546)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),c_Groups_Ozero__class_Ozero(U_4542)),U_4545))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),c_Groups_Ozero__class_Ozero(U_4542)),U_4543))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),U_4545),U_4546))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),U_4543),U_4544))
| ~ class_Rings_Oordered__semiring(U_4542) ),
inference(definitional_conversion,[status(esa)],[f_1160_2]) ).
cnf(f_1160_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4542),U_4543),U_4545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4542),U_4544),U_4546)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),c_Groups_Ozero__class_Ozero(U_4542)),U_4545))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),c_Groups_Ozero__class_Ozero(U_4542)),U_4543))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),U_4545),U_4546))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4542),U_4543),U_4544))
| ~ class_Rings_Oordered__semiring(U_4542) ),
inference(clausify,[status(thm)],[f_1160_3]) ).
fof(f_1161_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg]) ).
fof(f_1161_2,plain,
! [U_4550,U_4549,U_4548,U_4547] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4547),U_4550),U_4549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4547),U_4550),U_4548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),U_4550),c_Groups_Ozero__class_Ozero(U_4547)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),U_4548),U_4549))
| ~ class_Rings_Oordered__ring(U_4547) ),
inference(variable_rename,[status(thm)],[f_1161_1]) ).
fof(f_1161_3,plain,
! [U_4548,U_4549,U_4550,U_4547] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4547),U_4550),U_4549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4547),U_4550),U_4548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),U_4550),c_Groups_Ozero__class_Ozero(U_4547)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),U_4548),U_4549))
| ~ class_Rings_Oordered__ring(U_4547) ),
inference(definitional_conversion,[status(esa)],[f_1161_2]) ).
cnf(f_1161_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4547),U_4550),U_4549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4547),U_4550),U_4548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),U_4550),c_Groups_Ozero__class_Ozero(U_4547)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4547),U_4548),U_4549))
| ~ class_Rings_Oordered__ring(U_4547) ),
inference(clausify,[status(thm)],[f_1161_3]) ).
fof(f_1162_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg]) ).
fof(f_1162_2,plain,
! [U_4554,U_4553,U_4552,U_4551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4551),U_4553),U_4554)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4551),U_4552),U_4554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),U_4554),c_Groups_Ozero__class_Ozero(U_4551)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),U_4552),U_4553))
| ~ class_Rings_Oordered__ring(U_4551) ),
inference(variable_rename,[status(thm)],[f_1162_1]) ).
fof(f_1162_3,plain,
! [U_4551,U_4552,U_4553,U_4554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4551),U_4553),U_4554)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4551),U_4552),U_4554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),U_4554),c_Groups_Ozero__class_Ozero(U_4551)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),U_4552),U_4553))
| ~ class_Rings_Oordered__ring(U_4551) ),
inference(definitional_conversion,[status(esa)],[f_1162_2]) ).
cnf(f_1162_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4551),U_4553),U_4554)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4551),U_4552),U_4554)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),U_4554),c_Groups_Ozero__class_Ozero(U_4551)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4551),U_4552),U_4553))
| ~ class_Rings_Oordered__ring(U_4551) ),
inference(clausify,[status(thm)],[f_1162_3]) ).
fof(f_1163_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Rings_Oordered__comm__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono]) ).
fof(f_1163_2,plain,
! [U_4558,U_4557,U_4556,U_4555] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4555),U_4558),U_4556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4555),U_4558),U_4557)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),c_Groups_Ozero__class_Ozero(U_4555)),U_4558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),U_4556),U_4557))
| ~ class_Rings_Oordered__comm__semiring(U_4555) ),
inference(variable_rename,[status(thm)],[f_1163_1]) ).
fof(f_1163_3,plain,
! [U_4555,U_4556,U_4557,U_4558] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4555),U_4558),U_4556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4555),U_4558),U_4557)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),c_Groups_Ozero__class_Ozero(U_4555)),U_4558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),U_4556),U_4557))
| ~ class_Rings_Oordered__comm__semiring(U_4555) ),
inference(definitional_conversion,[status(esa)],[f_1163_2]) ).
cnf(f_1163_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4555),U_4558),U_4556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4555),U_4558),U_4557)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),c_Groups_Ozero__class_Ozero(U_4555)),U_4558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4555),U_4556),U_4557))
| ~ class_Rings_Oordered__comm__semiring(U_4555) ),
inference(clausify,[status(thm)],[f_1163_3]) ).
fof(f_1164_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__mono]) ).
fof(f_1164_2,plain,
! [U_4562,U_4561,U_4560,U_4559] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4559),U_4562),U_4560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4559),U_4562),U_4561)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),c_Groups_Ozero__class_Ozero(U_4559)),U_4562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),U_4560),U_4561))
| ~ class_Rings_Oordered__semiring(U_4559) ),
inference(variable_rename,[status(thm)],[f_1164_1]) ).
fof(f_1164_3,plain,
! [U_4559,U_4560,U_4561,U_4562] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4559),U_4562),U_4560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4559),U_4562),U_4561)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),c_Groups_Ozero__class_Ozero(U_4559)),U_4562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),U_4560),U_4561))
| ~ class_Rings_Oordered__semiring(U_4559) ),
inference(definitional_conversion,[status(esa)],[f_1164_2]) ).
cnf(f_1164_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4559),U_4562),U_4560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4559),U_4562),U_4561)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),c_Groups_Ozero__class_Ozero(U_4559)),U_4562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4559),U_4560),U_4561))
| ~ class_Rings_Oordered__semiring(U_4559) ),
inference(clausify,[status(thm)],[f_1164_3]) ).
fof(f_1165_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__mono]) ).
fof(f_1165_2,plain,
! [U_4566,U_4565,U_4564,U_4563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4563),U_4564),U_4566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4563),U_4565),U_4566)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),c_Groups_Ozero__class_Ozero(U_4563)),U_4566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),U_4564),U_4565))
| ~ class_Rings_Oordered__semiring(U_4563) ),
inference(variable_rename,[status(thm)],[f_1165_1]) ).
fof(f_1165_3,plain,
! [U_4563,U_4564,U_4565,U_4566] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4563),U_4564),U_4566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4563),U_4565),U_4566)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),c_Groups_Ozero__class_Ozero(U_4563)),U_4566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),U_4564),U_4565))
| ~ class_Rings_Oordered__semiring(U_4563) ),
inference(definitional_conversion,[status(esa)],[f_1165_2]) ).
cnf(f_1165_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4563),U_4564),U_4566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4563),U_4565),U_4566)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),c_Groups_Ozero__class_Ozero(U_4563)),U_4566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4563),U_4564),U_4565))
| ~ class_Rings_Oordered__semiring(U_4563) ),
inference(clausify,[status(thm)],[f_1165_3]) ).
fof(f_1166_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos]) ).
fof(f_1166_2,plain,
! [U_4569,U_4568,U_4567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),c_Groups_Ozero__class_Ozero(U_4567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4567),U_4568),U_4569)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),U_4569),c_Groups_Ozero__class_Ozero(U_4567)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),U_4568),c_Groups_Ozero__class_Ozero(U_4567)))
| ~ class_Rings_Oordered__ring(U_4567) ),
inference(variable_rename,[status(thm)],[f_1166_1]) ).
fof(f_1166_3,plain,
! [U_4568,U_4567,U_4569] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),c_Groups_Ozero__class_Ozero(U_4567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4567),U_4568),U_4569)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),U_4569),c_Groups_Ozero__class_Ozero(U_4567)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),U_4568),c_Groups_Ozero__class_Ozero(U_4567)))
| ~ class_Rings_Oordered__ring(U_4567) ),
inference(definitional_conversion,[status(esa)],[f_1166_2]) ).
cnf(f_1166_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),c_Groups_Ozero__class_Ozero(U_4567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4567),U_4568),U_4569)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),U_4569),c_Groups_Ozero__class_Ozero(U_4567)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4567),U_4568),c_Groups_Ozero__class_Ozero(U_4567)))
| ~ class_Rings_Oordered__ring(U_4567) ),
inference(clausify,[status(thm)],[f_1166_3]) ).
fof(f_1167_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg]) ).
fof(f_1167_2,plain,
! [U_4572,U_4571,U_4570] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4570),U_4571),U_4572)),c_Groups_Ozero__class_Ozero(U_4570)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),c_Groups_Ozero__class_Ozero(U_4570)),U_4572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),U_4571),c_Groups_Ozero__class_Ozero(U_4570)))
| ~ class_Rings_Oordered__cancel__semiring(U_4570) ),
inference(variable_rename,[status(thm)],[f_1167_1]) ).
fof(f_1167_3,plain,
! [U_4570,U_4571,U_4572] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4570),U_4571),U_4572)),c_Groups_Ozero__class_Ozero(U_4570)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),c_Groups_Ozero__class_Ozero(U_4570)),U_4572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),U_4571),c_Groups_Ozero__class_Ozero(U_4570)))
| ~ class_Rings_Oordered__cancel__semiring(U_4570) ),
inference(definitional_conversion,[status(esa)],[f_1167_2]) ).
cnf(f_1167_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4570),U_4571),U_4572)),c_Groups_Ozero__class_Ozero(U_4570)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),c_Groups_Ozero__class_Ozero(U_4570)),U_4572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4570),U_4571),c_Groups_Ozero__class_Ozero(U_4570)))
| ~ class_Rings_Oordered__cancel__semiring(U_4570) ),
inference(clausify,[status(thm)],[f_1167_3]) ).
fof(f_1168_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2]) ).
fof(f_1168_2,plain,
! [U_4575,U_4574,U_4573] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4573),U_4575),U_4574)),c_Groups_Ozero__class_Ozero(U_4573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),U_4575),c_Groups_Ozero__class_Ozero(U_4573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),c_Groups_Ozero__class_Ozero(U_4573)),U_4574))
| ~ class_Rings_Oordered__cancel__semiring(U_4573) ),
inference(variable_rename,[status(thm)],[f_1168_1]) ).
fof(f_1168_3,plain,
! [U_4573,U_4574,U_4575] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4573),U_4575),U_4574)),c_Groups_Ozero__class_Ozero(U_4573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),U_4575),c_Groups_Ozero__class_Ozero(U_4573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),c_Groups_Ozero__class_Ozero(U_4573)),U_4574))
| ~ class_Rings_Oordered__cancel__semiring(U_4573) ),
inference(definitional_conversion,[status(esa)],[f_1168_2]) ).
cnf(f_1168_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4573),U_4575),U_4574)),c_Groups_Ozero__class_Ozero(U_4573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),U_4575),c_Groups_Ozero__class_Ozero(U_4573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4573),c_Groups_Ozero__class_Ozero(U_4573)),U_4574))
| ~ class_Rings_Oordered__cancel__semiring(U_4573) ),
inference(clausify,[status(thm)],[f_1168_3]) ).
fof(f_1169_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos]) ).
fof(f_1169_2,plain,
! [U_4578,U_4577,U_4576] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4576),U_4577),U_4578)),c_Groups_Ozero__class_Ozero(U_4576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),U_4578),c_Groups_Ozero__class_Ozero(U_4576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),c_Groups_Ozero__class_Ozero(U_4576)),U_4577))
| ~ class_Rings_Oordered__cancel__semiring(U_4576) ),
inference(variable_rename,[status(thm)],[f_1169_1]) ).
fof(f_1169_3,plain,
! [U_4576,U_4577,U_4578] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4576),U_4577),U_4578)),c_Groups_Ozero__class_Ozero(U_4576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),U_4578),c_Groups_Ozero__class_Ozero(U_4576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),c_Groups_Ozero__class_Ozero(U_4576)),U_4577))
| ~ class_Rings_Oordered__cancel__semiring(U_4576) ),
inference(definitional_conversion,[status(esa)],[f_1169_2]) ).
cnf(f_1169_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4576),U_4577),U_4578)),c_Groups_Ozero__class_Ozero(U_4576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),U_4578),c_Groups_Ozero__class_Ozero(U_4576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4576),c_Groups_Ozero__class_Ozero(U_4576)),U_4577))
| ~ class_Rings_Oordered__cancel__semiring(U_4576) ),
inference(clausify,[status(thm)],[f_1169_3]) ).
fof(f_1170_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg]) ).
fof(f_1170_2,plain,
! [U_4581,U_4580,U_4579] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4579),U_4580),U_4581)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),U_4581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),U_4580))
| ~ class_Rings_Oordered__cancel__semiring(U_4579) ),
inference(variable_rename,[status(thm)],[f_1170_1]) ).
fof(f_1170_3,plain,
! [U_4580,U_4579,U_4581] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4579),U_4580),U_4581)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),U_4581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),U_4580))
| ~ class_Rings_Oordered__cancel__semiring(U_4579) ),
inference(definitional_conversion,[status(esa)],[f_1170_2]) ).
cnf(f_1170_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4579),U_4580),U_4581)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),U_4581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4579),c_Groups_Ozero__class_Ozero(U_4579)),U_4580))
| ~ class_Rings_Oordered__cancel__semiring(U_4579) ),
inference(clausify,[status(thm)],[f_1170_3]) ).
fof(f_1171_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ 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))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).
fof(f_1171_2,plain,
! [U_4584,U_4583,U_4582] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4582),U_4583),U_4584)),c_Groups_Ozero__class_Ozero(U_4582)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4583),c_Groups_Ozero__class_Ozero(U_4582))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4584),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4583)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4584))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4583),c_Groups_Ozero__class_Ozero(U_4582))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4584),c_Groups_Ozero__class_Ozero(U_4582)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4583)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4582),U_4583),U_4584)),c_Groups_Ozero__class_Ozero(U_4582))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_4582) ),
inference(variable_rename,[status(thm)],[f_1171_1]) ).
fof(f_1171_3,plain,
( ! [U_4582,U_4583,U_4584] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4583),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ sP288(U_4582,U_4583,U_4584) )
& ! [U_4582,U_4583,U_4584] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4584),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4583))
| ~ sP288(U_4582,U_4583,U_4584) )
& ! [U_4582,U_4583,U_4584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4584))
| ~ sP287(U_4582,U_4583,U_4584) )
& ! [U_4582,U_4583,U_4584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4583),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ sP287(U_4582,U_4583,U_4584) )
& ! [U_4582,U_4583,U_4584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4584),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ sP286(U_4582,U_4583,U_4584) )
& ! [U_4582,U_4583,U_4584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4583))
| ~ sP286(U_4582,U_4583,U_4584) )
& ! [U_4582,U_4583,U_4584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4582),U_4583),U_4584)),c_Groups_Ozero__class_Ozero(U_4582)))
| sP288(U_4582,U_4583,U_4584)
| ~ sP289(U_4582,U_4583,U_4584) )
& ! [U_4582,U_4583,U_4584] :
( sP287(U_4582,U_4583,U_4584)
| sP286(U_4582,U_4583,U_4584)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4582),U_4583),U_4584)),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ sP289(U_4582,U_4583,U_4584) )
& ! [U_4582,U_4583,U_4584] :
( sP289(U_4582,U_4583,U_4584)
| ~ class_Rings_Olinordered__ring__strict(U_4582) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286,sP287,sP288,sP289])],[f_1171_2]) ).
cnf(f_1171_4,plain,
( sP289(U_4582,U_4583,U_4584)
| ~ class_Rings_Olinordered__ring__strict(U_4582) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_5,plain,
( sP287(U_4582,U_4583,U_4584)
| sP286(U_4582,U_4583,U_4584)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4582),U_4583),U_4584)),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ sP289(U_4582,U_4583,U_4584) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4582),U_4583),U_4584)),c_Groups_Ozero__class_Ozero(U_4582)))
| sP288(U_4582,U_4583,U_4584)
| ~ sP289(U_4582,U_4583,U_4584) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4583))
| ~ sP286(U_4582,U_4583,U_4584) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4584),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ sP286(U_4582,U_4583,U_4584) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4583),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ sP287(U_4582,U_4583,U_4584) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4584))
| ~ sP287(U_4582,U_4583,U_4584) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4584),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4583))
| ~ sP288(U_4582,U_4583,U_4584) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),c_Groups_Ozero__class_Ozero(U_4582)),U_4584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4582),U_4583),c_Groups_Ozero__class_Ozero(U_4582)))
| ~ sP288(U_4582,U_4583,U_4584) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
fof(f_1172_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ 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))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).
fof(f_1172_2,plain,
! [U_4587,U_4586,U_4585] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4585),U_4586),U_4587)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4587),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4586),c_Groups_Ozero__class_Ozero(U_4585))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4587))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4586)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4587),c_Groups_Ozero__class_Ozero(U_4585)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4586),c_Groups_Ozero__class_Ozero(U_4585))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4587))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4586)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4585),U_4586),U_4587))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_4585) ),
inference(variable_rename,[status(thm)],[f_1172_1]) ).
fof(f_1172_3,plain,
( ! [U_4587,U_4585,U_4586] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4587),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4586),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ sP292(U_4587,U_4585,U_4586) )
& ! [U_4587,U_4585,U_4586] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4587))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4586))
| ~ sP292(U_4587,U_4585,U_4586) )
& ! [U_4587,U_4585,U_4586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4587),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ sP291(U_4587,U_4585,U_4586) )
& ! [U_4587,U_4585,U_4586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4586),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ sP291(U_4587,U_4585,U_4586) )
& ! [U_4587,U_4585,U_4586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4587))
| ~ sP290(U_4587,U_4585,U_4586) )
& ! [U_4587,U_4585,U_4586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4586))
| ~ sP290(U_4587,U_4585,U_4586) )
& ! [U_4587,U_4585,U_4586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4585),U_4586),U_4587)))
| sP292(U_4587,U_4585,U_4586)
| ~ sP293(U_4587,U_4585,U_4586) )
& ! [U_4587,U_4585,U_4586] :
( sP291(U_4587,U_4585,U_4586)
| sP290(U_4587,U_4585,U_4586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4585),U_4586),U_4587)))
| ~ sP293(U_4587,U_4585,U_4586) )
& ! [U_4587,U_4585,U_4586] :
( sP293(U_4587,U_4585,U_4586)
| ~ class_Rings_Olinordered__ring__strict(U_4585) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP290,sP291,sP292,sP293])],[f_1172_2]) ).
cnf(f_1172_4,plain,
( sP293(U_4587,U_4585,U_4586)
| ~ class_Rings_Olinordered__ring__strict(U_4585) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
cnf(f_1172_5,plain,
( sP291(U_4587,U_4585,U_4586)
| sP290(U_4587,U_4585,U_4586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4585),U_4586),U_4587)))
| ~ sP293(U_4587,U_4585,U_4586) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
cnf(f_1172_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4585),U_4586),U_4587)))
| sP292(U_4587,U_4585,U_4586)
| ~ sP293(U_4587,U_4585,U_4586) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
cnf(f_1172_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4586))
| ~ sP290(U_4587,U_4585,U_4586) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
cnf(f_1172_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4587))
| ~ sP290(U_4587,U_4585,U_4586) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
cnf(f_1172_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4586),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ sP291(U_4587,U_4585,U_4586) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
cnf(f_1172_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4587),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ sP291(U_4587,U_4585,U_4586) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
cnf(f_1172_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4587))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),c_Groups_Ozero__class_Ozero(U_4585)),U_4586))
| ~ sP292(U_4587,U_4585,U_4586) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
cnf(f_1172_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4587),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4585),U_4586),c_Groups_Ozero__class_Ozero(U_4585)))
| ~ sP292(U_4587,U_4585,U_4586) ),
inference(clausify,[status(thm)],[f_1172_3]) ).
fof(f_1173_1,plain,
! [V_a,T_a] :
( 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)))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__square]) ).
fof(f_1173_2,plain,
! [U_4589,U_4588] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4588),c_Groups_Ozero__class_Ozero(U_4588)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4588),U_4589),U_4589)))
| ~ class_Rings_Olinordered__ring(U_4588) ),
inference(variable_rename,[status(thm)],[f_1173_1]) ).
fof(f_1173_3,plain,
! [U_4589,U_4588] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4588),c_Groups_Ozero__class_Ozero(U_4588)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4588),U_4589),U_4589)))
| ~ class_Rings_Olinordered__ring(U_4588) ),
inference(definitional_conversion,[status(esa)],[f_1173_2]) ).
cnf(f_1173_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4588),c_Groups_Ozero__class_Ozero(U_4588)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4588),U_4589),U_4589)))
| ~ class_Rings_Olinordered__ring(U_4588) ),
inference(clausify,[status(thm)],[f_1173_3]) ).
fof(f_1174_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__add__strict]) ).
fof(f_1174_2,plain,
! [U_4593,U_4592,U_4591,U_4590] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),U_4592),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4590),U_4591),U_4593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),U_4592),U_4593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),c_Groups_Ozero__class_Ozero(U_4590)),U_4591))
| ~ class_Rings_Olinordered__semidom(U_4590) ),
inference(variable_rename,[status(thm)],[f_1174_1]) ).
fof(f_1174_3,plain,
! [U_4591,U_4592,U_4590,U_4593] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),U_4592),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4590),U_4591),U_4593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),U_4592),U_4593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),c_Groups_Ozero__class_Ozero(U_4590)),U_4591))
| ~ class_Rings_Olinordered__semidom(U_4590) ),
inference(definitional_conversion,[status(esa)],[f_1174_2]) ).
cnf(f_1174_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),U_4592),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4590),U_4591),U_4593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),U_4592),U_4593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4590),c_Groups_Ozero__class_Ozero(U_4590)),U_4591))
| ~ class_Rings_Olinordered__semidom(U_4590) ),
inference(clausify,[status(thm)],[f_1174_3]) ).
fof(f_1175_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__neg__neg]) ).
fof(f_1175_2,plain,
! [U_4596,U_4595,U_4594] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4594),U_4595),U_4596)),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),U_4596),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),U_4595),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4594) ),
inference(variable_rename,[status(thm)],[f_1175_1]) ).
fof(f_1175_3,plain,
! [U_4594,U_4595,U_4596] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4594),U_4595),U_4596)),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),U_4596),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),U_4595),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4594) ),
inference(definitional_conversion,[status(esa)],[f_1175_2]) ).
cnf(f_1175_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4594),U_4595),U_4596)),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),U_4596),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4594),U_4595),c_Groups_Ozero__class_Ozero(U_4594)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4594) ),
inference(clausify,[status(thm)],[f_1175_3]) ).
fof(f_1176_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pos__pos]) ).
fof(f_1176_2,plain,
! [U_4599,U_4598,U_4597] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4597),U_4598),U_4599)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),U_4599))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),U_4598))
| ~ class_Groups_Oordered__comm__monoid__add(U_4597) ),
inference(variable_rename,[status(thm)],[f_1176_1]) ).
fof(f_1176_3,plain,
! [U_4598,U_4597,U_4599] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4597),U_4598),U_4599)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),U_4599))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),U_4598))
| ~ class_Groups_Oordered__comm__monoid__add(U_4597) ),
inference(definitional_conversion,[status(esa)],[f_1176_2]) ).
cnf(f_1176_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4597),U_4598),U_4599)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),U_4599))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4597),c_Groups_Ozero__class_Ozero(U_4597)),U_4598))
| ~ class_Groups_Oordered__comm__monoid__add(U_4597) ),
inference(clausify,[status(thm)],[f_1176_3]) ).
fof(f_1177_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ 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))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).
fof(f_1177_2,plain,
! [U_4601,U_4600] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4600),U_4601),U_4601)),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),U_4601),c_Groups_Ozero__class_Ozero(U_4600))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),U_4601),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4600),U_4601),U_4601)),c_Groups_Ozero__class_Ozero(U_4600))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4600) ),
inference(variable_rename,[status(thm)],[f_1177_1]) ).
fof(f_1177_3,plain,
( ! [U_4601,U_4600] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4600),U_4601),U_4601)),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),U_4601),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ sP294(U_4601,U_4600) )
& ! [U_4601,U_4600] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),U_4601),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4600),U_4601),U_4601)),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ sP294(U_4601,U_4600) )
& ! [U_4601,U_4600] :
( sP294(U_4601,U_4600)
| ~ class_Groups_Olinordered__ab__group__add(U_4600) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_1177_2]) ).
cnf(f_1177_4,plain,
( sP294(U_4601,U_4600)
| ~ class_Groups_Olinordered__ab__group__add(U_4600) ),
inference(clausify,[status(thm)],[f_1177_3]) ).
cnf(f_1177_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),U_4601),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4600),U_4601),U_4601)),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ sP294(U_4601,U_4600) ),
inference(clausify,[status(thm)],[f_1177_3]) ).
cnf(f_1177_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4600),U_4601),U_4601)),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4600),U_4601),c_Groups_Ozero__class_Ozero(U_4600)))
| ~ sP294(U_4601,U_4600) ),
inference(clausify,[status(thm)],[f_1177_3]) ).
fof(f_1178_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ 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))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).
fof(f_1178_2,plain,
! [U_4603,U_4602] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4602),U_4603),U_4603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),U_4603)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),U_4603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4602),U_4603),U_4603))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4602) ),
inference(variable_rename,[status(thm)],[f_1178_1]) ).
fof(f_1178_3,plain,
( ! [U_4603,U_4602] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4602),U_4603),U_4603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),U_4603))
| ~ sP295(U_4603,U_4602) )
& ! [U_4603,U_4602] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),U_4603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4602),U_4603),U_4603)))
| ~ sP295(U_4603,U_4602) )
& ! [U_4603,U_4602] :
( sP295(U_4603,U_4602)
| ~ class_Groups_Olinordered__ab__group__add(U_4602) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295])],[f_1178_2]) ).
cnf(f_1178_4,plain,
( sP295(U_4603,U_4602)
| ~ class_Groups_Olinordered__ab__group__add(U_4602) ),
inference(clausify,[status(thm)],[f_1178_3]) ).
cnf(f_1178_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),U_4603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4602),U_4603),U_4603)))
| ~ sP295(U_4603,U_4602) ),
inference(clausify,[status(thm)],[f_1178_3]) ).
cnf(f_1178_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4602),U_4603),U_4603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4602),c_Groups_Ozero__class_Ozero(U_4602)),U_4603))
| ~ sP295(U_4603,U_4602) ),
inference(clausify,[status(thm)],[f_1178_3]) ).
fof(f_1179_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg]) ).
fof(f_1179_2,plain,
! [U_4607,U_4606,U_4605,U_4604] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4604),U_4607),U_4606)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4604),U_4607),U_4605)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),U_4607),c_Groups_Ozero__class_Ozero(U_4604)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),U_4605),U_4606))
| ~ class_Rings_Olinordered__ring__strict(U_4604) ),
inference(variable_rename,[status(thm)],[f_1179_1]) ).
fof(f_1179_3,plain,
! [U_4605,U_4604,U_4606,U_4607] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4604),U_4607),U_4606)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4604),U_4607),U_4605)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),U_4607),c_Groups_Ozero__class_Ozero(U_4604)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),U_4605),U_4606))
| ~ class_Rings_Olinordered__ring__strict(U_4604) ),
inference(definitional_conversion,[status(esa)],[f_1179_2]) ).
cnf(f_1179_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4604),U_4607),U_4606)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4604),U_4607),U_4605)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),U_4607),c_Groups_Ozero__class_Ozero(U_4604)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4604),U_4605),U_4606))
| ~ class_Rings_Olinordered__ring__strict(U_4604) ),
inference(clausify,[status(thm)],[f_1179_3]) ).
fof(f_1180_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg]) ).
fof(f_1180_2,plain,
! [U_4611,U_4610,U_4609,U_4608] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4608),U_4610),U_4611)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4608),U_4609),U_4611)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),U_4611),c_Groups_Ozero__class_Ozero(U_4608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),U_4609),U_4610))
| ~ class_Rings_Olinordered__ring__strict(U_4608) ),
inference(variable_rename,[status(thm)],[f_1180_1]) ).
fof(f_1180_3,plain,
! [U_4608,U_4609,U_4610,U_4611] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4608),U_4610),U_4611)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4608),U_4609),U_4611)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),U_4611),c_Groups_Ozero__class_Ozero(U_4608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),U_4609),U_4610))
| ~ class_Rings_Olinordered__ring__strict(U_4608) ),
inference(definitional_conversion,[status(esa)],[f_1180_2]) ).
cnf(f_1180_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4608),U_4610),U_4611)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4608),U_4609),U_4611)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),U_4611),c_Groups_Ozero__class_Ozero(U_4608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4608),U_4609),U_4610))
| ~ class_Rings_Olinordered__ring__strict(U_4608) ),
inference(clausify,[status(thm)],[f_1180_3]) ).
fof(f_1181_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__comm__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono]) ).
fof(f_1181_2,plain,
! [U_4615,U_4614,U_4613,U_4612] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4612),U_4615),U_4613)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4612),U_4615),U_4614)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),c_Groups_Ozero__class_Ozero(U_4612)),U_4615))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),U_4613),U_4614))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_4612) ),
inference(variable_rename,[status(thm)],[f_1181_1]) ).
fof(f_1181_3,plain,
! [U_4612,U_4613,U_4614,U_4615] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4612),U_4615),U_4613)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4612),U_4615),U_4614)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),c_Groups_Ozero__class_Ozero(U_4612)),U_4615))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),U_4613),U_4614))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_4612) ),
inference(definitional_conversion,[status(esa)],[f_1181_2]) ).
cnf(f_1181_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4612),U_4615),U_4613)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4612),U_4615),U_4614)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),c_Groups_Ozero__class_Ozero(U_4612)),U_4615))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4612),U_4613),U_4614))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_4612) ),
inference(clausify,[status(thm)],[f_1181_3]) ).
fof(f_1182_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono]) ).
fof(f_1182_2,plain,
! [U_4619,U_4618,U_4617,U_4616] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4616),U_4619),U_4617)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4616),U_4619),U_4618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),c_Groups_Ozero__class_Ozero(U_4616)),U_4619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),U_4617),U_4618))
| ~ class_Rings_Olinordered__semiring__strict(U_4616) ),
inference(variable_rename,[status(thm)],[f_1182_1]) ).
fof(f_1182_3,plain,
! [U_4616,U_4617,U_4618,U_4619] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4616),U_4619),U_4617)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4616),U_4619),U_4618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),c_Groups_Ozero__class_Ozero(U_4616)),U_4619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),U_4617),U_4618))
| ~ class_Rings_Olinordered__semiring__strict(U_4616) ),
inference(definitional_conversion,[status(esa)],[f_1182_2]) ).
cnf(f_1182_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4616),U_4619),U_4617)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4616),U_4619),U_4618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),c_Groups_Ozero__class_Ozero(U_4616)),U_4619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4616),U_4617),U_4618))
| ~ class_Rings_Olinordered__semiring__strict(U_4616) ),
inference(clausify,[status(thm)],[f_1182_3]) ).
fof(f_1183_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono]) ).
fof(f_1183_2,plain,
! [U_4623,U_4622,U_4621,U_4620] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4620),U_4621),U_4623)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4620),U_4622),U_4623)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),U_4623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),U_4621),U_4622))
| ~ class_Rings_Olinordered__semiring__strict(U_4620) ),
inference(variable_rename,[status(thm)],[f_1183_1]) ).
fof(f_1183_3,plain,
! [U_4620,U_4621,U_4622,U_4623] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4620),U_4621),U_4623)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4620),U_4622),U_4623)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),U_4623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),U_4621),U_4622))
| ~ class_Rings_Olinordered__semiring__strict(U_4620) ),
inference(definitional_conversion,[status(esa)],[f_1183_2]) ).
cnf(f_1183_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4620),U_4621),U_4623)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4620),U_4622),U_4623)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),U_4623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4620),U_4621),U_4622))
| ~ class_Rings_Olinordered__semiring__strict(U_4620) ),
inference(clausify,[status(thm)],[f_1183_3]) ).
fof(f_1184_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__neg__neg]) ).
fof(f_1184_2,plain,
! [U_4626,U_4625,U_4624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),c_Groups_Ozero__class_Ozero(U_4624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4624),U_4625),U_4626)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),U_4626),c_Groups_Ozero__class_Ozero(U_4624)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),U_4625),c_Groups_Ozero__class_Ozero(U_4624)))
| ~ class_Rings_Olinordered__ring__strict(U_4624) ),
inference(variable_rename,[status(thm)],[f_1184_1]) ).
fof(f_1184_3,plain,
! [U_4625,U_4624,U_4626] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),c_Groups_Ozero__class_Ozero(U_4624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4624),U_4625),U_4626)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),U_4626),c_Groups_Ozero__class_Ozero(U_4624)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),U_4625),c_Groups_Ozero__class_Ozero(U_4624)))
| ~ class_Rings_Olinordered__ring__strict(U_4624) ),
inference(definitional_conversion,[status(esa)],[f_1184_2]) ).
cnf(f_1184_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),c_Groups_Ozero__class_Ozero(U_4624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4624),U_4625),U_4626)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),U_4626),c_Groups_Ozero__class_Ozero(U_4624)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4624),U_4625),c_Groups_Ozero__class_Ozero(U_4624)))
| ~ class_Rings_Olinordered__ring__strict(U_4624) ),
inference(clausify,[status(thm)],[f_1184_3]) ).
fof(f_1185_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__neg__pos]) ).
fof(f_1185_2,plain,
! [U_4629,U_4628,U_4627] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4627),U_4628),U_4629)),c_Groups_Ozero__class_Ozero(U_4627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),U_4629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),U_4628),c_Groups_Ozero__class_Ozero(U_4627)))
| ~ class_Rings_Olinordered__semiring__strict(U_4627) ),
inference(variable_rename,[status(thm)],[f_1185_1]) ).
fof(f_1185_3,plain,
! [U_4627,U_4628,U_4629] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4627),U_4628),U_4629)),c_Groups_Ozero__class_Ozero(U_4627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),U_4629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),U_4628),c_Groups_Ozero__class_Ozero(U_4627)))
| ~ class_Rings_Olinordered__semiring__strict(U_4627) ),
inference(definitional_conversion,[status(esa)],[f_1185_2]) ).
cnf(f_1185_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4627),U_4628),U_4629)),c_Groups_Ozero__class_Ozero(U_4627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),U_4629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),U_4628),c_Groups_Ozero__class_Ozero(U_4627)))
| ~ class_Rings_Olinordered__semiring__strict(U_4627) ),
inference(clausify,[status(thm)],[f_1185_3]) ).
fof(f_1186_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).
fof(f_1186_2,plain,
! [U_4633,U_4632,U_4631,U_4630] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4633)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4633),U_4632)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4633),U_4632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4633))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4631),c_Groups_Ozero__class_Ozero(U_4630)))
| ~ class_Rings_Olinordered__ring__strict(U_4630) ),
inference(variable_rename,[status(thm)],[f_1186_1]) ).
fof(f_1186_3,plain,
( ! [U_4631,U_4630,U_4632,U_4633] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4633)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4633),U_4632))
| ~ sP296(U_4631,U_4630,U_4632,U_4633) )
& ! [U_4631,U_4630,U_4632,U_4633] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4633),U_4632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4633)))
| ~ sP296(U_4631,U_4630,U_4632,U_4633) )
& ! [U_4631,U_4630,U_4632,U_4633] :
( sP296(U_4631,U_4630,U_4632,U_4633)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4631),c_Groups_Ozero__class_Ozero(U_4630)))
| ~ class_Rings_Olinordered__ring__strict(U_4630) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP296])],[f_1186_2]) ).
cnf(f_1186_4,plain,
( sP296(U_4631,U_4630,U_4632,U_4633)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4631),c_Groups_Ozero__class_Ozero(U_4630)))
| ~ class_Rings_Olinordered__ring__strict(U_4630) ),
inference(clausify,[status(thm)],[f_1186_3]) ).
cnf(f_1186_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4633),U_4632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4633)))
| ~ sP296(U_4631,U_4630,U_4632,U_4633) ),
inference(clausify,[status(thm)],[f_1186_3]) ).
cnf(f_1186_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),U_4631),U_4633)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4630),U_4633),U_4632))
| ~ sP296(U_4631,U_4630,U_4632,U_4633) ),
inference(clausify,[status(thm)],[f_1186_3]) ).
fof(f_1187_1,plain,
! [V_a,V_b,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ 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)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2]) ).
fof(f_1187_2,plain,
! [U_4636,U_4635,U_4634] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),U_4635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),U_4636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4634),U_4635),U_4636)))
| ~ class_Rings_Olinordered__semiring__strict(U_4634) ),
inference(variable_rename,[status(thm)],[f_1187_1]) ).
fof(f_1187_3,plain,
! [U_4635,U_4636,U_4634] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),U_4635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),U_4636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4634),U_4635),U_4636)))
| ~ class_Rings_Olinordered__semiring__strict(U_4634) ),
inference(definitional_conversion,[status(esa)],[f_1187_2]) ).
cnf(f_1187_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),U_4635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),U_4636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4634),c_Groups_Ozero__class_Ozero(U_4634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4634),U_4635),U_4636)))
| ~ class_Rings_Olinordered__semiring__strict(U_4634) ),
inference(clausify,[status(thm)],[f_1187_3]) ).
fof(f_1188_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ 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)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos]) ).
fof(f_1188_2,plain,
! [U_4639,U_4638,U_4637] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),U_4639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),U_4638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4637),U_4638),U_4639)))
| ~ class_Rings_Olinordered__semiring__strict(U_4637) ),
inference(variable_rename,[status(thm)],[f_1188_1]) ).
fof(f_1188_3,plain,
! [U_4637,U_4638,U_4639] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),U_4639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),U_4638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4637),U_4638),U_4639)))
| ~ class_Rings_Olinordered__semiring__strict(U_4637) ),
inference(definitional_conversion,[status(esa)],[f_1188_2]) ).
cnf(f_1188_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),U_4639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),U_4638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4637),c_Groups_Ozero__class_Ozero(U_4637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4637),U_4638),U_4639)))
| ~ class_Rings_Olinordered__semiring__strict(U_4637) ),
inference(clausify,[status(thm)],[f_1188_3]) ).
fof(f_1189_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2]) ).
fof(f_1189_2,plain,
! [U_4642,U_4641,U_4640] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4640),U_4642),U_4641)),c_Groups_Ozero__class_Ozero(U_4640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),U_4642),c_Groups_Ozero__class_Ozero(U_4640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),c_Groups_Ozero__class_Ozero(U_4640)),U_4641))
| ~ class_Rings_Olinordered__semiring__strict(U_4640) ),
inference(variable_rename,[status(thm)],[f_1189_1]) ).
fof(f_1189_3,plain,
! [U_4640,U_4641,U_4642] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4640),U_4642),U_4641)),c_Groups_Ozero__class_Ozero(U_4640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),U_4642),c_Groups_Ozero__class_Ozero(U_4640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),c_Groups_Ozero__class_Ozero(U_4640)),U_4641))
| ~ class_Rings_Olinordered__semiring__strict(U_4640) ),
inference(definitional_conversion,[status(esa)],[f_1189_2]) ).
cnf(f_1189_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4640),U_4642),U_4641)),c_Groups_Ozero__class_Ozero(U_4640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),U_4642),c_Groups_Ozero__class_Ozero(U_4640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4640),c_Groups_Ozero__class_Ozero(U_4640)),U_4641))
| ~ class_Rings_Olinordered__semiring__strict(U_4640) ),
inference(clausify,[status(thm)],[f_1189_3]) ).
fof(f_1190_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__neg]) ).
fof(f_1190_2,plain,
! [U_4645,U_4644,U_4643] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4643),U_4644),U_4645)),c_Groups_Ozero__class_Ozero(U_4643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),U_4645),c_Groups_Ozero__class_Ozero(U_4643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),c_Groups_Ozero__class_Ozero(U_4643)),U_4644))
| ~ class_Rings_Olinordered__semiring__strict(U_4643) ),
inference(variable_rename,[status(thm)],[f_1190_1]) ).
fof(f_1190_3,plain,
! [U_4643,U_4644,U_4645] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4643),U_4644),U_4645)),c_Groups_Ozero__class_Ozero(U_4643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),U_4645),c_Groups_Ozero__class_Ozero(U_4643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),c_Groups_Ozero__class_Ozero(U_4643)),U_4644))
| ~ class_Rings_Olinordered__semiring__strict(U_4643) ),
inference(definitional_conversion,[status(esa)],[f_1190_2]) ).
cnf(f_1190_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4643),U_4644),U_4645)),c_Groups_Ozero__class_Ozero(U_4643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),U_4645),c_Groups_Ozero__class_Ozero(U_4643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4643),c_Groups_Ozero__class_Ozero(U_4643)),U_4644))
| ~ class_Rings_Olinordered__semiring__strict(U_4643) ),
inference(clausify,[status(thm)],[f_1190_3]) ).
fof(f_1191_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__pos]) ).
fof(f_1191_2,plain,
! [U_4648,U_4647,U_4646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4646),U_4647),U_4648)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),U_4648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),U_4647))
| ~ class_Rings_Olinordered__semiring__strict(U_4646) ),
inference(variable_rename,[status(thm)],[f_1191_1]) ).
fof(f_1191_3,plain,
! [U_4647,U_4646,U_4648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4646),U_4647),U_4648)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),U_4648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),U_4647))
| ~ class_Rings_Olinordered__semiring__strict(U_4646) ),
inference(definitional_conversion,[status(esa)],[f_1191_2]) ).
cnf(f_1191_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4646),U_4647),U_4648)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),U_4648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4646),c_Groups_Ozero__class_Ozero(U_4646)),U_4647))
| ~ class_Rings_Olinordered__semiring__strict(U_4646) ),
inference(clausify,[status(thm)],[f_1191_3]) ).
fof(f_1192_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).
fof(f_1192_2,plain,
! [U_4652,U_4651,U_4650,U_4649] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4652)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),U_4651),U_4652)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),U_4651),U_4652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4652))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),c_Groups_Ozero__class_Ozero(U_4649)),U_4650))
| ~ class_Rings_Olinordered__ring__strict(U_4649) ),
inference(variable_rename,[status(thm)],[f_1192_1]) ).
fof(f_1192_3,plain,
( ! [U_4650,U_4649,U_4651,U_4652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4652)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),U_4651),U_4652))
| ~ sP297(U_4650,U_4649,U_4651,U_4652) )
& ! [U_4650,U_4649,U_4651,U_4652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),U_4651),U_4652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4652)))
| ~ sP297(U_4650,U_4649,U_4651,U_4652) )
& ! [U_4650,U_4649,U_4651,U_4652] :
( sP297(U_4650,U_4649,U_4651,U_4652)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),c_Groups_Ozero__class_Ozero(U_4649)),U_4650))
| ~ class_Rings_Olinordered__ring__strict(U_4649) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP297])],[f_1192_2]) ).
cnf(f_1192_4,plain,
( sP297(U_4650,U_4649,U_4651,U_4652)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),c_Groups_Ozero__class_Ozero(U_4649)),U_4650))
| ~ class_Rings_Olinordered__ring__strict(U_4649) ),
inference(clausify,[status(thm)],[f_1192_3]) ).
cnf(f_1192_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),U_4651),U_4652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4652)))
| ~ sP297(U_4650,U_4649,U_4651,U_4652) ),
inference(clausify,[status(thm)],[f_1192_3]) ).
cnf(f_1192_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4649),U_4650),U_4652)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4649),U_4651),U_4652))
| ~ sP297(U_4650,U_4649,U_4651,U_4652) ),
inference(clausify,[status(thm)],[f_1192_3]) ).
fof(f_1193_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).
fof(f_1193_2,plain,
! [U_4656,U_4655,U_4654,U_4653] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4656)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4656),U_4655))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4654),c_Groups_Ozero__class_Ozero(U_4653))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4655),U_4656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Ozero__class_Ozero(U_4653)),U_4654)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4656),U_4655))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4654),c_Groups_Ozero__class_Ozero(U_4653))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4655),U_4656))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Ozero__class_Ozero(U_4653)),U_4654)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4656))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_4653) ),
inference(variable_rename,[status(thm)],[f_1193_1]) ).
fof(f_1193_3,plain,
( ! [U_4655,U_4654,U_4653,U_4656] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4656),U_4655))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4654),c_Groups_Ozero__class_Ozero(U_4653)))
| ~ sP300(U_4655,U_4654,U_4653,U_4656) )
& ! [U_4655,U_4654,U_4653,U_4656] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4655),U_4656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Ozero__class_Ozero(U_4653)),U_4654))
| ~ sP300(U_4655,U_4654,U_4653,U_4656) )
& ! [U_4655,U_4654,U_4653,U_4656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4656),U_4655))
| ~ sP299(U_4655,U_4654,U_4653,U_4656) )
& ! [U_4655,U_4654,U_4653,U_4656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4654),c_Groups_Ozero__class_Ozero(U_4653)))
| ~ sP299(U_4655,U_4654,U_4653,U_4656) )
& ! [U_4655,U_4654,U_4653,U_4656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4655),U_4656))
| ~ sP298(U_4655,U_4654,U_4653,U_4656) )
& ! [U_4655,U_4654,U_4653,U_4656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Ozero__class_Ozero(U_4653)),U_4654))
| ~ sP298(U_4655,U_4654,U_4653,U_4656) )
& ! [U_4655,U_4654,U_4653,U_4656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4656)))
| sP300(U_4655,U_4654,U_4653,U_4656)
| ~ sP301(U_4655,U_4654,U_4653,U_4656) )
& ! [U_4655,U_4654,U_4653,U_4656] :
( sP299(U_4655,U_4654,U_4653,U_4656)
| sP298(U_4655,U_4654,U_4653,U_4656)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4656)))
| ~ sP301(U_4655,U_4654,U_4653,U_4656) )
& ! [U_4655,U_4654,U_4653,U_4656] :
( sP301(U_4655,U_4654,U_4653,U_4656)
| ~ class_Rings_Olinordered__ring__strict(U_4653) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298,sP299,sP300,sP301])],[f_1193_2]) ).
cnf(f_1193_4,plain,
( sP301(U_4655,U_4654,U_4653,U_4656)
| ~ class_Rings_Olinordered__ring__strict(U_4653) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
cnf(f_1193_5,plain,
( sP299(U_4655,U_4654,U_4653,U_4656)
| sP298(U_4655,U_4654,U_4653,U_4656)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4656)))
| ~ sP301(U_4655,U_4654,U_4653,U_4656) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
cnf(f_1193_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4653),U_4654),U_4656)))
| sP300(U_4655,U_4654,U_4653,U_4656)
| ~ sP301(U_4655,U_4654,U_4653,U_4656) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
cnf(f_1193_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Ozero__class_Ozero(U_4653)),U_4654))
| ~ sP298(U_4655,U_4654,U_4653,U_4656) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
cnf(f_1193_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4655),U_4656))
| ~ sP298(U_4655,U_4654,U_4653,U_4656) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
cnf(f_1193_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4654),c_Groups_Ozero__class_Ozero(U_4653)))
| ~ sP299(U_4655,U_4654,U_4653,U_4656) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
cnf(f_1193_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4656),U_4655))
| ~ sP299(U_4655,U_4654,U_4653,U_4656) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
cnf(f_1193_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4655),U_4656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Ozero__class_Ozero(U_4653)),U_4654))
| ~ sP300(U_4655,U_4654,U_4653,U_4656) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
cnf(f_1193_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4656),U_4655))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),U_4654),c_Groups_Ozero__class_Ozero(U_4653)))
| ~ sP300(U_4655,U_4654,U_4653,U_4656) ),
inference(clausify,[status(thm)],[f_1193_3]) ).
fof(f_1194_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).
fof(f_1194_2,plain,
! [U_4660,U_4659,U_4658,U_4657] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4660),U_4659)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4660),U_4658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4659),c_Groups_Ozero__class_Ozero(U_4657))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4659)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4660),U_4658))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4659),c_Groups_Ozero__class_Ozero(U_4657))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4659)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4660),U_4659))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_4657) ),
inference(variable_rename,[status(thm)],[f_1194_1]) ).
fof(f_1194_3,plain,
( ! [U_4659,U_4658,U_4660,U_4657] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4660),U_4658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4659),c_Groups_Ozero__class_Ozero(U_4657)))
| ~ sP304(U_4659,U_4658,U_4660,U_4657) )
& ! [U_4659,U_4658,U_4660,U_4657] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4659))
| ~ sP304(U_4659,U_4658,U_4660,U_4657) )
& ! [U_4659,U_4658,U_4660,U_4657] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4660),U_4658))
| ~ sP303(U_4659,U_4658,U_4660,U_4657) )
& ! [U_4659,U_4658,U_4660,U_4657] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4659),c_Groups_Ozero__class_Ozero(U_4657)))
| ~ sP303(U_4659,U_4658,U_4660,U_4657) )
& ! [U_4659,U_4658,U_4660,U_4657] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
| ~ sP302(U_4659,U_4658,U_4660,U_4657) )
& ! [U_4659,U_4658,U_4660,U_4657] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4659))
| ~ sP302(U_4659,U_4658,U_4660,U_4657) )
& ! [U_4659,U_4658,U_4660,U_4657] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4660),U_4659)))
| sP304(U_4659,U_4658,U_4660,U_4657)
| ~ sP305(U_4659,U_4658,U_4660,U_4657) )
& ! [U_4659,U_4658,U_4660,U_4657] :
( sP303(U_4659,U_4658,U_4660,U_4657)
| sP302(U_4659,U_4658,U_4660,U_4657)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4660),U_4659)))
| ~ sP305(U_4659,U_4658,U_4660,U_4657) )
& ! [U_4659,U_4658,U_4660,U_4657] :
( sP305(U_4659,U_4658,U_4660,U_4657)
| ~ class_Rings_Olinordered__ring__strict(U_4657) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302,sP303,sP304,sP305])],[f_1194_2]) ).
cnf(f_1194_4,plain,
( sP305(U_4659,U_4658,U_4660,U_4657)
| ~ class_Rings_Olinordered__ring__strict(U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
cnf(f_1194_5,plain,
( sP303(U_4659,U_4658,U_4660,U_4657)
| sP302(U_4659,U_4658,U_4660,U_4657)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4660),U_4659)))
| ~ sP305(U_4659,U_4658,U_4660,U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
cnf(f_1194_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4657),U_4660),U_4659)))
| sP304(U_4659,U_4658,U_4660,U_4657)
| ~ sP305(U_4659,U_4658,U_4660,U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
cnf(f_1194_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4659))
| ~ sP302(U_4659,U_4658,U_4660,U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
cnf(f_1194_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
| ~ sP302(U_4659,U_4658,U_4660,U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
cnf(f_1194_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4659),c_Groups_Ozero__class_Ozero(U_4657)))
| ~ sP303(U_4659,U_4658,U_4660,U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
cnf(f_1194_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4660),U_4658))
| ~ sP303(U_4659,U_4658,U_4660,U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
cnf(f_1194_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4659))
| ~ sP304(U_4659,U_4658,U_4660,U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
cnf(f_1194_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4660),U_4658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4659),c_Groups_Ozero__class_Ozero(U_4657)))
| ~ sP304(U_4659,U_4658,U_4660,U_4657) ),
inference(clausify,[status(thm)],[f_1194_3]) ).
fof(f_1195_1,plain,
! [V_a,T_a] :
( ~ 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)))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__square__less__zero]) ).
fof(f_1195_2,plain,
! [U_4662,U_4661] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4661),U_4662),U_4662)),c_Groups_Ozero__class_Ozero(U_4661)))
| ~ class_Rings_Olinordered__ring(U_4661) ),
inference(variable_rename,[status(thm)],[f_1195_1]) ).
fof(f_1195_3,plain,
! [U_4662,U_4661] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4661),U_4662),U_4662)),c_Groups_Ozero__class_Ozero(U_4661)))
| ~ class_Rings_Olinordered__ring(U_4661) ),
inference(definitional_conversion,[status(esa)],[f_1195_2]) ).
cnf(f_1195_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4661),U_4662),U_4662)),c_Groups_Ozero__class_Ozero(U_4661)))
| ~ class_Rings_Olinordered__ring(U_4661) ),
inference(clausify,[status(thm)],[f_1195_3]) ).
fof(f_1196_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).
fof(f_1196_2,plain,
! [U_4665,U_4664,U_4663] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),U_4664),U_4665))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4663),U_4664),U_4665)),c_Groups_Ozero__class_Ozero(U_4663))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4663),U_4664),U_4665)),c_Groups_Ozero__class_Ozero(U_4663)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),U_4664),U_4665)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_4663) ),
inference(variable_rename,[status(thm)],[f_1196_1]) ).
fof(f_1196_3,plain,
( ! [U_4665,U_4663,U_4664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),U_4664),U_4665))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4663),U_4664),U_4665)),c_Groups_Ozero__class_Ozero(U_4663)))
| ~ sP306(U_4665,U_4663,U_4664) )
& ! [U_4665,U_4663,U_4664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4663),U_4664),U_4665)),c_Groups_Ozero__class_Ozero(U_4663)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),U_4664),U_4665))
| ~ sP306(U_4665,U_4663,U_4664) )
& ! [U_4665,U_4663,U_4664] :
( sP306(U_4665,U_4663,U_4664)
| ~ class_Groups_Oordered__ab__group__add(U_4663) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306])],[f_1196_2]) ).
cnf(f_1196_4,plain,
( sP306(U_4665,U_4663,U_4664)
| ~ class_Groups_Oordered__ab__group__add(U_4663) ),
inference(clausify,[status(thm)],[f_1196_3]) ).
cnf(f_1196_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4663),U_4664),U_4665)),c_Groups_Ozero__class_Ozero(U_4663)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),U_4664),U_4665))
| ~ sP306(U_4665,U_4663,U_4664) ),
inference(clausify,[status(thm)],[f_1196_3]) ).
cnf(f_1196_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),U_4664),U_4665))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4663),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4663),U_4664),U_4665)),c_Groups_Ozero__class_Ozero(U_4663)))
| ~ sP306(U_4665,U_4663,U_4664) ),
inference(clausify,[status(thm)],[f_1196_3]) ).
fof(f_1197_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).
fof(f_1197_2,plain,
! [U_4668,U_4667,U_4666] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),U_4667),U_4668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4666),U_4667),U_4668)),c_Groups_Ozero__class_Ozero(U_4666))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4666),U_4667),U_4668)),c_Groups_Ozero__class_Ozero(U_4666)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),U_4667),U_4668)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_4666) ),
inference(variable_rename,[status(thm)],[f_1197_1]) ).
fof(f_1197_3,plain,
( ! [U_4668,U_4667,U_4666] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),U_4667),U_4668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4666),U_4667),U_4668)),c_Groups_Ozero__class_Ozero(U_4666)))
| ~ sP307(U_4668,U_4667,U_4666) )
& ! [U_4668,U_4667,U_4666] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4666),U_4667),U_4668)),c_Groups_Ozero__class_Ozero(U_4666)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),U_4667),U_4668))
| ~ sP307(U_4668,U_4667,U_4666) )
& ! [U_4668,U_4667,U_4666] :
( sP307(U_4668,U_4667,U_4666)
| ~ class_Groups_Oordered__ab__group__add(U_4666) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP307])],[f_1197_2]) ).
cnf(f_1197_4,plain,
( sP307(U_4668,U_4667,U_4666)
| ~ class_Groups_Oordered__ab__group__add(U_4666) ),
inference(clausify,[status(thm)],[f_1197_3]) ).
cnf(f_1197_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4666),U_4667),U_4668)),c_Groups_Ozero__class_Ozero(U_4666)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),U_4667),U_4668))
| ~ sP307(U_4668,U_4667,U_4666) ),
inference(clausify,[status(thm)],[f_1197_3]) ).
cnf(f_1197_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),U_4667),U_4668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4666),U_4667),U_4668)),c_Groups_Ozero__class_Ozero(U_4666)))
| ~ sP307(U_4668,U_4667,U_4666) ),
inference(clausify,[status(thm)],[f_1197_3]) ).
fof(f_1198_1,plain,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( 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))
| V_c = V_d
| V_a != V_b
| V_r = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq]) ).
fof(f_1198_2,plain,
! [U_4674,U_4673,U_4672,U_4671,U_4670,U_4669] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4669),U_4671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),U_4673)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4669),U_4672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),U_4674))
| U_4673 = U_4674
| U_4671 != U_4672
| U_4670 = c_Groups_Ozero__class_Ozero(U_4669)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4669) ),
inference(variable_rename,[status(thm)],[f_1198_1]) ).
fof(f_1198_3,plain,
! [U_4670,U_4669,U_4671,U_4672,U_4673,U_4674] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4669),U_4671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),U_4673)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4669),U_4672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),U_4674))
| U_4673 = U_4674
| U_4671 != U_4672
| U_4670 = c_Groups_Ozero__class_Ozero(U_4669)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4669) ),
inference(definitional_conversion,[status(esa)],[f_1198_2]) ).
cnf(f_1198_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4669),U_4671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),U_4673)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4669),U_4672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),U_4674))
| U_4673 = U_4674
| U_4671 != U_4672
| U_4670 = c_Groups_Ozero__class_Ozero(U_4669)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4669) ),
inference(clausify,[status(thm)],[f_1198_3]) ).
fof(f_1199_1,plain,
! [T_a] :
( 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)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__one]) ).
fof(f_1199_2,plain,
! [U_4675] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),c_Groups_Oone__class_Oone(U_4675)))
| ~ class_Rings_Olinordered__semidom(U_4675) ),
inference(variable_rename,[status(thm)],[f_1199_1]) ).
fof(f_1199_3,plain,
! [U_4675] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),c_Groups_Oone__class_Oone(U_4675)))
| ~ class_Rings_Olinordered__semidom(U_4675) ),
inference(definitional_conversion,[status(esa)],[f_1199_2]) ).
cnf(f_1199_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),c_Groups_Oone__class_Oone(U_4675)))
| ~ class_Rings_Olinordered__semidom(U_4675) ),
inference(clausify,[status(thm)],[f_1199_3]) ).
fof(f_1200_1,plain,
! [T_a] :
( ~ 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)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__one__le__zero]) ).
fof(f_1200_2,plain,
! [U_4676] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4676),c_Groups_Oone__class_Oone(U_4676)),c_Groups_Ozero__class_Ozero(U_4676)))
| ~ class_Rings_Olinordered__semidom(U_4676) ),
inference(variable_rename,[status(thm)],[f_1200_1]) ).
fof(f_1200_3,plain,
! [U_4676] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4676),c_Groups_Oone__class_Oone(U_4676)),c_Groups_Ozero__class_Ozero(U_4676)))
| ~ class_Rings_Olinordered__semidom(U_4676) ),
inference(definitional_conversion,[status(esa)],[f_1200_2]) ).
cnf(f_1200_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4676),c_Groups_Oone__class_Oone(U_4676)),c_Groups_Ozero__class_Ozero(U_4676)))
| ~ class_Rings_Olinordered__semidom(U_4676) ),
inference(clausify,[status(thm)],[f_1200_3]) ).
fof(f_1201_1,plain,
! [T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__one]) ).
fof(f_1201_2,plain,
! [U_4677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Ozero__class_Ozero(U_4677)),c_Groups_Oone__class_Oone(U_4677)))
| ~ class_Rings_Olinordered__semidom(U_4677) ),
inference(variable_rename,[status(thm)],[f_1201_1]) ).
fof(f_1201_3,plain,
! [U_4677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Ozero__class_Ozero(U_4677)),c_Groups_Oone__class_Oone(U_4677)))
| ~ class_Rings_Olinordered__semidom(U_4677) ),
inference(definitional_conversion,[status(esa)],[f_1201_2]) ).
cnf(f_1201_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Ozero__class_Ozero(U_4677)),c_Groups_Oone__class_Oone(U_4677)))
| ~ class_Rings_Olinordered__semidom(U_4677) ),
inference(clausify,[status(thm)],[f_1201_3]) ).
fof(f_1202_1,plain,
! [T_a] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__one__less__zero]) ).
fof(f_1202_2,plain,
! [U_4678] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4678),c_Groups_Oone__class_Oone(U_4678)),c_Groups_Ozero__class_Ozero(U_4678)))
| ~ class_Rings_Olinordered__semidom(U_4678) ),
inference(variable_rename,[status(thm)],[f_1202_1]) ).
fof(f_1202_3,plain,
! [U_4678] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4678),c_Groups_Oone__class_Oone(U_4678)),c_Groups_Ozero__class_Ozero(U_4678)))
| ~ class_Rings_Olinordered__semidom(U_4678) ),
inference(definitional_conversion,[status(esa)],[f_1202_2]) ).
cnf(f_1202_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4678),c_Groups_Oone__class_Oone(U_4678)),c_Groups_Ozero__class_Ozero(U_4678)))
| ~ class_Rings_Olinordered__semidom(U_4678) ),
inference(clausify,[status(thm)],[f_1202_3]) ).
fof(f_1203_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_diff__Suc__1]) ).
fof(f_1203_2,plain,
! [U_4679] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4679)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4679,
inference(variable_rename,[status(thm)],[f_1203_1]) ).
fof(f_1203_3,plain,
! [U_4679] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4679)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4679,
inference(definitional_conversion,[status(esa)],[f_1203_2]) ).
cnf(f_1203_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4679)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4679,
inference(clausify,[status(thm)],[f_1203_3]) ).
fof(f_1204_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).
fof(f_1204_2,plain,
! [U_4681,U_4680] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),c_Groups_Ozero__class_Ozero(U_4680)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4680),U_4681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),U_4681),c_Groups_Ozero__class_Ozero(U_4680))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),U_4681),c_Groups_Ozero__class_Ozero(U_4680)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),c_Groups_Ozero__class_Ozero(U_4680)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4680),U_4681))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_4680) ),
inference(variable_rename,[status(thm)],[f_1204_1]) ).
fof(f_1204_3,plain,
( ! [U_4680,U_4681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),c_Groups_Ozero__class_Ozero(U_4680)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4680),U_4681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),U_4681),c_Groups_Ozero__class_Ozero(U_4680)))
| ~ sP308(U_4680,U_4681) )
& ! [U_4680,U_4681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),U_4681),c_Groups_Ozero__class_Ozero(U_4680)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),c_Groups_Ozero__class_Ozero(U_4680)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4680),U_4681)))
| ~ sP308(U_4680,U_4681) )
& ! [U_4680,U_4681] :
( sP308(U_4680,U_4681)
| ~ class_Groups_Oordered__ab__group__add(U_4680) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308])],[f_1204_2]) ).
cnf(f_1204_4,plain,
( sP308(U_4680,U_4681)
| ~ class_Groups_Oordered__ab__group__add(U_4680) ),
inference(clausify,[status(thm)],[f_1204_3]) ).
cnf(f_1204_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),U_4681),c_Groups_Ozero__class_Ozero(U_4680)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),c_Groups_Ozero__class_Ozero(U_4680)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4680),U_4681)))
| ~ sP308(U_4680,U_4681) ),
inference(clausify,[status(thm)],[f_1204_3]) ).
cnf(f_1204_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),c_Groups_Ozero__class_Ozero(U_4680)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4680),U_4681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4680),U_4681),c_Groups_Ozero__class_Ozero(U_4680)))
| ~ sP308(U_4680,U_4681) ),
inference(clausify,[status(thm)],[f_1204_3]) ).
fof(f_1205_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ 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))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).
fof(f_1205_2,plain,
! [U_4683,U_4682] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),hAPP(c_Groups_Ouminus__class_Ouminus(U_4682),U_4683)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),c_Groups_Ozero__class_Ozero(U_4682))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),c_Groups_Ozero__class_Ozero(U_4682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),hAPP(c_Groups_Ouminus__class_Ouminus(U_4682),U_4683))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4682) ),
inference(variable_rename,[status(thm)],[f_1205_1]) ).
fof(f_1205_3,plain,
( ! [U_4683,U_4682] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),hAPP(c_Groups_Ouminus__class_Ouminus(U_4682),U_4683)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),c_Groups_Ozero__class_Ozero(U_4682)))
| ~ sP309(U_4683,U_4682) )
& ! [U_4683,U_4682] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),c_Groups_Ozero__class_Ozero(U_4682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),hAPP(c_Groups_Ouminus__class_Ouminus(U_4682),U_4683)))
| ~ sP309(U_4683,U_4682) )
& ! [U_4683,U_4682] :
( sP309(U_4683,U_4682)
| ~ class_Groups_Olinordered__ab__group__add(U_4682) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP309])],[f_1205_2]) ).
cnf(f_1205_4,plain,
( sP309(U_4683,U_4682)
| ~ class_Groups_Olinordered__ab__group__add(U_4682) ),
inference(clausify,[status(thm)],[f_1205_3]) ).
cnf(f_1205_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),c_Groups_Ozero__class_Ozero(U_4682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),hAPP(c_Groups_Ouminus__class_Ouminus(U_4682),U_4683)))
| ~ sP309(U_4683,U_4682) ),
inference(clausify,[status(thm)],[f_1205_3]) ).
cnf(f_1205_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),hAPP(c_Groups_Ouminus__class_Ouminus(U_4682),U_4683)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4682),U_4683),c_Groups_Ozero__class_Ozero(U_4682)))
| ~ sP309(U_4683,U_4682) ),
inference(clausify,[status(thm)],[f_1205_3]) ).
fof(f_1206_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).
fof(f_1206_2,plain,
! [U_4685,U_4684] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),hAPP(c_Groups_Ouminus__class_Ouminus(U_4684),U_4685)),c_Groups_Ozero__class_Ozero(U_4684)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),c_Groups_Ozero__class_Ozero(U_4684)),U_4685)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),c_Groups_Ozero__class_Ozero(U_4684)),U_4685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),hAPP(c_Groups_Ouminus__class_Ouminus(U_4684),U_4685)),c_Groups_Ozero__class_Ozero(U_4684))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_4684) ),
inference(variable_rename,[status(thm)],[f_1206_1]) ).
fof(f_1206_3,plain,
( ! [U_4685,U_4684] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),hAPP(c_Groups_Ouminus__class_Ouminus(U_4684),U_4685)),c_Groups_Ozero__class_Ozero(U_4684)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),c_Groups_Ozero__class_Ozero(U_4684)),U_4685))
| ~ sP310(U_4685,U_4684) )
& ! [U_4685,U_4684] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),c_Groups_Ozero__class_Ozero(U_4684)),U_4685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),hAPP(c_Groups_Ouminus__class_Ouminus(U_4684),U_4685)),c_Groups_Ozero__class_Ozero(U_4684)))
| ~ sP310(U_4685,U_4684) )
& ! [U_4685,U_4684] :
( sP310(U_4685,U_4684)
| ~ class_Groups_Oordered__ab__group__add(U_4684) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP310])],[f_1206_2]) ).
cnf(f_1206_4,plain,
( sP310(U_4685,U_4684)
| ~ class_Groups_Oordered__ab__group__add(U_4684) ),
inference(clausify,[status(thm)],[f_1206_3]) ).
cnf(f_1206_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),c_Groups_Ozero__class_Ozero(U_4684)),U_4685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),hAPP(c_Groups_Ouminus__class_Ouminus(U_4684),U_4685)),c_Groups_Ozero__class_Ozero(U_4684)))
| ~ sP310(U_4685,U_4684) ),
inference(clausify,[status(thm)],[f_1206_3]) ).
cnf(f_1206_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),hAPP(c_Groups_Ouminus__class_Ouminus(U_4684),U_4685)),c_Groups_Ozero__class_Ozero(U_4684)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4684),c_Groups_Ozero__class_Ozero(U_4684)),U_4685))
| ~ sP310(U_4685,U_4684) ),
inference(clausify,[status(thm)],[f_1206_3]) ).
fof(f_1207_1,plain,
! [V_a_2,T_b] :
( ( ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ 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)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).
fof(f_1207_2,plain,
! [U_4687,U_4686] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),hAPP(c_Groups_Ouminus__class_Ouminus(U_4686),U_4687)),U_4687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),c_Groups_Ozero__class_Ozero(U_4686)),U_4687)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),c_Groups_Ozero__class_Ozero(U_4686)),U_4687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),hAPP(c_Groups_Ouminus__class_Ouminus(U_4686),U_4687)),U_4687)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4686) ),
inference(variable_rename,[status(thm)],[f_1207_1]) ).
fof(f_1207_3,plain,
( ! [U_4687,U_4686] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),hAPP(c_Groups_Ouminus__class_Ouminus(U_4686),U_4687)),U_4687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),c_Groups_Ozero__class_Ozero(U_4686)),U_4687))
| ~ sP311(U_4687,U_4686) )
& ! [U_4687,U_4686] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),c_Groups_Ozero__class_Ozero(U_4686)),U_4687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),hAPP(c_Groups_Ouminus__class_Ouminus(U_4686),U_4687)),U_4687))
| ~ sP311(U_4687,U_4686) )
& ! [U_4687,U_4686] :
( sP311(U_4687,U_4686)
| ~ class_Groups_Olinordered__ab__group__add(U_4686) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP311])],[f_1207_2]) ).
cnf(f_1207_4,plain,
( sP311(U_4687,U_4686)
| ~ class_Groups_Olinordered__ab__group__add(U_4686) ),
inference(clausify,[status(thm)],[f_1207_3]) ).
cnf(f_1207_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),c_Groups_Ozero__class_Ozero(U_4686)),U_4687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),hAPP(c_Groups_Ouminus__class_Ouminus(U_4686),U_4687)),U_4687))
| ~ sP311(U_4687,U_4686) ),
inference(clausify,[status(thm)],[f_1207_3]) ).
cnf(f_1207_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),hAPP(c_Groups_Ouminus__class_Ouminus(U_4686),U_4687)),U_4687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4686),c_Groups_Ozero__class_Ozero(U_4686)),U_4687))
| ~ sP311(U_4687,U_4686) ),
inference(clausify,[status(thm)],[f_1207_3]) ).
fof(f_1208_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).
fof(f_1208_2,plain,
! [U_4689,U_4688] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Ozero__class_Ozero(U_4688)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4688),U_4689)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),U_4689),c_Groups_Ozero__class_Ozero(U_4688))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),U_4689),c_Groups_Ozero__class_Ozero(U_4688)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Ozero__class_Ozero(U_4688)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4688),U_4689))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_4688) ),
inference(variable_rename,[status(thm)],[f_1208_1]) ).
fof(f_1208_3,plain,
( ! [U_4689,U_4688] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Ozero__class_Ozero(U_4688)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4688),U_4689)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),U_4689),c_Groups_Ozero__class_Ozero(U_4688)))
| ~ sP312(U_4689,U_4688) )
& ! [U_4689,U_4688] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),U_4689),c_Groups_Ozero__class_Ozero(U_4688)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Ozero__class_Ozero(U_4688)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4688),U_4689)))
| ~ sP312(U_4689,U_4688) )
& ! [U_4689,U_4688] :
( sP312(U_4689,U_4688)
| ~ class_Groups_Oordered__ab__group__add(U_4688) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP312])],[f_1208_2]) ).
cnf(f_1208_4,plain,
( sP312(U_4689,U_4688)
| ~ class_Groups_Oordered__ab__group__add(U_4688) ),
inference(clausify,[status(thm)],[f_1208_3]) ).
cnf(f_1208_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),U_4689),c_Groups_Ozero__class_Ozero(U_4688)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Ozero__class_Ozero(U_4688)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4688),U_4689)))
| ~ sP312(U_4689,U_4688) ),
inference(clausify,[status(thm)],[f_1208_3]) ).
cnf(f_1208_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Ozero__class_Ozero(U_4688)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4688),U_4689)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),U_4689),c_Groups_Ozero__class_Ozero(U_4688)))
| ~ sP312(U_4689,U_4688) ),
inference(clausify,[status(thm)],[f_1208_3]) ).
fof(f_1209_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).
fof(f_1209_2,plain,
! [U_4691,U_4690] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),hAPP(c_Groups_Ouminus__class_Ouminus(U_4690),U_4691)),c_Groups_Ozero__class_Ozero(U_4690)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),c_Groups_Ozero__class_Ozero(U_4690)),U_4691)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),c_Groups_Ozero__class_Ozero(U_4690)),U_4691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),hAPP(c_Groups_Ouminus__class_Ouminus(U_4690),U_4691)),c_Groups_Ozero__class_Ozero(U_4690))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_4690) ),
inference(variable_rename,[status(thm)],[f_1209_1]) ).
fof(f_1209_3,plain,
( ! [U_4691,U_4690] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),hAPP(c_Groups_Ouminus__class_Ouminus(U_4690),U_4691)),c_Groups_Ozero__class_Ozero(U_4690)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),c_Groups_Ozero__class_Ozero(U_4690)),U_4691))
| ~ sP313(U_4691,U_4690) )
& ! [U_4691,U_4690] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),c_Groups_Ozero__class_Ozero(U_4690)),U_4691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),hAPP(c_Groups_Ouminus__class_Ouminus(U_4690),U_4691)),c_Groups_Ozero__class_Ozero(U_4690)))
| ~ sP313(U_4691,U_4690) )
& ! [U_4691,U_4690] :
( sP313(U_4691,U_4690)
| ~ class_Groups_Oordered__ab__group__add(U_4690) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP313])],[f_1209_2]) ).
cnf(f_1209_4,plain,
( sP313(U_4691,U_4690)
| ~ class_Groups_Oordered__ab__group__add(U_4690) ),
inference(clausify,[status(thm)],[f_1209_3]) ).
cnf(f_1209_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),c_Groups_Ozero__class_Ozero(U_4690)),U_4691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),hAPP(c_Groups_Ouminus__class_Ouminus(U_4690),U_4691)),c_Groups_Ozero__class_Ozero(U_4690)))
| ~ sP313(U_4691,U_4690) ),
inference(clausify,[status(thm)],[f_1209_3]) ).
cnf(f_1209_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),hAPP(c_Groups_Ouminus__class_Ouminus(U_4690),U_4691)),c_Groups_Ozero__class_Ozero(U_4690)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4690),c_Groups_Ozero__class_Ozero(U_4690)),U_4691))
| ~ sP313(U_4691,U_4690) ),
inference(clausify,[status(thm)],[f_1209_3]) ).
fof(f_1210_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).
fof(f_1210_2,plain,
! [U_4693,U_4692] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),U_4693)),U_4693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),U_4693)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),U_4693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),U_4693)),U_4693)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_4692) ),
inference(variable_rename,[status(thm)],[f_1210_1]) ).
fof(f_1210_3,plain,
( ! [U_4692,U_4693] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),U_4693)),U_4693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),U_4693))
| ~ sP314(U_4692,U_4693) )
& ! [U_4692,U_4693] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),U_4693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),U_4693)),U_4693))
| ~ sP314(U_4692,U_4693) )
& ! [U_4692,U_4693] :
( sP314(U_4692,U_4693)
| ~ class_Groups_Olinordered__ab__group__add(U_4692) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP314])],[f_1210_2]) ).
cnf(f_1210_4,plain,
( sP314(U_4692,U_4693)
| ~ class_Groups_Olinordered__ab__group__add(U_4692) ),
inference(clausify,[status(thm)],[f_1210_3]) ).
cnf(f_1210_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),U_4693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),U_4693)),U_4693))
| ~ sP314(U_4692,U_4693) ),
inference(clausify,[status(thm)],[f_1210_3]) ).
cnf(f_1210_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),U_4693)),U_4693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),U_4693))
| ~ sP314(U_4692,U_4693) ),
inference(clausify,[status(thm)],[f_1210_3]) ).
fof(f_1211_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).
fof(f_1211_2,plain,
! [U_4695,U_4694] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),hAPP(c_Groups_Ouminus__class_Ouminus(U_4694),U_4695)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),c_Groups_Ozero__class_Ozero(U_4694))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),c_Groups_Ozero__class_Ozero(U_4694)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),hAPP(c_Groups_Ouminus__class_Ouminus(U_4694),U_4695))) ) )
| ~ class_Rings_Olinordered__idom(U_4694) ),
inference(variable_rename,[status(thm)],[f_1211_1]) ).
fof(f_1211_3,plain,
( ! [U_4695,U_4694] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),hAPP(c_Groups_Ouminus__class_Ouminus(U_4694),U_4695)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),c_Groups_Ozero__class_Ozero(U_4694)))
| ~ sP315(U_4695,U_4694) )
& ! [U_4695,U_4694] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),c_Groups_Ozero__class_Ozero(U_4694)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),hAPP(c_Groups_Ouminus__class_Ouminus(U_4694),U_4695)))
| ~ sP315(U_4695,U_4694) )
& ! [U_4695,U_4694] :
( sP315(U_4695,U_4694)
| ~ class_Rings_Olinordered__idom(U_4694) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP315])],[f_1211_2]) ).
cnf(f_1211_4,plain,
( sP315(U_4695,U_4694)
| ~ class_Rings_Olinordered__idom(U_4694) ),
inference(clausify,[status(thm)],[f_1211_3]) ).
cnf(f_1211_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),c_Groups_Ozero__class_Ozero(U_4694)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),hAPP(c_Groups_Ouminus__class_Ouminus(U_4694),U_4695)))
| ~ sP315(U_4695,U_4694) ),
inference(clausify,[status(thm)],[f_1211_3]) ).
cnf(f_1211_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),hAPP(c_Groups_Ouminus__class_Ouminus(U_4694),U_4695)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4694),U_4695),c_Groups_Ozero__class_Ozero(U_4694)))
| ~ sP315(U_4695,U_4694) ),
inference(clausify,[status(thm)],[f_1211_3]) ).
fof(f_1212_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__minus]) ).
fof(f_1212_2,plain,
! [U_4697,U_4696] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4696),U_4697),hAPP(c_Groups_Ouminus__class_Ouminus(U_4696),U_4697)) = c_Groups_Ozero__class_Ozero(U_4696)
| ~ class_Groups_Ogroup__add(U_4696) ),
inference(variable_rename,[status(thm)],[f_1212_1]) ).
fof(f_1212_3,plain,
! [U_4697,U_4696] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4696),U_4697),hAPP(c_Groups_Ouminus__class_Ouminus(U_4696),U_4697)) = c_Groups_Ozero__class_Ozero(U_4696)
| ~ class_Groups_Ogroup__add(U_4696) ),
inference(definitional_conversion,[status(esa)],[f_1212_2]) ).
cnf(f_1212_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4696),U_4697),hAPP(c_Groups_Ouminus__class_Ouminus(U_4696),U_4697)) = c_Groups_Ozero__class_Ozero(U_4696)
| ~ class_Groups_Ogroup__add(U_4696) ),
inference(clausify,[status(thm)],[f_1212_3]) ).
fof(f_1213_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).
fof(f_1213_2,plain,
! [U_4700,U_4699,U_4698] :
( ( ( U_4699 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4698),U_4700)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4698),U_4699),U_4700) != c_Groups_Ozero__class_Ozero(U_4698) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4698),U_4699),U_4700) = c_Groups_Ozero__class_Ozero(U_4698)
| U_4699 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4698),U_4700) ) )
| ~ class_Groups_Ogroup__add(U_4698) ),
inference(variable_rename,[status(thm)],[f_1213_1]) ).
fof(f_1213_3,plain,
( ! [U_4698,U_4699,U_4700] :
( U_4699 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4698),U_4700)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4698),U_4699),U_4700) != c_Groups_Ozero__class_Ozero(U_4698)
| ~ sP316(U_4698,U_4699,U_4700) )
& ! [U_4698,U_4699,U_4700] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4698),U_4699),U_4700) = c_Groups_Ozero__class_Ozero(U_4698)
| U_4699 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4698),U_4700)
| ~ sP316(U_4698,U_4699,U_4700) )
& ! [U_4698,U_4699,U_4700] :
( sP316(U_4698,U_4699,U_4700)
| ~ class_Groups_Ogroup__add(U_4698) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP316])],[f_1213_2]) ).
cnf(f_1213_4,plain,
( sP316(U_4698,U_4699,U_4700)
| ~ class_Groups_Ogroup__add(U_4698) ),
inference(clausify,[status(thm)],[f_1213_3]) ).
cnf(f_1213_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4698),U_4699),U_4700) = c_Groups_Ozero__class_Ozero(U_4698)
| U_4699 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4698),U_4700)
| ~ sP316(U_4698,U_4699,U_4700) ),
inference(clausify,[status(thm)],[f_1213_3]) ).
cnf(f_1213_6,plain,
( U_4699 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4698),U_4700)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4698),U_4699),U_4700) != c_Groups_Ozero__class_Ozero(U_4698)
| ~ sP316(U_4698,U_4699,U_4700) ),
inference(clausify,[status(thm)],[f_1213_3]) ).
fof(f_1214_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_left__minus]) ).
fof(f_1214_2,plain,
! [U_4702,U_4701] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4701),hAPP(c_Groups_Ouminus__class_Ouminus(U_4701),U_4702)),U_4702) = c_Groups_Ozero__class_Ozero(U_4701)
| ~ class_Groups_Ogroup__add(U_4701) ),
inference(variable_rename,[status(thm)],[f_1214_1]) ).
fof(f_1214_3,plain,
! [U_4702,U_4701] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4701),hAPP(c_Groups_Ouminus__class_Ouminus(U_4701),U_4702)),U_4702) = c_Groups_Ozero__class_Ozero(U_4701)
| ~ class_Groups_Ogroup__add(U_4701) ),
inference(definitional_conversion,[status(esa)],[f_1214_2]) ).
cnf(f_1214_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4701),hAPP(c_Groups_Ouminus__class_Ouminus(U_4701),U_4702)),U_4702) = c_Groups_Ozero__class_Ozero(U_4701)
| ~ class_Groups_Ogroup__add(U_4701) ),
inference(clausify,[status(thm)],[f_1214_3]) ).
fof(f_1215_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__left__minus]) ).
fof(f_1215_2,plain,
! [U_4704,U_4703] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4703),hAPP(c_Groups_Ouminus__class_Ouminus(U_4703),U_4704)),U_4704) = c_Groups_Ozero__class_Ozero(U_4703)
| ~ class_Groups_Oab__group__add(U_4703) ),
inference(variable_rename,[status(thm)],[f_1215_1]) ).
fof(f_1215_3,plain,
! [U_4703,U_4704] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4703),hAPP(c_Groups_Ouminus__class_Ouminus(U_4703),U_4704)),U_4704) = c_Groups_Ozero__class_Ozero(U_4703)
| ~ class_Groups_Oab__group__add(U_4703) ),
inference(definitional_conversion,[status(esa)],[f_1215_2]) ).
cnf(f_1215_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4703),hAPP(c_Groups_Ouminus__class_Ouminus(U_4703),U_4704)),U_4704) = c_Groups_Ozero__class_Ozero(U_4703)
| ~ class_Groups_Oab__group__add(U_4703) ),
inference(clausify,[status(thm)],[f_1215_3]) ).
fof(f_1216_1,plain,
! [V_b,V_a,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__unique]) ).
fof(f_1216_2,plain,
! [U_4707,U_4706,U_4705] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4705),U_4706) = U_4707
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4705),U_4706),U_4707) != c_Groups_Ozero__class_Ozero(U_4705)
| ~ class_Groups_Ogroup__add(U_4705) ),
inference(variable_rename,[status(thm)],[f_1216_1]) ).
fof(f_1216_3,plain,
! [U_4705,U_4706,U_4707] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4705),U_4706) = U_4707
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4705),U_4706),U_4707) != c_Groups_Ozero__class_Ozero(U_4705)
| ~ class_Groups_Ogroup__add(U_4705) ),
inference(definitional_conversion,[status(esa)],[f_1216_2]) ).
cnf(f_1216_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4705),U_4706) = U_4707
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4705),U_4706),U_4707) != c_Groups_Ozero__class_Ozero(U_4705)
| ~ class_Groups_Ogroup__add(U_4705) ),
inference(clausify,[status(thm)],[f_1216_3]) ).
fof(f_1217_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__0]) ).
fof(f_1217_2,plain,
! [U_4709,U_4708] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4708),c_Groups_Ozero__class_Ozero(U_4708)),U_4709) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4708),U_4709)
| ~ class_Groups_Ogroup__add(U_4708) ),
inference(variable_rename,[status(thm)],[f_1217_1]) ).
fof(f_1217_3,plain,
! [U_4708,U_4709] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4708),c_Groups_Ozero__class_Ozero(U_4708)),U_4709) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4708),U_4709)
| ~ class_Groups_Ogroup__add(U_4708) ),
inference(definitional_conversion,[status(esa)],[f_1217_2]) ).
cnf(f_1217_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4708),c_Groups_Ozero__class_Ozero(U_4708)),U_4709) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4708),U_4709)
| ~ class_Groups_Ogroup__add(U_4708) ),
inference(clausify,[status(thm)],[f_1217_3]) ).
fof(f_1218_1,plain,
! [V_n_2,V_m_2] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThanSuc]) ).
fof(f_1218_2,plain,
! [U_4711,U_4710] :
( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4710),hAPP(c_Nat_OSuc,U_4711)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4710),U_4711)) )
& ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4710),hAPP(c_Nat_OSuc,U_4711)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4711),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4710),U_4711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4710),U_4711)) ) ),
inference(variable_rename,[status(thm)],[f_1218_1]) ).
fof(f_1218_3,plain,
( ! [U_4715,U_4713] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4713),hAPP(c_Nat_OSuc,U_4715)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4713),U_4715)) )
& ! [U_4714,U_4712] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4712),hAPP(c_Nat_OSuc,U_4714)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4714),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4712),U_4714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4712),U_4714)) ) ),
inference(miniscope,[status(thm)],[f_1218_2]) ).
fof(f_1218_4,plain,
( ! [U_4713,U_4715] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4713),hAPP(c_Nat_OSuc,U_4715)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4713),U_4715)) )
& ! [U_4714,U_4712] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4712),hAPP(c_Nat_OSuc,U_4714)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4714),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4712),U_4714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4712),U_4714)) ) ),
inference(definitional_conversion,[status(esa)],[f_1218_3]) ).
cnf(f_1218_5,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4712),hAPP(c_Nat_OSuc,U_4714)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4714),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4712),U_4714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4712),U_4714)) ),
inference(clausify,[status(thm)],[f_1218_4]) ).
cnf(f_1218_6,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4713),hAPP(c_Nat_OSuc,U_4715)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4713),U_4715)) ),
inference(clausify,[status(thm)],[f_1218_4]) ).
fof(f_1219_1,plain,
! [V_f_2,T_c,T_b] :
( 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)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__empty]) ).
fof(f_1219_2,plain,
! [U_4718,U_4717,U_4716] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4717,U_4716),U_4718),c_Orderings_Obot__class_Obot(tc_fun(U_4717,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_4716)
| ~ class_Groups_Ocomm__monoid__add(U_4716) ),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
fof(f_1219_3,plain,
! [U_4717,U_4716,U_4718] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4717,U_4716),U_4718),c_Orderings_Obot__class_Obot(tc_fun(U_4717,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_4716)
| ~ class_Groups_Ocomm__monoid__add(U_4716) ),
inference(definitional_conversion,[status(esa)],[f_1219_2]) ).
cnf(f_1219_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4717,U_4716),U_4718),c_Orderings_Obot__class_Obot(tc_fun(U_4717,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_4716)
| ~ class_Groups_Ocomm__monoid__add(U_4716) ),
inference(clausify,[status(thm)],[f_1219_3]) ).
fof(f_1220_1,plain,
! [V_g_2,T_c,T_b] :
( 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)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oempty]) ).
fof(f_1220_2,plain,
! [U_4721,U_4720,U_4719] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4720,U_4719),U_4721),c_Orderings_Obot__class_Obot(tc_fun(U_4720,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_4719)
| ~ class_Groups_Ocomm__monoid__add(U_4719) ),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
fof(f_1220_3,plain,
! [U_4719,U_4720,U_4721] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4720,U_4719),U_4721),c_Orderings_Obot__class_Obot(tc_fun(U_4720,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_4719)
| ~ class_Groups_Ocomm__monoid__add(U_4719) ),
inference(definitional_conversion,[status(esa)],[f_1220_2]) ).
cnf(f_1220_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4720,U_4719),U_4721),c_Orderings_Obot__class_Obot(tc_fun(U_4720,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_4719)
| ~ class_Groups_Ocomm__monoid__add(U_4719) ),
inference(clausify,[status(thm)],[f_1220_3]) ).
fof(f_1221_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( 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)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__infinite]) ).
fof(f_1221_2,plain,
! [U_4725,U_4724,U_4723,U_4722] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4723,U_4722),U_4725),U_4724) = c_Groups_Ozero__class_Ozero(U_4722)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4724))
| ~ class_Groups_Ocomm__monoid__add(U_4722) ),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
fof(f_1221_3,plain,
! [U_4722,U_4723,U_4724,U_4725] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4723,U_4722),U_4725),U_4724) = c_Groups_Ozero__class_Ozero(U_4722)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4724))
| ~ class_Groups_Ocomm__monoid__add(U_4722) ),
inference(definitional_conversion,[status(esa)],[f_1221_2]) ).
cnf(f_1221_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4723,U_4722),U_4725),U_4724) = c_Groups_Ozero__class_Ozero(U_4722)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4724))
| ~ class_Groups_Ocomm__monoid__add(U_4722) ),
inference(clausify,[status(thm)],[f_1221_3]) ).
fof(f_1222_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( 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)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinfinite]) ).
fof(f_1222_2,plain,
! [U_4729,U_4728,U_4727,U_4726] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4727,U_4726),U_4729),U_4728) = c_Groups_Ozero__class_Ozero(U_4726)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4727),U_4728))
| ~ class_Groups_Ocomm__monoid__add(U_4726) ),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
fof(f_1222_3,plain,
! [U_4727,U_4726,U_4728,U_4729] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4727,U_4726),U_4729),U_4728) = c_Groups_Ozero__class_Ozero(U_4726)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4727),U_4728))
| ~ class_Groups_Ocomm__monoid__add(U_4726) ),
inference(definitional_conversion,[status(esa)],[f_1222_2]) ).
cnf(f_1222_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4727,U_4726),U_4729),U_4728) = c_Groups_Ozero__class_Ozero(U_4726)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4727),U_4728))
| ~ class_Groups_Ocomm__monoid__add(U_4726) ),
inference(clausify,[status(thm)],[f_1222_3]) ).
fof(f_1223_1,plain,
! [V_f_2,V_S_2,T_b] :
( ( ( 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)))
| ? [B_x] :
( ~ 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)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
& ( ! [B_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ 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))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff]) ).
fof(f_1223_2,plain,
! [U_4734,U_4733,U_4732] :
( ( ( 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(U_4732,tc_Nat_Onat),U_4734),U_4733)))
| ? [U_4731] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4734,U_4731)))
& hBOOL(hAPP(hAPP(c_member(U_4732),U_4731),U_4733)) ) )
& ( ! [U_4730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4734,U_4730)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4732),U_4730),U_4733)) )
| ~ 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(U_4732,tc_Nat_Onat),U_4734),U_4733))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4732),U_4733)) ),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
fof(f_1223_3,plain,
! [U_4734,U_4733,U_4732] :
( ( ( 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(U_4732,tc_Nat_Onat),U_4734),U_4733)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4734,sK106(U_4734,U_4733,U_4732))))
& hBOOL(hAPP(hAPP(c_member(U_4732),sK106(U_4734,U_4733,U_4732)),U_4733)) ) )
& ( ! [U_4730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4734,U_4730)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4732),U_4730),U_4733)) )
| ~ 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(U_4732,tc_Nat_Onat),U_4734),U_4733))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4732),U_4733)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_4731,sK106(U_4734,U_4733,U_4732))],[f_1223_2]) ).
fof(f_1223_4,plain,
( ! [U_4732,U_4733,U_4734] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4734,sK106(U_4734,U_4733,U_4732))))
| ~ sP317(U_4732,U_4733,U_4734) )
& ! [U_4732,U_4733,U_4734] :
( hBOOL(hAPP(hAPP(c_member(U_4732),sK106(U_4734,U_4733,U_4732)),U_4733))
| ~ sP317(U_4732,U_4733,U_4734) )
& ! [U_4730,U_4732,U_4733,U_4734] :
( 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(U_4732,tc_Nat_Onat),U_4734),U_4733)))
| sP317(U_4732,U_4733,U_4734)
| ~ sP318(U_4730,U_4732,U_4733,U_4734) )
& ! [U_4730,U_4732,U_4733,U_4734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4734,U_4730)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4732),U_4730),U_4733))
| ~ 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(U_4732,tc_Nat_Onat),U_4734),U_4733)))
| ~ sP318(U_4730,U_4732,U_4733,U_4734) )
& ! [U_4730,U_4732,U_4733,U_4734] :
( sP318(U_4730,U_4732,U_4733,U_4734)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4732),U_4733)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP317,sP318])],[f_1223_3]) ).
cnf(f_1223_5,plain,
( sP318(U_4730,U_4732,U_4733,U_4734)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4732),U_4733)) ),
inference(clausify,[status(thm)],[f_1223_4]) ).
cnf(f_1223_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4734,U_4730)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4732),U_4730),U_4733))
| ~ 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(U_4732,tc_Nat_Onat),U_4734),U_4733)))
| ~ sP318(U_4730,U_4732,U_4733,U_4734) ),
inference(clausify,[status(thm)],[f_1223_4]) ).
cnf(f_1223_7,plain,
( 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(U_4732,tc_Nat_Onat),U_4734),U_4733)))
| sP317(U_4732,U_4733,U_4734)
| ~ sP318(U_4730,U_4732,U_4733,U_4734) ),
inference(clausify,[status(thm)],[f_1223_4]) ).
cnf(f_1223_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4732),sK106(U_4734,U_4733,U_4732)),U_4733))
| ~ sP317(U_4732,U_4733,U_4734) ),
inference(clausify,[status(thm)],[f_1223_4]) ).
cnf(f_1223_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4734,sK106(U_4734,U_4733,U_4732))))
| ~ sP317(U_4732,U_4733,U_4734) ),
inference(clausify,[status(thm)],[f_1223_4]) ).
fof(f_1224_1,plain,
! [V_n_2,V_m_2] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv]) ).
fof(f_1224_2,plain,
! [U_4736,U_4735] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4735,hAPP(c_Nat_OSuc,U_4736)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4736)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4735,U_4736))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4735),hAPP(c_Nat_OSuc,U_4736))) ),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
fof(f_1224_3,plain,
! [U_4736,U_4735] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4735,hAPP(c_Nat_OSuc,U_4736)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4736)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4735,U_4736))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4735),hAPP(c_Nat_OSuc,U_4736))) ),
inference(definitional_conversion,[status(esa)],[f_1224_2]) ).
cnf(f_1224_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4735,hAPP(c_Nat_OSuc,U_4736)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4736)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4735,U_4736))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4735),hAPP(c_Nat_OSuc,U_4736))) ),
inference(clausify,[status(thm)],[f_1224_3]) ).
fof(f_1225_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( ( ( 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)
| ! [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| 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) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Rings_Ono__zero__divisors(T_c)
| ~ class_Rings_Ocomm__semiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff]) ).
fof(f_1225_2,plain,
! [U_4742,U_4741,U_4740,U_4739] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4740,U_4739),U_4742),U_4741) = c_Groups_Ozero__class_Ozero(U_4739)
| ! [U_4738] :
( hAPP(U_4742,U_4738) != c_Groups_Ozero__class_Ozero(U_4739)
| ~ hBOOL(hAPP(hAPP(c_member(U_4740),U_4738),U_4741)) ) )
& ( ? [U_4737] :
( hAPP(U_4742,U_4737) = c_Groups_Ozero__class_Ozero(U_4739)
& hBOOL(hAPP(hAPP(c_member(U_4740),U_4737),U_4741)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4740,U_4739),U_4742),U_4741) != c_Groups_Ozero__class_Ozero(U_4739) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4740),U_4741))
| ~ class_Rings_Ono__zero__divisors(U_4739)
| ~ class_Rings_Ocomm__semiring__1(U_4739) ),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
fof(f_1225_3,plain,
! [U_4742,U_4741,U_4740,U_4739] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4740,U_4739),U_4742),U_4741) = c_Groups_Ozero__class_Ozero(U_4739)
| ! [U_4738] :
( hAPP(U_4742,U_4738) != c_Groups_Ozero__class_Ozero(U_4739)
| ~ hBOOL(hAPP(hAPP(c_member(U_4740),U_4738),U_4741)) ) )
& ( ( hAPP(U_4742,sK107(U_4742,U_4741,U_4740,U_4739)) = c_Groups_Ozero__class_Ozero(U_4739)
& hBOOL(hAPP(hAPP(c_member(U_4740),sK107(U_4742,U_4741,U_4740,U_4739)),U_4741)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4740,U_4739),U_4742),U_4741) != c_Groups_Ozero__class_Ozero(U_4739) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4740),U_4741))
| ~ class_Rings_Ono__zero__divisors(U_4739)
| ~ class_Rings_Ocomm__semiring__1(U_4739) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_4737,sK107(U_4742,U_4741,U_4740,U_4739))],[f_1225_2]) ).
fof(f_1225_4,plain,
( ! [U_4739,U_4740,U_4741,U_4742] :
( hAPP(U_4742,sK107(U_4742,U_4741,U_4740,U_4739)) = c_Groups_Ozero__class_Ozero(U_4739)
| ~ sP319(U_4739,U_4740,U_4741,U_4742) )
& ! [U_4739,U_4740,U_4741,U_4742] :
( hBOOL(hAPP(hAPP(c_member(U_4740),sK107(U_4742,U_4741,U_4740,U_4739)),U_4741))
| ~ sP319(U_4739,U_4740,U_4741,U_4742) )
& ! [U_4738,U_4739,U_4740,U_4741,U_4742] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4740,U_4739),U_4742),U_4741) = c_Groups_Ozero__class_Ozero(U_4739)
| hAPP(U_4742,U_4738) != c_Groups_Ozero__class_Ozero(U_4739)
| ~ hBOOL(hAPP(hAPP(c_member(U_4740),U_4738),U_4741))
| ~ sP320(U_4738,U_4739,U_4740,U_4741,U_4742) )
& ! [U_4738,U_4739,U_4740,U_4741,U_4742] :
( sP319(U_4739,U_4740,U_4741,U_4742)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4740,U_4739),U_4742),U_4741) != c_Groups_Ozero__class_Ozero(U_4739)
| ~ sP320(U_4738,U_4739,U_4740,U_4741,U_4742) )
& ! [U_4738,U_4739,U_4740,U_4741,U_4742] :
( sP320(U_4738,U_4739,U_4740,U_4741,U_4742)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4740),U_4741))
| ~ class_Rings_Ono__zero__divisors(U_4739)
| ~ class_Rings_Ocomm__semiring__1(U_4739) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP319,sP320])],[f_1225_3]) ).
cnf(f_1225_5,plain,
( sP320(U_4738,U_4739,U_4740,U_4741,U_4742)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4740),U_4741))
| ~ class_Rings_Ono__zero__divisors(U_4739)
| ~ class_Rings_Ocomm__semiring__1(U_4739) ),
inference(clausify,[status(thm)],[f_1225_4]) ).
cnf(f_1225_6,plain,
( sP319(U_4739,U_4740,U_4741,U_4742)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4740,U_4739),U_4742),U_4741) != c_Groups_Ozero__class_Ozero(U_4739)
| ~ sP320(U_4738,U_4739,U_4740,U_4741,U_4742) ),
inference(clausify,[status(thm)],[f_1225_4]) ).
cnf(f_1225_7,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4740,U_4739),U_4742),U_4741) = c_Groups_Ozero__class_Ozero(U_4739)
| hAPP(U_4742,U_4738) != c_Groups_Ozero__class_Ozero(U_4739)
| ~ hBOOL(hAPP(hAPP(c_member(U_4740),U_4738),U_4741))
| ~ sP320(U_4738,U_4739,U_4740,U_4741,U_4742) ),
inference(clausify,[status(thm)],[f_1225_4]) ).
cnf(f_1225_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4740),sK107(U_4742,U_4741,U_4740,U_4739)),U_4741))
| ~ sP319(U_4739,U_4740,U_4741,U_4742) ),
inference(clausify,[status(thm)],[f_1225_4]) ).
cnf(f_1225_9,plain,
( hAPP(U_4742,sK107(U_4742,U_4741,U_4740,U_4739)) = c_Groups_Ozero__class_Ozero(U_4739)
| ~ sP319(U_4739,U_4740,U_4741,U_4742) ),
inference(clausify,[status(thm)],[f_1225_4]) ).
fof(f_1226_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( 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)
| ! [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Rings_Ocomm__semiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__zero]) ).
fof(f_1226_2,plain,
! [U_4747,U_4746,U_4745,U_4744] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4745,U_4744),U_4747),U_4746) = c_Groups_Ozero__class_Ozero(U_4744)
| ! [U_4743] :
( hAPP(U_4747,U_4743) != c_Groups_Ozero__class_Ozero(U_4744)
| ~ hBOOL(hAPP(hAPP(c_member(U_4745),U_4743),U_4746)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4745),U_4746))
| ~ class_Rings_Ocomm__semiring__1(U_4744) ),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
fof(f_1226_3,plain,
! [U_4746,U_4747,U_4745,U_4743,U_4744] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4745,U_4744),U_4747),U_4746) = c_Groups_Ozero__class_Ozero(U_4744)
| hAPP(U_4747,U_4743) != c_Groups_Ozero__class_Ozero(U_4744)
| ~ hBOOL(hAPP(hAPP(c_member(U_4745),U_4743),U_4746))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4745),U_4746))
| ~ class_Rings_Ocomm__semiring__1(U_4744) ),
inference(definitional_conversion,[status(esa)],[f_1226_2]) ).
cnf(f_1226_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4745,U_4744),U_4747),U_4746) = c_Groups_Ozero__class_Ozero(U_4744)
| hAPP(U_4747,U_4743) != c_Groups_Ozero__class_Ozero(U_4744)
| ~ hBOOL(hAPP(hAPP(c_member(U_4745),U_4743),U_4746))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4745),U_4746))
| ~ class_Rings_Ocomm__semiring__1(U_4744) ),
inference(clausify,[status(thm)],[f_1226_3]) ).
fof(f_1227_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_card__atLeastAtMost]) ).
fof(f_1227_2,plain,
! [U_4749,U_4748] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4748,U_4749)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4749)),U_4748),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
fof(f_1227_3,plain,
! [U_4749,U_4748] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4748,U_4749)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4749)),U_4748),
inference(definitional_conversion,[status(esa)],[f_1227_2]) ).
cnf(f_1227_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4748,U_4749)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4749)),U_4748),
inference(clausify,[status(thm)],[f_1227_3]) ).
fof(f_1228_1,plain,
! [V_n_2,V_m_2] :
( ( 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)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).
fof(f_1228_2,plain,
! [U_4751,U_4750] :
( ( 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),U_4750),U_4751)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4751))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4750)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4751))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4750))
| ~ 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),U_4750),U_4751))) ) ),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
fof(f_1228_3,plain,
( ! [U_4755,U_4753] :
( 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),U_4753),U_4755)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4755))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4753)) ) )
& ! [U_4754,U_4752] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4752))
| ~ 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),U_4752),U_4754))) ) ),
inference(miniscope,[status(thm)],[f_1228_2]) ).
fof(f_1228_4,plain,
( ! [U_4753,U_4755] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4755))
| ~ sP321(U_4753,U_4755) )
& ! [U_4753,U_4755] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4753))
| ~ sP321(U_4753,U_4755) )
& ! [U_4753,U_4755] :
( 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),U_4753),U_4755)))
| sP321(U_4753,U_4755) )
& ! [U_4754,U_4752] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4752))
| ~ 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),U_4752),U_4754))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP321])],[f_1228_3]) ).
cnf(f_1228_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4752))
| ~ 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),U_4752),U_4754))) ),
inference(clausify,[status(thm)],[f_1228_4]) ).
cnf(f_1228_6,plain,
( 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),U_4753),U_4755)))
| sP321(U_4753,U_4755) ),
inference(clausify,[status(thm)],[f_1228_4]) ).
cnf(f_1228_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4753))
| ~ sP321(U_4753,U_4755) ),
inference(clausify,[status(thm)],[f_1228_4]) ).
cnf(f_1228_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4755))
| ~ sP321(U_4753,U_4755) ),
inference(clausify,[status(thm)],[f_1228_4]) ).
fof(f_1229_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_card_Oempty]) ).
fof(f_1229_2,plain,
! [U_4756] : hAPP(c_Finite__Set_Ocard(U_4756),c_Orderings_Obot__class_Obot(tc_fun(U_4756,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
fof(f_1229_3,plain,
! [U_4756] : hAPP(c_Finite__Set_Ocard(U_4756),c_Orderings_Obot__class_Obot(tc_fun(U_4756,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1229_2]) ).
cnf(f_1229_4,plain,
hAPP(c_Finite__Set_Ocard(U_4756),c_Orderings_Obot__class_Obot(tc_fun(U_4756,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1229_3]) ).
fof(f_1230_1,plain,
! [V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__infinite]) ).
fof(f_1230_2,plain,
! [U_4758,U_4757] :
( hAPP(c_Finite__Set_Ocard(U_4757),U_4758) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4758)) ),
inference(variable_rename,[status(thm)],[f_1230_1]) ).
fof(f_1230_3,plain,
! [U_4758,U_4757] :
( hAPP(c_Finite__Set_Ocard(U_4757),U_4758) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4758)) ),
inference(definitional_conversion,[status(esa)],[f_1230_2]) ).
cnf(f_1230_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4757),U_4758) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4758)) ),
inference(clausify,[status(thm)],[f_1230_3]) ).
fof(f_1231_1,plain,
! [V_m,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__less]) ).
fof(f_1231_2,plain,
! [U_4760,U_4759] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4760),U_4759)),U_4760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4759)) ),
inference(variable_rename,[status(thm)],[f_1231_1]) ).
fof(f_1231_3,plain,
! [U_4759,U_4760] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4760),U_4759)),U_4760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4759)) ),
inference(definitional_conversion,[status(esa)],[f_1231_2]) ).
cnf(f_1231_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4760),U_4759)),U_4760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4759)) ),
inference(clausify,[status(thm)],[f_1231_3]) ).
fof(f_1232_1,plain,
! [V_m_2,V_n_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).
fof(f_1232_2,plain,
! [U_4762,U_4761] :
( ( 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),U_4761),U_4762)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4762),U_4761)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4762),U_4761))
| ~ 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),U_4761),U_4762))) ) ),
inference(variable_rename,[status(thm)],[f_1232_1]) ).
fof(f_1232_3,plain,
( ! [U_4766,U_4764] :
( 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),U_4764),U_4766)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4766),U_4764)) )
& ! [U_4765,U_4763] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4765),U_4763))
| ~ 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),U_4763),U_4765))) ) ),
inference(miniscope,[status(thm)],[f_1232_2]) ).
fof(f_1232_4,plain,
( ! [U_4764,U_4766] :
( 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),U_4764),U_4766)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4766),U_4764)) )
& ! [U_4765,U_4763] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4765),U_4763))
| ~ 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),U_4763),U_4765))) ) ),
inference(definitional_conversion,[status(esa)],[f_1232_3]) ).
cnf(f_1232_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4765),U_4763))
| ~ 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),U_4763),U_4765))) ),
inference(clausify,[status(thm)],[f_1232_4]) ).
cnf(f_1232_6,plain,
( 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),U_4764),U_4766)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4766),U_4764)) ),
inference(clausify,[status(thm)],[f_1232_4]) ).
fof(f_1233_1,plain,
! [V_n_2,V_m_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).
fof(f_1233_2,plain,
! [U_4768,U_4767] :
( ( 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),U_4767),U_4768)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4768))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4767)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4768))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4767)) )
| ~ 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),U_4767),U_4768))) ) ),
inference(variable_rename,[status(thm)],[f_1233_1]) ).
fof(f_1233_3,plain,
( ! [U_4772,U_4770] :
( 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),U_4770),U_4772)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4772))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4770)) )
& ! [U_4771,U_4769] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4771))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4769)) )
| ~ 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),U_4769),U_4771))) ) ),
inference(miniscope,[status(thm)],[f_1233_2]) ).
fof(f_1233_4,plain,
( ! [U_4771,U_4769] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4771))
| ~ sP322(U_4771,U_4769) )
& ! [U_4771,U_4769] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4769))
| ~ sP322(U_4771,U_4769) )
& ! [U_4772,U_4770] :
( 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),U_4770),U_4772)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4772))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4770)) )
& ! [U_4771,U_4769] :
( sP322(U_4771,U_4769)
| ~ 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),U_4769),U_4771))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP322])],[f_1233_3]) ).
cnf(f_1233_5,plain,
( sP322(U_4771,U_4769)
| ~ 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),U_4769),U_4771))) ),
inference(clausify,[status(thm)],[f_1233_4]) ).
cnf(f_1233_6,plain,
( 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),U_4770),U_4772)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4772))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4770)) ),
inference(clausify,[status(thm)],[f_1233_4]) ).
cnf(f_1233_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4769))
| ~ sP322(U_4771,U_4769) ),
inference(clausify,[status(thm)],[f_1233_4]) ).
cnf(f_1233_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4771))
| ~ sP322(U_4771,U_4769) ),
inference(clausify,[status(thm)],[f_1233_4]) ).
fof(f_1234_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).
fof(f_1234_2,plain,
! [U_4775,U_4774,U_4773] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4773),U_4774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4773),U_4775)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4774),U_4775))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4773)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4774),U_4775))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4773)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4773),U_4774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4773),U_4775))) ) ),
inference(variable_rename,[status(thm)],[f_1234_1]) ).
fof(f_1234_3,plain,
( ! [U_4781,U_4779,U_4777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4777),U_4779)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4777),U_4781)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4779),U_4781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4777)) )
& ! [U_4780,U_4778,U_4776] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4778),U_4780))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4776)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4776),U_4778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4776),U_4780))) ) ),
inference(miniscope,[status(thm)],[f_1234_2]) ).
fof(f_1234_4,plain,
( ! [U_4776,U_4780,U_4778] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4778),U_4780))
| ~ sP323(U_4776,U_4780,U_4778) )
& ! [U_4776,U_4780,U_4778] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4776))
| ~ sP323(U_4776,U_4780,U_4778) )
& ! [U_4781,U_4779,U_4777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4777),U_4779)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4777),U_4781)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4779),U_4781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4777)) )
& ! [U_4776,U_4780,U_4778] :
( sP323(U_4776,U_4780,U_4778)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4776),U_4778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4776),U_4780))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP323])],[f_1234_3]) ).
cnf(f_1234_5,plain,
( sP323(U_4776,U_4780,U_4778)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4776),U_4778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4776),U_4780))) ),
inference(clausify,[status(thm)],[f_1234_4]) ).
cnf(f_1234_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4777),U_4779)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4777),U_4781)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4779),U_4781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4777)) ),
inference(clausify,[status(thm)],[f_1234_4]) ).
cnf(f_1234_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4776))
| ~ sP323(U_4776,U_4780,U_4778) ),
inference(clausify,[status(thm)],[f_1234_4]) ).
cnf(f_1234_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4778),U_4780))
| ~ sP323(U_4776,U_4780,U_4778) ),
inference(clausify,[status(thm)],[f_1234_4]) ).
fof(f_1235_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).
fof(f_1235_2,plain,
! [U_4784,U_4783,U_4782] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4782),U_4783)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4784),U_4783)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4782),U_4784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4783)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4782),U_4784))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4783)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4782),U_4783)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4784),U_4783))) ) ),
inference(variable_rename,[status(thm)],[f_1235_1]) ).
fof(f_1235_3,plain,
( ! [U_4790,U_4788,U_4786] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4786),U_4788)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4790),U_4788)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4786),U_4790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4788)) )
& ! [U_4789,U_4787,U_4785] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4785),U_4789))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4787)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4785),U_4787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4789),U_4787))) ) ),
inference(miniscope,[status(thm)],[f_1235_2]) ).
fof(f_1235_4,plain,
( ! [U_4787,U_4785,U_4789] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4785),U_4789))
| ~ sP324(U_4787,U_4785,U_4789) )
& ! [U_4787,U_4785,U_4789] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4787))
| ~ sP324(U_4787,U_4785,U_4789) )
& ! [U_4788,U_4786,U_4790] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4786),U_4788)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4790),U_4788)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4786),U_4790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4788)) )
& ! [U_4787,U_4785,U_4789] :
( sP324(U_4787,U_4785,U_4789)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4785),U_4787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4789),U_4787))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP324])],[f_1235_3]) ).
cnf(f_1235_5,plain,
( sP324(U_4787,U_4785,U_4789)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4785),U_4787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4789),U_4787))) ),
inference(clausify,[status(thm)],[f_1235_4]) ).
cnf(f_1235_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4786),U_4788)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4790),U_4788)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4786),U_4790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4788)) ),
inference(clausify,[status(thm)],[f_1235_4]) ).
cnf(f_1235_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4787))
| ~ sP324(U_4787,U_4785,U_4789) ),
inference(clausify,[status(thm)],[f_1235_4]) ).
cnf(f_1235_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4785),U_4789))
| ~ sP324(U_4787,U_4785,U_4789) ),
inference(clausify,[status(thm)],[f_1235_4]) ).
fof(f_1236_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono1]) ).
fof(f_1236_2,plain,
! [U_4793,U_4792,U_4791] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4791),U_4793)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4792),U_4793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4791),U_4792)) ),
inference(variable_rename,[status(thm)],[f_1236_1]) ).
fof(f_1236_3,plain,
! [U_4793,U_4791,U_4792] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4791),U_4793)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4792),U_4793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4791),U_4792)) ),
inference(definitional_conversion,[status(esa)],[f_1236_2]) ).
cnf(f_1236_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4791),U_4793)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4792),U_4793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4791),U_4792)) ),
inference(clausify,[status(thm)],[f_1236_3]) ).
fof(f_1237_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono2]) ).
fof(f_1237_2,plain,
! [U_4796,U_4795,U_4794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4796),U_4794)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4796),U_4795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4794),U_4795)) ),
inference(variable_rename,[status(thm)],[f_1237_1]) ).
fof(f_1237_3,plain,
! [U_4795,U_4794,U_4796] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4796),U_4794)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4796),U_4795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4794),U_4795)) ),
inference(definitional_conversion,[status(esa)],[f_1237_2]) ).
cnf(f_1237_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4796),U_4794)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4796),U_4795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4794),U_4795)) ),
inference(clausify,[status(thm)],[f_1237_3]) ).
fof(f_1238_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( 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)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| 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) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1]) ).
fof(f_1238_2,plain,
! [U_4799,U_4798,U_4797] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4798) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4799)
| U_4798 != U_4799 )
& ( U_4798 = U_4799
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4798) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4799) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4797)) ),
inference(variable_rename,[status(thm)],[f_1238_1]) ).
fof(f_1238_3,plain,
( ! [U_4797,U_4798,U_4799] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4798) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4799)
| U_4798 != U_4799
| ~ sP325(U_4797,U_4798,U_4799) )
& ! [U_4797,U_4798,U_4799] :
( U_4798 = U_4799
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4798) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4799)
| ~ sP325(U_4797,U_4798,U_4799) )
& ! [U_4797,U_4798,U_4799] :
( sP325(U_4797,U_4798,U_4799)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4797)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP325])],[f_1238_2]) ).
cnf(f_1238_4,plain,
( sP325(U_4797,U_4798,U_4799)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4797)) ),
inference(clausify,[status(thm)],[f_1238_3]) ).
cnf(f_1238_5,plain,
( U_4798 = U_4799
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4798) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4799)
| ~ sP325(U_4797,U_4798,U_4799) ),
inference(clausify,[status(thm)],[f_1238_3]) ).
cnf(f_1238_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4798) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4797),U_4799)
| U_4798 != U_4799
| ~ sP325(U_4797,U_4798,U_4799) ),
inference(clausify,[status(thm)],[f_1238_3]) ).
fof(f_1239_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1]) ).
fof(f_1239_2,plain,
! [U_4802,U_4801,U_4800] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4801),U_4802)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4801),U_4802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4802))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4800)) ),
inference(variable_rename,[status(thm)],[f_1239_1]) ).
fof(f_1239_3,plain,
( ! [U_4801,U_4800,U_4802] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4801),U_4802))
| ~ sP326(U_4801,U_4800,U_4802) )
& ! [U_4801,U_4800,U_4802] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4801),U_4802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4802)))
| ~ sP326(U_4801,U_4800,U_4802) )
& ! [U_4801,U_4800,U_4802] :
( sP326(U_4801,U_4800,U_4802)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4800)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP326])],[f_1239_2]) ).
cnf(f_1239_4,plain,
( sP326(U_4801,U_4800,U_4802)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4800)) ),
inference(clausify,[status(thm)],[f_1239_3]) ).
cnf(f_1239_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4801),U_4802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4802)))
| ~ sP326(U_4801,U_4800,U_4802) ),
inference(clausify,[status(thm)],[f_1239_3]) ).
cnf(f_1239_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4800),U_4802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4801),U_4802))
| ~ sP326(U_4801,U_4800,U_4802) ),
inference(clausify,[status(thm)],[f_1239_3]) ).
fof(f_1240_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_diff__add__0]) ).
fof(f_1240_2,plain,
! [U_4804,U_4803] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4803),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4803),U_4804)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1240_1]) ).
fof(f_1240_3,plain,
! [U_4803,U_4804] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4803),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4803),U_4804)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1240_2]) ).
cnf(f_1240_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4803),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4803),U_4804)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1240_3]) ).
fof(f_1241_1,plain,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H]) ).
fof(f_1241_2,plain,
! [U_4806,U_4805] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4805),U_4806) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4805),U_4806)) ),
inference(variable_rename,[status(thm)],[f_1241_1]) ).
fof(f_1241_3,plain,
! [U_4805,U_4806] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4805),U_4806) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4805),U_4806)) ),
inference(definitional_conversion,[status(esa)],[f_1241_2]) ).
cnf(f_1241_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4805),U_4806) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4805),U_4806)) ),
inference(clausify,[status(thm)],[f_1241_3]) ).
fof(f_1242_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).
fof(f_1242_2,plain,
! [U_4808,U_4807] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4807),U_4808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4807),U_4808)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4807),U_4808))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4807),U_4808) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1242_1]) ).
fof(f_1242_3,plain,
( ! [U_4812,U_4810] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4810),U_4812) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4810),U_4812)) )
& ! [U_4811,U_4809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4809),U_4811))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4809),U_4811) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1242_2]) ).
fof(f_1242_4,plain,
( ! [U_4810,U_4812] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4810),U_4812) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4810),U_4812)) )
& ! [U_4811,U_4809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4809),U_4811))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4809),U_4811) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1242_3]) ).
cnf(f_1242_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4809),U_4811))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4809),U_4811) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1242_4]) ).
cnf(f_1242_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4810),U_4812) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4810),U_4812)) ),
inference(clausify,[status(thm)],[f_1242_4]) ).
fof(f_1243_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).
fof(f_1243_2,plain,
! [U_4814,U_4813] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4813),hAPP(c_Nat_OSuc,U_4814)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4813,U_4814),
inference(variable_rename,[status(thm)],[f_1243_1]) ).
fof(f_1243_3,plain,
! [U_4813,U_4814] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4813),hAPP(c_Nat_OSuc,U_4814)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4813,U_4814),
inference(definitional_conversion,[status(esa)],[f_1243_2]) ).
cnf(f_1243_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4813),hAPP(c_Nat_OSuc,U_4814)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4813,U_4814),
inference(clausify,[status(thm)],[f_1243_3]) ).
fof(f_1244_1,plain,
! [V_n,V_m] :
( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10]) ).
fof(f_1244_2,plain,
! [U_4816,U_4815] :
( U_4815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4816 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_4815 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4815),U_4816) ),
inference(variable_rename,[status(thm)],[f_1244_1]) ).
fof(f_1244_3,plain,
! [U_4815,U_4816] :
( U_4815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4816 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_4815 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4815),U_4816) ),
inference(definitional_conversion,[status(esa)],[f_1244_2]) ).
cnf(f_1244_4,plain,
( U_4815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4816 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_4815 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4815),U_4816) ),
inference(clausify,[status(thm)],[f_1244_3]) ).
fof(f_1245_1,plain,
! [V_f_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_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) ) )
& ( ! [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) )
| 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) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__0__iff]) ).
fof(f_1245_2,plain,
! [U_4821,U_4820,U_4819] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4819,tc_Nat_Onat),U_4821),U_4820) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [U_4818] :
( hAPP(U_4821,U_4818) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4819),U_4818),U_4820)) ) )
& ( ! [U_4817] :
( hAPP(U_4821,U_4817) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4819),U_4817),U_4820)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4819,tc_Nat_Onat),U_4821),U_4820) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4820)) ),
inference(variable_rename,[status(thm)],[f_1245_1]) ).
fof(f_1245_3,plain,
! [U_4821,U_4820,U_4819] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4819,tc_Nat_Onat),U_4821),U_4820) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hAPP(U_4821,sK108(U_4821,U_4820,U_4819)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4819),sK108(U_4821,U_4820,U_4819)),U_4820)) ) )
& ( ! [U_4817] :
( hAPP(U_4821,U_4817) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4819),U_4817),U_4820)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4819,tc_Nat_Onat),U_4821),U_4820) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4820)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_4818,sK108(U_4821,U_4820,U_4819))],[f_1245_2]) ).
fof(f_1245_4,plain,
( ! [U_4819,U_4820,U_4821] :
( hAPP(U_4821,sK108(U_4821,U_4820,U_4819)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP327(U_4819,U_4820,U_4821) )
& ! [U_4819,U_4820,U_4821] :
( hBOOL(hAPP(hAPP(c_member(U_4819),sK108(U_4821,U_4820,U_4819)),U_4820))
| ~ sP327(U_4819,U_4820,U_4821) )
& ! [U_4817,U_4819,U_4820,U_4821] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4819,tc_Nat_Onat),U_4821),U_4820) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP327(U_4819,U_4820,U_4821)
| ~ sP328(U_4817,U_4819,U_4820,U_4821) )
& ! [U_4817,U_4819,U_4820,U_4821] :
( hAPP(U_4821,U_4817) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4819),U_4817),U_4820))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4819,tc_Nat_Onat),U_4821),U_4820) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP328(U_4817,U_4819,U_4820,U_4821) )
& ! [U_4817,U_4819,U_4820,U_4821] :
( sP328(U_4817,U_4819,U_4820,U_4821)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4820)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP327,sP328])],[f_1245_3]) ).
cnf(f_1245_5,plain,
( sP328(U_4817,U_4819,U_4820,U_4821)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4820)) ),
inference(clausify,[status(thm)],[f_1245_4]) ).
cnf(f_1245_6,plain,
( hAPP(U_4821,U_4817) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4819),U_4817),U_4820))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4819,tc_Nat_Onat),U_4821),U_4820) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP328(U_4817,U_4819,U_4820,U_4821) ),
inference(clausify,[status(thm)],[f_1245_4]) ).
cnf(f_1245_7,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4819,tc_Nat_Onat),U_4821),U_4820) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP327(U_4819,U_4820,U_4821)
| ~ sP328(U_4817,U_4819,U_4820,U_4821) ),
inference(clausify,[status(thm)],[f_1245_4]) ).
cnf(f_1245_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4819),sK108(U_4821,U_4820,U_4819)),U_4820))
| ~ sP327(U_4819,U_4820,U_4821) ),
inference(clausify,[status(thm)],[f_1245_4]) ).
cnf(f_1245_9,plain,
( hAPP(U_4821,sK108(U_4821,U_4820,U_4819)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP327(U_4819,U_4820,U_4821) ),
inference(clausify,[status(thm)],[f_1245_4]) ).
fof(f_1246_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_lessThan__Suc__atMost]) ).
fof(f_1246_2,plain,
! [U_4822] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4822)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4822),
inference(variable_rename,[status(thm)],[f_1246_1]) ).
fof(f_1246_3,plain,
! [U_4822] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4822)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4822),
inference(definitional_conversion,[status(esa)],[f_1246_2]) ).
cnf(f_1246_4,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4822)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4822),
inference(clausify,[status(thm)],[f_1246_3]) ).
fof(f_1247_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeast0LessThan]) ).
fof(f_1247_2,plain,
! [U_4823] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4823) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4823),
inference(variable_rename,[status(thm)],[f_1247_1]) ).
fof(f_1247_3,plain,
! [U_4823] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4823) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4823),
inference(definitional_conversion,[status(esa)],[f_1247_2]) ).
cnf(f_1247_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4823) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4823),
inference(clausify,[status(thm)],[f_1247_3]) ).
fof(f_1248_1,plain,
! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g]) ).
fof(f_1248_2,plain,
! [U_4830,U_4829,U_4828,U_4827,U_4826,U_4825,U_4824] :
( hAPP(U_4829,U_4830) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4824,U_4825,U_4826),U_4828),U_4827),U_4830)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4825),U_4830))
| ~ c_Finite__Set_Ofolding__image__simple(U_4824,U_4825,U_4826,U_4827,U_4828,U_4829) ),
inference(variable_rename,[status(thm)],[f_1248_1]) ).
fof(f_1248_3,plain,
! [U_4826,U_4827,U_4825,U_4824,U_4828,U_4829,U_4830] :
( hAPP(U_4829,U_4830) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4824,U_4825,U_4826),U_4828),U_4827),U_4830)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4825),U_4830))
| ~ c_Finite__Set_Ofolding__image__simple(U_4824,U_4825,U_4826,U_4827,U_4828,U_4829) ),
inference(definitional_conversion,[status(esa)],[f_1248_2]) ).
cnf(f_1248_4,plain,
( hAPP(U_4829,U_4830) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4824,U_4825,U_4826),U_4828),U_4827),U_4830)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4825),U_4830))
| ~ c_Finite__Set_Ofolding__image__simple(U_4824,U_4825,U_4826,U_4827,U_4828,U_4829) ),
inference(clausify,[status(thm)],[f_1248_3]) ).
fof(f_1249_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_card__greaterThanLessThan]) ).
fof(f_1249_2,plain,
! [U_4832,U_4831] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4831,U_4832)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4832),hAPP(c_Nat_OSuc,U_4831)),
inference(variable_rename,[status(thm)],[f_1249_1]) ).
fof(f_1249_3,plain,
! [U_4832,U_4831] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4831,U_4832)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4832),hAPP(c_Nat_OSuc,U_4831)),
inference(definitional_conversion,[status(esa)],[f_1249_2]) ).
cnf(f_1249_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4831,U_4832)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4832),hAPP(c_Nat_OSuc,U_4831)),
inference(clausify,[status(thm)],[f_1249_3]) ).
fof(f_1250_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeast0AtMost]) ).
fof(f_1250_2,plain,
! [U_4833] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_4833) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4833),
inference(variable_rename,[status(thm)],[f_1250_1]) ).
fof(f_1250_3,plain,
! [U_4833] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_4833) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4833),
inference(definitional_conversion,[status(esa)],[f_1250_2]) ).
cnf(f_1250_4,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_4833) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4833),
inference(clausify,[status(thm)],[f_1250_3]) ).
fof(f_1251_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).
fof(f_1251_2,plain,
! [U_4835,U_4834] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4834),U_4835) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4834,U_4835),
inference(variable_rename,[status(thm)],[f_1251_1]) ).
fof(f_1251_3,plain,
! [U_4835,U_4834] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4834),U_4835) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4834,U_4835),
inference(definitional_conversion,[status(esa)],[f_1251_2]) ).
cnf(f_1251_4,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4834),U_4835) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4834,U_4835),
inference(clausify,[status(thm)],[f_1251_3]) ).
fof(f_1252_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).
fof(f_1252_2,plain,
! [U_4837,U_4836] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4836)),U_4837) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4836,U_4837),
inference(variable_rename,[status(thm)],[f_1252_1]) ).
fof(f_1252_3,plain,
! [U_4836,U_4837] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4836)),U_4837) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4836,U_4837),
inference(definitional_conversion,[status(esa)],[f_1252_2]) ).
cnf(f_1252_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4836)),U_4837) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4836,U_4837),
inference(clausify,[status(thm)],[f_1252_3]) ).
fof(f_1253_1,plain,
! [V_m,V_j,V_k] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2]) ).
fof(f_1253_2,plain,
! [U_4840,U_4839,U_4838] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4839),U_4838))),U_4840) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4838),U_4840))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4838),U_4839)) ),
inference(variable_rename,[status(thm)],[f_1253_1]) ).
fof(f_1253_3,plain,
! [U_4838,U_4839,U_4840] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4839),U_4838))),U_4840) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4838),U_4840))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4838),U_4839)) ),
inference(definitional_conversion,[status(esa)],[f_1253_2]) ).
cnf(f_1253_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4839),U_4838))),U_4840) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4838),U_4840))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4838),U_4839)) ),
inference(clausify,[status(thm)],[f_1253_3]) ).
fof(f_1254_1,plain,
! [V_m,V_j,V_k] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1]) ).
fof(f_1254_2,plain,
! [U_4843,U_4842,U_4841] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4843),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4842),U_4841))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4843),U_4841)),hAPP(c_Nat_OSuc,U_4842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4841),U_4842)) ),
inference(variable_rename,[status(thm)],[f_1254_1]) ).
fof(f_1254_3,plain,
! [U_4841,U_4842,U_4843] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4843),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4842),U_4841))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4843),U_4841)),hAPP(c_Nat_OSuc,U_4842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4841),U_4842)) ),
inference(definitional_conversion,[status(esa)],[f_1254_2]) ).
cnf(f_1254_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4843),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4842),U_4841))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4843),U_4841)),hAPP(c_Nat_OSuc,U_4842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4841),U_4842)) ),
inference(clausify,[status(thm)],[f_1254_3]) ).
fof(f_1255_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg]) ).
fof(f_1255_2,plain,
! [U_4846,U_4845,U_4844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4844),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4844),U_4845),U_4846)),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4844),U_4846),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4844),U_4845),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4844) ),
inference(variable_rename,[status(thm)],[f_1255_1]) ).
fof(f_1255_3,plain,
! [U_4844,U_4845,U_4846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4844),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4844),U_4845),U_4846)),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4844),U_4846),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4844),U_4845),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4844) ),
inference(definitional_conversion,[status(esa)],[f_1255_2]) ).
cnf(f_1255_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4844),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4844),U_4845),U_4846)),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4844),U_4846),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4844),U_4845),c_Groups_Ozero__class_Ozero(U_4844)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4844) ),
inference(clausify,[status(thm)],[f_1255_3]) ).
fof(f_1256_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos]) ).
fof(f_1256_2,plain,
! [U_4849,U_4848,U_4847] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4847),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4847),U_4848),U_4849)),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4847),U_4849),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4847),U_4848),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4847) ),
inference(variable_rename,[status(thm)],[f_1256_1]) ).
fof(f_1256_3,plain,
! [U_4847,U_4848,U_4849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4847),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4847),U_4848),U_4849)),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4847),U_4849),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4847),U_4848),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4847) ),
inference(definitional_conversion,[status(esa)],[f_1256_2]) ).
cnf(f_1256_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4847),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4847),U_4848),U_4849)),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4847),U_4849),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4847),U_4848),c_Groups_Ozero__class_Ozero(U_4847)))
| ~ class_Groups_Oordered__comm__monoid__add(U_4847) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
fof(f_1257_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2]) ).
fof(f_1257_2,plain,
! [U_4853,U_4852,U_4851,U_4850] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4850),U_4852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4850),U_4851),U_4853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4850),U_4852),U_4853))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4850),c_Groups_Ozero__class_Ozero(U_4850)),U_4851))
| ~ class_Groups_Oordered__comm__monoid__add(U_4850) ),
inference(variable_rename,[status(thm)],[f_1257_1]) ).
fof(f_1257_3,plain,
! [U_4850,U_4851,U_4852,U_4853] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4850),U_4852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4850),U_4851),U_4853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4850),U_4852),U_4853))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4850),c_Groups_Ozero__class_Ozero(U_4850)),U_4851))
| ~ class_Groups_Oordered__comm__monoid__add(U_4850) ),
inference(definitional_conversion,[status(esa)],[f_1257_2]) ).
cnf(f_1257_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4850),U_4852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4850),U_4851),U_4853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4850),U_4852),U_4853))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4850),c_Groups_Ozero__class_Ozero(U_4850)),U_4851))
| ~ class_Groups_Oordered__comm__monoid__add(U_4850) ),
inference(clausify,[status(thm)],[f_1257_3]) ).
fof(f_1258_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__increasing]) ).
fof(f_1258_2,plain,
! [U_4857,U_4856,U_4855,U_4854] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4854),U_4856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4854),U_4855),U_4857)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4856),U_4857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4854),c_Groups_Ozero__class_Ozero(U_4854)),U_4855))
| ~ class_Groups_Oordered__comm__monoid__add(U_4854) ),
inference(variable_rename,[status(thm)],[f_1258_1]) ).
fof(f_1258_3,plain,
! [U_4854,U_4855,U_4856,U_4857] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4854),U_4856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4854),U_4855),U_4857)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4856),U_4857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4854),c_Groups_Ozero__class_Ozero(U_4854)),U_4855))
| ~ class_Groups_Oordered__comm__monoid__add(U_4854) ),
inference(definitional_conversion,[status(esa)],[f_1258_2]) ).
cnf(f_1258_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4854),U_4856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4854),U_4855),U_4857)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4856),U_4857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4854),c_Groups_Ozero__class_Ozero(U_4854)),U_4855))
| ~ class_Groups_Oordered__comm__monoid__add(U_4854) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
fof(f_1259_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos]) ).
fof(f_1259_2,plain,
! [U_4860,U_4859,U_4858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4858),U_4859),U_4860)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),U_4860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),U_4859))
| ~ class_Groups_Oordered__comm__monoid__add(U_4858) ),
inference(variable_rename,[status(thm)],[f_1259_1]) ).
fof(f_1259_3,plain,
! [U_4859,U_4858,U_4860] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4858),U_4859),U_4860)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),U_4860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),U_4859))
| ~ class_Groups_Oordered__comm__monoid__add(U_4858) ),
inference(definitional_conversion,[status(esa)],[f_1259_2]) ).
cnf(f_1259_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4858),U_4859),U_4860)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),U_4860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4858),c_Groups_Ozero__class_Ozero(U_4858)),U_4859))
| ~ class_Groups_Oordered__comm__monoid__add(U_4858) ),
inference(clausify,[status(thm)],[f_1259_3]) ).
fof(f_1260_1,plain,
! [V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg]) ).
fof(f_1260_2,plain,
! [U_4863,U_4862,U_4861] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4861),U_4862),U_4863)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),U_4863))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),U_4862))
| ~ class_Groups_Oordered__comm__monoid__add(U_4861) ),
inference(variable_rename,[status(thm)],[f_1260_1]) ).
fof(f_1260_3,plain,
! [U_4861,U_4862,U_4863] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4861),U_4862),U_4863)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),U_4863))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),U_4862))
| ~ class_Groups_Oordered__comm__monoid__add(U_4861) ),
inference(definitional_conversion,[status(esa)],[f_1260_2]) ).
cnf(f_1260_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4861),U_4862),U_4863)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),U_4863))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4861),c_Groups_Ozero__class_Ozero(U_4861)),U_4862))
| ~ class_Groups_Oordered__comm__monoid__add(U_4861) ),
inference(clausify,[status(thm)],[f_1260_3]) ).
fof(f_1261_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ 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)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le]) ).
fof(f_1261_2,plain,
! [U_4867,U_4866,U_4865,U_4864] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4864),U_4866),U_4867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4864),c_Groups_Ozero__class_Ozero(U_4864)),U_4865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4864),U_4865),U_4866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4864),U_4865),U_4867)))
| ~ class_Rings_Olinordered__semiring__strict(U_4864) ),
inference(variable_rename,[status(thm)],[f_1261_1]) ).
fof(f_1261_3,plain,
! [U_4864,U_4865,U_4866,U_4867] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4864),U_4866),U_4867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4864),c_Groups_Ozero__class_Ozero(U_4864)),U_4865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4864),U_4865),U_4866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4864),U_4865),U_4867)))
| ~ class_Rings_Olinordered__semiring__strict(U_4864) ),
inference(definitional_conversion,[status(esa)],[f_1261_2]) ).
cnf(f_1261_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4864),U_4866),U_4867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4864),c_Groups_Ozero__class_Ozero(U_4864)),U_4865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4864),U_4865),U_4866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4864),U_4865),U_4867)))
| ~ class_Rings_Olinordered__semiring__strict(U_4864) ),
inference(clausify,[status(thm)],[f_1261_3]) ).
fof(f_1262_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ 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)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le]) ).
fof(f_1262_2,plain,
! [U_4871,U_4870,U_4869,U_4868] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),U_4869),U_4871))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4868),c_Groups_Ozero__class_Ozero(U_4868)),U_4870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4868),U_4869),U_4870)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4868),U_4871),U_4870)))
| ~ class_Rings_Olinordered__semiring__strict(U_4868) ),
inference(variable_rename,[status(thm)],[f_1262_1]) ).
fof(f_1262_3,plain,
! [U_4868,U_4869,U_4870,U_4871] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),U_4869),U_4871))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4868),c_Groups_Ozero__class_Ozero(U_4868)),U_4870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4868),U_4869),U_4870)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4868),U_4871),U_4870)))
| ~ class_Rings_Olinordered__semiring__strict(U_4868) ),
inference(definitional_conversion,[status(esa)],[f_1262_2]) ).
cnf(f_1262_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),U_4869),U_4871))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4868),c_Groups_Ozero__class_Ozero(U_4868)),U_4870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4868),U_4869),U_4870)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4868),U_4871),U_4870)))
| ~ class_Rings_Olinordered__semiring__strict(U_4868) ),
inference(clausify,[status(thm)],[f_1262_3]) ).
fof(f_1263_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ 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)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left]) ).
fof(f_1263_2,plain,
! [U_4875,U_4874,U_4873,U_4872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4872),U_4874),U_4875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4872),U_4873),U_4874)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4872),U_4873),U_4875)))
| ~ class_Rings_Olinordered__semiring__strict(U_4872) ),
inference(variable_rename,[status(thm)],[f_1263_1]) ).
fof(f_1263_3,plain,
! [U_4872,U_4873,U_4874,U_4875] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4872),U_4874),U_4875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4872),U_4873),U_4874)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4872),U_4873),U_4875)))
| ~ class_Rings_Olinordered__semiring__strict(U_4872) ),
inference(definitional_conversion,[status(esa)],[f_1263_2]) ).
cnf(f_1263_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4872),U_4874),U_4875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4872),U_4873),U_4874)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4872),U_4873),U_4875)))
| ~ class_Rings_Olinordered__semiring__strict(U_4872) ),
inference(clausify,[status(thm)],[f_1263_3]) ).
fof(f_1264_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ 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)))
| ~ class_Rings_Olinordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less]) ).
fof(f_1264_2,plain,
! [U_4879,U_4878,U_4877,U_4876] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4876),U_4878),U_4879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4876),c_Groups_Ozero__class_Ozero(U_4876)),U_4877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4876),U_4877),U_4878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4876),U_4877),U_4879)))
| ~ class_Rings_Olinordered__semiring(U_4876) ),
inference(variable_rename,[status(thm)],[f_1264_1]) ).
fof(f_1264_3,plain,
! [U_4876,U_4877,U_4878,U_4879] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4876),U_4878),U_4879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4876),c_Groups_Ozero__class_Ozero(U_4876)),U_4877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4876),U_4877),U_4878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4876),U_4877),U_4879)))
| ~ class_Rings_Olinordered__semiring(U_4876) ),
inference(definitional_conversion,[status(esa)],[f_1264_2]) ).
cnf(f_1264_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4876),U_4878),U_4879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4876),c_Groups_Ozero__class_Ozero(U_4876)),U_4877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4876),U_4877),U_4878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4876),U_4877),U_4879)))
| ~ class_Rings_Olinordered__semiring(U_4876) ),
inference(clausify,[status(thm)],[f_1264_3]) ).
fof(f_1265_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ 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)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right]) ).
fof(f_1265_2,plain,
! [U_4883,U_4882,U_4881,U_4880] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),U_4881),U_4883))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),U_4882))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4880),U_4881),U_4882)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4880),U_4883),U_4882)))
| ~ class_Rings_Olinordered__semiring__strict(U_4880) ),
inference(variable_rename,[status(thm)],[f_1265_1]) ).
fof(f_1265_3,plain,
! [U_4880,U_4881,U_4882,U_4883] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),U_4881),U_4883))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),U_4882))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4880),U_4881),U_4882)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4880),U_4883),U_4882)))
| ~ class_Rings_Olinordered__semiring__strict(U_4880) ),
inference(definitional_conversion,[status(esa)],[f_1265_2]) ).
cnf(f_1265_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),U_4881),U_4883))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),U_4882))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4880),U_4881),U_4882)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4880),U_4883),U_4882)))
| ~ class_Rings_Olinordered__semiring__strict(U_4880) ),
inference(clausify,[status(thm)],[f_1265_3]) ).
fof(f_1266_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ 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)))
| ~ class_Rings_Olinordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less]) ).
fof(f_1266_2,plain,
! [U_4887,U_4886,U_4885,U_4884] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4884),U_4885),U_4887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4884),c_Groups_Ozero__class_Ozero(U_4884)),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4884),U_4885),U_4886)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4884),U_4887),U_4886)))
| ~ class_Rings_Olinordered__semiring(U_4884) ),
inference(variable_rename,[status(thm)],[f_1266_1]) ).
fof(f_1266_3,plain,
! [U_4884,U_4885,U_4886,U_4887] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4884),U_4885),U_4887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4884),c_Groups_Ozero__class_Ozero(U_4884)),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4884),U_4885),U_4886)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4884),U_4887),U_4886)))
| ~ class_Rings_Olinordered__semiring(U_4884) ),
inference(definitional_conversion,[status(esa)],[f_1266_2]) ).
cnf(f_1266_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4884),U_4885),U_4887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4884),c_Groups_Ozero__class_Ozero(U_4884)),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4884),U_4885),U_4886)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4884),U_4887),U_4886)))
| ~ class_Rings_Olinordered__semiring(U_4884) ),
inference(clausify,[status(thm)],[f_1266_3]) ).
fof(f_1267_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less]) ).
fof(f_1267_2,plain,
! [U_4892,U_4891,U_4890,U_4889,U_4888] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4888),U_4889),U_4891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4888),U_4890),U_4892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4888),c_Groups_Ozero__class_Ozero(U_4888)),U_4891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),c_Groups_Ozero__class_Ozero(U_4888)),U_4889))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),U_4891),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4888),U_4889),U_4890))
| ~ class_Rings_Olinordered__semiring__strict(U_4888) ),
inference(variable_rename,[status(thm)],[f_1267_1]) ).
fof(f_1267_3,plain,
! [U_4888,U_4889,U_4890,U_4891,U_4892] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4888),U_4889),U_4891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4888),U_4890),U_4892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4888),c_Groups_Ozero__class_Ozero(U_4888)),U_4891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),c_Groups_Ozero__class_Ozero(U_4888)),U_4889))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),U_4891),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4888),U_4889),U_4890))
| ~ class_Rings_Olinordered__semiring__strict(U_4888) ),
inference(definitional_conversion,[status(esa)],[f_1267_2]) ).
cnf(f_1267_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4888),U_4889),U_4891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4888),U_4890),U_4892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4888),c_Groups_Ozero__class_Ozero(U_4888)),U_4891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),c_Groups_Ozero__class_Ozero(U_4888)),U_4889))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4888),U_4891),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4888),U_4889),U_4890))
| ~ class_Rings_Olinordered__semiring__strict(U_4888) ),
inference(clausify,[status(thm)],[f_1267_3]) ).
fof(f_1268_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less]) ).
fof(f_1268_2,plain,
! [U_4897,U_4896,U_4895,U_4894,U_4893] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4893),U_4894),U_4896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4893),U_4895),U_4897)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),c_Groups_Ozero__class_Ozero(U_4893)),U_4896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4893),c_Groups_Ozero__class_Ozero(U_4893)),U_4894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4893),U_4896),U_4897))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),U_4894),U_4895))
| ~ class_Rings_Olinordered__semiring__strict(U_4893) ),
inference(variable_rename,[status(thm)],[f_1268_1]) ).
fof(f_1268_3,plain,
! [U_4894,U_4895,U_4893,U_4896,U_4897] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4893),U_4894),U_4896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4893),U_4895),U_4897)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),c_Groups_Ozero__class_Ozero(U_4893)),U_4896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4893),c_Groups_Ozero__class_Ozero(U_4893)),U_4894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4893),U_4896),U_4897))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),U_4894),U_4895))
| ~ class_Rings_Olinordered__semiring__strict(U_4893) ),
inference(definitional_conversion,[status(esa)],[f_1268_2]) ).
cnf(f_1268_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4893),U_4894),U_4896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4893),U_4895),U_4897)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),c_Groups_Ozero__class_Ozero(U_4893)),U_4896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4893),c_Groups_Ozero__class_Ozero(U_4893)),U_4894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4893),U_4896),U_4897))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4893),U_4894),U_4895))
| ~ class_Rings_Olinordered__semiring__strict(U_4893) ),
inference(clausify,[status(thm)],[f_1268_3]) ).
fof(f_1269_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H]) ).
fof(f_1269_2,plain,
! [U_4902,U_4901,U_4900,U_4899,U_4898] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4898),U_4899),U_4901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4898),U_4900),U_4902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4901),U_4902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4899),U_4900))
| ~ class_Rings_Olinordered__semiring__strict(U_4898) ),
inference(variable_rename,[status(thm)],[f_1269_1]) ).
fof(f_1269_3,plain,
! [U_4899,U_4901,U_4900,U_4898,U_4902] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4898),U_4899),U_4901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4898),U_4900),U_4902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4901),U_4902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4899),U_4900))
| ~ class_Rings_Olinordered__semiring__strict(U_4898) ),
inference(definitional_conversion,[status(esa)],[f_1269_2]) ).
cnf(f_1269_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4898),U_4899),U_4901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4898),U_4900),U_4902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4901),U_4902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4899),U_4900))
| ~ class_Rings_Olinordered__semiring__strict(U_4898) ),
inference(clausify,[status(thm)],[f_1269_3]) ).
fof(f_1270_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__mono]) ).
fof(f_1270_2,plain,
! [U_4907,U_4906,U_4905,U_4904,U_4903] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4903),U_4904),U_4906)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4903),U_4905),U_4907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4903),c_Groups_Ozero__class_Ozero(U_4903)),U_4906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),c_Groups_Ozero__class_Ozero(U_4903)),U_4905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),U_4906),U_4907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),U_4904),U_4905))
| ~ class_Rings_Olinordered__semiring__strict(U_4903) ),
inference(variable_rename,[status(thm)],[f_1270_1]) ).
fof(f_1270_3,plain,
! [U_4904,U_4903,U_4905,U_4906,U_4907] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4903),U_4904),U_4906)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4903),U_4905),U_4907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4903),c_Groups_Ozero__class_Ozero(U_4903)),U_4906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),c_Groups_Ozero__class_Ozero(U_4903)),U_4905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),U_4906),U_4907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),U_4904),U_4905))
| ~ class_Rings_Olinordered__semiring__strict(U_4903) ),
inference(definitional_conversion,[status(esa)],[f_1270_2]) ).
cnf(f_1270_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4903),U_4904),U_4906)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4903),U_4905),U_4907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4903),c_Groups_Ozero__class_Ozero(U_4903)),U_4906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),c_Groups_Ozero__class_Ozero(U_4903)),U_4905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),U_4906),U_4907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4903),U_4904),U_4905))
| ~ class_Rings_Olinordered__semiring__strict(U_4903) ),
inference(clausify,[status(thm)],[f_1270_3]) ).
fof(f_1271_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).
fof(f_1271_2,plain,
! [U_4911,U_4910,U_4909,U_4908] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),U_4911),U_4910)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),U_4911),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4911))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4908),U_4909),c_Groups_Ozero__class_Ozero(U_4908)))
| ~ class_Rings_Olinordered__ring__strict(U_4908) ),
inference(variable_rename,[status(thm)],[f_1271_1]) ).
fof(f_1271_3,plain,
( ! [U_4909,U_4910,U_4908,U_4911] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),U_4911),U_4910))
| ~ sP329(U_4909,U_4910,U_4908,U_4911) )
& ! [U_4909,U_4910,U_4908,U_4911] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),U_4911),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4911)))
| ~ sP329(U_4909,U_4910,U_4908,U_4911) )
& ! [U_4909,U_4910,U_4908,U_4911] :
( sP329(U_4909,U_4910,U_4908,U_4911)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4908),U_4909),c_Groups_Ozero__class_Ozero(U_4908)))
| ~ class_Rings_Olinordered__ring__strict(U_4908) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP329])],[f_1271_2]) ).
cnf(f_1271_4,plain,
( sP329(U_4909,U_4910,U_4908,U_4911)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4908),U_4909),c_Groups_Ozero__class_Ozero(U_4908)))
| ~ class_Rings_Olinordered__ring__strict(U_4908) ),
inference(clausify,[status(thm)],[f_1271_3]) ).
cnf(f_1271_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),U_4911),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4911)))
| ~ sP329(U_4909,U_4910,U_4908,U_4911) ),
inference(clausify,[status(thm)],[f_1271_3]) ).
cnf(f_1271_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4908),U_4909),U_4911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4908),U_4911),U_4910))
| ~ sP329(U_4909,U_4910,U_4908,U_4911) ),
inference(clausify,[status(thm)],[f_1271_3]) ).
fof(f_1272_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).
fof(f_1272_2,plain,
! [U_4915,U_4914,U_4913,U_4912] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),U_4914),U_4915)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),U_4914),U_4915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4915))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4912),c_Groups_Ozero__class_Ozero(U_4912)),U_4913))
| ~ class_Rings_Olinordered__ring__strict(U_4912) ),
inference(variable_rename,[status(thm)],[f_1272_1]) ).
fof(f_1272_3,plain,
( ! [U_4912,U_4914,U_4913,U_4915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),U_4914),U_4915))
| ~ sP330(U_4912,U_4914,U_4913,U_4915) )
& ! [U_4912,U_4914,U_4913,U_4915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),U_4914),U_4915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4915)))
| ~ sP330(U_4912,U_4914,U_4913,U_4915) )
& ! [U_4912,U_4914,U_4913,U_4915] :
( sP330(U_4912,U_4914,U_4913,U_4915)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4912),c_Groups_Ozero__class_Ozero(U_4912)),U_4913))
| ~ class_Rings_Olinordered__ring__strict(U_4912) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP330])],[f_1272_2]) ).
cnf(f_1272_4,plain,
( sP330(U_4912,U_4914,U_4913,U_4915)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4912),c_Groups_Ozero__class_Ozero(U_4912)),U_4913))
| ~ class_Rings_Olinordered__ring__strict(U_4912) ),
inference(clausify,[status(thm)],[f_1272_3]) ).
cnf(f_1272_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),U_4914),U_4915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4915)))
| ~ sP330(U_4912,U_4914,U_4913,U_4915) ),
inference(clausify,[status(thm)],[f_1272_3]) ).
cnf(f_1272_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4912),U_4913),U_4915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4912),U_4914),U_4915))
| ~ sP330(U_4912,U_4914,U_4913,U_4915) ),
inference(clausify,[status(thm)],[f_1272_3]) ).
fof(f_1273_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le]) ).
fof(f_1273_2,plain,
! [U_4918,U_4917,U_4916] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4916),U_4918),U_4917)),U_4917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),U_4918),c_Groups_Oone__class_Oone(U_4916)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),U_4918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),U_4917))
| ~ class_Rings_Olinordered__idom(U_4916) ),
inference(variable_rename,[status(thm)],[f_1273_1]) ).
fof(f_1273_3,plain,
! [U_4916,U_4917,U_4918] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4916),U_4918),U_4917)),U_4917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),U_4918),c_Groups_Oone__class_Oone(U_4916)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),U_4918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),U_4917))
| ~ class_Rings_Olinordered__idom(U_4916) ),
inference(definitional_conversion,[status(esa)],[f_1273_2]) ).
cnf(f_1273_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4916),U_4918),U_4917)),U_4917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),U_4918),c_Groups_Oone__class_Oone(U_4916)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),U_4918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),U_4917))
| ~ class_Rings_Olinordered__idom(U_4916) ),
inference(clausify,[status(thm)],[f_1273_3]) ).
fof(f_1274_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le]) ).
fof(f_1274_2,plain,
! [U_4921,U_4920,U_4919] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),U_4920),U_4921)),U_4920))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),U_4921),c_Groups_Oone__class_Oone(U_4919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),U_4921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),U_4920))
| ~ class_Rings_Olinordered__idom(U_4919) ),
inference(variable_rename,[status(thm)],[f_1274_1]) ).
fof(f_1274_3,plain,
! [U_4919,U_4920,U_4921] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),U_4920),U_4921)),U_4920))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),U_4921),c_Groups_Oone__class_Oone(U_4919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),U_4921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),U_4920))
| ~ class_Rings_Olinordered__idom(U_4919) ),
inference(definitional_conversion,[status(esa)],[f_1274_2]) ).
cnf(f_1274_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),U_4920),U_4921)),U_4920))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),U_4921),c_Groups_Oone__class_Oone(U_4919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),U_4921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),U_4920))
| ~ class_Rings_Olinordered__idom(U_4919) ),
inference(clausify,[status(thm)],[f_1274_3]) ).
fof(f_1275_1,plain,
! [T_a] :
( 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))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__two]) ).
fof(f_1275_2,plain,
! [U_4922] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4922),c_Groups_Ozero__class_Ozero(U_4922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4922),c_Groups_Oone__class_Oone(U_4922)),c_Groups_Oone__class_Oone(U_4922))))
| ~ class_Rings_Olinordered__semidom(U_4922) ),
inference(variable_rename,[status(thm)],[f_1275_1]) ).
fof(f_1275_3,plain,
! [U_4922] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4922),c_Groups_Ozero__class_Ozero(U_4922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4922),c_Groups_Oone__class_Oone(U_4922)),c_Groups_Oone__class_Oone(U_4922))))
| ~ class_Rings_Olinordered__semidom(U_4922) ),
inference(definitional_conversion,[status(esa)],[f_1275_2]) ).
cnf(f_1275_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4922),c_Groups_Ozero__class_Ozero(U_4922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4922),c_Groups_Oone__class_Oone(U_4922)),c_Groups_Oone__class_Oone(U_4922))))
| ~ class_Rings_Olinordered__semidom(U_4922) ),
inference(clausify,[status(thm)],[f_1275_3]) ).
fof(f_1276_1,plain,
! [V_A_2,T_b] :
( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_card__eq__0__iff]) ).
fof(f_1276_2,plain,
! [U_4924,U_4923] :
( ( hAPP(c_Finite__Set_Ocard(U_4923),U_4924) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4923),U_4924))
& U_4924 != c_Orderings_Obot__class_Obot(tc_fun(U_4923,tc_HOL_Obool)) ) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4923),U_4924))
| U_4924 = c_Orderings_Obot__class_Obot(tc_fun(U_4923,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4923),U_4924) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1276_1]) ).
fof(f_1276_3,plain,
( ! [U_4928,U_4926] :
( hAPP(c_Finite__Set_Ocard(U_4926),U_4928) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4926),U_4928))
& U_4928 != c_Orderings_Obot__class_Obot(tc_fun(U_4926,tc_HOL_Obool)) ) )
& ! [U_4927,U_4925] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4925),U_4927))
| U_4927 = c_Orderings_Obot__class_Obot(tc_fun(U_4925,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4925),U_4927) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1276_2]) ).
fof(f_1276_4,plain,
( ! [U_4926,U_4928] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4926),U_4928))
| ~ sP331(U_4926,U_4928) )
& ! [U_4926,U_4928] :
( U_4928 != c_Orderings_Obot__class_Obot(tc_fun(U_4926,tc_HOL_Obool))
| ~ sP331(U_4926,U_4928) )
& ! [U_4926,U_4928] :
( hAPP(c_Finite__Set_Ocard(U_4926),U_4928) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP331(U_4926,U_4928) )
& ! [U_4927,U_4925] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4925),U_4927))
| U_4927 = c_Orderings_Obot__class_Obot(tc_fun(U_4925,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4925),U_4927) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP331])],[f_1276_3]) ).
cnf(f_1276_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4925),U_4927))
| U_4927 = c_Orderings_Obot__class_Obot(tc_fun(U_4925,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4925),U_4927) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1276_4]) ).
cnf(f_1276_6,plain,
( hAPP(c_Finite__Set_Ocard(U_4926),U_4928) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP331(U_4926,U_4928) ),
inference(clausify,[status(thm)],[f_1276_4]) ).
cnf(f_1276_7,plain,
( U_4928 != c_Orderings_Obot__class_Obot(tc_fun(U_4926,tc_HOL_Obool))
| ~ sP331(U_4926,U_4928) ),
inference(clausify,[status(thm)],[f_1276_4]) ).
cnf(f_1276_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4926),U_4928))
| ~ sP331(U_4926,U_4928) ),
inference(clausify,[status(thm)],[f_1276_4]) ).
fof(f_1277_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite]) ).
fof(f_1277_2,plain,
! [U_4930,U_4929] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4929),U_4930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4929),U_4930))) ),
inference(variable_rename,[status(thm)],[f_1277_1]) ).
fof(f_1277_3,plain,
! [U_4930,U_4929] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4929),U_4930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4929),U_4930))) ),
inference(definitional_conversion,[status(esa)],[f_1277_2]) ).
cnf(f_1277_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4929),U_4930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4929),U_4930))) ),
inference(clausify,[status(thm)],[f_1277_3]) ).
fof(f_1278_1,plain,
! [V_b_2,V_a_2,V_Pa_2] :
( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_Pa_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_Pa_2,B_d))
| V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
& ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
| ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).
fof(f_1278_2,plain,
! [U_4935,U_4934,U_4933] :
( ( hBOOL(hAPP(U_4933,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4934),U_4935)))
| ? [U_4932] :
( ~ hBOOL(hAPP(U_4933,U_4932))
& U_4934 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4935),U_4932) )
| ( ~ hBOOL(hAPP(U_4933,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4934),U_4935)) ) )
& ( ( ! [U_4931] :
( hBOOL(hAPP(U_4933,U_4931))
| U_4934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4935),U_4931) )
& ( hBOOL(hAPP(U_4933,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4934),U_4935)) ) )
| ~ hBOOL(hAPP(U_4933,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4934),U_4935))) ) ),
inference(variable_rename,[status(thm)],[f_1278_1]) ).
fof(f_1278_3,plain,
( ! [U_4941,U_4939,U_4937] :
( hBOOL(hAPP(U_4937,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4939),U_4941)))
| ? [U_4932] :
( ~ hBOOL(hAPP(U_4937,U_4932))
& U_4939 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4941),U_4932) )
| ( ~ hBOOL(hAPP(U_4937,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4939),U_4941)) ) )
& ! [U_4940,U_4938,U_4936] :
( ( ! [U_4931] :
( hBOOL(hAPP(U_4936,U_4931))
| U_4938 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4940),U_4931) )
& ( hBOOL(hAPP(U_4936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4938),U_4940)) ) )
| ~ hBOOL(hAPP(U_4936,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4938),U_4940))) ) ),
inference(miniscope,[status(thm)],[f_1278_2]) ).
fof(f_1278_4,plain,
( ! [U_4941,U_4939,U_4937] :
( hBOOL(hAPP(U_4937,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4939),U_4941)))
| ( ~ hBOOL(hAPP(U_4937,sK109(U_4941,U_4939,U_4937)))
& U_4939 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4941),sK109(U_4941,U_4939,U_4937)) )
| ( ~ hBOOL(hAPP(U_4937,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4939),U_4941)) ) )
& ! [U_4940,U_4938,U_4936] :
( ( ! [U_4931] :
( hBOOL(hAPP(U_4936,U_4931))
| U_4938 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4940),U_4931) )
& ( hBOOL(hAPP(U_4936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4938),U_4940)) ) )
| ~ hBOOL(hAPP(U_4936,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4938),U_4940))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_4932,sK109(U_4941,U_4939,U_4937))],[f_1278_3]) ).
fof(f_1278_5,plain,
( ! [U_4939,U_4937,U_4941] :
( ~ hBOOL(hAPP(U_4937,sK109(U_4941,U_4939,U_4937)))
| ~ sP334(U_4939,U_4937,U_4941) )
& ! [U_4939,U_4937,U_4941] :
( U_4939 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4941),sK109(U_4941,U_4939,U_4937))
| ~ sP334(U_4939,U_4937,U_4941) )
& ! [U_4939,U_4937,U_4941] :
( ~ hBOOL(hAPP(U_4937,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP333(U_4939,U_4937,U_4941) )
& ! [U_4939,U_4937,U_4941] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4939),U_4941))
| ~ sP333(U_4939,U_4937,U_4941) )
& ! [U_4931,U_4936,U_4938,U_4940] :
( hBOOL(hAPP(U_4936,U_4931))
| U_4938 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4940),U_4931)
| ~ sP332(U_4931,U_4936,U_4938,U_4940) )
& ! [U_4931,U_4936,U_4938,U_4940] :
( hBOOL(hAPP(U_4936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4938),U_4940))
| ~ sP332(U_4931,U_4936,U_4938,U_4940) )
& ! [U_4939,U_4937,U_4941] :
( hBOOL(hAPP(U_4937,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4939),U_4941)))
| sP334(U_4939,U_4937,U_4941)
| sP333(U_4939,U_4937,U_4941) )
& ! [U_4931,U_4936,U_4938,U_4940] :
( sP332(U_4931,U_4936,U_4938,U_4940)
| ~ hBOOL(hAPP(U_4936,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4938),U_4940))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP332,sP333,sP334])],[f_1278_4]) ).
cnf(f_1278_6,plain,
( sP332(U_4931,U_4936,U_4938,U_4940)
| ~ hBOOL(hAPP(U_4936,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4938),U_4940))) ),
inference(clausify,[status(thm)],[f_1278_5]) ).
cnf(f_1278_7,plain,
( hBOOL(hAPP(U_4937,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4939),U_4941)))
| sP334(U_4939,U_4937,U_4941)
| sP333(U_4939,U_4937,U_4941) ),
inference(clausify,[status(thm)],[f_1278_5]) ).
cnf(f_1278_8,plain,
( hBOOL(hAPP(U_4936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4938),U_4940))
| ~ sP332(U_4931,U_4936,U_4938,U_4940) ),
inference(clausify,[status(thm)],[f_1278_5]) ).
cnf(f_1278_9,plain,
( hBOOL(hAPP(U_4936,U_4931))
| U_4938 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4940),U_4931)
| ~ sP332(U_4931,U_4936,U_4938,U_4940) ),
inference(clausify,[status(thm)],[f_1278_5]) ).
cnf(f_1278_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4939),U_4941))
| ~ sP333(U_4939,U_4937,U_4941) ),
inference(clausify,[status(thm)],[f_1278_5]) ).
cnf(f_1278_11,plain,
( ~ hBOOL(hAPP(U_4937,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP333(U_4939,U_4937,U_4941) ),
inference(clausify,[status(thm)],[f_1278_5]) ).
cnf(f_1278_12,plain,
( U_4939 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4941),sK109(U_4941,U_4939,U_4937))
| ~ sP334(U_4939,U_4937,U_4941) ),
inference(clausify,[status(thm)],[f_1278_5]) ).
cnf(f_1278_13,plain,
( ~ hBOOL(hAPP(U_4937,sK109(U_4941,U_4939,U_4937)))
| ~ sP334(U_4939,U_4937,U_4941) ),
inference(clausify,[status(thm)],[f_1278_5]) ).
fof(f_1279_1,plain,
! [V_b_2,V_a_2,V_Pa_2] :
( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_Pa_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_Pa_2,B_d))
| V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
& ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
| ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(f_1279_2,plain,
! [U_4946,U_4945,U_4944] :
( ( hBOOL(hAPP(U_4944,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4945),U_4946)))
| ? [U_4943] :
( ~ hBOOL(hAPP(U_4944,U_4943))
& U_4945 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4946),U_4943) )
| ( ~ hBOOL(hAPP(U_4944,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4945),U_4946)) ) )
& ( ( ! [U_4942] :
( hBOOL(hAPP(U_4944,U_4942))
| U_4945 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4946),U_4942) )
& ( hBOOL(hAPP(U_4944,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4945),U_4946)) ) )
| ~ hBOOL(hAPP(U_4944,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4945),U_4946))) ) ),
inference(variable_rename,[status(thm)],[f_1279_1]) ).
fof(f_1279_3,plain,
( ! [U_4952,U_4950,U_4948] :
( hBOOL(hAPP(U_4948,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4950),U_4952)))
| ? [U_4943] :
( ~ hBOOL(hAPP(U_4948,U_4943))
& U_4950 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4952),U_4943) )
| ( ~ hBOOL(hAPP(U_4948,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4950),U_4952)) ) )
& ! [U_4951,U_4949,U_4947] :
( ( ! [U_4942] :
( hBOOL(hAPP(U_4947,U_4942))
| U_4949 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4951),U_4942) )
& ( hBOOL(hAPP(U_4947,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4949),U_4951)) ) )
| ~ hBOOL(hAPP(U_4947,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4949),U_4951))) ) ),
inference(miniscope,[status(thm)],[f_1279_2]) ).
fof(f_1279_4,plain,
( ! [U_4952,U_4950,U_4948] :
( hBOOL(hAPP(U_4948,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4950),U_4952)))
| ( ~ hBOOL(hAPP(U_4948,sK110(U_4952,U_4950,U_4948)))
& U_4950 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4952),sK110(U_4952,U_4950,U_4948)) )
| ( ~ hBOOL(hAPP(U_4948,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4950),U_4952)) ) )
& ! [U_4951,U_4949,U_4947] :
( ( ! [U_4942] :
( hBOOL(hAPP(U_4947,U_4942))
| U_4949 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4951),U_4942) )
& ( hBOOL(hAPP(U_4947,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4949),U_4951)) ) )
| ~ hBOOL(hAPP(U_4947,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4949),U_4951))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_4943,sK110(U_4952,U_4950,U_4948))],[f_1279_3]) ).
fof(f_1279_5,plain,
( ! [U_4950,U_4948,U_4952] :
( ~ hBOOL(hAPP(U_4948,sK110(U_4952,U_4950,U_4948)))
| ~ sP337(U_4950,U_4948,U_4952) )
& ! [U_4950,U_4948,U_4952] :
( U_4950 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4952),sK110(U_4952,U_4950,U_4948))
| ~ sP337(U_4950,U_4948,U_4952) )
& ! [U_4950,U_4948,U_4952] :
( ~ hBOOL(hAPP(U_4948,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP336(U_4950,U_4948,U_4952) )
& ! [U_4950,U_4948,U_4952] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4950),U_4952))
| ~ sP336(U_4950,U_4948,U_4952) )
& ! [U_4942,U_4949,U_4947,U_4951] :
( hBOOL(hAPP(U_4947,U_4942))
| U_4949 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4951),U_4942)
| ~ sP335(U_4942,U_4949,U_4947,U_4951) )
& ! [U_4942,U_4949,U_4947,U_4951] :
( hBOOL(hAPP(U_4947,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4949),U_4951))
| ~ sP335(U_4942,U_4949,U_4947,U_4951) )
& ! [U_4950,U_4948,U_4952] :
( hBOOL(hAPP(U_4948,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4950),U_4952)))
| sP337(U_4950,U_4948,U_4952)
| sP336(U_4950,U_4948,U_4952) )
& ! [U_4942,U_4949,U_4947,U_4951] :
( sP335(U_4942,U_4949,U_4947,U_4951)
| ~ hBOOL(hAPP(U_4947,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4949),U_4951))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP335,sP336,sP337])],[f_1279_4]) ).
cnf(f_1279_6,plain,
( sP335(U_4942,U_4949,U_4947,U_4951)
| ~ hBOOL(hAPP(U_4947,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4949),U_4951))) ),
inference(clausify,[status(thm)],[f_1279_5]) ).
cnf(f_1279_7,plain,
( hBOOL(hAPP(U_4948,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4950),U_4952)))
| sP337(U_4950,U_4948,U_4952)
| sP336(U_4950,U_4948,U_4952) ),
inference(clausify,[status(thm)],[f_1279_5]) ).
cnf(f_1279_8,plain,
( hBOOL(hAPP(U_4947,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4949),U_4951))
| ~ sP335(U_4942,U_4949,U_4947,U_4951) ),
inference(clausify,[status(thm)],[f_1279_5]) ).
cnf(f_1279_9,plain,
( hBOOL(hAPP(U_4947,U_4942))
| U_4949 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4951),U_4942)
| ~ sP335(U_4942,U_4949,U_4947,U_4951) ),
inference(clausify,[status(thm)],[f_1279_5]) ).
cnf(f_1279_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4950),U_4952))
| ~ sP336(U_4950,U_4948,U_4952) ),
inference(clausify,[status(thm)],[f_1279_5]) ).
cnf(f_1279_11,plain,
( ~ hBOOL(hAPP(U_4948,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP336(U_4950,U_4948,U_4952) ),
inference(clausify,[status(thm)],[f_1279_5]) ).
cnf(f_1279_12,plain,
( U_4950 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4952),sK110(U_4952,U_4950,U_4948))
| ~ sP337(U_4950,U_4948,U_4952) ),
inference(clausify,[status(thm)],[f_1279_5]) ).
cnf(f_1279_13,plain,
( ~ hBOOL(hAPP(U_4948,sK110(U_4952,U_4950,U_4948)))
| ~ sP337(U_4950,U_4948,U_4952) ),
inference(clausify,[status(thm)],[f_1279_5]) ).
fof(f_1280_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( 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)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).
fof(f_1280_2,plain,
! [U_4955,U_4954,U_4953] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4953),U_4954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4953),U_4955)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4954),U_4955))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4953)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4954),U_4955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4953),U_4954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4953),U_4955))) ) ),
inference(variable_rename,[status(thm)],[f_1280_1]) ).
fof(f_1280_3,plain,
( ! [U_4961,U_4959,U_4957] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4957),U_4959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4957),U_4961)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4959),U_4961))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4957)) ) )
& ! [U_4960,U_4958,U_4956] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4958),U_4960))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4956),U_4958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4956),U_4960))) ) ),
inference(miniscope,[status(thm)],[f_1280_2]) ).
fof(f_1280_4,plain,
( ! [U_4957,U_4961,U_4959] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4959),U_4961))
| ~ sP338(U_4957,U_4961,U_4959) )
& ! [U_4957,U_4961,U_4959] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4957))
| ~ sP338(U_4957,U_4961,U_4959) )
& ! [U_4957,U_4961,U_4959] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4957),U_4959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4957),U_4961)))
| sP338(U_4957,U_4961,U_4959) )
& ! [U_4960,U_4956,U_4958] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4958),U_4960))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4956),U_4958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4956),U_4960))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP338])],[f_1280_3]) ).
cnf(f_1280_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4958),U_4960))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4956),U_4958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4956),U_4960))) ),
inference(clausify,[status(thm)],[f_1280_4]) ).
cnf(f_1280_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4957),U_4959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4957),U_4961)))
| sP338(U_4957,U_4961,U_4959) ),
inference(clausify,[status(thm)],[f_1280_4]) ).
cnf(f_1280_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4957))
| ~ sP338(U_4957,U_4961,U_4959) ),
inference(clausify,[status(thm)],[f_1280_4]) ).
cnf(f_1280_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4959),U_4961))
| ~ sP338(U_4957,U_4961,U_4959) ),
inference(clausify,[status(thm)],[f_1280_4]) ).
fof(f_1281_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( 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)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2]) ).
fof(f_1281_2,plain,
! [U_4964,U_4963,U_4962] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4962),U_4963)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4964),U_4963)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),U_4964))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4963)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),U_4964))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4963))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4962),U_4963)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4964),U_4963))) ) ),
inference(variable_rename,[status(thm)],[f_1281_1]) ).
fof(f_1281_3,plain,
( ! [U_4970,U_4968,U_4966] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4966),U_4968)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4970),U_4968)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4966),U_4970))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4968)) ) )
& ! [U_4969,U_4967,U_4965] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4965),U_4969))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4965),U_4967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4969),U_4967))) ) ),
inference(miniscope,[status(thm)],[f_1281_2]) ).
fof(f_1281_4,plain,
( ! [U_4968,U_4970,U_4966] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4966),U_4970))
| ~ sP339(U_4968,U_4970,U_4966) )
& ! [U_4968,U_4970,U_4966] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4968))
| ~ sP339(U_4968,U_4970,U_4966) )
& ! [U_4968,U_4970,U_4966] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4966),U_4968)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4970),U_4968)))
| sP339(U_4968,U_4970,U_4966) )
& ! [U_4967,U_4965,U_4969] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4965),U_4969))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4965),U_4967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4969),U_4967))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP339])],[f_1281_3]) ).
cnf(f_1281_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4965),U_4969))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4965),U_4967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4969),U_4967))) ),
inference(clausify,[status(thm)],[f_1281_4]) ).
cnf(f_1281_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4966),U_4968)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4970),U_4968)))
| sP339(U_4968,U_4970,U_4966) ),
inference(clausify,[status(thm)],[f_1281_4]) ).
cnf(f_1281_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4968))
| ~ sP339(U_4968,U_4970,U_4966) ),
inference(clausify,[status(thm)],[f_1281_4]) ).
cnf(f_1281_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4966),U_4970))
| ~ sP339(U_4968,U_4970,U_4966) ),
inference(clausify,[status(thm)],[f_1281_4]) ).
fof(f_1282_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1]) ).
fof(f_1282_2,plain,
! [U_4973,U_4972,U_4971] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4973)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4972),U_4973)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4972),U_4973))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4973))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4971)) ),
inference(variable_rename,[status(thm)],[f_1282_1]) ).
fof(f_1282_3,plain,
( ! [U_4972,U_4973,U_4971] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4973)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4972),U_4973))
| ~ sP340(U_4972,U_4973,U_4971) )
& ! [U_4972,U_4973,U_4971] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4972),U_4973))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4973)))
| ~ sP340(U_4972,U_4973,U_4971) )
& ! [U_4972,U_4973,U_4971] :
( sP340(U_4972,U_4973,U_4971)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4971)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP340])],[f_1282_2]) ).
cnf(f_1282_4,plain,
( sP340(U_4972,U_4973,U_4971)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4971)) ),
inference(clausify,[status(thm)],[f_1282_3]) ).
cnf(f_1282_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4972),U_4973))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4973)))
| ~ sP340(U_4972,U_4973,U_4971) ),
inference(clausify,[status(thm)],[f_1282_3]) ).
cnf(f_1282_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4971),U_4973)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4972),U_4973))
| ~ sP340(U_4972,U_4973,U_4971) ),
inference(clausify,[status(thm)],[f_1282_3]) ).
fof(f_1283_1,plain,
! [V_f_2,V_A_2,T_b] :
( ( ( 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)
| ! [B_x] :
( ? [B_xa] :
( hAPP(V_f_2,B_xa) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& B_x != B_xa
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
| hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( ! [B_xa] :
( hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| B_x = B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
& hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| 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) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__1__iff]) ).
fof(f_1283_2,plain,
! [U_4980,U_4979,U_4978] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_4977] :
( ? [U_4976] :
( hAPP(U_4980,U_4976) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4977 != U_4976
& hBOOL(hAPP(hAPP(c_member(U_4978),U_4976),U_4979)) )
| hAPP(U_4980,U_4977) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4977),U_4979)) ) )
& ( ? [U_4975] :
( ! [U_4974] :
( hAPP(U_4980,U_4974) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4975 = U_4974
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4974),U_4979)) )
& hAPP(U_4980,U_4975) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4978),U_4975),U_4979)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4978),U_4979)) ),
inference(variable_rename,[status(thm)],[f_1283_1]) ).
fof(f_1283_3,plain,
! [U_4980,U_4979,U_4978] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_4977] :
( ? [U_4976] :
( hAPP(U_4980,U_4976) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4977 != U_4976
& hBOOL(hAPP(hAPP(c_member(U_4978),U_4976),U_4979)) )
| hAPP(U_4980,U_4977) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4977),U_4979)) ) )
& ( ( ! [U_4974] :
( hAPP(U_4980,U_4974) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK111(U_4980,U_4979,U_4978) = U_4974
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4974),U_4979)) )
& hAPP(U_4980,sK111(U_4980,U_4979,U_4978)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4978),sK111(U_4980,U_4979,U_4978)),U_4979)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4978),U_4979)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_4975,sK111(U_4980,U_4979,U_4978))],[f_1283_2]) ).
fof(f_1283_4,plain,
! [U_4980,U_4979,U_4978] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_4977] :
( ( hAPP(U_4980,sK112(U_4980,U_4979,U_4978,U_4977)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4977 != sK112(U_4980,U_4979,U_4978,U_4977)
& hBOOL(hAPP(hAPP(c_member(U_4978),sK112(U_4980,U_4979,U_4978,U_4977)),U_4979)) )
| hAPP(U_4980,U_4977) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4977),U_4979)) ) )
& ( ( ! [U_4974] :
( hAPP(U_4980,U_4974) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK111(U_4980,U_4979,U_4978) = U_4974
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4974),U_4979)) )
& hAPP(U_4980,sK111(U_4980,U_4979,U_4978)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4978),sK111(U_4980,U_4979,U_4978)),U_4979)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4978),U_4979)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_4976,sK112(U_4980,U_4979,U_4978,U_4977))],[f_1283_3]) ).
fof(f_1283_5,plain,
( ! [U_4977,U_4978,U_4979,U_4980] :
( hAPP(U_4980,sK112(U_4980,U_4979,U_4978,U_4977)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP342(U_4977,U_4978,U_4979,U_4980) )
& ! [U_4977,U_4978,U_4979,U_4980] :
( U_4977 != sK112(U_4980,U_4979,U_4978,U_4977)
| ~ sP342(U_4977,U_4978,U_4979,U_4980) )
& ! [U_4977,U_4978,U_4979,U_4980] :
( hBOOL(hAPP(hAPP(c_member(U_4978),sK112(U_4980,U_4979,U_4978,U_4977)),U_4979))
| ~ sP342(U_4977,U_4978,U_4979,U_4980) )
& ! [U_4974,U_4978,U_4979,U_4980] :
( hAPP(U_4980,U_4974) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK111(U_4980,U_4979,U_4978) = U_4974
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4974),U_4979))
| ~ sP341(U_4974,U_4978,U_4979,U_4980) )
& ! [U_4974,U_4978,U_4979,U_4980] :
( hAPP(U_4980,sK111(U_4980,U_4979,U_4978)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP341(U_4974,U_4978,U_4979,U_4980) )
& ! [U_4974,U_4978,U_4979,U_4980] :
( hBOOL(hAPP(hAPP(c_member(U_4978),sK111(U_4980,U_4979,U_4978)),U_4979))
| ~ sP341(U_4974,U_4978,U_4979,U_4980) )
& ! [U_4974,U_4977,U_4978,U_4979,U_4980] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| sP342(U_4977,U_4978,U_4979,U_4980)
| hAPP(U_4980,U_4977) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4977),U_4979))
| ~ sP343(U_4974,U_4977,U_4978,U_4979,U_4980) )
& ! [U_4974,U_4977,U_4978,U_4979,U_4980] :
( sP341(U_4974,U_4978,U_4979,U_4980)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP343(U_4974,U_4977,U_4978,U_4979,U_4980) )
& ! [U_4974,U_4977,U_4978,U_4979,U_4980] :
( sP343(U_4974,U_4977,U_4978,U_4979,U_4980)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4978),U_4979)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP341,sP342,sP343])],[f_1283_4]) ).
cnf(f_1283_6,plain,
( sP343(U_4974,U_4977,U_4978,U_4979,U_4980)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4978),U_4979)) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
cnf(f_1283_7,plain,
( sP341(U_4974,U_4978,U_4979,U_4980)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP343(U_4974,U_4977,U_4978,U_4979,U_4980) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
cnf(f_1283_8,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4978,tc_Nat_Onat),U_4980),U_4979) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| sP342(U_4977,U_4978,U_4979,U_4980)
| hAPP(U_4980,U_4977) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4977),U_4979))
| ~ sP343(U_4974,U_4977,U_4978,U_4979,U_4980) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
cnf(f_1283_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_4978),sK111(U_4980,U_4979,U_4978)),U_4979))
| ~ sP341(U_4974,U_4978,U_4979,U_4980) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
cnf(f_1283_10,plain,
( hAPP(U_4980,sK111(U_4980,U_4979,U_4978)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP341(U_4974,U_4978,U_4979,U_4980) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
cnf(f_1283_11,plain,
( hAPP(U_4980,U_4974) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK111(U_4980,U_4979,U_4978) = U_4974
| ~ hBOOL(hAPP(hAPP(c_member(U_4978),U_4974),U_4979))
| ~ sP341(U_4974,U_4978,U_4979,U_4980) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
cnf(f_1283_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_4978),sK112(U_4980,U_4979,U_4978,U_4977)),U_4979))
| ~ sP342(U_4977,U_4978,U_4979,U_4980) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
cnf(f_1283_13,plain,
( U_4977 != sK112(U_4980,U_4979,U_4978,U_4977)
| ~ sP342(U_4977,U_4978,U_4979,U_4980) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
cnf(f_1283_14,plain,
( hAPP(U_4980,sK112(U_4980,U_4979,U_4978,U_4977)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP342(U_4977,U_4978,U_4979,U_4980) ),
inference(clausify,[status(thm)],[f_1283_5]) ).
fof(f_1284_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__if]) ).
fof(f_1284_2,plain,
! [U_4983,U_4982,U_4981] :
( ( ( hAPP(c_Finite__Set_Ocard(U_4981),hAPP(hAPP(c_Set_Oinsert(U_4981),U_4983),U_4982)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4981),U_4982))
| hBOOL(hAPP(hAPP(c_member(U_4981),U_4983),U_4982)) )
& ( hAPP(c_Finite__Set_Ocard(U_4981),hAPP(hAPP(c_Set_Oinsert(U_4981),U_4983),U_4982)) = hAPP(c_Finite__Set_Ocard(U_4981),U_4982)
| ~ hBOOL(hAPP(hAPP(c_member(U_4981),U_4983),U_4982)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4981),U_4982)) ),
inference(variable_rename,[status(thm)],[f_1284_1]) ).
fof(f_1284_3,plain,
( ! [U_4982,U_4983,U_4981] :
( hAPP(c_Finite__Set_Ocard(U_4981),hAPP(hAPP(c_Set_Oinsert(U_4981),U_4983),U_4982)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4981),U_4982))
| hBOOL(hAPP(hAPP(c_member(U_4981),U_4983),U_4982))
| ~ sP344(U_4982,U_4983,U_4981) )
& ! [U_4982,U_4983,U_4981] :
( hAPP(c_Finite__Set_Ocard(U_4981),hAPP(hAPP(c_Set_Oinsert(U_4981),U_4983),U_4982)) = hAPP(c_Finite__Set_Ocard(U_4981),U_4982)
| ~ hBOOL(hAPP(hAPP(c_member(U_4981),U_4983),U_4982))
| ~ sP344(U_4982,U_4983,U_4981) )
& ! [U_4982,U_4983,U_4981] :
( sP344(U_4982,U_4983,U_4981)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4981),U_4982)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP344])],[f_1284_2]) ).
cnf(f_1284_4,plain,
( sP344(U_4982,U_4983,U_4981)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4981),U_4982)) ),
inference(clausify,[status(thm)],[f_1284_3]) ).
cnf(f_1284_5,plain,
( hAPP(c_Finite__Set_Ocard(U_4981),hAPP(hAPP(c_Set_Oinsert(U_4981),U_4983),U_4982)) = hAPP(c_Finite__Set_Ocard(U_4981),U_4982)
| ~ hBOOL(hAPP(hAPP(c_member(U_4981),U_4983),U_4982))
| ~ sP344(U_4982,U_4983,U_4981) ),
inference(clausify,[status(thm)],[f_1284_3]) ).
cnf(f_1284_6,plain,
( hAPP(c_Finite__Set_Ocard(U_4981),hAPP(hAPP(c_Set_Oinsert(U_4981),U_4983),U_4982)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4981),U_4982))
| hBOOL(hAPP(hAPP(c_member(U_4981),U_4983),U_4982))
| ~ sP344(U_4982,U_4983,U_4981) ),
inference(clausify,[status(thm)],[f_1284_3]) ).
fof(f_1285_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__disjoint]) ).
fof(f_1285_2,plain,
! [U_4986,U_4985,U_4984] :
( hAPP(c_Finite__Set_Ocard(U_4984),hAPP(hAPP(c_Set_Oinsert(U_4984),U_4986),U_4985)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4984),U_4985))
| hBOOL(hAPP(hAPP(c_member(U_4984),U_4986),U_4985))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4984),U_4985)) ),
inference(variable_rename,[status(thm)],[f_1285_1]) ).
fof(f_1285_3,plain,
! [U_4984,U_4985,U_4986] :
( hAPP(c_Finite__Set_Ocard(U_4984),hAPP(hAPP(c_Set_Oinsert(U_4984),U_4986),U_4985)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4984),U_4985))
| hBOOL(hAPP(hAPP(c_member(U_4984),U_4986),U_4985))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4984),U_4985)) ),
inference(definitional_conversion,[status(esa)],[f_1285_2]) ).
cnf(f_1285_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4984),hAPP(hAPP(c_Set_Oinsert(U_4984),U_4986),U_4985)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4984),U_4985))
| hBOOL(hAPP(hAPP(c_member(U_4984),U_4986),U_4985))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4984),U_4985)) ),
inference(clausify,[status(thm)],[f_1285_3]) ).
fof(f_1286_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( 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))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
| ~ class_Rings_Olinordered__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convex__bound__le]) ).
fof(f_1286_2,plain,
! [U_4992,U_4991,U_4990,U_4989,U_4988,U_4987] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4987),U_4991),U_4988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4987),U_4992),U_4990))),U_4989))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4987),U_4991),U_4992) != c_Groups_Oone__class_Oone(U_4987)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),c_Groups_Ozero__class_Ozero(U_4987)),U_4992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),c_Groups_Ozero__class_Ozero(U_4987)),U_4991))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),U_4990),U_4989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),U_4988),U_4989))
| ~ class_Rings_Olinordered__semiring__1(U_4987) ),
inference(variable_rename,[status(thm)],[f_1286_1]) ).
fof(f_1286_3,plain,
! [U_4988,U_4987,U_4989,U_4990,U_4991,U_4992] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4987),U_4991),U_4988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4987),U_4992),U_4990))),U_4989))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4987),U_4991),U_4992) != c_Groups_Oone__class_Oone(U_4987)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),c_Groups_Ozero__class_Ozero(U_4987)),U_4992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),c_Groups_Ozero__class_Ozero(U_4987)),U_4991))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),U_4990),U_4989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),U_4988),U_4989))
| ~ class_Rings_Olinordered__semiring__1(U_4987) ),
inference(definitional_conversion,[status(esa)],[f_1286_2]) ).
cnf(f_1286_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4987),U_4991),U_4988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4987),U_4992),U_4990))),U_4989))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4987),U_4991),U_4992) != c_Groups_Oone__class_Oone(U_4987)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),c_Groups_Ozero__class_Ozero(U_4987)),U_4992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),c_Groups_Ozero__class_Ozero(U_4987)),U_4991))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),U_4990),U_4989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),U_4988),U_4989))
| ~ class_Rings_Olinordered__semiring__1(U_4987) ),
inference(clausify,[status(thm)],[f_1286_3]) ).
fof(f_1287_1,plain,
! [V_f_2,V_n_2,V_m_2,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_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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc]) ).
fof(f_1287_2,plain,
! [U_4996,U_4995,U_4994,U_4993] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4993),U_4996),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4994),U_4995)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4993),hAPP(U_4996,U_4994)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4993),U_4996),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4994)),U_4995)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4994),U_4995))
| ~ class_Groups_Ocomm__monoid__add(U_4993) ),
inference(variable_rename,[status(thm)],[f_1287_1]) ).
fof(f_1287_3,plain,
! [U_4993,U_4994,U_4995,U_4996] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4993),U_4996),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4994),U_4995)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4993),hAPP(U_4996,U_4994)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4993),U_4996),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4994)),U_4995)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4994),U_4995))
| ~ class_Groups_Ocomm__monoid__add(U_4993) ),
inference(definitional_conversion,[status(esa)],[f_1287_2]) ).
cnf(f_1287_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4993),U_4996),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4994),U_4995)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4993),hAPP(U_4996,U_4994)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4993),U_4996),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4994)),U_4995)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4994),U_4995))
| ~ class_Groups_Ocomm__monoid__add(U_4993) ),
inference(clausify,[status(thm)],[f_1287_3]) ).
fof(f_1288_1,plain,
! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
( 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))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__insert]) ).
fof(f_1288_2,plain,
! [U_5002,U_5001,U_5000,U_4999,U_4998,U_4997] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4997,U_4998,c_Groups_Otimes__class_Otimes(U_4997)),U_5001),U_5002),hAPP(hAPP(c_Set_Oinsert(U_4998),U_5000),U_4999)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4997),hAPP(U_5001,U_5000)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4997,U_4998,c_Groups_Otimes__class_Otimes(U_4997)),U_5001),U_5002),U_4999))
| hBOOL(hAPP(hAPP(c_member(U_4998),U_5000),U_4999))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4998),U_4999))
| ~ class_Groups_Oab__semigroup__mult(U_4997) ),
inference(variable_rename,[status(thm)],[f_1288_1]) ).
fof(f_1288_3,plain,
! [U_4997,U_4998,U_4999,U_5000,U_5001,U_5002] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4997,U_4998,c_Groups_Otimes__class_Otimes(U_4997)),U_5001),U_5002),hAPP(hAPP(c_Set_Oinsert(U_4998),U_5000),U_4999)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4997),hAPP(U_5001,U_5000)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4997,U_4998,c_Groups_Otimes__class_Otimes(U_4997)),U_5001),U_5002),U_4999))
| hBOOL(hAPP(hAPP(c_member(U_4998),U_5000),U_4999))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4998),U_4999))
| ~ class_Groups_Oab__semigroup__mult(U_4997) ),
inference(definitional_conversion,[status(esa)],[f_1288_2]) ).
cnf(f_1288_4,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4997,U_4998,c_Groups_Otimes__class_Otimes(U_4997)),U_5001),U_5002),hAPP(hAPP(c_Set_Oinsert(U_4998),U_5000),U_4999)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4997),hAPP(U_5001,U_5000)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4997,U_4998,c_Groups_Otimes__class_Otimes(U_4997)),U_5001),U_5002),U_4999))
| hBOOL(hAPP(hAPP(c_member(U_4998),U_5000),U_4999))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4998),U_4999))
| ~ class_Groups_Oab__semigroup__mult(U_4997) ),
inference(clausify,[status(thm)],[f_1288_3]) ).
fof(f_1289_1,plain,
! [V_f_2,V_n_2,V_m_2,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_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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc]) ).
fof(f_1289_2,plain,
! [U_5006,U_5005,U_5004,U_5003] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5003),U_5006),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5004,U_5005)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5003),hAPP(U_5006,U_5004)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5003),U_5006),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5004),U_5005)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5004),U_5005))
| ~ class_Groups_Ocomm__monoid__add(U_5003) ),
inference(variable_rename,[status(thm)],[f_1289_1]) ).
fof(f_1289_3,plain,
! [U_5003,U_5004,U_5005,U_5006] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5003),U_5006),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5004,U_5005)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5003),hAPP(U_5006,U_5004)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5003),U_5006),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5004),U_5005)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5004),U_5005))
| ~ class_Groups_Ocomm__monoid__add(U_5003) ),
inference(definitional_conversion,[status(esa)],[f_1289_2]) ).
cnf(f_1289_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5003),U_5006),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5004,U_5005)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5003),hAPP(U_5006,U_5004)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5003),U_5006),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5004),U_5005)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5004),U_5005))
| ~ class_Groups_Ocomm__monoid__add(U_5003) ),
inference(clausify,[status(thm)],[f_1289_3]) ).
fof(f_1290_1,plain,
! [V_A_2,T_b] :
( ( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff]) ).
fof(f_1290_2,plain,
! [U_5008,U_5007] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5007),U_5008)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5007),U_5008))
| U_5008 = c_Orderings_Obot__class_Obot(tc_fun(U_5007,tc_HOL_Obool)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5007),U_5008))
& U_5008 != c_Orderings_Obot__class_Obot(tc_fun(U_5007,tc_HOL_Obool)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5007),U_5008))) ) ),
inference(variable_rename,[status(thm)],[f_1290_1]) ).
fof(f_1290_3,plain,
( ! [U_5012,U_5010] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5010),U_5012)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5010),U_5012))
| U_5012 = c_Orderings_Obot__class_Obot(tc_fun(U_5010,tc_HOL_Obool)) )
& ! [U_5011,U_5009] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5009),U_5011))
& U_5011 != c_Orderings_Obot__class_Obot(tc_fun(U_5009,tc_HOL_Obool)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5009),U_5011))) ) ),
inference(miniscope,[status(thm)],[f_1290_2]) ).
fof(f_1290_4,plain,
( ! [U_5011,U_5009] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5009),U_5011))
| ~ sP345(U_5011,U_5009) )
& ! [U_5011,U_5009] :
( U_5011 != c_Orderings_Obot__class_Obot(tc_fun(U_5009,tc_HOL_Obool))
| ~ sP345(U_5011,U_5009) )
& ! [U_5012,U_5010] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5010),U_5012)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5010),U_5012))
| U_5012 = c_Orderings_Obot__class_Obot(tc_fun(U_5010,tc_HOL_Obool)) )
& ! [U_5011,U_5009] :
( sP345(U_5011,U_5009)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5009),U_5011))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP345])],[f_1290_3]) ).
cnf(f_1290_5,plain,
( sP345(U_5011,U_5009)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5009),U_5011))) ),
inference(clausify,[status(thm)],[f_1290_4]) ).
cnf(f_1290_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5010),U_5012)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5010),U_5012))
| U_5012 = c_Orderings_Obot__class_Obot(tc_fun(U_5010,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1290_4]) ).
cnf(f_1290_7,plain,
( U_5011 != c_Orderings_Obot__class_Obot(tc_fun(U_5009,tc_HOL_Obool))
| ~ sP345(U_5011,U_5009) ),
inference(clausify,[status(thm)],[f_1290_4]) ).
cnf(f_1290_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5009),U_5011))
| ~ sP345(U_5011,U_5009) ),
inference(clausify,[status(thm)],[f_1290_4]) ).
fof(f_1291_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( ( ( 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)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_OF__eq]) ).
fof(f_1291_2,plain,
! [U_5016,U_5015,U_5014,U_5013] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5014,U_5013),U_5016),U_5015) = c_Groups_Oone__class_Oone(U_5013)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5014),U_5015)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5014,U_5013),U_5016),U_5015) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5013,U_5014,c_Groups_Otimes__class_Otimes(U_5013)),U_5016),c_Groups_Oone__class_Oone(U_5013)),U_5015)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5014),U_5015)) ) )
| ~ class_Groups_Ocomm__monoid__mult(U_5013) ),
inference(variable_rename,[status(thm)],[f_1291_1]) ).
fof(f_1291_3,plain,
( ! [U_5014,U_5013,U_5015,U_5016] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5014,U_5013),U_5016),U_5015) = c_Groups_Oone__class_Oone(U_5013)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5014),U_5015))
| ~ sP346(U_5014,U_5013,U_5015,U_5016) )
& ! [U_5014,U_5013,U_5015,U_5016] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5014,U_5013),U_5016),U_5015) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5013,U_5014,c_Groups_Otimes__class_Otimes(U_5013)),U_5016),c_Groups_Oone__class_Oone(U_5013)),U_5015)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5014),U_5015))
| ~ sP346(U_5014,U_5013,U_5015,U_5016) )
& ! [U_5014,U_5013,U_5015,U_5016] :
( sP346(U_5014,U_5013,U_5015,U_5016)
| ~ class_Groups_Ocomm__monoid__mult(U_5013) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP346])],[f_1291_2]) ).
cnf(f_1291_4,plain,
( sP346(U_5014,U_5013,U_5015,U_5016)
| ~ class_Groups_Ocomm__monoid__mult(U_5013) ),
inference(clausify,[status(thm)],[f_1291_3]) ).
cnf(f_1291_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5014,U_5013),U_5016),U_5015) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5013,U_5014,c_Groups_Otimes__class_Otimes(U_5013)),U_5016),c_Groups_Oone__class_Oone(U_5013)),U_5015)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5014),U_5015))
| ~ sP346(U_5014,U_5013,U_5015,U_5016) ),
inference(clausify,[status(thm)],[f_1291_3]) ).
cnf(f_1291_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5014,U_5013),U_5016),U_5015) = c_Groups_Oone__class_Oone(U_5013)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5014),U_5015))
| ~ sP346(U_5014,U_5013,U_5015,U_5016) ),
inference(clausify,[status(thm)],[f_1291_3]) ).
fof(f_1292_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold]) ).
fof(f_1292_2,plain,
! [U_5020,U_5019,U_5018,U_5017] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5018,U_5017),U_5020),U_5019) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5017,U_5018,c_Groups_Otimes__class_Otimes(U_5017)),U_5020),c_Groups_Oone__class_Oone(U_5017)),U_5019)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5018),U_5019))
| ~ class_Groups_Ocomm__monoid__mult(U_5017) ),
inference(variable_rename,[status(thm)],[f_1292_1]) ).
fof(f_1292_3,plain,
! [U_5019,U_5018,U_5017,U_5020] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5018,U_5017),U_5020),U_5019) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5017,U_5018,c_Groups_Otimes__class_Otimes(U_5017)),U_5020),c_Groups_Oone__class_Oone(U_5017)),U_5019)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5018),U_5019))
| ~ class_Groups_Ocomm__monoid__mult(U_5017) ),
inference(definitional_conversion,[status(esa)],[f_1292_2]) ).
cnf(f_1292_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5018,U_5017),U_5020),U_5019) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5017,U_5018,c_Groups_Otimes__class_Otimes(U_5017)),U_5020),c_Groups_Oone__class_Oone(U_5017)),U_5019)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5018),U_5019))
| ~ class_Groups_Ocomm__monoid__mult(U_5017) ),
inference(clausify,[status(thm)],[f_1292_3]) ).
fof(f_1293_1,plain,
! [T_b] :
( 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)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0]) ).
fof(f_1293_2,plain,
! [U_5021] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5021),c_Orderings_Otop__class_Otop(tc_fun(U_5021,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5021),c_Orderings_Otop__class_Otop(tc_fun(U_5021,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_1293_1]) ).
fof(f_1293_3,plain,
! [U_5021] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5021),c_Orderings_Otop__class_Otop(tc_fun(U_5021,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5021),c_Orderings_Otop__class_Otop(tc_fun(U_5021,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_1293_2]) ).
cnf(f_1293_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5021),c_Orderings_Otop__class_Otop(tc_fun(U_5021,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5021),c_Orderings_Otop__class_Otop(tc_fun(U_5021,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_1293_3]) ).
fof(f_1294_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert]) ).
fof(f_1294_2,plain,
! [U_5024,U_5023,U_5022] :
( hAPP(c_Finite__Set_Ocard(U_5022),hAPP(hAPP(c_Set_Oinsert(U_5022),U_5024),U_5023)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5022),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5022,tc_HOL_Obool)),U_5023),hAPP(hAPP(c_Set_Oinsert(U_5022),U_5024),c_Orderings_Obot__class_Obot(tc_fun(U_5022,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5022),U_5023)) ),
inference(variable_rename,[status(thm)],[f_1294_1]) ).
fof(f_1294_3,plain,
! [U_5022,U_5023,U_5024] :
( hAPP(c_Finite__Set_Ocard(U_5022),hAPP(hAPP(c_Set_Oinsert(U_5022),U_5024),U_5023)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5022),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5022,tc_HOL_Obool)),U_5023),hAPP(hAPP(c_Set_Oinsert(U_5022),U_5024),c_Orderings_Obot__class_Obot(tc_fun(U_5022,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5022),U_5023)) ),
inference(definitional_conversion,[status(esa)],[f_1294_2]) ).
cnf(f_1294_4,plain,
( hAPP(c_Finite__Set_Ocard(U_5022),hAPP(hAPP(c_Set_Oinsert(U_5022),U_5024),U_5023)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5022),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5022,tc_HOL_Obool)),U_5023),hAPP(hAPP(c_Set_Oinsert(U_5022),U_5024),c_Orderings_Obot__class_Obot(tc_fun(U_5022,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5022),U_5023)) ),
inference(clausify,[status(thm)],[f_1294_3]) ).
fof(f_1295_1,plain,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| 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))
| ~ 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)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1]) ).
fof(f_1295_2,plain,
! [U_5026,U_5025] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5025),c_Orderings_Otop__class_Otop(tc_fun(U_5025,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_5026),c_Orderings_Otop__class_Otop(tc_fun(U_5026,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5025,U_5026)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5025,U_5026),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_1295_1]) ).
fof(f_1295_3,plain,
! [U_5025,U_5026] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5025),c_Orderings_Otop__class_Otop(tc_fun(U_5025,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_5026),c_Orderings_Otop__class_Otop(tc_fun(U_5026,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5025,U_5026)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5025,U_5026),tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_1295_2]) ).
cnf(f_1295_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5025),c_Orderings_Otop__class_Otop(tc_fun(U_5025,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_5026),c_Orderings_Otop__class_Otop(tc_fun(U_5026,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5025,U_5026)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5025,U_5026),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_1295_3]) ).
fof(f_1296_1,plain,
! [V_n,V_m] :
( ( 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))
| V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__if]) ).
fof(f_1296_2,plain,
! [U_5028,U_5027] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5027),U_5028) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5027),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5028))
| U_5027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5027),U_5028) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5027 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1296_1]) ).
fof(f_1296_3,plain,
( ! [U_5032,U_5030] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5030),U_5032) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5030),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5032))
| U_5030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5031,U_5029] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5029),U_5031) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5029 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1296_2]) ).
fof(f_1296_4,plain,
( ! [U_5030,U_5032] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5030),U_5032) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5030),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5032))
| U_5030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5031,U_5029] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5029),U_5031) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5029 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1296_3]) ).
cnf(f_1296_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5029),U_5031) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5029 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1296_4]) ).
cnf(f_1296_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5030),U_5032) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5030),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5032))
| U_5030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1296_4]) ).
fof(f_1297_1,plain,
! [V_n,V_m] :
( ( 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))
| V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__eq__if]) ).
fof(f_1297_2,plain,
! [U_5034,U_5033] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5033),U_5034) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5033),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5034))
| U_5033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5033),U_5034) = U_5034
| U_5033 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1297_1]) ).
fof(f_1297_3,plain,
( ! [U_5038,U_5036] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5036),U_5038) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5036),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5038))
| U_5036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5037,U_5035] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5035),U_5037) = U_5037
| U_5035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1297_2]) ).
fof(f_1297_4,plain,
( ! [U_5036,U_5038] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5036),U_5038) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5036),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5038))
| U_5036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5037,U_5035] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5035),U_5037) = U_5037
| U_5035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1297_3]) ).
cnf(f_1297_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5035),U_5037) = U_5037
| U_5035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1297_4]) ).
cnf(f_1297_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5036),U_5038) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5036),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5038))
| U_5036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1297_4]) ).
fof(f_1298_1,plain,
! [V_n] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred_H]) ).
fof(f_1298_2,plain,
! [U_5039] :
( U_5039 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5039),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5039)) ),
inference(variable_rename,[status(thm)],[f_1298_1]) ).
fof(f_1298_3,plain,
! [U_5039] :
( U_5039 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5039),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5039)) ),
inference(definitional_conversion,[status(esa)],[f_1298_2]) ).
cnf(f_1298_4,plain,
( U_5039 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5039),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5039)) ),
inference(clausify,[status(thm)],[f_1298_3]) ).
fof(f_1299_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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))))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
| ~ 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)))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).
fof(f_1299_2,plain,
! [U_5042,U_5041,U_5040] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5040),c_Groups_Ozero__class_Ozero(U_5040)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))))
| ( U_5042 = c_Groups_Ozero__class_Ozero(U_5040)
& U_5041 = c_Groups_Ozero__class_Ozero(U_5040) ) )
& ( U_5042 != c_Groups_Ozero__class_Ozero(U_5040)
| U_5041 != c_Groups_Ozero__class_Ozero(U_5040)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5040),c_Groups_Ozero__class_Ozero(U_5040)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042)))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_5040) ),
inference(variable_rename,[status(thm)],[f_1299_1]) ).
fof(f_1299_3,plain,
( ! [U_5040,U_5041,U_5042] :
( U_5042 = c_Groups_Ozero__class_Ozero(U_5040)
| ~ sP347(U_5040,U_5041,U_5042) )
& ! [U_5040,U_5041,U_5042] :
( U_5041 = c_Groups_Ozero__class_Ozero(U_5040)
| ~ sP347(U_5040,U_5041,U_5042) )
& ! [U_5040,U_5041,U_5042] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5040),c_Groups_Ozero__class_Ozero(U_5040)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))))
| sP347(U_5040,U_5041,U_5042)
| ~ sP348(U_5040,U_5041,U_5042) )
& ! [U_5040,U_5041,U_5042] :
( U_5042 != c_Groups_Ozero__class_Ozero(U_5040)
| U_5041 != c_Groups_Ozero__class_Ozero(U_5040)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5040),c_Groups_Ozero__class_Ozero(U_5040)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))))
| ~ sP348(U_5040,U_5041,U_5042) )
& ! [U_5040,U_5041,U_5042] :
( sP348(U_5040,U_5041,U_5042)
| ~ class_Rings_Olinordered__ring__strict(U_5040) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP347,sP348])],[f_1299_2]) ).
cnf(f_1299_4,plain,
( sP348(U_5040,U_5041,U_5042)
| ~ class_Rings_Olinordered__ring__strict(U_5040) ),
inference(clausify,[status(thm)],[f_1299_3]) ).
cnf(f_1299_5,plain,
( U_5042 != c_Groups_Ozero__class_Ozero(U_5040)
| U_5041 != c_Groups_Ozero__class_Ozero(U_5040)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5040),c_Groups_Ozero__class_Ozero(U_5040)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))))
| ~ sP348(U_5040,U_5041,U_5042) ),
inference(clausify,[status(thm)],[f_1299_3]) ).
cnf(f_1299_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5040),c_Groups_Ozero__class_Ozero(U_5040)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))))
| sP347(U_5040,U_5041,U_5042)
| ~ sP348(U_5040,U_5041,U_5042) ),
inference(clausify,[status(thm)],[f_1299_3]) ).
cnf(f_1299_7,plain,
( U_5041 = c_Groups_Ozero__class_Ozero(U_5040)
| ~ sP347(U_5040,U_5041,U_5042) ),
inference(clausify,[status(thm)],[f_1299_3]) ).
cnf(f_1299_8,plain,
( U_5042 = c_Groups_Ozero__class_Ozero(U_5040)
| ~ sP347(U_5040,U_5041,U_5042) ),
inference(clausify,[status(thm)],[f_1299_3]) ).
fof(f_1300_1,plain,
! [V_y,V_x,T_a] :
( ~ 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)))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(f_1300_2,plain,
! [U_5045,U_5044,U_5043] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5044),U_5044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5045),U_5045))),c_Groups_Ozero__class_Ozero(U_5043)))
| ~ class_Rings_Olinordered__ring(U_5043) ),
inference(variable_rename,[status(thm)],[f_1300_1]) ).
fof(f_1300_3,plain,
! [U_5044,U_5045,U_5043] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5044),U_5044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5045),U_5045))),c_Groups_Ozero__class_Ozero(U_5043)))
| ~ class_Rings_Olinordered__ring(U_5043) ),
inference(definitional_conversion,[status(esa)],[f_1300_2]) ).
cnf(f_1300_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5044),U_5044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5045),U_5045))),c_Groups_Ozero__class_Ozero(U_5043)))
| ~ class_Rings_Olinordered__ring(U_5043) ),
inference(clausify,[status(thm)],[f_1300_3]) ).
fof(f_1301_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ~ 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))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).
fof(f_1301_2,plain,
! [U_5048,U_5047,U_5046] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))),c_Groups_Ozero__class_Ozero(U_5046)))
| U_5048 != c_Groups_Ozero__class_Ozero(U_5046)
| U_5047 != c_Groups_Ozero__class_Ozero(U_5046) )
& ( ( U_5048 = c_Groups_Ozero__class_Ozero(U_5046)
& U_5047 = c_Groups_Ozero__class_Ozero(U_5046) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))),c_Groups_Ozero__class_Ozero(U_5046))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_5046) ),
inference(variable_rename,[status(thm)],[f_1301_1]) ).
fof(f_1301_3,plain,
( ! [U_5046,U_5048,U_5047] :
( U_5048 = c_Groups_Ozero__class_Ozero(U_5046)
| ~ sP349(U_5046,U_5048,U_5047) )
& ! [U_5046,U_5048,U_5047] :
( U_5047 = c_Groups_Ozero__class_Ozero(U_5046)
| ~ sP349(U_5046,U_5048,U_5047) )
& ! [U_5046,U_5048,U_5047] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))),c_Groups_Ozero__class_Ozero(U_5046)))
| U_5048 != c_Groups_Ozero__class_Ozero(U_5046)
| U_5047 != c_Groups_Ozero__class_Ozero(U_5046)
| ~ sP350(U_5046,U_5048,U_5047) )
& ! [U_5046,U_5048,U_5047] :
( sP349(U_5046,U_5048,U_5047)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))),c_Groups_Ozero__class_Ozero(U_5046)))
| ~ sP350(U_5046,U_5048,U_5047) )
& ! [U_5046,U_5048,U_5047] :
( sP350(U_5046,U_5048,U_5047)
| ~ class_Rings_Olinordered__ring__strict(U_5046) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP349,sP350])],[f_1301_2]) ).
cnf(f_1301_4,plain,
( sP350(U_5046,U_5048,U_5047)
| ~ class_Rings_Olinordered__ring__strict(U_5046) ),
inference(clausify,[status(thm)],[f_1301_3]) ).
cnf(f_1301_5,plain,
( sP349(U_5046,U_5048,U_5047)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))),c_Groups_Ozero__class_Ozero(U_5046)))
| ~ sP350(U_5046,U_5048,U_5047) ),
inference(clausify,[status(thm)],[f_1301_3]) ).
cnf(f_1301_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))),c_Groups_Ozero__class_Ozero(U_5046)))
| U_5048 != c_Groups_Ozero__class_Ozero(U_5046)
| U_5047 != c_Groups_Ozero__class_Ozero(U_5046)
| ~ sP350(U_5046,U_5048,U_5047) ),
inference(clausify,[status(thm)],[f_1301_3]) ).
cnf(f_1301_7,plain,
( U_5047 = c_Groups_Ozero__class_Ozero(U_5046)
| ~ sP349(U_5046,U_5048,U_5047) ),
inference(clausify,[status(thm)],[f_1301_3]) ).
cnf(f_1301_8,plain,
( U_5048 = c_Groups_Ozero__class_Ozero(U_5046)
| ~ sP349(U_5046,U_5048,U_5047) ),
inference(clausify,[status(thm)],[f_1301_3]) ).
fof(f_1302_1,plain,
! [V_y,V_x,T_a] :
( 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))))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero]) ).
fof(f_1302_2,plain,
! [U_5051,U_5050,U_5049] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),c_Groups_Ozero__class_Ozero(U_5049)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5049),U_5050),U_5050)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5049),U_5051),U_5051))))
| ~ class_Rings_Olinordered__ring(U_5049) ),
inference(variable_rename,[status(thm)],[f_1302_1]) ).
fof(f_1302_3,plain,
! [U_5050,U_5051,U_5049] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),c_Groups_Ozero__class_Ozero(U_5049)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5049),U_5050),U_5050)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5049),U_5051),U_5051))))
| ~ class_Rings_Olinordered__ring(U_5049) ),
inference(definitional_conversion,[status(esa)],[f_1302_2]) ).
cnf(f_1302_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),c_Groups_Ozero__class_Ozero(U_5049)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5049),U_5050),U_5050)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5049),U_5051),U_5051))))
| ~ class_Rings_Olinordered__ring(U_5049) ),
inference(clausify,[status(thm)],[f_1302_3]) ).
fof(f_1303_1,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_bot__nat__def]) ).
fof(f_1303_2,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1303_1]) ).
cnf(f_1303_3,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1303_2]) ).
fof(f_1304_1,plain,
! [V_y_2,V_x_2,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)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = 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)) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).
fof(f_1304_2,plain,
! [U_5054,U_5053,U_5052] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5053),U_5053)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5054),U_5054)) = c_Groups_Ozero__class_Ozero(U_5052)
| U_5054 != c_Groups_Ozero__class_Ozero(U_5052)
| U_5053 != c_Groups_Ozero__class_Ozero(U_5052) )
& ( ( U_5054 = c_Groups_Ozero__class_Ozero(U_5052)
& U_5053 = c_Groups_Ozero__class_Ozero(U_5052) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5053),U_5053)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5054),U_5054)) != c_Groups_Ozero__class_Ozero(U_5052) ) )
| ~ class_Rings_Olinordered__ring__strict(U_5052) ),
inference(variable_rename,[status(thm)],[f_1304_1]) ).
fof(f_1304_3,plain,
( ! [U_5052,U_5053,U_5054] :
( U_5054 = c_Groups_Ozero__class_Ozero(U_5052)
| ~ sP351(U_5052,U_5053,U_5054) )
& ! [U_5052,U_5053,U_5054] :
( U_5053 = c_Groups_Ozero__class_Ozero(U_5052)
| ~ sP351(U_5052,U_5053,U_5054) )
& ! [U_5052,U_5053,U_5054] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5053),U_5053)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5054),U_5054)) = c_Groups_Ozero__class_Ozero(U_5052)
| U_5054 != c_Groups_Ozero__class_Ozero(U_5052)
| U_5053 != c_Groups_Ozero__class_Ozero(U_5052)
| ~ sP352(U_5052,U_5053,U_5054) )
& ! [U_5052,U_5053,U_5054] :
( sP351(U_5052,U_5053,U_5054)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5053),U_5053)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5054),U_5054)) != c_Groups_Ozero__class_Ozero(U_5052)
| ~ sP352(U_5052,U_5053,U_5054) )
& ! [U_5052,U_5053,U_5054] :
( sP352(U_5052,U_5053,U_5054)
| ~ class_Rings_Olinordered__ring__strict(U_5052) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP351,sP352])],[f_1304_2]) ).
cnf(f_1304_4,plain,
( sP352(U_5052,U_5053,U_5054)
| ~ class_Rings_Olinordered__ring__strict(U_5052) ),
inference(clausify,[status(thm)],[f_1304_3]) ).
cnf(f_1304_5,plain,
( sP351(U_5052,U_5053,U_5054)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5053),U_5053)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5054),U_5054)) != c_Groups_Ozero__class_Ozero(U_5052)
| ~ sP352(U_5052,U_5053,U_5054) ),
inference(clausify,[status(thm)],[f_1304_3]) ).
cnf(f_1304_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5053),U_5053)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5052),U_5054),U_5054)) = c_Groups_Ozero__class_Ozero(U_5052)
| U_5054 != c_Groups_Ozero__class_Ozero(U_5052)
| U_5053 != c_Groups_Ozero__class_Ozero(U_5052)
| ~ sP352(U_5052,U_5053,U_5054) ),
inference(clausify,[status(thm)],[f_1304_3]) ).
cnf(f_1304_7,plain,
( U_5053 = c_Groups_Ozero__class_Ozero(U_5052)
| ~ sP351(U_5052,U_5053,U_5054) ),
inference(clausify,[status(thm)],[f_1304_3]) ).
cnf(f_1304_8,plain,
( U_5054 = c_Groups_Ozero__class_Ozero(U_5052)
| ~ sP351(U_5052,U_5053,U_5054) ),
inference(clausify,[status(thm)],[f_1304_3]) ).
fof(f_1305_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(f_1305_2,plain,
! [U_5055] : hAPP(c_Nat_OSuc,U_5055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5055),
inference(variable_rename,[status(thm)],[f_1305_1]) ).
fof(f_1305_3,plain,
! [U_5055] : hAPP(c_Nat_OSuc,U_5055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5055),
inference(definitional_conversion,[status(esa)],[f_1305_2]) ).
cnf(f_1305_4,plain,
hAPP(c_Nat_OSuc,U_5055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5055),
inference(clausify,[status(thm)],[f_1305_3]) ).
fof(f_1306_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(f_1306_2,plain,
! [U_5056] : hAPP(c_Nat_OSuc,U_5056) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5056),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_1306_1]) ).
fof(f_1306_3,plain,
! [U_5056] : hAPP(c_Nat_OSuc,U_5056) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5056),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_1306_2]) ).
cnf(f_1306_4,plain,
hAPP(c_Nat_OSuc,U_5056) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5056),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1306_3]) ).
fof(f_1307_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(f_1307_2,plain,
! [U_5058,U_5057] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5057),hAPP(c_Nat_OSuc,U_5058)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5057),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5058),
inference(variable_rename,[status(thm)],[f_1307_1]) ).
fof(f_1307_3,plain,
! [U_5058,U_5057] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5057),hAPP(c_Nat_OSuc,U_5058)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5057),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5058),
inference(definitional_conversion,[status(esa)],[f_1307_2]) ).
cnf(f_1307_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5057),hAPP(c_Nat_OSuc,U_5058)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5057),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5058),
inference(clausify,[status(thm)],[f_1307_3]) ).
fof(f_1308_1,plain,
! [V_Pa_2,V_n_2] :
( ( ? [B_m] :
( hBOOL(hAPP(V_Pa_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ 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))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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))) )
| ! [B_m] :
( ~ hBOOL(hAPP(V_Pa_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat__less]) ).
fof(f_1308_2,plain,
! [U_5064,U_5063] :
( ( ? [U_5062] :
( hBOOL(hAPP(U_5064,U_5062))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5062),U_5063)) )
| ! [U_5061] :
( ~ hBOOL(hAPP(U_5064,U_5061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5063))) ) )
& ( ? [U_5060] :
( hBOOL(hAPP(U_5064,U_5060))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5060),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5063))) )
| ! [U_5059] :
( ~ hBOOL(hAPP(U_5064,U_5059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5059),U_5063)) ) ) ),
inference(variable_rename,[status(thm)],[f_1308_1]) ).
fof(f_1308_3,plain,
( ! [U_5068,U_5066] :
( ? [U_5062] :
( hBOOL(hAPP(U_5068,U_5062))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5062),U_5066)) )
| ! [U_5061] :
( ~ hBOOL(hAPP(U_5068,U_5061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5066))) ) )
& ! [U_5067,U_5065] :
( ? [U_5060] :
( hBOOL(hAPP(U_5067,U_5060))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5060),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5065))) )
| ! [U_5059] :
( ~ hBOOL(hAPP(U_5067,U_5059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5059),U_5065)) ) ) ),
inference(miniscope,[status(thm)],[f_1308_2]) ).
fof(f_1308_4,plain,
( ! [U_5068,U_5066] :
( ? [U_5062] :
( hBOOL(hAPP(U_5068,U_5062))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5062),U_5066)) )
| ! [U_5061] :
( ~ hBOOL(hAPP(U_5068,U_5061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5066))) ) )
& ! [U_5067,U_5065] :
( ( hBOOL(hAPP(U_5067,sK113(U_5067,U_5065)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK113(U_5067,U_5065)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5065))) )
| ! [U_5059] :
( ~ hBOOL(hAPP(U_5067,U_5059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5059),U_5065)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_5060,sK113(U_5067,U_5065))],[f_1308_3]) ).
fof(f_1308_5,plain,
( ! [U_5068,U_5066] :
( ( hBOOL(hAPP(U_5068,sK114(U_5068,U_5066)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK114(U_5068,U_5066)),U_5066)) )
| ! [U_5061] :
( ~ hBOOL(hAPP(U_5068,U_5061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5066))) ) )
& ! [U_5067,U_5065] :
( ( hBOOL(hAPP(U_5067,sK113(U_5067,U_5065)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK113(U_5067,U_5065)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5065))) )
| ! [U_5059] :
( ~ hBOOL(hAPP(U_5067,U_5059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5059),U_5065)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_5062,sK114(U_5068,U_5066))],[f_1308_4]) ).
fof(f_1308_6,plain,
( ! [U_5068,U_5066] :
( hBOOL(hAPP(U_5068,sK114(U_5068,U_5066)))
| ~ sP354(U_5068,U_5066) )
& ! [U_5068,U_5066] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK114(U_5068,U_5066)),U_5066))
| ~ sP354(U_5068,U_5066) )
& ! [U_5065,U_5067] :
( hBOOL(hAPP(U_5067,sK113(U_5067,U_5065)))
| ~ sP353(U_5065,U_5067) )
& ! [U_5065,U_5067] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK113(U_5067,U_5065)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5065)))
| ~ sP353(U_5065,U_5067) )
& ! [U_5061,U_5068,U_5066] :
( sP354(U_5068,U_5066)
| ~ hBOOL(hAPP(U_5068,U_5061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5066))) )
& ! [U_5059,U_5065,U_5067] :
( sP353(U_5065,U_5067)
| ~ hBOOL(hAPP(U_5067,U_5059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5059),U_5065)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP353,sP354])],[f_1308_5]) ).
cnf(f_1308_7,plain,
( sP353(U_5065,U_5067)
| ~ hBOOL(hAPP(U_5067,U_5059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5059),U_5065)) ),
inference(clausify,[status(thm)],[f_1308_6]) ).
cnf(f_1308_8,plain,
( sP354(U_5068,U_5066)
| ~ hBOOL(hAPP(U_5068,U_5061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5066))) ),
inference(clausify,[status(thm)],[f_1308_6]) ).
cnf(f_1308_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK113(U_5067,U_5065)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5065)))
| ~ sP353(U_5065,U_5067) ),
inference(clausify,[status(thm)],[f_1308_6]) ).
cnf(f_1308_10,plain,
( hBOOL(hAPP(U_5067,sK113(U_5067,U_5065)))
| ~ sP353(U_5065,U_5067) ),
inference(clausify,[status(thm)],[f_1308_6]) ).
cnf(f_1308_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK114(U_5068,U_5066)),U_5066))
| ~ sP354(U_5068,U_5066) ),
inference(clausify,[status(thm)],[f_1308_6]) ).
cnf(f_1308_12,plain,
( hBOOL(hAPP(U_5068,sK114(U_5068,U_5066)))
| ~ sP354(U_5068,U_5066) ),
inference(clausify,[status(thm)],[f_1308_6]) ).
fof(f_1309_1,plain,
! [V_Pa_2,V_n_2] :
( ( ! [B_m] :
( hBOOL(hAPP(V_Pa_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& 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))) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ 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))) )
| ? [B_m] :
( ~ hBOOL(hAPP(V_Pa_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat__less]) ).
fof(f_1309_2,plain,
! [U_5074,U_5073] :
( ( ! [U_5072] :
( hBOOL(hAPP(U_5074,U_5072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5072),U_5073)) )
| ? [U_5071] :
( ~ hBOOL(hAPP(U_5074,U_5071))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5071),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5073))) ) )
& ( ! [U_5070] :
( hBOOL(hAPP(U_5074,U_5070))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5070),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5073))) )
| ? [U_5069] :
( ~ hBOOL(hAPP(U_5074,U_5069))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5069),U_5073)) ) ) ),
inference(variable_rename,[status(thm)],[f_1309_1]) ).
fof(f_1309_3,plain,
( ! [U_5078,U_5076] :
( ! [U_5072] :
( hBOOL(hAPP(U_5078,U_5072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5072),U_5076)) )
| ? [U_5071] :
( ~ hBOOL(hAPP(U_5078,U_5071))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5071),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5076))) ) )
& ! [U_5077,U_5075] :
( ! [U_5070] :
( hBOOL(hAPP(U_5077,U_5070))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5070),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5075))) )
| ? [U_5069] :
( ~ hBOOL(hAPP(U_5077,U_5069))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5069),U_5075)) ) ) ),
inference(miniscope,[status(thm)],[f_1309_2]) ).
fof(f_1309_4,plain,
( ! [U_5078,U_5076] :
( ! [U_5072] :
( hBOOL(hAPP(U_5078,U_5072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5072),U_5076)) )
| ? [U_5071] :
( ~ hBOOL(hAPP(U_5078,U_5071))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5071),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5076))) ) )
& ! [U_5077,U_5075] :
( ! [U_5070] :
( hBOOL(hAPP(U_5077,U_5070))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5070),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5075))) )
| ( ~ hBOOL(hAPP(U_5077,sK115(U_5077,U_5075)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK115(U_5077,U_5075)),U_5075)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_5069,sK115(U_5077,U_5075))],[f_1309_3]) ).
fof(f_1309_5,plain,
( ! [U_5078,U_5076] :
( ! [U_5072] :
( hBOOL(hAPP(U_5078,U_5072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5072),U_5076)) )
| ( ~ hBOOL(hAPP(U_5078,sK116(U_5078,U_5076)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK116(U_5078,U_5076)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5076))) ) )
& ! [U_5077,U_5075] :
( ! [U_5070] :
( hBOOL(hAPP(U_5077,U_5070))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5070),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5075))) )
| ( ~ hBOOL(hAPP(U_5077,sK115(U_5077,U_5075)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK115(U_5077,U_5075)),U_5075)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_5071,sK116(U_5078,U_5076))],[f_1309_4]) ).
fof(f_1309_6,plain,
( ! [U_5078,U_5076] :
( ~ hBOOL(hAPP(U_5078,sK116(U_5078,U_5076)))
| ~ sP356(U_5078,U_5076) )
& ! [U_5078,U_5076] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK116(U_5078,U_5076)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5076)))
| ~ sP356(U_5078,U_5076) )
& ! [U_5075,U_5077] :
( ~ hBOOL(hAPP(U_5077,sK115(U_5077,U_5075)))
| ~ sP355(U_5075,U_5077) )
& ! [U_5075,U_5077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK115(U_5077,U_5075)),U_5075))
| ~ sP355(U_5075,U_5077) )
& ! [U_5078,U_5072,U_5076] :
( hBOOL(hAPP(U_5078,U_5072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5072),U_5076))
| sP356(U_5078,U_5076) )
& ! [U_5070,U_5075,U_5077] :
( hBOOL(hAPP(U_5077,U_5070))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5070),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5075)))
| sP355(U_5075,U_5077) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP355,sP356])],[f_1309_5]) ).
cnf(f_1309_7,plain,
( hBOOL(hAPP(U_5077,U_5070))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5070),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5075)))
| sP355(U_5075,U_5077) ),
inference(clausify,[status(thm)],[f_1309_6]) ).
cnf(f_1309_8,plain,
( hBOOL(hAPP(U_5078,U_5072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5072),U_5076))
| sP356(U_5078,U_5076) ),
inference(clausify,[status(thm)],[f_1309_6]) ).
cnf(f_1309_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK115(U_5077,U_5075)),U_5075))
| ~ sP355(U_5075,U_5077) ),
inference(clausify,[status(thm)],[f_1309_6]) ).
cnf(f_1309_10,plain,
( ~ hBOOL(hAPP(U_5077,sK115(U_5077,U_5075)))
| ~ sP355(U_5075,U_5077) ),
inference(clausify,[status(thm)],[f_1309_6]) ).
cnf(f_1309_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK116(U_5078,U_5076)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5076)))
| ~ sP356(U_5078,U_5076) ),
inference(clausify,[status(thm)],[f_1309_6]) ).
cnf(f_1309_12,plain,
( ~ hBOOL(hAPP(U_5078,sK116(U_5078,U_5076)))
| ~ sP356(U_5078,U_5076) ),
inference(clausify,[status(thm)],[f_1309_6]) ).
fof(f_1310_1,plain,
! [V_Pa_2,V_n_2] :
( ( ? [B_m] :
( hBOOL(hAPP(V_Pa_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ 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))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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))) )
| ! [B_m] :
( ~ hBOOL(hAPP(V_Pa_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq]) ).
fof(f_1310_2,plain,
! [U_5084,U_5083] :
( ( ? [U_5082] :
( hBOOL(hAPP(U_5084,U_5082))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5082),U_5083)) )
| ! [U_5081] :
( ~ hBOOL(hAPP(U_5084,U_5081))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5081),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5083))) ) )
& ( ? [U_5080] :
( hBOOL(hAPP(U_5084,U_5080))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5080),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5083))) )
| ! [U_5079] :
( ~ hBOOL(hAPP(U_5084,U_5079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5079),U_5083)) ) ) ),
inference(variable_rename,[status(thm)],[f_1310_1]) ).
fof(f_1310_3,plain,
( ! [U_5088,U_5086] :
( ? [U_5082] :
( hBOOL(hAPP(U_5088,U_5082))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5082),U_5086)) )
| ! [U_5081] :
( ~ hBOOL(hAPP(U_5088,U_5081))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5081),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5086))) ) )
& ! [U_5087,U_5085] :
( ? [U_5080] :
( hBOOL(hAPP(U_5087,U_5080))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5080),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5085))) )
| ! [U_5079] :
( ~ hBOOL(hAPP(U_5087,U_5079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5079),U_5085)) ) ) ),
inference(miniscope,[status(thm)],[f_1310_2]) ).
fof(f_1310_4,plain,
( ! [U_5088,U_5086] :
( ? [U_5082] :
( hBOOL(hAPP(U_5088,U_5082))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5082),U_5086)) )
| ! [U_5081] :
( ~ hBOOL(hAPP(U_5088,U_5081))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5081),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5086))) ) )
& ! [U_5087,U_5085] :
( ( hBOOL(hAPP(U_5087,sK117(U_5087,U_5085)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK117(U_5087,U_5085)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5085))) )
| ! [U_5079] :
( ~ hBOOL(hAPP(U_5087,U_5079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5079),U_5085)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_5080,sK117(U_5087,U_5085))],[f_1310_3]) ).
fof(f_1310_5,plain,
( ! [U_5088,U_5086] :
( ( hBOOL(hAPP(U_5088,sK118(U_5088,U_5086)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK118(U_5088,U_5086)),U_5086)) )
| ! [U_5081] :
( ~ hBOOL(hAPP(U_5088,U_5081))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5081),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5086))) ) )
& ! [U_5087,U_5085] :
( ( hBOOL(hAPP(U_5087,sK117(U_5087,U_5085)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK117(U_5087,U_5085)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5085))) )
| ! [U_5079] :
( ~ hBOOL(hAPP(U_5087,U_5079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5079),U_5085)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_5082,sK118(U_5088,U_5086))],[f_1310_4]) ).
fof(f_1310_6,plain,
( ! [U_5088,U_5086] :
( hBOOL(hAPP(U_5088,sK118(U_5088,U_5086)))
| ~ sP358(U_5088,U_5086) )
& ! [U_5088,U_5086] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK118(U_5088,U_5086)),U_5086))
| ~ sP358(U_5088,U_5086) )
& ! [U_5085,U_5087] :
( hBOOL(hAPP(U_5087,sK117(U_5087,U_5085)))
| ~ sP357(U_5085,U_5087) )
& ! [U_5085,U_5087] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK117(U_5087,U_5085)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5085)))
| ~ sP357(U_5085,U_5087) )
& ! [U_5081,U_5088,U_5086] :
( sP358(U_5088,U_5086)
| ~ hBOOL(hAPP(U_5088,U_5081))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5081),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5086))) )
& ! [U_5079,U_5085,U_5087] :
( sP357(U_5085,U_5087)
| ~ hBOOL(hAPP(U_5087,U_5079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5079),U_5085)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP357,sP358])],[f_1310_5]) ).
cnf(f_1310_7,plain,
( sP357(U_5085,U_5087)
| ~ hBOOL(hAPP(U_5087,U_5079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5079),U_5085)) ),
inference(clausify,[status(thm)],[f_1310_6]) ).
cnf(f_1310_8,plain,
( sP358(U_5088,U_5086)
| ~ hBOOL(hAPP(U_5088,U_5081))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5081),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5086))) ),
inference(clausify,[status(thm)],[f_1310_6]) ).
cnf(f_1310_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK117(U_5087,U_5085)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5085)))
| ~ sP357(U_5085,U_5087) ),
inference(clausify,[status(thm)],[f_1310_6]) ).
cnf(f_1310_10,plain,
( hBOOL(hAPP(U_5087,sK117(U_5087,U_5085)))
| ~ sP357(U_5085,U_5087) ),
inference(clausify,[status(thm)],[f_1310_6]) ).
cnf(f_1310_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK118(U_5088,U_5086)),U_5086))
| ~ sP358(U_5088,U_5086) ),
inference(clausify,[status(thm)],[f_1310_6]) ).
cnf(f_1310_12,plain,
( hBOOL(hAPP(U_5088,sK118(U_5088,U_5086)))
| ~ sP358(U_5088,U_5086) ),
inference(clausify,[status(thm)],[f_1310_6]) ).
fof(f_1311_1,plain,
! [V_Pa_2,V_n_2] :
( ( ! [B_m] :
( hBOOL(hAPP(V_Pa_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& 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))) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ 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))) )
| ? [B_m] :
( ~ hBOOL(hAPP(V_Pa_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat__less__eq]) ).
fof(f_1311_2,plain,
! [U_5094,U_5093] :
( ( ! [U_5092] :
( hBOOL(hAPP(U_5094,U_5092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5092),U_5093)) )
| ? [U_5091] :
( ~ hBOOL(hAPP(U_5094,U_5091))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5091),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5093))) ) )
& ( ! [U_5090] :
( hBOOL(hAPP(U_5094,U_5090))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5090),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5093))) )
| ? [U_5089] :
( ~ hBOOL(hAPP(U_5094,U_5089))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5089),U_5093)) ) ) ),
inference(variable_rename,[status(thm)],[f_1311_1]) ).
fof(f_1311_3,plain,
( ! [U_5098,U_5096] :
( ! [U_5092] :
( hBOOL(hAPP(U_5098,U_5092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5092),U_5096)) )
| ? [U_5091] :
( ~ hBOOL(hAPP(U_5098,U_5091))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5091),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5096))) ) )
& ! [U_5097,U_5095] :
( ! [U_5090] :
( hBOOL(hAPP(U_5097,U_5090))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5090),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5095))) )
| ? [U_5089] :
( ~ hBOOL(hAPP(U_5097,U_5089))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5089),U_5095)) ) ) ),
inference(miniscope,[status(thm)],[f_1311_2]) ).
fof(f_1311_4,plain,
( ! [U_5098,U_5096] :
( ! [U_5092] :
( hBOOL(hAPP(U_5098,U_5092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5092),U_5096)) )
| ? [U_5091] :
( ~ hBOOL(hAPP(U_5098,U_5091))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5091),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5096))) ) )
& ! [U_5097,U_5095] :
( ! [U_5090] :
( hBOOL(hAPP(U_5097,U_5090))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5090),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5095))) )
| ( ~ hBOOL(hAPP(U_5097,sK119(U_5097,U_5095)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK119(U_5097,U_5095)),U_5095)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_5089,sK119(U_5097,U_5095))],[f_1311_3]) ).
fof(f_1311_5,plain,
( ! [U_5098,U_5096] :
( ! [U_5092] :
( hBOOL(hAPP(U_5098,U_5092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5092),U_5096)) )
| ( ~ hBOOL(hAPP(U_5098,sK120(U_5098,U_5096)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK120(U_5098,U_5096)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5096))) ) )
& ! [U_5097,U_5095] :
( ! [U_5090] :
( hBOOL(hAPP(U_5097,U_5090))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5090),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5095))) )
| ( ~ hBOOL(hAPP(U_5097,sK119(U_5097,U_5095)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK119(U_5097,U_5095)),U_5095)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_5091,sK120(U_5098,U_5096))],[f_1311_4]) ).
fof(f_1311_6,plain,
( ! [U_5098,U_5096] :
( ~ hBOOL(hAPP(U_5098,sK120(U_5098,U_5096)))
| ~ sP360(U_5098,U_5096) )
& ! [U_5098,U_5096] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK120(U_5098,U_5096)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5096)))
| ~ sP360(U_5098,U_5096) )
& ! [U_5095,U_5097] :
( ~ hBOOL(hAPP(U_5097,sK119(U_5097,U_5095)))
| ~ sP359(U_5095,U_5097) )
& ! [U_5095,U_5097] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK119(U_5097,U_5095)),U_5095))
| ~ sP359(U_5095,U_5097) )
& ! [U_5092,U_5098,U_5096] :
( hBOOL(hAPP(U_5098,U_5092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5092),U_5096))
| sP360(U_5098,U_5096) )
& ! [U_5090,U_5095,U_5097] :
( hBOOL(hAPP(U_5097,U_5090))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5090),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5095)))
| sP359(U_5095,U_5097) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP359,sP360])],[f_1311_5]) ).
cnf(f_1311_7,plain,
( hBOOL(hAPP(U_5097,U_5090))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5090),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5095)))
| sP359(U_5095,U_5097) ),
inference(clausify,[status(thm)],[f_1311_6]) ).
cnf(f_1311_8,plain,
( hBOOL(hAPP(U_5098,U_5092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5092),U_5096))
| sP360(U_5098,U_5096) ),
inference(clausify,[status(thm)],[f_1311_6]) ).
cnf(f_1311_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK119(U_5097,U_5095)),U_5095))
| ~ sP359(U_5095,U_5097) ),
inference(clausify,[status(thm)],[f_1311_6]) ).
cnf(f_1311_10,plain,
( ~ hBOOL(hAPP(U_5097,sK119(U_5097,U_5095)))
| ~ sP359(U_5095,U_5097) ),
inference(clausify,[status(thm)],[f_1311_6]) ).
cnf(f_1311_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK120(U_5098,U_5096)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5096)))
| ~ sP360(U_5098,U_5096) ),
inference(clausify,[status(thm)],[f_1311_6]) ).
cnf(f_1311_12,plain,
( ~ hBOOL(hAPP(U_5098,sK120(U_5098,U_5096)))
| ~ sP360(U_5098,U_5096) ),
inference(clausify,[status(thm)],[f_1311_6]) ).
fof(f_1312_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).
fof(f_1312_2,plain,
! [U_5100,U_5099] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),U_5100),U_5100)),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),U_5100),c_Groups_Ozero__class_Ozero(U_5099))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),U_5100),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),U_5100),U_5100)),c_Groups_Ozero__class_Ozero(U_5099))) ) )
| ~ class_Rings_Olinordered__idom(U_5099) ),
inference(variable_rename,[status(thm)],[f_1312_1]) ).
fof(f_1312_3,plain,
( ! [U_5100,U_5099] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),U_5100),U_5100)),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),U_5100),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ sP361(U_5100,U_5099) )
& ! [U_5100,U_5099] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),U_5100),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),U_5100),U_5100)),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ sP361(U_5100,U_5099) )
& ! [U_5100,U_5099] :
( sP361(U_5100,U_5099)
| ~ class_Rings_Olinordered__idom(U_5099) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP361])],[f_1312_2]) ).
cnf(f_1312_4,plain,
( sP361(U_5100,U_5099)
| ~ class_Rings_Olinordered__idom(U_5099) ),
inference(clausify,[status(thm)],[f_1312_3]) ).
cnf(f_1312_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),U_5100),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),U_5100),U_5100)),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ sP361(U_5100,U_5099) ),
inference(clausify,[status(thm)],[f_1312_3]) ).
cnf(f_1312_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),U_5100),U_5100)),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5099),U_5100),c_Groups_Ozero__class_Ozero(U_5099)))
| ~ sP361(U_5100,U_5099) ),
inference(clausify,[status(thm)],[f_1312_3]) ).
fof(f_1313_1,plain,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( ( ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) )
| ~ c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).
fof(f_1313_2,plain,
! [U_5107,U_5106,U_5105,U_5104,U_5103,U_5102,U_5101] :
( ( ( hAPP(hAPP(U_5105,U_5107),U_5106) = U_5104
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5102),U_5106)) )
& ( hAPP(hAPP(U_5105,U_5107),U_5106) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5101,U_5102,U_5103),U_5107),U_5104),U_5106)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5102),U_5106)) ) )
| ~ c_Big__Operators_Ocomm__monoid__big(U_5101,U_5102,U_5103,U_5104,U_5105) ),
inference(variable_rename,[status(thm)],[f_1313_1]) ).
fof(f_1313_3,plain,
( ! [U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107] :
( hAPP(hAPP(U_5105,U_5107),U_5106) = U_5104
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5102),U_5106))
| ~ sP362(U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107) )
& ! [U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107] :
( hAPP(hAPP(U_5105,U_5107),U_5106) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5101,U_5102,U_5103),U_5107),U_5104),U_5106)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5102),U_5106))
| ~ sP362(U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107) )
& ! [U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107] :
( sP362(U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107)
| ~ c_Big__Operators_Ocomm__monoid__big(U_5101,U_5102,U_5103,U_5104,U_5105) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP362])],[f_1313_2]) ).
cnf(f_1313_4,plain,
( sP362(U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107)
| ~ c_Big__Operators_Ocomm__monoid__big(U_5101,U_5102,U_5103,U_5104,U_5105) ),
inference(clausify,[status(thm)],[f_1313_3]) ).
cnf(f_1313_5,plain,
( hAPP(hAPP(U_5105,U_5107),U_5106) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5101,U_5102,U_5103),U_5107),U_5104),U_5106)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5102),U_5106))
| ~ sP362(U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107) ),
inference(clausify,[status(thm)],[f_1313_3]) ).
cnf(f_1313_6,plain,
( hAPP(hAPP(U_5105,U_5107),U_5106) = U_5104
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5102),U_5106))
| ~ sP362(U_5101,U_5103,U_5102,U_5104,U_5105,U_5106,U_5107) ),
inference(clausify,[status(thm)],[f_1313_3]) ).
fof(f_1314_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [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))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter__neutral]) ).
fof(f_1314_2,plain,
! [U_5111,U_5110,U_5109] :
( hAPP(c_Finite__Set_Ocard(U_5109),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5109,tc_HOL_Obool)),U_5110),U_5111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5109),U_5110)),hAPP(c_Finite__Set_Ocard(U_5109),U_5111))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [U_5108] : hBOOL(hAPP(hAPP(c_member(U_5109),U_5108),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5109,tc_HOL_Obool)),U_5110),U_5111))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5109),U_5111))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5109),U_5110)) ),
inference(variable_rename,[status(thm)],[f_1314_1]) ).
fof(f_1314_3,plain,
! [U_5111,U_5110,U_5109] :
( hAPP(c_Finite__Set_Ocard(U_5109),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5109,tc_HOL_Obool)),U_5110),U_5111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5109),U_5110)),hAPP(c_Finite__Set_Ocard(U_5109),U_5111))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_5109),sK121(U_5111,U_5110,U_5109)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5109,tc_HOL_Obool)),U_5110),U_5111))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5109),U_5111))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5109),U_5110)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_5108,sK121(U_5111,U_5110,U_5109))],[f_1314_2]) ).
fof(f_1314_4,plain,
( ! [U_5110,U_5109,U_5111] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP363(U_5110,U_5109,U_5111) )
& ! [U_5110,U_5109,U_5111] :
( hBOOL(hAPP(hAPP(c_member(U_5109),sK121(U_5111,U_5110,U_5109)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5109,tc_HOL_Obool)),U_5110),U_5111)))
| ~ sP363(U_5110,U_5109,U_5111) )
& ! [U_5110,U_5109,U_5111] :
( hAPP(c_Finite__Set_Ocard(U_5109),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5109,tc_HOL_Obool)),U_5110),U_5111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5109),U_5110)),hAPP(c_Finite__Set_Ocard(U_5109),U_5111))
| sP363(U_5110,U_5109,U_5111)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5109),U_5111))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5109),U_5110)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP363])],[f_1314_3]) ).
cnf(f_1314_5,plain,
( hAPP(c_Finite__Set_Ocard(U_5109),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5109,tc_HOL_Obool)),U_5110),U_5111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5109),U_5110)),hAPP(c_Finite__Set_Ocard(U_5109),U_5111))
| sP363(U_5110,U_5109,U_5111)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5109),U_5111))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5109),U_5110)) ),
inference(clausify,[status(thm)],[f_1314_4]) ).
cnf(f_1314_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5109),sK121(U_5111,U_5110,U_5109)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5109,tc_HOL_Obool)),U_5110),U_5111)))
| ~ sP363(U_5110,U_5109,U_5111) ),
inference(clausify,[status(thm)],[f_1314_4]) ).
cnf(f_1314_7,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP363(U_5110,U_5109,U_5111) ),
inference(clausify,[status(thm)],[f_1314_4]) ).
fof(f_1315_1,plain,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).
fof(f_1315_2,plain,
! [U_5118,U_5117,U_5116,U_5115,U_5114,U_5113,U_5112] :
( hAPP(hAPP(U_5116,U_5118),U_5117) = U_5115
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5113),U_5117))
| ~ c_Big__Operators_Ocomm__monoid__big(U_5112,U_5113,U_5114,U_5115,U_5116) ),
inference(variable_rename,[status(thm)],[f_1315_1]) ).
fof(f_1315_3,plain,
! [U_5118,U_5117,U_5116,U_5115,U_5114,U_5113] :
( ! [U_5112] : ~ c_Big__Operators_Ocomm__monoid__big(U_5112,U_5113,U_5114,U_5115,U_5116)
| hAPP(hAPP(U_5116,U_5118),U_5117) = U_5115
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5113),U_5117)) ),
inference(miniscope,[status(thm)],[f_1315_2]) ).
fof(f_1315_4,plain,
! [U_5117,U_5114,U_5113,U_5112,U_5115,U_5116,U_5118] :
( ~ c_Big__Operators_Ocomm__monoid__big(U_5112,U_5113,U_5114,U_5115,U_5116)
| hAPP(hAPP(U_5116,U_5118),U_5117) = U_5115
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5113),U_5117)) ),
inference(definitional_conversion,[status(esa)],[f_1315_3]) ).
cnf(f_1315_5,plain,
( ~ c_Big__Operators_Ocomm__monoid__big(U_5112,U_5113,U_5114,U_5115,U_5116)
| hAPP(hAPP(U_5116,U_5118),U_5117) = U_5115
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5113),U_5117)) ),
inference(clausify,[status(thm)],[f_1315_4]) ).
fof(f_1316_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).
fof(f_1316_2,plain,
! [U_5120,U_5119] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5119),U_5120),U_5120) = c_Groups_Ozero__class_Ozero(U_5119)
| U_5120 != c_Groups_Ozero__class_Ozero(U_5119) )
& ( U_5120 = c_Groups_Ozero__class_Ozero(U_5119)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5119),U_5120),U_5120) != c_Groups_Ozero__class_Ozero(U_5119) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_5119) ),
inference(variable_rename,[status(thm)],[f_1316_1]) ).
fof(f_1316_3,plain,
( ! [U_5119,U_5120] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5119),U_5120),U_5120) = c_Groups_Ozero__class_Ozero(U_5119)
| U_5120 != c_Groups_Ozero__class_Ozero(U_5119)
| ~ sP364(U_5119,U_5120) )
& ! [U_5119,U_5120] :
( U_5120 = c_Groups_Ozero__class_Ozero(U_5119)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5119),U_5120),U_5120) != c_Groups_Ozero__class_Ozero(U_5119)
| ~ sP364(U_5119,U_5120) )
& ! [U_5119,U_5120] :
( sP364(U_5119,U_5120)
| ~ class_Groups_Olinordered__ab__group__add(U_5119) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP364])],[f_1316_2]) ).
cnf(f_1316_4,plain,
( sP364(U_5119,U_5120)
| ~ class_Groups_Olinordered__ab__group__add(U_5119) ),
inference(clausify,[status(thm)],[f_1316_3]) ).
cnf(f_1316_5,plain,
( U_5120 = c_Groups_Ozero__class_Ozero(U_5119)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5119),U_5120),U_5120) != c_Groups_Ozero__class_Ozero(U_5119)
| ~ sP364(U_5119,U_5120) ),
inference(clausify,[status(thm)],[f_1316_3]) ).
cnf(f_1316_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5119),U_5120),U_5120) = c_Groups_Ozero__class_Ozero(U_5119)
| U_5120 != c_Groups_Ozero__class_Ozero(U_5119)
| ~ sP364(U_5119,U_5120) ),
inference(clausify,[status(thm)],[f_1316_3]) ).
fof(f_1317_1,plain,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( 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)))
| ? [B_b] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b)))
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ class_Groups_Oordered__comm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono2]) ).
fof(f_1317_2,plain,
! [U_5126,U_5125,U_5124,U_5123,U_5122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5122),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5123,U_5122),U_5126),U_5125)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5123,U_5122),U_5126),U_5124)))
| ? [U_5121] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5122),c_Groups_Ozero__class_Ozero(U_5122)),hAPP(U_5126,U_5121)))
& hBOOL(hAPP(hAPP(c_member(U_5123),U_5121),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5123,tc_HOL_Obool)),U_5124),U_5125))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5123,tc_HOL_Obool)),U_5125),U_5124))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5123),U_5124))
| ~ class_Groups_Oordered__comm__monoid__add(U_5122) ),
inference(variable_rename,[status(thm)],[f_1317_1]) ).
fof(f_1317_3,plain,
! [U_5126,U_5125,U_5124,U_5123,U_5122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5122),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5123,U_5122),U_5126),U_5125)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5123,U_5122),U_5126),U_5124)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5122),c_Groups_Ozero__class_Ozero(U_5122)),hAPP(U_5126,sK122(U_5126,U_5125,U_5124,U_5123,U_5122))))
& hBOOL(hAPP(hAPP(c_member(U_5123),sK122(U_5126,U_5125,U_5124,U_5123,U_5122)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5123,tc_HOL_Obool)),U_5124),U_5125))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5123,tc_HOL_Obool)),U_5125),U_5124))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5123),U_5124))
| ~ class_Groups_Oordered__comm__monoid__add(U_5122) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_5121,sK122(U_5126,U_5125,U_5124,U_5123,U_5122))],[f_1317_2]) ).
fof(f_1317_4,plain,
( ! [U_5123,U_5122,U_5124,U_5125,U_5126] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5122),c_Groups_Ozero__class_Ozero(U_5122)),hAPP(U_5126,sK122(U_5126,U_5125,U_5124,U_5123,U_5122))))
| ~ sP365(U_5123,U_5122,U_5124,U_5125,U_5126) )
& ! [U_5123,U_5122,U_5124,U_5125,U_5126] :
( hBOOL(hAPP(hAPP(c_member(U_5123),sK122(U_5126,U_5125,U_5124,U_5123,U_5122)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5123,tc_HOL_Obool)),U_5124),U_5125)))
| ~ sP365(U_5123,U_5122,U_5124,U_5125,U_5126) )
& ! [U_5123,U_5122,U_5124,U_5125,U_5126] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5122),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5123,U_5122),U_5126),U_5125)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5123,U_5122),U_5126),U_5124)))
| sP365(U_5123,U_5122,U_5124,U_5125,U_5126)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5123,tc_HOL_Obool)),U_5125),U_5124))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5123),U_5124))
| ~ class_Groups_Oordered__comm__monoid__add(U_5122) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP365])],[f_1317_3]) ).
cnf(f_1317_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5122),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5123,U_5122),U_5126),U_5125)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5123,U_5122),U_5126),U_5124)))
| sP365(U_5123,U_5122,U_5124,U_5125,U_5126)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5123,tc_HOL_Obool)),U_5125),U_5124))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5123),U_5124))
| ~ class_Groups_Oordered__comm__monoid__add(U_5122) ),
inference(clausify,[status(thm)],[f_1317_4]) ).
cnf(f_1317_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5123),sK122(U_5126,U_5125,U_5124,U_5123,U_5122)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5123,tc_HOL_Obool)),U_5124),U_5125)))
| ~ sP365(U_5123,U_5122,U_5124,U_5125,U_5126) ),
inference(clausify,[status(thm)],[f_1317_4]) ).
cnf(f_1317_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5122),c_Groups_Ozero__class_Ozero(U_5122)),hAPP(U_5126,sK122(U_5126,U_5125,U_5124,U_5123,U_5122))))
| ~ sP365(U_5123,U_5122,U_5124,U_5125,U_5126) ),
inference(clausify,[status(thm)],[f_1317_4]) ).
fof(f_1318_1,plain,
! [V_f_2,V_T_2,V_S_2,T_b,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)),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))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& 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))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__Un__one]) ).
fof(f_1318_2,plain,
! [U_5132,U_5131,U_5130,U_5129,U_5128] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5129,tc_HOL_Obool)),U_5130),U_5131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5128),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),U_5130)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),U_5131))
| ? [U_5127] :
( hAPP(U_5132,U_5127) != c_Groups_Oone__class_Oone(U_5128)
& hBOOL(hAPP(hAPP(c_member(U_5129),U_5127),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5129,tc_HOL_Obool)),U_5130),U_5131))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5129),U_5131))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5129),U_5130))
| ~ class_Groups_Ocomm__monoid__mult(U_5128) ),
inference(variable_rename,[status(thm)],[f_1318_1]) ).
fof(f_1318_3,plain,
! [U_5132,U_5131,U_5130,U_5129,U_5128] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5129,tc_HOL_Obool)),U_5130),U_5131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5128),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),U_5130)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),U_5131))
| ( hAPP(U_5132,sK123(U_5132,U_5131,U_5130,U_5129,U_5128)) != c_Groups_Oone__class_Oone(U_5128)
& hBOOL(hAPP(hAPP(c_member(U_5129),sK123(U_5132,U_5131,U_5130,U_5129,U_5128)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5129,tc_HOL_Obool)),U_5130),U_5131))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5129),U_5131))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5129),U_5130))
| ~ class_Groups_Ocomm__monoid__mult(U_5128) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_5127,sK123(U_5132,U_5131,U_5130,U_5129,U_5128))],[f_1318_2]) ).
fof(f_1318_4,plain,
( ! [U_5128,U_5129,U_5130,U_5131,U_5132] :
( hAPP(U_5132,sK123(U_5132,U_5131,U_5130,U_5129,U_5128)) != c_Groups_Oone__class_Oone(U_5128)
| ~ sP366(U_5128,U_5129,U_5130,U_5131,U_5132) )
& ! [U_5128,U_5129,U_5130,U_5131,U_5132] :
( hBOOL(hAPP(hAPP(c_member(U_5129),sK123(U_5132,U_5131,U_5130,U_5129,U_5128)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5129,tc_HOL_Obool)),U_5130),U_5131)))
| ~ sP366(U_5128,U_5129,U_5130,U_5131,U_5132) )
& ! [U_5128,U_5129,U_5130,U_5131,U_5132] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5129,tc_HOL_Obool)),U_5130),U_5131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5128),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),U_5130)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),U_5131))
| sP366(U_5128,U_5129,U_5130,U_5131,U_5132)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5129),U_5131))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5129),U_5130))
| ~ class_Groups_Ocomm__monoid__mult(U_5128) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP366])],[f_1318_3]) ).
cnf(f_1318_5,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5129,tc_HOL_Obool)),U_5130),U_5131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5128),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),U_5130)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5128,U_5129,c_Groups_Otimes__class_Otimes(U_5128)),U_5132),c_Groups_Oone__class_Oone(U_5128)),U_5131))
| sP366(U_5128,U_5129,U_5130,U_5131,U_5132)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5129),U_5131))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5129),U_5130))
| ~ class_Groups_Ocomm__monoid__mult(U_5128) ),
inference(clausify,[status(thm)],[f_1318_4]) ).
cnf(f_1318_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5129),sK123(U_5132,U_5131,U_5130,U_5129,U_5128)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5129,tc_HOL_Obool)),U_5130),U_5131)))
| ~ sP366(U_5128,U_5129,U_5130,U_5131,U_5132) ),
inference(clausify,[status(thm)],[f_1318_4]) ).
cnf(f_1318_7,plain,
( hAPP(U_5132,sK123(U_5132,U_5131,U_5130,U_5129,U_5128)) != c_Groups_Oone__class_Oone(U_5128)
| ~ sP366(U_5128,U_5129,U_5130,U_5131,U_5132) ),
inference(clausify,[status(thm)],[f_1318_4]) ).
fof(f_1319_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,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_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))
| ? [B_x] :
( hAPP(V_g_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
& 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))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Ounion__inter__neutral]) ).
fof(f_1319_2,plain,
! [U_5138,U_5137,U_5136,U_5135,U_5134] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5135,tc_HOL_Obool)),U_5136),U_5137)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5134),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),U_5136)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),U_5137))
| ? [U_5133] :
( hAPP(U_5138,U_5133) != c_Groups_Ozero__class_Ozero(U_5134)
& hBOOL(hAPP(hAPP(c_member(U_5135),U_5133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5135,tc_HOL_Obool)),U_5136),U_5137))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5135),U_5137))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5135),U_5136))
| ~ class_Groups_Ocomm__monoid__add(U_5134) ),
inference(variable_rename,[status(thm)],[f_1319_1]) ).
fof(f_1319_3,plain,
! [U_5138,U_5137,U_5136,U_5135,U_5134] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5135,tc_HOL_Obool)),U_5136),U_5137)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5134),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),U_5136)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),U_5137))
| ( hAPP(U_5138,sK124(U_5138,U_5137,U_5136,U_5135,U_5134)) != c_Groups_Ozero__class_Ozero(U_5134)
& hBOOL(hAPP(hAPP(c_member(U_5135),sK124(U_5138,U_5137,U_5136,U_5135,U_5134)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5135,tc_HOL_Obool)),U_5136),U_5137))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5135),U_5137))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5135),U_5136))
| ~ class_Groups_Ocomm__monoid__add(U_5134) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_5133,sK124(U_5138,U_5137,U_5136,U_5135,U_5134))],[f_1319_2]) ).
fof(f_1319_4,plain,
( ! [U_5137,U_5136,U_5134,U_5135,U_5138] :
( hAPP(U_5138,sK124(U_5138,U_5137,U_5136,U_5135,U_5134)) != c_Groups_Ozero__class_Ozero(U_5134)
| ~ sP367(U_5137,U_5136,U_5134,U_5135,U_5138) )
& ! [U_5137,U_5136,U_5134,U_5135,U_5138] :
( hBOOL(hAPP(hAPP(c_member(U_5135),sK124(U_5138,U_5137,U_5136,U_5135,U_5134)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5135,tc_HOL_Obool)),U_5136),U_5137)))
| ~ sP367(U_5137,U_5136,U_5134,U_5135,U_5138) )
& ! [U_5137,U_5136,U_5134,U_5135,U_5138] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5135,tc_HOL_Obool)),U_5136),U_5137)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5134),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),U_5136)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),U_5137))
| sP367(U_5137,U_5136,U_5134,U_5135,U_5138)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5135),U_5137))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5135),U_5136))
| ~ class_Groups_Ocomm__monoid__add(U_5134) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP367])],[f_1319_3]) ).
cnf(f_1319_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5135,tc_HOL_Obool)),U_5136),U_5137)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5134),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),U_5136)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5135,U_5134),U_5138),U_5137))
| sP367(U_5137,U_5136,U_5134,U_5135,U_5138)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5135),U_5137))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5135),U_5136))
| ~ class_Groups_Ocomm__monoid__add(U_5134) ),
inference(clausify,[status(thm)],[f_1319_4]) ).
cnf(f_1319_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5135),sK124(U_5138,U_5137,U_5136,U_5135,U_5134)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5135,tc_HOL_Obool)),U_5136),U_5137)))
| ~ sP367(U_5137,U_5136,U_5134,U_5135,U_5138) ),
inference(clausify,[status(thm)],[f_1319_4]) ).
cnf(f_1319_7,plain,
( hAPP(U_5138,sK124(U_5138,U_5137,U_5136,U_5135,U_5134)) != c_Groups_Ozero__class_Ozero(U_5134)
| ~ sP367(U_5137,U_5136,U_5134,U_5135,U_5138) ),
inference(clausify,[status(thm)],[f_1319_4]) ).
fof(f_1320_1,plain,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( 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))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
& 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))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__zero]) ).
fof(f_1320_2,plain,
! [U_5144,U_5143,U_5142,U_5141,U_5140] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5141,tc_HOL_Obool)),U_5142),U_5143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5140),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),U_5142)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),U_5143))
| ? [U_5139] :
( hAPP(U_5144,U_5139) != c_Groups_Ozero__class_Ozero(U_5140)
& hBOOL(hAPP(hAPP(c_member(U_5141),U_5139),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5141,tc_HOL_Obool)),U_5142),U_5143))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5141),U_5143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5141),U_5142))
| ~ class_Groups_Ocomm__monoid__add(U_5140) ),
inference(variable_rename,[status(thm)],[f_1320_1]) ).
fof(f_1320_3,plain,
! [U_5144,U_5143,U_5142,U_5141,U_5140] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5141,tc_HOL_Obool)),U_5142),U_5143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5140),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),U_5142)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),U_5143))
| ( hAPP(U_5144,sK125(U_5144,U_5143,U_5142,U_5141,U_5140)) != c_Groups_Ozero__class_Ozero(U_5140)
& hBOOL(hAPP(hAPP(c_member(U_5141),sK125(U_5144,U_5143,U_5142,U_5141,U_5140)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5141,tc_HOL_Obool)),U_5142),U_5143))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5141),U_5143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5141),U_5142))
| ~ class_Groups_Ocomm__monoid__add(U_5140) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_5139,sK125(U_5144,U_5143,U_5142,U_5141,U_5140))],[f_1320_2]) ).
fof(f_1320_4,plain,
( ! [U_5141,U_5142,U_5140,U_5143,U_5144] :
( hAPP(U_5144,sK125(U_5144,U_5143,U_5142,U_5141,U_5140)) != c_Groups_Ozero__class_Ozero(U_5140)
| ~ sP368(U_5141,U_5142,U_5140,U_5143,U_5144) )
& ! [U_5141,U_5142,U_5140,U_5143,U_5144] :
( hBOOL(hAPP(hAPP(c_member(U_5141),sK125(U_5144,U_5143,U_5142,U_5141,U_5140)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5141,tc_HOL_Obool)),U_5142),U_5143)))
| ~ sP368(U_5141,U_5142,U_5140,U_5143,U_5144) )
& ! [U_5141,U_5142,U_5140,U_5143,U_5144] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5141,tc_HOL_Obool)),U_5142),U_5143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5140),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),U_5142)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),U_5143))
| sP368(U_5141,U_5142,U_5140,U_5143,U_5144)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5141),U_5143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5141),U_5142))
| ~ class_Groups_Ocomm__monoid__add(U_5140) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP368])],[f_1320_3]) ).
cnf(f_1320_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5141,tc_HOL_Obool)),U_5142),U_5143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5140),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),U_5142)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5141,U_5140),U_5144),U_5143))
| sP368(U_5141,U_5142,U_5140,U_5143,U_5144)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5141),U_5143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5141),U_5142))
| ~ class_Groups_Ocomm__monoid__add(U_5140) ),
inference(clausify,[status(thm)],[f_1320_4]) ).
cnf(f_1320_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5141),sK125(U_5144,U_5143,U_5142,U_5141,U_5140)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5141,tc_HOL_Obool)),U_5142),U_5143)))
| ~ sP368(U_5141,U_5142,U_5140,U_5143,U_5144) ),
inference(clausify,[status(thm)],[f_1320_4]) ).
cnf(f_1320_7,plain,
( hAPP(U_5144,sK125(U_5144,U_5143,U_5142,U_5141,U_5140)) != c_Groups_Ozero__class_Ozero(U_5140)
| ~ sP368(U_5141,U_5142,U_5140,U_5143,U_5144) ),
inference(clausify,[status(thm)],[f_1320_4]) ).
fof(f_1321_1,plain,
! [V_k_2,V_A_2,T_b] :
( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
| ! [B_b,B_B] :
( ( B_B != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(T_b),B_B) != V_k_2
| hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
| V_A_2 != hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) ) )
& ( ? [B_b,B_B] :
( ( B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
& V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) )
| hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != hAPP(c_Nat_OSuc,V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_card__Suc__eq]) ).
fof(f_1321_2,plain,
! [U_5151,U_5150,U_5149] :
( ( hAPP(c_Finite__Set_Ocard(U_5149),U_5150) = hAPP(c_Nat_OSuc,U_5151)
| ! [U_5148,U_5147] :
( ( U_5147 != c_Orderings_Obot__class_Obot(tc_fun(U_5149,tc_HOL_Obool))
& U_5151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_5149),U_5147) != U_5151
| hBOOL(hAPP(hAPP(c_member(U_5149),U_5148),U_5147))
| U_5150 != hAPP(hAPP(c_Set_Oinsert(U_5149),U_5148),U_5147) ) )
& ( ? [U_5146,U_5145] :
( ( U_5145 = c_Orderings_Obot__class_Obot(tc_fun(U_5149,tc_HOL_Obool))
| U_5151 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_5149),U_5145) = U_5151
& ~ hBOOL(hAPP(hAPP(c_member(U_5149),U_5146),U_5145))
& U_5150 = hAPP(hAPP(c_Set_Oinsert(U_5149),U_5146),U_5145) )
| hAPP(c_Finite__Set_Ocard(U_5149),U_5150) != hAPP(c_Nat_OSuc,U_5151) ) ),
inference(variable_rename,[status(thm)],[f_1321_1]) ).
fof(f_1321_3,plain,
( ! [U_5157,U_5155,U_5153] :
( hAPP(c_Finite__Set_Ocard(U_5153),U_5155) = hAPP(c_Nat_OSuc,U_5157)
| ! [U_5148,U_5147] :
( ( U_5147 != c_Orderings_Obot__class_Obot(tc_fun(U_5153,tc_HOL_Obool))
& U_5157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_5153),U_5147) != U_5157
| hBOOL(hAPP(hAPP(c_member(U_5153),U_5148),U_5147))
| U_5155 != hAPP(hAPP(c_Set_Oinsert(U_5153),U_5148),U_5147) ) )
& ! [U_5156,U_5154,U_5152] :
( ? [U_5146,U_5145] :
( ( U_5145 = c_Orderings_Obot__class_Obot(tc_fun(U_5152,tc_HOL_Obool))
| U_5156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_5152),U_5145) = U_5156
& ~ hBOOL(hAPP(hAPP(c_member(U_5152),U_5146),U_5145))
& U_5154 = hAPP(hAPP(c_Set_Oinsert(U_5152),U_5146),U_5145) )
| hAPP(c_Finite__Set_Ocard(U_5152),U_5154) != hAPP(c_Nat_OSuc,U_5156) ) ),
inference(miniscope,[status(thm)],[f_1321_2]) ).
fof(f_1321_4,plain,
( ! [U_5157,U_5155,U_5153] :
( hAPP(c_Finite__Set_Ocard(U_5153),U_5155) = hAPP(c_Nat_OSuc,U_5157)
| ! [U_5148,U_5147] :
( ( U_5147 != c_Orderings_Obot__class_Obot(tc_fun(U_5153,tc_HOL_Obool))
& U_5157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_5153),U_5147) != U_5157
| hBOOL(hAPP(hAPP(c_member(U_5153),U_5148),U_5147))
| U_5155 != hAPP(hAPP(c_Set_Oinsert(U_5153),U_5148),U_5147) ) )
& ! [U_5156,U_5154,U_5152] :
( ? [U_5145] :
( ( U_5145 = c_Orderings_Obot__class_Obot(tc_fun(U_5152,tc_HOL_Obool))
| U_5156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_5152),U_5145) = U_5156
& ~ hBOOL(hAPP(hAPP(c_member(U_5152),sK126(U_5156,U_5154,U_5152)),U_5145))
& U_5154 = hAPP(hAPP(c_Set_Oinsert(U_5152),sK126(U_5156,U_5154,U_5152)),U_5145) )
| hAPP(c_Finite__Set_Ocard(U_5152),U_5154) != hAPP(c_Nat_OSuc,U_5156) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_5146,sK126(U_5156,U_5154,U_5152))],[f_1321_3]) ).
fof(f_1321_5,plain,
( ! [U_5157,U_5155,U_5153] :
( hAPP(c_Finite__Set_Ocard(U_5153),U_5155) = hAPP(c_Nat_OSuc,U_5157)
| ! [U_5148,U_5147] :
( ( U_5147 != c_Orderings_Obot__class_Obot(tc_fun(U_5153,tc_HOL_Obool))
& U_5157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_5153),U_5147) != U_5157
| hBOOL(hAPP(hAPP(c_member(U_5153),U_5148),U_5147))
| U_5155 != hAPP(hAPP(c_Set_Oinsert(U_5153),U_5148),U_5147) ) )
& ! [U_5156,U_5154,U_5152] :
( ( ( sK127(U_5156,U_5154,U_5152) = c_Orderings_Obot__class_Obot(tc_fun(U_5152,tc_HOL_Obool))
| U_5156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_5152),sK127(U_5156,U_5154,U_5152)) = U_5156
& ~ hBOOL(hAPP(hAPP(c_member(U_5152),sK126(U_5156,U_5154,U_5152)),sK127(U_5156,U_5154,U_5152)))
& U_5154 = hAPP(hAPP(c_Set_Oinsert(U_5152),sK126(U_5156,U_5154,U_5152)),sK127(U_5156,U_5154,U_5152)) )
| hAPP(c_Finite__Set_Ocard(U_5152),U_5154) != hAPP(c_Nat_OSuc,U_5156) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_5145,sK127(U_5156,U_5154,U_5152))],[f_1321_4]) ).
fof(f_1321_6,plain,
( ! [U_5147,U_5157,U_5153] :
( U_5147 != c_Orderings_Obot__class_Obot(tc_fun(U_5153,tc_HOL_Obool))
| ~ sP370(U_5147,U_5157,U_5153) )
& ! [U_5147,U_5157,U_5153] :
( U_5157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP370(U_5147,U_5157,U_5153) )
& ! [U_5154,U_5156,U_5152] :
( sK127(U_5156,U_5154,U_5152) = c_Orderings_Obot__class_Obot(tc_fun(U_5152,tc_HOL_Obool))
| U_5156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP369(U_5154,U_5156,U_5152) )
& ! [U_5154,U_5156,U_5152] :
( hAPP(c_Finite__Set_Ocard(U_5152),sK127(U_5156,U_5154,U_5152)) = U_5156
| ~ sP369(U_5154,U_5156,U_5152) )
& ! [U_5154,U_5156,U_5152] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5152),sK126(U_5156,U_5154,U_5152)),sK127(U_5156,U_5154,U_5152)))
| ~ sP369(U_5154,U_5156,U_5152) )
& ! [U_5154,U_5156,U_5152] :
( U_5154 = hAPP(hAPP(c_Set_Oinsert(U_5152),sK126(U_5156,U_5154,U_5152)),sK127(U_5156,U_5154,U_5152))
| ~ sP369(U_5154,U_5156,U_5152) )
& ! [U_5147,U_5155,U_5157,U_5148,U_5153] :
( hAPP(c_Finite__Set_Ocard(U_5153),U_5155) = hAPP(c_Nat_OSuc,U_5157)
| sP370(U_5147,U_5157,U_5153)
| hAPP(c_Finite__Set_Ocard(U_5153),U_5147) != U_5157
| hBOOL(hAPP(hAPP(c_member(U_5153),U_5148),U_5147))
| U_5155 != hAPP(hAPP(c_Set_Oinsert(U_5153),U_5148),U_5147) )
& ! [U_5154,U_5156,U_5152] :
( sP369(U_5154,U_5156,U_5152)
| hAPP(c_Finite__Set_Ocard(U_5152),U_5154) != hAPP(c_Nat_OSuc,U_5156) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP369,sP370])],[f_1321_5]) ).
cnf(f_1321_7,plain,
( sP369(U_5154,U_5156,U_5152)
| hAPP(c_Finite__Set_Ocard(U_5152),U_5154) != hAPP(c_Nat_OSuc,U_5156) ),
inference(clausify,[status(thm)],[f_1321_6]) ).
cnf(f_1321_8,plain,
( hAPP(c_Finite__Set_Ocard(U_5153),U_5155) = hAPP(c_Nat_OSuc,U_5157)
| sP370(U_5147,U_5157,U_5153)
| hAPP(c_Finite__Set_Ocard(U_5153),U_5147) != U_5157
| hBOOL(hAPP(hAPP(c_member(U_5153),U_5148),U_5147))
| U_5155 != hAPP(hAPP(c_Set_Oinsert(U_5153),U_5148),U_5147) ),
inference(clausify,[status(thm)],[f_1321_6]) ).
cnf(f_1321_9,plain,
( U_5154 = hAPP(hAPP(c_Set_Oinsert(U_5152),sK126(U_5156,U_5154,U_5152)),sK127(U_5156,U_5154,U_5152))
| ~ sP369(U_5154,U_5156,U_5152) ),
inference(clausify,[status(thm)],[f_1321_6]) ).
cnf(f_1321_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_5152),sK126(U_5156,U_5154,U_5152)),sK127(U_5156,U_5154,U_5152)))
| ~ sP369(U_5154,U_5156,U_5152) ),
inference(clausify,[status(thm)],[f_1321_6]) ).
cnf(f_1321_11,plain,
( hAPP(c_Finite__Set_Ocard(U_5152),sK127(U_5156,U_5154,U_5152)) = U_5156
| ~ sP369(U_5154,U_5156,U_5152) ),
inference(clausify,[status(thm)],[f_1321_6]) ).
cnf(f_1321_12,plain,
( sK127(U_5156,U_5154,U_5152) = c_Orderings_Obot__class_Obot(tc_fun(U_5152,tc_HOL_Obool))
| U_5156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP369(U_5154,U_5156,U_5152) ),
inference(clausify,[status(thm)],[f_1321_6]) ).
cnf(f_1321_13,plain,
( U_5157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP370(U_5147,U_5157,U_5153) ),
inference(clausify,[status(thm)],[f_1321_6]) ).
cnf(f_1321_14,plain,
( U_5147 != c_Orderings_Obot__class_Obot(tc_fun(U_5153,tc_HOL_Obool))
| ~ sP370(U_5147,U_5157,U_5153) ),
inference(clausify,[status(thm)],[f_1321_6]) ).
fof(f_1322_1,plain,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ class_Groups_Oordered__ab__semigroup__add(T_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono3]) ).
fof(f_1322_2,plain,
! [U_5163,U_5162,U_5161,U_5160,U_5159] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5159),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5160,U_5159),U_5163),U_5162)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5160,U_5159),U_5163),U_5161)))
| ? [U_5158] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5159),c_Groups_Ozero__class_Ozero(U_5159)),hAPP(U_5163,U_5158)))
& hBOOL(hAPP(hAPP(c_member(U_5160),U_5158),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5160,tc_HOL_Obool)),U_5161),U_5162))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5160,tc_HOL_Obool)),U_5162),U_5161))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5160),U_5161))
| ~ class_Groups_Oordered__ab__semigroup__add(U_5159)
| ~ class_Groups_Ocomm__monoid__add(U_5159) ),
inference(variable_rename,[status(thm)],[f_1322_1]) ).
fof(f_1322_3,plain,
! [U_5163,U_5162,U_5161,U_5160,U_5159] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5159),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5160,U_5159),U_5163),U_5162)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5160,U_5159),U_5163),U_5161)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5159),c_Groups_Ozero__class_Ozero(U_5159)),hAPP(U_5163,sK128(U_5163,U_5162,U_5161,U_5160,U_5159))))
& hBOOL(hAPP(hAPP(c_member(U_5160),sK128(U_5163,U_5162,U_5161,U_5160,U_5159)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5160,tc_HOL_Obool)),U_5161),U_5162))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5160,tc_HOL_Obool)),U_5162),U_5161))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5160),U_5161))
| ~ class_Groups_Oordered__ab__semigroup__add(U_5159)
| ~ class_Groups_Ocomm__monoid__add(U_5159) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_5158,sK128(U_5163,U_5162,U_5161,U_5160,U_5159))],[f_1322_2]) ).
fof(f_1322_4,plain,
( ! [U_5160,U_5162,U_5161,U_5159,U_5163] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5159),c_Groups_Ozero__class_Ozero(U_5159)),hAPP(U_5163,sK128(U_5163,U_5162,U_5161,U_5160,U_5159))))
| ~ sP371(U_5160,U_5162,U_5161,U_5159,U_5163) )
& ! [U_5160,U_5162,U_5161,U_5159,U_5163] :
( hBOOL(hAPP(hAPP(c_member(U_5160),sK128(U_5163,U_5162,U_5161,U_5160,U_5159)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5160,tc_HOL_Obool)),U_5161),U_5162)))
| ~ sP371(U_5160,U_5162,U_5161,U_5159,U_5163) )
& ! [U_5160,U_5162,U_5161,U_5159,U_5163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5159),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5160,U_5159),U_5163),U_5162)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5160,U_5159),U_5163),U_5161)))
| sP371(U_5160,U_5162,U_5161,U_5159,U_5163)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5160,tc_HOL_Obool)),U_5162),U_5161))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5160),U_5161))
| ~ class_Groups_Oordered__ab__semigroup__add(U_5159)
| ~ class_Groups_Ocomm__monoid__add(U_5159) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP371])],[f_1322_3]) ).
cnf(f_1322_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5159),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5160,U_5159),U_5163),U_5162)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5160,U_5159),U_5163),U_5161)))
| sP371(U_5160,U_5162,U_5161,U_5159,U_5163)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5160,tc_HOL_Obool)),U_5162),U_5161))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5160),U_5161))
| ~ class_Groups_Oordered__ab__semigroup__add(U_5159)
| ~ class_Groups_Ocomm__monoid__add(U_5159) ),
inference(clausify,[status(thm)],[f_1322_4]) ).
cnf(f_1322_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5160),sK128(U_5163,U_5162,U_5161,U_5160,U_5159)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5160,tc_HOL_Obool)),U_5161),U_5162)))
| ~ sP371(U_5160,U_5162,U_5161,U_5159,U_5163) ),
inference(clausify,[status(thm)],[f_1322_4]) ).
cnf(f_1322_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5159),c_Groups_Ozero__class_Ozero(U_5159)),hAPP(U_5163,sK128(U_5163,U_5162,U_5161,U_5160,U_5159))))
| ~ sP371(U_5160,U_5162,U_5161,U_5159,U_5163) ),
inference(clausify,[status(thm)],[f_1322_4]) ).
fof(f_1323_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0]) ).
fof(f_1323_2,plain,
! [U_5165,U_5164] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),c_Groups_Oone__class_Oone(U_5164)),U_5165)),U_5165)),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),U_5165),c_Groups_Ozero__class_Ozero(U_5164))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),U_5165),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),c_Groups_Oone__class_Oone(U_5164)),U_5165)),U_5165)),c_Groups_Ozero__class_Ozero(U_5164))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_5164),U_5165),c_Int_Oring__1__class_OInts(U_5164)))
| ~ class_Rings_Olinordered__idom(U_5164) ),
inference(variable_rename,[status(thm)],[f_1323_1]) ).
fof(f_1323_3,plain,
( ! [U_5165,U_5164] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),c_Groups_Oone__class_Oone(U_5164)),U_5165)),U_5165)),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),U_5165),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ sP372(U_5165,U_5164) )
& ! [U_5165,U_5164] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),U_5165),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),c_Groups_Oone__class_Oone(U_5164)),U_5165)),U_5165)),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ sP372(U_5165,U_5164) )
& ! [U_5165,U_5164] :
( sP372(U_5165,U_5164)
| ~ hBOOL(hAPP(hAPP(c_member(U_5164),U_5165),c_Int_Oring__1__class_OInts(U_5164)))
| ~ class_Rings_Olinordered__idom(U_5164) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP372])],[f_1323_2]) ).
cnf(f_1323_4,plain,
( sP372(U_5165,U_5164)
| ~ hBOOL(hAPP(hAPP(c_member(U_5164),U_5165),c_Int_Oring__1__class_OInts(U_5164)))
| ~ class_Rings_Olinordered__idom(U_5164) ),
inference(clausify,[status(thm)],[f_1323_3]) ).
cnf(f_1323_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),U_5165),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),c_Groups_Oone__class_Oone(U_5164)),U_5165)),U_5165)),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ sP372(U_5165,U_5164) ),
inference(clausify,[status(thm)],[f_1323_3]) ).
cnf(f_1323_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5164),c_Groups_Oone__class_Oone(U_5164)),U_5165)),U_5165)),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5164),U_5165),c_Groups_Ozero__class_Ozero(U_5164)))
| ~ sP372(U_5165,U_5164) ),
inference(clausify,[status(thm)],[f_1323_3]) ).
fof(f_1324_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__0]) ).
fof(f_1324_2,plain,
! [U_5166] :
( hBOOL(hAPP(hAPP(c_member(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),c_Int_Oring__1__class_OInts(U_5166)))
| ~ class_Rings_Oring__1(U_5166) ),
inference(variable_rename,[status(thm)],[f_1324_1]) ).
fof(f_1324_3,plain,
! [U_5166] :
( hBOOL(hAPP(hAPP(c_member(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),c_Int_Oring__1__class_OInts(U_5166)))
| ~ class_Rings_Oring__1(U_5166) ),
inference(definitional_conversion,[status(esa)],[f_1324_2]) ).
cnf(f_1324_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),c_Int_Oring__1__class_OInts(U_5166)))
| ~ class_Rings_Oring__1(U_5166) ),
inference(clausify,[status(thm)],[f_1324_3]) ).
fof(f_1325_1,plain,
! [V_b_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__add]) ).
fof(f_1325_2,plain,
! [U_5169,U_5168,U_5167] :
( hBOOL(hAPP(hAPP(c_member(U_5167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5167),U_5168),U_5169)),c_Int_Oring__1__class_OInts(U_5167)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5167),U_5169),c_Int_Oring__1__class_OInts(U_5167)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5167),U_5168),c_Int_Oring__1__class_OInts(U_5167)))
| ~ class_Rings_Oring__1(U_5167) ),
inference(variable_rename,[status(thm)],[f_1325_1]) ).
fof(f_1325_3,plain,
! [U_5167,U_5168,U_5169] :
( hBOOL(hAPP(hAPP(c_member(U_5167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5167),U_5168),U_5169)),c_Int_Oring__1__class_OInts(U_5167)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5167),U_5169),c_Int_Oring__1__class_OInts(U_5167)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5167),U_5168),c_Int_Oring__1__class_OInts(U_5167)))
| ~ class_Rings_Oring__1(U_5167) ),
inference(definitional_conversion,[status(esa)],[f_1325_2]) ).
cnf(f_1325_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5167),U_5168),U_5169)),c_Int_Oring__1__class_OInts(U_5167)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5167),U_5169),c_Int_Oring__1__class_OInts(U_5167)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5167),U_5168),c_Int_Oring__1__class_OInts(U_5167)))
| ~ class_Rings_Oring__1(U_5167) ),
inference(clausify,[status(thm)],[f_1325_3]) ).
fof(f_1326_1,plain,
! [V_b_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__mult]) ).
fof(f_1326_2,plain,
! [U_5172,U_5171,U_5170] :
( hBOOL(hAPP(hAPP(c_member(U_5170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5170),U_5171),U_5172)),c_Int_Oring__1__class_OInts(U_5170)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5170),U_5172),c_Int_Oring__1__class_OInts(U_5170)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5170),U_5171),c_Int_Oring__1__class_OInts(U_5170)))
| ~ class_Rings_Oring__1(U_5170) ),
inference(variable_rename,[status(thm)],[f_1326_1]) ).
fof(f_1326_3,plain,
! [U_5170,U_5171,U_5172] :
( hBOOL(hAPP(hAPP(c_member(U_5170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5170),U_5171),U_5172)),c_Int_Oring__1__class_OInts(U_5170)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5170),U_5172),c_Int_Oring__1__class_OInts(U_5170)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5170),U_5171),c_Int_Oring__1__class_OInts(U_5170)))
| ~ class_Rings_Oring__1(U_5170) ),
inference(definitional_conversion,[status(esa)],[f_1326_2]) ).
cnf(f_1326_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5170),U_5171),U_5172)),c_Int_Oring__1__class_OInts(U_5170)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5170),U_5172),c_Int_Oring__1__class_OInts(U_5170)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5170),U_5171),c_Int_Oring__1__class_OInts(U_5170)))
| ~ class_Rings_Oring__1(U_5170) ),
inference(clausify,[status(thm)],[f_1326_3]) ).
fof(f_1327_1,plain,
! [V_b_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__diff]) ).
fof(f_1327_2,plain,
! [U_5175,U_5174,U_5173] :
( hBOOL(hAPP(hAPP(c_member(U_5173),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5173),U_5174),U_5175)),c_Int_Oring__1__class_OInts(U_5173)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5173),U_5175),c_Int_Oring__1__class_OInts(U_5173)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5173),U_5174),c_Int_Oring__1__class_OInts(U_5173)))
| ~ class_Rings_Oring__1(U_5173) ),
inference(variable_rename,[status(thm)],[f_1327_1]) ).
fof(f_1327_3,plain,
! [U_5173,U_5174,U_5175] :
( hBOOL(hAPP(hAPP(c_member(U_5173),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5173),U_5174),U_5175)),c_Int_Oring__1__class_OInts(U_5173)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5173),U_5175),c_Int_Oring__1__class_OInts(U_5173)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5173),U_5174),c_Int_Oring__1__class_OInts(U_5173)))
| ~ class_Rings_Oring__1(U_5173) ),
inference(definitional_conversion,[status(esa)],[f_1327_2]) ).
cnf(f_1327_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5173),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5173),U_5174),U_5175)),c_Int_Oring__1__class_OInts(U_5173)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5173),U_5175),c_Int_Oring__1__class_OInts(U_5173)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5173),U_5174),c_Int_Oring__1__class_OInts(U_5173)))
| ~ class_Rings_Oring__1(U_5173) ),
inference(clausify,[status(thm)],[f_1327_3]) ).
fof(f_1328_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__1]) ).
fof(f_1328_2,plain,
! [U_5176] :
( hBOOL(hAPP(hAPP(c_member(U_5176),c_Groups_Oone__class_Oone(U_5176)),c_Int_Oring__1__class_OInts(U_5176)))
| ~ class_Rings_Oring__1(U_5176) ),
inference(variable_rename,[status(thm)],[f_1328_1]) ).
fof(f_1328_3,plain,
! [U_5176] :
( hBOOL(hAPP(hAPP(c_member(U_5176),c_Groups_Oone__class_Oone(U_5176)),c_Int_Oring__1__class_OInts(U_5176)))
| ~ class_Rings_Oring__1(U_5176) ),
inference(definitional_conversion,[status(esa)],[f_1328_2]) ).
cnf(f_1328_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5176),c_Groups_Oone__class_Oone(U_5176)),c_Int_Oring__1__class_OInts(U_5176)))
| ~ class_Rings_Oring__1(U_5176) ),
inference(clausify,[status(thm)],[f_1328_3]) ).
fof(f_1329_1,plain,
! [V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__minus]) ).
fof(f_1329_2,plain,
! [U_5178,U_5177] :
( hBOOL(hAPP(hAPP(c_member(U_5177),hAPP(c_Groups_Ouminus__class_Ouminus(U_5177),U_5178)),c_Int_Oring__1__class_OInts(U_5177)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5177),U_5178),c_Int_Oring__1__class_OInts(U_5177)))
| ~ class_Rings_Oring__1(U_5177) ),
inference(variable_rename,[status(thm)],[f_1329_1]) ).
fof(f_1329_3,plain,
! [U_5177,U_5178] :
( hBOOL(hAPP(hAPP(c_member(U_5177),hAPP(c_Groups_Ouminus__class_Ouminus(U_5177),U_5178)),c_Int_Oring__1__class_OInts(U_5177)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5177),U_5178),c_Int_Oring__1__class_OInts(U_5177)))
| ~ class_Rings_Oring__1(U_5177) ),
inference(definitional_conversion,[status(esa)],[f_1329_2]) ).
cnf(f_1329_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5177),hAPP(c_Groups_Ouminus__class_Ouminus(U_5177),U_5178)),c_Int_Oring__1__class_OInts(U_5177)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5177),U_5178),c_Int_Oring__1__class_OInts(U_5177)))
| ~ class_Rings_Oring__1(U_5177) ),
inference(clausify,[status(thm)],[f_1329_3]) ).
fof(f_1330_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff]) ).
fof(f_1330_2,plain,
! [U_5180,U_5179] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5179),U_5180),U_5180) = c_Groups_Ozero__class_Ozero(U_5179)
| U_5180 != c_Groups_Ozero__class_Ozero(U_5179) )
& ( U_5180 = c_Groups_Ozero__class_Ozero(U_5179)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5179),U_5180),U_5180) != c_Groups_Ozero__class_Ozero(U_5179) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_5179),U_5180),c_Int_Oring__1__class_OInts(U_5179)))
| ~ class_Int_Oring__char__0(U_5179) ),
inference(variable_rename,[status(thm)],[f_1330_1]) ).
fof(f_1330_3,plain,
( ! [U_5179,U_5180] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5179),U_5180),U_5180) = c_Groups_Ozero__class_Ozero(U_5179)
| U_5180 != c_Groups_Ozero__class_Ozero(U_5179)
| ~ sP373(U_5179,U_5180) )
& ! [U_5179,U_5180] :
( U_5180 = c_Groups_Ozero__class_Ozero(U_5179)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5179),U_5180),U_5180) != c_Groups_Ozero__class_Ozero(U_5179)
| ~ sP373(U_5179,U_5180) )
& ! [U_5179,U_5180] :
( sP373(U_5179,U_5180)
| ~ hBOOL(hAPP(hAPP(c_member(U_5179),U_5180),c_Int_Oring__1__class_OInts(U_5179)))
| ~ class_Int_Oring__char__0(U_5179) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP373])],[f_1330_2]) ).
cnf(f_1330_4,plain,
( sP373(U_5179,U_5180)
| ~ hBOOL(hAPP(hAPP(c_member(U_5179),U_5180),c_Int_Oring__1__class_OInts(U_5179)))
| ~ class_Int_Oring__char__0(U_5179) ),
inference(clausify,[status(thm)],[f_1330_3]) ).
cnf(f_1330_5,plain,
( U_5180 = c_Groups_Ozero__class_Ozero(U_5179)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5179),U_5180),U_5180) != c_Groups_Ozero__class_Ozero(U_5179)
| ~ sP373(U_5179,U_5180) ),
inference(clausify,[status(thm)],[f_1330_3]) ).
cnf(f_1330_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5179),U_5180),U_5180) = c_Groups_Ozero__class_Ozero(U_5179)
| U_5180 != c_Groups_Ozero__class_Ozero(U_5179)
| ~ sP373(U_5179,U_5180) ),
inference(clausify,[status(thm)],[f_1330_3]) ).
fof(f_1331_1,plain,
! [V_a_2,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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero]) ).
fof(f_1331_2,plain,
! [U_5182,U_5181] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5181),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5181),c_Groups_Oone__class_Oone(U_5181)),U_5182)),U_5182) != c_Groups_Ozero__class_Ozero(U_5181)
| ~ hBOOL(hAPP(hAPP(c_member(U_5181),U_5182),c_Int_Oring__1__class_OInts(U_5181)))
| ~ class_Int_Oring__char__0(U_5181) ),
inference(variable_rename,[status(thm)],[f_1331_1]) ).
fof(f_1331_3,plain,
! [U_5182,U_5181] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5181),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5181),c_Groups_Oone__class_Oone(U_5181)),U_5182)),U_5182) != c_Groups_Ozero__class_Ozero(U_5181)
| ~ hBOOL(hAPP(hAPP(c_member(U_5181),U_5182),c_Int_Oring__1__class_OInts(U_5181)))
| ~ class_Int_Oring__char__0(U_5181) ),
inference(definitional_conversion,[status(esa)],[f_1331_2]) ).
cnf(f_1331_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5181),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5181),c_Groups_Oone__class_Oone(U_5181)),U_5182)),U_5182) != c_Groups_Ozero__class_Ozero(U_5181)
| ~ hBOOL(hAPP(hAPP(c_member(U_5181),U_5182),c_Int_Oring__1__class_OInts(U_5181)))
| ~ class_Int_Oring__char__0(U_5181) ),
inference(clausify,[status(thm)],[f_1331_3]) ).
fof(f_1332_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( ( 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)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
& ( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if]) ).
fof(f_1332_2,plain,
! [U_5186,U_5185,U_5184,U_5183] :
( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5183,U_5185)),c_Sum__Type_OPlus(U_5183,U_5185,U_5184,U_5186)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5185),U_5186))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_5183),U_5184)) ) )
& ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5183,U_5185)),c_Sum__Type_OPlus(U_5183,U_5185,U_5184,U_5186)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5183),U_5184)),hAPP(c_Finite__Set_Ocard(U_5185),U_5186))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5185),U_5186))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5183),U_5184)) ) ),
inference(variable_rename,[status(thm)],[f_1332_1]) ).
fof(f_1332_3,plain,
( ! [U_5194,U_5192,U_5190,U_5188] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5188,U_5192)),c_Sum__Type_OPlus(U_5188,U_5192,U_5190,U_5194)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5192),U_5194))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_5188),U_5190)) ) )
& ! [U_5193,U_5191,U_5189,U_5187] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5187,U_5191)),c_Sum__Type_OPlus(U_5187,U_5191,U_5189,U_5193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5187),U_5189)),hAPP(c_Finite__Set_Ocard(U_5191),U_5193))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5191),U_5193))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5187),U_5189)) ) ),
inference(miniscope,[status(thm)],[f_1332_2]) ).
fof(f_1332_4,plain,
( ! [U_5188,U_5190,U_5192,U_5194] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5192),U_5194))
| ~ sP374(U_5188,U_5190,U_5192,U_5194) )
& ! [U_5188,U_5190,U_5192,U_5194] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5188),U_5190))
| ~ sP374(U_5188,U_5190,U_5192,U_5194) )
& ! [U_5188,U_5190,U_5192,U_5194] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5188,U_5192)),c_Sum__Type_OPlus(U_5188,U_5192,U_5190,U_5194)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP374(U_5188,U_5190,U_5192,U_5194) )
& ! [U_5187,U_5189,U_5191,U_5193] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5187,U_5191)),c_Sum__Type_OPlus(U_5187,U_5191,U_5189,U_5193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5187),U_5189)),hAPP(c_Finite__Set_Ocard(U_5191),U_5193))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5191),U_5193))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5187),U_5189)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP374])],[f_1332_3]) ).
cnf(f_1332_5,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5187,U_5191)),c_Sum__Type_OPlus(U_5187,U_5191,U_5189,U_5193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5187),U_5189)),hAPP(c_Finite__Set_Ocard(U_5191),U_5193))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5191),U_5193))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5187),U_5189)) ),
inference(clausify,[status(thm)],[f_1332_4]) ).
cnf(f_1332_6,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5188,U_5192)),c_Sum__Type_OPlus(U_5188,U_5192,U_5190,U_5194)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP374(U_5188,U_5190,U_5192,U_5194) ),
inference(clausify,[status(thm)],[f_1332_4]) ).
cnf(f_1332_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5188),U_5190))
| ~ sP374(U_5188,U_5190,U_5192,U_5194) ),
inference(clausify,[status(thm)],[f_1332_4]) ).
cnf(f_1332_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5192),U_5194))
| ~ sP374(U_5188,U_5190,U_5192,U_5194) ),
inference(clausify,[status(thm)],[f_1332_4]) ).
fof(f_1333_1,plain,
! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) )
| hAPP(V_f_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Fields_Ofield(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__diff1]) ).
fof(f_1333_2,plain,
! [U_5199,U_5198,U_5197,U_5196,U_5195] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5196,tc_HOL_Obool)),U_5197),hAPP(hAPP(c_Set_Oinsert(U_5196),U_5199),c_Orderings_Obot__class_Obot(tc_fun(U_5196,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),U_5197)
| hBOOL(hAPP(hAPP(c_member(U_5196),U_5199),U_5197)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5196,tc_HOL_Obool)),U_5197),hAPP(hAPP(c_Set_Oinsert(U_5196),U_5199),c_Orderings_Obot__class_Obot(tc_fun(U_5196,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5195),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),U_5197)),hAPP(U_5198,U_5199))
| ~ hBOOL(hAPP(hAPP(c_member(U_5196),U_5199),U_5197)) ) )
| hAPP(U_5198,U_5199) = c_Groups_Ozero__class_Ozero(U_5195)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5196),U_5197))
| ~ class_Fields_Ofield(U_5195) ),
inference(variable_rename,[status(thm)],[f_1333_1]) ).
fof(f_1333_3,plain,
( ! [U_5196,U_5195,U_5197,U_5198,U_5199] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5196,tc_HOL_Obool)),U_5197),hAPP(hAPP(c_Set_Oinsert(U_5196),U_5199),c_Orderings_Obot__class_Obot(tc_fun(U_5196,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),U_5197)
| hBOOL(hAPP(hAPP(c_member(U_5196),U_5199),U_5197))
| ~ sP375(U_5196,U_5195,U_5197,U_5198,U_5199) )
& ! [U_5196,U_5195,U_5197,U_5198,U_5199] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5196,tc_HOL_Obool)),U_5197),hAPP(hAPP(c_Set_Oinsert(U_5196),U_5199),c_Orderings_Obot__class_Obot(tc_fun(U_5196,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5195),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),U_5197)),hAPP(U_5198,U_5199))
| ~ hBOOL(hAPP(hAPP(c_member(U_5196),U_5199),U_5197))
| ~ sP375(U_5196,U_5195,U_5197,U_5198,U_5199) )
& ! [U_5196,U_5195,U_5197,U_5198,U_5199] :
( sP375(U_5196,U_5195,U_5197,U_5198,U_5199)
| hAPP(U_5198,U_5199) = c_Groups_Ozero__class_Ozero(U_5195)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5196),U_5197))
| ~ class_Fields_Ofield(U_5195) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP375])],[f_1333_2]) ).
cnf(f_1333_4,plain,
( sP375(U_5196,U_5195,U_5197,U_5198,U_5199)
| hAPP(U_5198,U_5199) = c_Groups_Ozero__class_Ozero(U_5195)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5196),U_5197))
| ~ class_Fields_Ofield(U_5195) ),
inference(clausify,[status(thm)],[f_1333_3]) ).
cnf(f_1333_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5196,tc_HOL_Obool)),U_5197),hAPP(hAPP(c_Set_Oinsert(U_5196),U_5199),c_Orderings_Obot__class_Obot(tc_fun(U_5196,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5195),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),U_5197)),hAPP(U_5198,U_5199))
| ~ hBOOL(hAPP(hAPP(c_member(U_5196),U_5199),U_5197))
| ~ sP375(U_5196,U_5195,U_5197,U_5198,U_5199) ),
inference(clausify,[status(thm)],[f_1333_3]) ).
cnf(f_1333_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5196,tc_HOL_Obool)),U_5197),hAPP(hAPP(c_Set_Oinsert(U_5196),U_5199),c_Orderings_Obot__class_Obot(tc_fun(U_5196,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5196,U_5195),U_5198),U_5197)
| hBOOL(hAPP(hAPP(c_member(U_5196),U_5199),U_5197))
| ~ sP375(U_5196,U_5195,U_5197,U_5198,U_5199) ),
inference(clausify,[status(thm)],[f_1333_3]) ).
fof(f_1334_1,plain,
! [V_n_2,V_Pa_2] :
( ? [B_k] :
( 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))))
& ! [B_i] :
( ~ hBOOL(hAPP(V_Pa_2,B_i))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) )
| ~ hBOOL(hAPP(V_Pa_2,V_n_2))
| hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).
fof(f_1334_2,plain,
! [U_5203,U_5202] :
( ? [U_5201] :
( hBOOL(hAPP(U_5202,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5201),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_5200] :
( ~ hBOOL(hAPP(U_5202,U_5200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5200),U_5201)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5201),U_5203)) )
| ~ hBOOL(hAPP(U_5202,U_5203))
| hBOOL(hAPP(U_5202,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[f_1334_1]) ).
fof(f_1334_3,plain,
! [U_5203,U_5202] :
( ( hBOOL(hAPP(U_5202,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK129(U_5203,U_5202)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_5200] :
( ~ hBOOL(hAPP(U_5202,U_5200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5200),sK129(U_5203,U_5202))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK129(U_5203,U_5202)),U_5203)) )
| ~ hBOOL(hAPP(U_5202,U_5203))
| hBOOL(hAPP(U_5202,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_5201,sK129(U_5203,U_5202))],[f_1334_2]) ).
fof(f_1334_4,plain,
( ! [U_5200,U_5202,U_5203] :
( hBOOL(hAPP(U_5202,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK129(U_5203,U_5202)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ sP376(U_5200,U_5202,U_5203) )
& ! [U_5200,U_5202,U_5203] :
( ~ hBOOL(hAPP(U_5202,U_5200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5200),sK129(U_5203,U_5202)))
| ~ sP376(U_5200,U_5202,U_5203) )
& ! [U_5200,U_5202,U_5203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK129(U_5203,U_5202)),U_5203))
| ~ sP376(U_5200,U_5202,U_5203) )
& ! [U_5200,U_5202,U_5203] :
( sP376(U_5200,U_5202,U_5203)
| ~ hBOOL(hAPP(U_5202,U_5203))
| hBOOL(hAPP(U_5202,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP376])],[f_1334_3]) ).
cnf(f_1334_5,plain,
( sP376(U_5200,U_5202,U_5203)
| ~ hBOOL(hAPP(U_5202,U_5203))
| hBOOL(hAPP(U_5202,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_1334_4]) ).
cnf(f_1334_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK129(U_5203,U_5202)),U_5203))
| ~ sP376(U_5200,U_5202,U_5203) ),
inference(clausify,[status(thm)],[f_1334_4]) ).
cnf(f_1334_7,plain,
( ~ hBOOL(hAPP(U_5202,U_5200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5200),sK129(U_5203,U_5202)))
| ~ sP376(U_5200,U_5202,U_5203) ),
inference(clausify,[status(thm)],[f_1334_4]) ).
cnf(f_1334_8,plain,
( hBOOL(hAPP(U_5202,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK129(U_5203,U_5202)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ sP376(U_5200,U_5202,U_5203) ),
inference(clausify,[status(thm)],[f_1334_4]) ).
fof(f_1335_1,plain,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( 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)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right]) ).
fof(f_1335_2,plain,
! [U_5209,U_5208,U_5207,U_5206,U_5205] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5206,U_5205),U_5209),U_5207) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5206,U_5205),U_5209),U_5208)
| ? [U_5204] :
( hAPP(U_5209,U_5204) != c_Groups_Ozero__class_Ozero(U_5205)
& hBOOL(hAPP(hAPP(c_member(U_5206),U_5204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5206,tc_HOL_Obool)),U_5207),U_5208))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5206,tc_HOL_Obool)),U_5208),U_5207))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5206),U_5207))
| ~ class_Groups_Ocomm__monoid__add(U_5205) ),
inference(variable_rename,[status(thm)],[f_1335_1]) ).
fof(f_1335_3,plain,
! [U_5209,U_5208,U_5207,U_5206,U_5205] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5206,U_5205),U_5209),U_5207) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5206,U_5205),U_5209),U_5208)
| ( hAPP(U_5209,sK130(U_5209,U_5208,U_5207,U_5206,U_5205)) != c_Groups_Ozero__class_Ozero(U_5205)
& hBOOL(hAPP(hAPP(c_member(U_5206),sK130(U_5209,U_5208,U_5207,U_5206,U_5205)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5206,tc_HOL_Obool)),U_5207),U_5208))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5206,tc_HOL_Obool)),U_5208),U_5207))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5206),U_5207))
| ~ class_Groups_Ocomm__monoid__add(U_5205) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_5204,sK130(U_5209,U_5208,U_5207,U_5206,U_5205))],[f_1335_2]) ).
fof(f_1335_4,plain,
( ! [U_5205,U_5206,U_5207,U_5208,U_5209] :
( hAPP(U_5209,sK130(U_5209,U_5208,U_5207,U_5206,U_5205)) != c_Groups_Ozero__class_Ozero(U_5205)
| ~ sP377(U_5205,U_5206,U_5207,U_5208,U_5209) )
& ! [U_5205,U_5206,U_5207,U_5208,U_5209] :
( hBOOL(hAPP(hAPP(c_member(U_5206),sK130(U_5209,U_5208,U_5207,U_5206,U_5205)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5206,tc_HOL_Obool)),U_5207),U_5208)))
| ~ sP377(U_5205,U_5206,U_5207,U_5208,U_5209) )
& ! [U_5205,U_5206,U_5207,U_5208,U_5209] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5206,U_5205),U_5209),U_5207) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5206,U_5205),U_5209),U_5208)
| sP377(U_5205,U_5206,U_5207,U_5208,U_5209)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5206,tc_HOL_Obool)),U_5208),U_5207))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5206),U_5207))
| ~ class_Groups_Ocomm__monoid__add(U_5205) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP377])],[f_1335_3]) ).
cnf(f_1335_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5206,U_5205),U_5209),U_5207) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5206,U_5205),U_5209),U_5208)
| sP377(U_5205,U_5206,U_5207,U_5208,U_5209)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5206,tc_HOL_Obool)),U_5208),U_5207))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5206),U_5207))
| ~ class_Groups_Ocomm__monoid__add(U_5205) ),
inference(clausify,[status(thm)],[f_1335_4]) ).
cnf(f_1335_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5206),sK130(U_5209,U_5208,U_5207,U_5206,U_5205)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5206,tc_HOL_Obool)),U_5207),U_5208)))
| ~ sP377(U_5205,U_5206,U_5207,U_5208,U_5209) ),
inference(clausify,[status(thm)],[f_1335_4]) ).
cnf(f_1335_7,plain,
( hAPP(U_5209,sK130(U_5209,U_5208,U_5207,U_5206,U_5205)) != c_Groups_Ozero__class_Ozero(U_5205)
| ~ sP377(U_5205,U_5206,U_5207,U_5208,U_5209) ),
inference(clausify,[status(thm)],[f_1335_4]) ).
fof(f_1336_1,plain,
! [V_f_2,V_S_2,V_T_2,T_b,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)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__left]) ).
fof(f_1336_2,plain,
! [U_5215,U_5214,U_5213,U_5212,U_5211] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5212,U_5211),U_5215),U_5214) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5212,U_5211),U_5215),U_5213)
| ? [U_5210] :
( hAPP(U_5215,U_5210) != c_Groups_Ozero__class_Ozero(U_5211)
& hBOOL(hAPP(hAPP(c_member(U_5212),U_5210),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5212,tc_HOL_Obool)),U_5213),U_5214))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5212,tc_HOL_Obool)),U_5214),U_5213))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5212),U_5213))
| ~ class_Groups_Ocomm__monoid__add(U_5211) ),
inference(variable_rename,[status(thm)],[f_1336_1]) ).
fof(f_1336_3,plain,
! [U_5215,U_5214,U_5213,U_5212,U_5211] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5212,U_5211),U_5215),U_5214) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5212,U_5211),U_5215),U_5213)
| ( hAPP(U_5215,sK131(U_5215,U_5214,U_5213,U_5212,U_5211)) != c_Groups_Ozero__class_Ozero(U_5211)
& hBOOL(hAPP(hAPP(c_member(U_5212),sK131(U_5215,U_5214,U_5213,U_5212,U_5211)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5212,tc_HOL_Obool)),U_5213),U_5214))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5212,tc_HOL_Obool)),U_5214),U_5213))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5212),U_5213))
| ~ class_Groups_Ocomm__monoid__add(U_5211) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_5210,sK131(U_5215,U_5214,U_5213,U_5212,U_5211))],[f_1336_2]) ).
fof(f_1336_4,plain,
( ! [U_5212,U_5211,U_5214,U_5213,U_5215] :
( hAPP(U_5215,sK131(U_5215,U_5214,U_5213,U_5212,U_5211)) != c_Groups_Ozero__class_Ozero(U_5211)
| ~ sP378(U_5212,U_5211,U_5214,U_5213,U_5215) )
& ! [U_5212,U_5211,U_5214,U_5213,U_5215] :
( hBOOL(hAPP(hAPP(c_member(U_5212),sK131(U_5215,U_5214,U_5213,U_5212,U_5211)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5212,tc_HOL_Obool)),U_5213),U_5214)))
| ~ sP378(U_5212,U_5211,U_5214,U_5213,U_5215) )
& ! [U_5212,U_5211,U_5214,U_5213,U_5215] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5212,U_5211),U_5215),U_5214) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5212,U_5211),U_5215),U_5213)
| sP378(U_5212,U_5211,U_5214,U_5213,U_5215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5212,tc_HOL_Obool)),U_5214),U_5213))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5212),U_5213))
| ~ class_Groups_Ocomm__monoid__add(U_5211) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP378])],[f_1336_3]) ).
cnf(f_1336_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5212,U_5211),U_5215),U_5214) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5212,U_5211),U_5215),U_5213)
| sP378(U_5212,U_5211,U_5214,U_5213,U_5215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5212,tc_HOL_Obool)),U_5214),U_5213))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5212),U_5213))
| ~ class_Groups_Ocomm__monoid__add(U_5211) ),
inference(clausify,[status(thm)],[f_1336_4]) ).
cnf(f_1336_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5212),sK131(U_5215,U_5214,U_5213,U_5212,U_5211)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5212,tc_HOL_Obool)),U_5213),U_5214)))
| ~ sP378(U_5212,U_5211,U_5214,U_5213,U_5215) ),
inference(clausify,[status(thm)],[f_1336_4]) ).
cnf(f_1336_7,plain,
( hAPP(U_5215,sK131(U_5215,U_5214,U_5213,U_5212,U_5211)) != c_Groups_Ozero__class_Ozero(U_5211)
| ~ sP378(U_5212,U_5211,U_5214,U_5213,U_5215) ),
inference(clausify,[status(thm)],[f_1336_4]) ).
fof(f_1337_1,plain,
! [V_a_2,T_b] :
( ( ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| 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)) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).
fof(f_1337_2,plain,
! [U_5217,U_5216] :
( ( ( c_Groups_Osgn__class_Osgn(U_5216,U_5217) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5216),c_Groups_Oone__class_Oone(U_5216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5216),U_5217),c_Groups_Ozero__class_Ozero(U_5216))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5216),U_5217),c_Groups_Ozero__class_Ozero(U_5216)))
| c_Groups_Osgn__class_Osgn(U_5216,U_5217) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5216),c_Groups_Oone__class_Oone(U_5216)) ) )
| ~ class_Rings_Olinordered__idom(U_5216) ),
inference(variable_rename,[status(thm)],[f_1337_1]) ).
fof(f_1337_3,plain,
( ! [U_5217,U_5216] :
( c_Groups_Osgn__class_Osgn(U_5216,U_5217) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5216),c_Groups_Oone__class_Oone(U_5216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5216),U_5217),c_Groups_Ozero__class_Ozero(U_5216)))
| ~ sP379(U_5217,U_5216) )
& ! [U_5217,U_5216] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5216),U_5217),c_Groups_Ozero__class_Ozero(U_5216)))
| c_Groups_Osgn__class_Osgn(U_5216,U_5217) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5216),c_Groups_Oone__class_Oone(U_5216))
| ~ sP379(U_5217,U_5216) )
& ! [U_5217,U_5216] :
( sP379(U_5217,U_5216)
| ~ class_Rings_Olinordered__idom(U_5216) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP379])],[f_1337_2]) ).
cnf(f_1337_4,plain,
( sP379(U_5217,U_5216)
| ~ class_Rings_Olinordered__idom(U_5216) ),
inference(clausify,[status(thm)],[f_1337_3]) ).
cnf(f_1337_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5216),U_5217),c_Groups_Ozero__class_Ozero(U_5216)))
| c_Groups_Osgn__class_Osgn(U_5216,U_5217) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5216),c_Groups_Oone__class_Oone(U_5216))
| ~ sP379(U_5217,U_5216) ),
inference(clausify,[status(thm)],[f_1337_3]) ).
cnf(f_1337_6,plain,
( c_Groups_Osgn__class_Osgn(U_5216,U_5217) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5216),c_Groups_Oone__class_Oone(U_5216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5216),U_5217),c_Groups_Ozero__class_Ozero(U_5216)))
| ~ sP379(U_5217,U_5216) ),
inference(clausify,[status(thm)],[f_1337_3]) ).
fof(f_1338_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__sgn]) ).
fof(f_1338_2,plain,
! [U_5219,U_5218] :
( c_Groups_Osgn__class_Osgn(U_5218,c_Groups_Osgn__class_Osgn(U_5218,U_5219)) = c_Groups_Osgn__class_Osgn(U_5218,U_5219)
| ~ class_Rings_Olinordered__idom(U_5218) ),
inference(variable_rename,[status(thm)],[f_1338_1]) ).
fof(f_1338_3,plain,
! [U_5218,U_5219] :
( c_Groups_Osgn__class_Osgn(U_5218,c_Groups_Osgn__class_Osgn(U_5218,U_5219)) = c_Groups_Osgn__class_Osgn(U_5218,U_5219)
| ~ class_Rings_Olinordered__idom(U_5218) ),
inference(definitional_conversion,[status(esa)],[f_1338_2]) ).
cnf(f_1338_4,plain,
( c_Groups_Osgn__class_Osgn(U_5218,c_Groups_Osgn__class_Osgn(U_5218,U_5219)) = c_Groups_Osgn__class_Osgn(U_5218,U_5219)
| ~ class_Rings_Olinordered__idom(U_5218) ),
inference(clausify,[status(thm)],[f_1338_3]) ).
fof(f_1339_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__zero__left]) ).
fof(f_1339_2,plain,
! [U_5221,U_5220] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5220),c_Groups_Ozero__class_Ozero(U_5220)),U_5221) = c_Groups_Ozero__class_Ozero(U_5220)
| ~ class_Rings_Odivision__ring(U_5220) ),
inference(variable_rename,[status(thm)],[f_1339_1]) ).
fof(f_1339_3,plain,
! [U_5220,U_5221] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5220),c_Groups_Ozero__class_Ozero(U_5220)),U_5221) = c_Groups_Ozero__class_Ozero(U_5220)
| ~ class_Rings_Odivision__ring(U_5220) ),
inference(definitional_conversion,[status(esa)],[f_1339_2]) ).
cnf(f_1339_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5220),c_Groups_Ozero__class_Ozero(U_5220)),U_5221) = c_Groups_Ozero__class_Ozero(U_5220)
| ~ class_Rings_Odivision__ring(U_5220) ),
inference(clausify,[status(thm)],[f_1339_3]) ).
fof(f_1340_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__zero]) ).
fof(f_1340_2,plain,
! [U_5223,U_5222] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5223),c_Groups_Ozero__class_Ozero(U_5222)) = c_Groups_Ozero__class_Ozero(U_5222)
| ~ class_Rings_Odivision__ring__inverse__zero(U_5222) ),
inference(variable_rename,[status(thm)],[f_1340_1]) ).
fof(f_1340_3,plain,
! [U_5222,U_5223] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5223),c_Groups_Ozero__class_Ozero(U_5222)) = c_Groups_Ozero__class_Ozero(U_5222)
| ~ class_Rings_Odivision__ring__inverse__zero(U_5222) ),
inference(definitional_conversion,[status(esa)],[f_1340_2]) ).
cnf(f_1340_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5223),c_Groups_Ozero__class_Ozero(U_5222)) = c_Groups_Ozero__class_Ozero(U_5222)
| ~ class_Rings_Odivision__ring__inverse__zero(U_5222) ),
inference(clausify,[status(thm)],[f_1340_3]) ).
fof(f_1341_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__divide__distrib]) ).
fof(f_1341_2,plain,
! [U_5227,U_5226,U_5225,U_5224] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5224),U_5225),U_5226)),U_5227) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5224),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),U_5225),U_5227)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),U_5226),U_5227))
| ~ class_Rings_Odivision__ring(U_5224) ),
inference(variable_rename,[status(thm)],[f_1341_1]) ).
fof(f_1341_3,plain,
! [U_5224,U_5225,U_5226,U_5227] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5224),U_5225),U_5226)),U_5227) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5224),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),U_5225),U_5227)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),U_5226),U_5227))
| ~ class_Rings_Odivision__ring(U_5224) ),
inference(definitional_conversion,[status(esa)],[f_1341_2]) ).
cnf(f_1341_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5224),U_5225),U_5226)),U_5227) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5224),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),U_5225),U_5227)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5224),U_5226),U_5227))
| ~ class_Rings_Odivision__ring(U_5224) ),
inference(clausify,[status(thm)],[f_1341_3]) ).
fof(f_1342_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right]) ).
fof(f_1342_2,plain,
! [U_5231,U_5230,U_5229,U_5228] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5228),U_5229),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5228),U_5230),U_5231)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5228),U_5229),U_5230)),U_5231)
| ~ class_Rings_Odivision__ring(U_5228) ),
inference(variable_rename,[status(thm)],[f_1342_1]) ).
fof(f_1342_3,plain,
! [U_5228,U_5229,U_5230,U_5231] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5228),U_5229),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5228),U_5230),U_5231)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5228),U_5229),U_5230)),U_5231)
| ~ class_Rings_Odivision__ring(U_5228) ),
inference(definitional_conversion,[status(esa)],[f_1342_2]) ).
cnf(f_1342_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5228),U_5229),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5228),U_5230),U_5231)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5228),U_5229),U_5230)),U_5231)
| ~ class_Rings_Odivision__ring(U_5228) ),
inference(clausify,[status(thm)],[f_1342_3]) ).
fof(f_1343_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib]) ).
fof(f_1343_2,plain,
! [U_5235,U_5234,U_5233,U_5232] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5232),U_5233),U_5234)),U_5235) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5232),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),U_5233),U_5235)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),U_5234),U_5235))
| ~ class_Rings_Odivision__ring(U_5232) ),
inference(variable_rename,[status(thm)],[f_1343_1]) ).
fof(f_1343_3,plain,
! [U_5232,U_5233,U_5234,U_5235] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5232),U_5233),U_5234)),U_5235) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5232),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),U_5233),U_5235)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),U_5234),U_5235))
| ~ class_Rings_Odivision__ring(U_5232) ),
inference(definitional_conversion,[status(esa)],[f_1343_2]) ).
cnf(f_1343_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5232),U_5233),U_5234)),U_5235) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5232),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),U_5233),U_5235)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5232),U_5234),U_5235))
| ~ class_Rings_Odivision__ring(U_5232) ),
inference(clausify,[status(thm)],[f_1343_3]) ).
fof(f_1344_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__1]) ).
fof(f_1344_2,plain,
! [U_5237,U_5236] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5236),U_5237),c_Groups_Oone__class_Oone(U_5236)) = U_5237
| ~ class_Rings_Odivision__ring(U_5236) ),
inference(variable_rename,[status(thm)],[f_1344_1]) ).
fof(f_1344_3,plain,
! [U_5237,U_5236] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5236),U_5237),c_Groups_Oone__class_Oone(U_5236)) = U_5237
| ~ class_Rings_Odivision__ring(U_5236) ),
inference(definitional_conversion,[status(esa)],[f_1344_2]) ).
cnf(f_1344_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5236),U_5237),c_Groups_Oone__class_Oone(U_5236)) = U_5237
| ~ class_Rings_Odivision__ring(U_5236) ),
inference(clausify,[status(thm)],[f_1344_3]) ).
fof(f_1345_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__left]) ).
fof(f_1345_2,plain,
! [U_5240,U_5239,U_5238] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5238),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),U_5239),U_5240)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),hAPP(c_Groups_Ouminus__class_Ouminus(U_5238),U_5239)),U_5240)
| ~ class_Rings_Odivision__ring(U_5238) ),
inference(variable_rename,[status(thm)],[f_1345_1]) ).
fof(f_1345_3,plain,
! [U_5238,U_5239,U_5240] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5238),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),U_5239),U_5240)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),hAPP(c_Groups_Ouminus__class_Ouminus(U_5238),U_5239)),U_5240)
| ~ class_Rings_Odivision__ring(U_5238) ),
inference(definitional_conversion,[status(esa)],[f_1345_2]) ).
cnf(f_1345_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5238),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),U_5239),U_5240)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),hAPP(c_Groups_Ouminus__class_Ouminus(U_5238),U_5239)),U_5240)
| ~ class_Rings_Odivision__ring(U_5238) ),
inference(clausify,[status(thm)],[f_1345_3]) ).
fof(f_1346_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| c_Groups_Osgn__class_Osgn(T_b,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__0__0]) ).
fof(f_1346_2,plain,
! [U_5242,U_5241] :
( ( ( c_Groups_Osgn__class_Osgn(U_5241,U_5242) = c_Groups_Ozero__class_Ozero(U_5241)
| U_5242 != c_Groups_Ozero__class_Ozero(U_5241) )
& ( U_5242 = c_Groups_Ozero__class_Ozero(U_5241)
| c_Groups_Osgn__class_Osgn(U_5241,U_5242) != c_Groups_Ozero__class_Ozero(U_5241) ) )
| ~ class_Rings_Olinordered__idom(U_5241) ),
inference(variable_rename,[status(thm)],[f_1346_1]) ).
fof(f_1346_3,plain,
( ! [U_5241,U_5242] :
( c_Groups_Osgn__class_Osgn(U_5241,U_5242) = c_Groups_Ozero__class_Ozero(U_5241)
| U_5242 != c_Groups_Ozero__class_Ozero(U_5241)
| ~ sP380(U_5241,U_5242) )
& ! [U_5241,U_5242] :
( U_5242 = c_Groups_Ozero__class_Ozero(U_5241)
| c_Groups_Osgn__class_Osgn(U_5241,U_5242) != c_Groups_Ozero__class_Ozero(U_5241)
| ~ sP380(U_5241,U_5242) )
& ! [U_5241,U_5242] :
( sP380(U_5241,U_5242)
| ~ class_Rings_Olinordered__idom(U_5241) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP380])],[f_1346_2]) ).
cnf(f_1346_4,plain,
( sP380(U_5241,U_5242)
| ~ class_Rings_Olinordered__idom(U_5241) ),
inference(clausify,[status(thm)],[f_1346_3]) ).
cnf(f_1346_5,plain,
( U_5242 = c_Groups_Ozero__class_Ozero(U_5241)
| c_Groups_Osgn__class_Osgn(U_5241,U_5242) != c_Groups_Ozero__class_Ozero(U_5241)
| ~ sP380(U_5241,U_5242) ),
inference(clausify,[status(thm)],[f_1346_3]) ).
cnf(f_1346_6,plain,
( c_Groups_Osgn__class_Osgn(U_5241,U_5242) = c_Groups_Ozero__class_Ozero(U_5241)
| U_5242 != c_Groups_Ozero__class_Ozero(U_5241)
| ~ sP380(U_5241,U_5242) ),
inference(clausify,[status(thm)],[f_1346_3]) ).
fof(f_1347_1,plain,
! [T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Osgn__if(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn0]) ).
fof(f_1347_2,plain,
! [U_5243] :
( c_Groups_Osgn__class_Osgn(U_5243,c_Groups_Ozero__class_Ozero(U_5243)) = c_Groups_Ozero__class_Ozero(U_5243)
| ~ class_Groups_Osgn__if(U_5243) ),
inference(variable_rename,[status(thm)],[f_1347_1]) ).
fof(f_1347_3,plain,
! [U_5243] :
( c_Groups_Osgn__class_Osgn(U_5243,c_Groups_Ozero__class_Ozero(U_5243)) = c_Groups_Ozero__class_Ozero(U_5243)
| ~ class_Groups_Osgn__if(U_5243) ),
inference(definitional_conversion,[status(esa)],[f_1347_2]) ).
cnf(f_1347_4,plain,
( c_Groups_Osgn__class_Osgn(U_5243,c_Groups_Ozero__class_Ozero(U_5243)) = c_Groups_Ozero__class_Ozero(U_5243)
| ~ class_Groups_Osgn__if(U_5243) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
fof(f_1348_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__times]) ).
fof(f_1348_2,plain,
! [U_5246,U_5245,U_5244] :
( c_Groups_Osgn__class_Osgn(U_5244,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5244),U_5245),U_5246)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5244),c_Groups_Osgn__class_Osgn(U_5244,U_5245)),c_Groups_Osgn__class_Osgn(U_5244,U_5246))
| ~ class_Rings_Olinordered__idom(U_5244) ),
inference(variable_rename,[status(thm)],[f_1348_1]) ).
fof(f_1348_3,plain,
! [U_5244,U_5245,U_5246] :
( c_Groups_Osgn__class_Osgn(U_5244,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5244),U_5245),U_5246)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5244),c_Groups_Osgn__class_Osgn(U_5244,U_5245)),c_Groups_Osgn__class_Osgn(U_5244,U_5246))
| ~ class_Rings_Olinordered__idom(U_5244) ),
inference(definitional_conversion,[status(esa)],[f_1348_2]) ).
cnf(f_1348_4,plain,
( c_Groups_Osgn__class_Osgn(U_5244,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5244),U_5245),U_5246)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5244),c_Groups_Osgn__class_Osgn(U_5244,U_5245)),c_Groups_Osgn__class_Osgn(U_5244,U_5246))
| ~ class_Rings_Olinordered__idom(U_5244) ),
inference(clausify,[status(thm)],[f_1348_3]) ).
fof(f_1349_1,plain,
! [V_b,V_a,V_c,T_a] :
( V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) != V_b
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__imp]) ).
fof(f_1349_2,plain,
! [U_5250,U_5249,U_5248,U_5247] :
( U_5249 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5247),U_5250),U_5248)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5247),U_5249),U_5248) != U_5250
| U_5248 = c_Groups_Ozero__class_Ozero(U_5247)
| ~ class_Rings_Odivision__ring(U_5247) ),
inference(variable_rename,[status(thm)],[f_1349_1]) ).
fof(f_1349_3,plain,
! [U_5247,U_5248,U_5249,U_5250] :
( U_5249 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5247),U_5250),U_5248)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5247),U_5249),U_5248) != U_5250
| U_5248 = c_Groups_Ozero__class_Ozero(U_5247)
| ~ class_Rings_Odivision__ring(U_5247) ),
inference(definitional_conversion,[status(esa)],[f_1349_2]) ).
cnf(f_1349_4,plain,
( U_5249 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5247),U_5250),U_5248)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5247),U_5249),U_5248) != U_5250
| U_5248 = c_Groups_Ozero__class_Ozero(U_5247)
| ~ class_Rings_Odivision__ring(U_5247) ),
inference(clausify,[status(thm)],[f_1349_3]) ).
fof(f_1350_1,plain,
! [V_a,V_b,V_c,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a
| V_b != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__imp]) ).
fof(f_1350_2,plain,
! [U_5254,U_5253,U_5252,U_5251] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5251),U_5253),U_5252) = U_5254
| U_5253 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5251),U_5254),U_5252)
| U_5252 = c_Groups_Ozero__class_Ozero(U_5251)
| ~ class_Rings_Odivision__ring(U_5251) ),
inference(variable_rename,[status(thm)],[f_1350_1]) ).
fof(f_1350_3,plain,
! [U_5253,U_5252,U_5251,U_5254] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5251),U_5253),U_5252) = U_5254
| U_5253 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5251),U_5254),U_5252)
| U_5252 = c_Groups_Ozero__class_Ozero(U_5251)
| ~ class_Rings_Odivision__ring(U_5251) ),
inference(definitional_conversion,[status(esa)],[f_1350_2]) ).
cnf(f_1350_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5251),U_5253),U_5252) = U_5254
| U_5253 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5251),U_5254),U_5252)
| U_5252 = c_Groups_Ozero__class_Ozero(U_5251)
| ~ class_Rings_Odivision__ring(U_5251) ),
inference(clausify,[status(thm)],[f_1350_3]) ).
fof(f_1351_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
| V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) != V_a_2 ) )
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Rings_Odivision__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).
fof(f_1351_2,plain,
! [U_5258,U_5257,U_5256,U_5255] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5256) = U_5258
| U_5257 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5258),U_5256) )
& ( U_5257 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5258),U_5256)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5256) != U_5258 ) )
| U_5256 = c_Groups_Ozero__class_Ozero(U_5255)
| ~ class_Rings_Odivision__ring(U_5255) ),
inference(variable_rename,[status(thm)],[f_1351_1]) ).
fof(f_1351_3,plain,
( ! [U_5255,U_5256,U_5257,U_5258] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5256) = U_5258
| U_5257 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5258),U_5256)
| ~ sP381(U_5255,U_5256,U_5257,U_5258) )
& ! [U_5255,U_5256,U_5257,U_5258] :
( U_5257 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5258),U_5256)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5256) != U_5258
| ~ sP381(U_5255,U_5256,U_5257,U_5258) )
& ! [U_5255,U_5256,U_5257,U_5258] :
( sP381(U_5255,U_5256,U_5257,U_5258)
| U_5256 = c_Groups_Ozero__class_Ozero(U_5255)
| ~ class_Rings_Odivision__ring(U_5255) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP381])],[f_1351_2]) ).
cnf(f_1351_4,plain,
( sP381(U_5255,U_5256,U_5257,U_5258)
| U_5256 = c_Groups_Ozero__class_Ozero(U_5255)
| ~ class_Rings_Odivision__ring(U_5255) ),
inference(clausify,[status(thm)],[f_1351_3]) ).
cnf(f_1351_5,plain,
( U_5257 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5258),U_5256)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5256) != U_5258
| ~ sP381(U_5255,U_5256,U_5257,U_5258) ),
inference(clausify,[status(thm)],[f_1351_3]) ).
cnf(f_1351_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5256) = U_5258
| U_5257 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5258),U_5256)
| ~ sP381(U_5255,U_5256,U_5257,U_5258) ),
inference(clausify,[status(thm)],[f_1351_3]) ).
fof(f_1352_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) != V_b_2 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) ) )
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Rings_Odivision__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).
fof(f_1352_2,plain,
! [U_5262,U_5261,U_5260,U_5259] :
( ( ( U_5261 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5262),U_5260)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5261),U_5260) != U_5262 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5261),U_5260) = U_5262
| U_5261 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5262),U_5260) ) )
| U_5260 = c_Groups_Ozero__class_Ozero(U_5259)
| ~ class_Rings_Odivision__ring(U_5259) ),
inference(variable_rename,[status(thm)],[f_1352_1]) ).
fof(f_1352_3,plain,
( ! [U_5262,U_5259,U_5260,U_5261] :
( U_5261 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5262),U_5260)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5261),U_5260) != U_5262
| ~ sP382(U_5262,U_5259,U_5260,U_5261) )
& ! [U_5262,U_5259,U_5260,U_5261] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5261),U_5260) = U_5262
| U_5261 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5262),U_5260)
| ~ sP382(U_5262,U_5259,U_5260,U_5261) )
& ! [U_5262,U_5259,U_5260,U_5261] :
( sP382(U_5262,U_5259,U_5260,U_5261)
| U_5260 = c_Groups_Ozero__class_Ozero(U_5259)
| ~ class_Rings_Odivision__ring(U_5259) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP382])],[f_1352_2]) ).
cnf(f_1352_4,plain,
( sP382(U_5262,U_5259,U_5260,U_5261)
| U_5260 = c_Groups_Ozero__class_Ozero(U_5259)
| ~ class_Rings_Odivision__ring(U_5259) ),
inference(clausify,[status(thm)],[f_1352_3]) ).
cnf(f_1352_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5261),U_5260) = U_5262
| U_5261 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5262),U_5260)
| ~ sP382(U_5262,U_5259,U_5260,U_5261) ),
inference(clausify,[status(thm)],[f_1352_3]) ).
cnf(f_1352_6,plain,
( U_5261 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5262),U_5260)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5261),U_5260) != U_5262
| ~ sP382(U_5262,U_5259,U_5260,U_5261) ),
inference(clausify,[status(thm)],[f_1352_3]) ).
fof(f_1353_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) != c_Groups_Oone__class_Oone(T_b) ) )
| V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Rings_Odivision__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).
fof(f_1353_2,plain,
! [U_5265,U_5264,U_5263] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5265),U_5264) = c_Groups_Oone__class_Oone(U_5263)
| U_5265 != U_5264 )
& ( U_5265 = U_5264
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5265),U_5264) != c_Groups_Oone__class_Oone(U_5263) ) )
| U_5264 = c_Groups_Ozero__class_Ozero(U_5263)
| ~ class_Rings_Odivision__ring(U_5263) ),
inference(variable_rename,[status(thm)],[f_1353_1]) ).
fof(f_1353_3,plain,
( ! [U_5263,U_5264,U_5265] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5265),U_5264) = c_Groups_Oone__class_Oone(U_5263)
| U_5265 != U_5264
| ~ sP383(U_5263,U_5264,U_5265) )
& ! [U_5263,U_5264,U_5265] :
( U_5265 = U_5264
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5265),U_5264) != c_Groups_Oone__class_Oone(U_5263)
| ~ sP383(U_5263,U_5264,U_5265) )
& ! [U_5263,U_5264,U_5265] :
( sP383(U_5263,U_5264,U_5265)
| U_5264 = c_Groups_Ozero__class_Ozero(U_5263)
| ~ class_Rings_Odivision__ring(U_5263) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP383])],[f_1353_2]) ).
cnf(f_1353_4,plain,
( sP383(U_5263,U_5264,U_5265)
| U_5264 = c_Groups_Ozero__class_Ozero(U_5263)
| ~ class_Rings_Odivision__ring(U_5263) ),
inference(clausify,[status(thm)],[f_1353_3]) ).
cnf(f_1353_5,plain,
( U_5265 = U_5264
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5265),U_5264) != c_Groups_Oone__class_Oone(U_5263)
| ~ sP383(U_5263,U_5264,U_5265) ),
inference(clausify,[status(thm)],[f_1353_3]) ).
cnf(f_1353_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5265),U_5264) = c_Groups_Oone__class_Oone(U_5263)
| U_5265 != U_5264
| ~ sP383(U_5263,U_5264,U_5265) ),
inference(clausify,[status(thm)],[f_1353_3]) ).
fof(f_1354_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__self]) ).
fof(f_1354_2,plain,
! [U_5267,U_5266] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5266),U_5267),U_5267) = c_Groups_Oone__class_Oone(U_5266)
| U_5267 = c_Groups_Ozero__class_Ozero(U_5266)
| ~ class_Rings_Odivision__ring(U_5266) ),
inference(variable_rename,[status(thm)],[f_1354_1]) ).
fof(f_1354_3,plain,
! [U_5267,U_5266] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5266),U_5267),U_5267) = c_Groups_Oone__class_Oone(U_5266)
| U_5267 = c_Groups_Ozero__class_Ozero(U_5266)
| ~ class_Rings_Odivision__ring(U_5266) ),
inference(definitional_conversion,[status(esa)],[f_1354_2]) ).
cnf(f_1354_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5266),U_5267),U_5267) = c_Groups_Oone__class_Oone(U_5266)
| U_5267 = c_Groups_Ozero__class_Ozero(U_5266)
| ~ class_Rings_Odivision__ring(U_5266) ),
inference(clausify,[status(thm)],[f_1354_3]) ).
fof(f_1355_1,plain,
! [V_a,T_a] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| V_a != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__self__if]) ).
fof(f_1355_2,plain,
! [U_5269,U_5268] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5268),U_5269),U_5269) = c_Groups_Oone__class_Oone(U_5268)
| U_5269 = c_Groups_Ozero__class_Ozero(U_5268) )
& ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5268),U_5269),U_5269) = c_Groups_Ozero__class_Ozero(U_5268)
| U_5269 != c_Groups_Ozero__class_Ozero(U_5268) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_5268) ),
inference(variable_rename,[status(thm)],[f_1355_1]) ).
fof(f_1355_3,plain,
( ! [U_5269,U_5268] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5268),U_5269),U_5269) = c_Groups_Oone__class_Oone(U_5268)
| U_5269 = c_Groups_Ozero__class_Ozero(U_5268)
| ~ sP384(U_5269,U_5268) )
& ! [U_5269,U_5268] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5268),U_5269),U_5269) = c_Groups_Ozero__class_Ozero(U_5268)
| U_5269 != c_Groups_Ozero__class_Ozero(U_5268)
| ~ sP384(U_5269,U_5268) )
& ! [U_5269,U_5268] :
( sP384(U_5269,U_5268)
| ~ class_Rings_Odivision__ring__inverse__zero(U_5268) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP384])],[f_1355_2]) ).
cnf(f_1355_4,plain,
( sP384(U_5269,U_5268)
| ~ class_Rings_Odivision__ring__inverse__zero(U_5268) ),
inference(clausify,[status(thm)],[f_1355_3]) ).
cnf(f_1355_5,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5268),U_5269),U_5269) = c_Groups_Ozero__class_Ozero(U_5268)
| U_5269 != c_Groups_Ozero__class_Ozero(U_5268)
| ~ sP384(U_5269,U_5268) ),
inference(clausify,[status(thm)],[f_1355_3]) ).
cnf(f_1355_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5268),U_5269),U_5269) = c_Groups_Oone__class_Oone(U_5268)
| U_5269 = c_Groups_Ozero__class_Ozero(U_5268)
| ~ sP384(U_5269,U_5268) ),
inference(clausify,[status(thm)],[f_1355_3]) ).
fof(f_1356_1,plain,
! [V_a,V_b,T_a] :
( 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)
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide]) ).
fof(f_1356_2,plain,
! [U_5272,U_5271,U_5270] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5270),hAPP(c_Groups_Ouminus__class_Ouminus(U_5270),U_5272)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5270),U_5271)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5270),U_5272),U_5271)
| U_5271 = c_Groups_Ozero__class_Ozero(U_5270)
| ~ class_Rings_Odivision__ring(U_5270) ),
inference(variable_rename,[status(thm)],[f_1356_1]) ).
fof(f_1356_3,plain,
! [U_5271,U_5272,U_5270] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5270),hAPP(c_Groups_Ouminus__class_Ouminus(U_5270),U_5272)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5270),U_5271)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5270),U_5272),U_5271)
| U_5271 = c_Groups_Ozero__class_Ozero(U_5270)
| ~ class_Rings_Odivision__ring(U_5270) ),
inference(definitional_conversion,[status(esa)],[f_1356_2]) ).
cnf(f_1356_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5270),hAPP(c_Groups_Ouminus__class_Ouminus(U_5270),U_5272)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5270),U_5271)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5270),U_5272),U_5271)
| U_5271 = c_Groups_Ozero__class_Ozero(U_5270)
| ~ class_Rings_Odivision__ring(U_5270) ),
inference(clausify,[status(thm)],[f_1356_3]) ).
fof(f_1357_1,plain,
! [V_a,V_b,T_a] :
( 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))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right]) ).
fof(f_1357_2,plain,
! [U_5275,U_5274,U_5273] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5273),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5273),U_5275),U_5274)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5273),U_5275),hAPP(c_Groups_Ouminus__class_Ouminus(U_5273),U_5274))
| U_5274 = c_Groups_Ozero__class_Ozero(U_5273)
| ~ class_Rings_Odivision__ring(U_5273) ),
inference(variable_rename,[status(thm)],[f_1357_1]) ).
fof(f_1357_3,plain,
! [U_5273,U_5274,U_5275] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5273),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5273),U_5275),U_5274)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5273),U_5275),hAPP(c_Groups_Ouminus__class_Ouminus(U_5273),U_5274))
| U_5274 = c_Groups_Ozero__class_Ozero(U_5273)
| ~ class_Rings_Odivision__ring(U_5273) ),
inference(definitional_conversion,[status(esa)],[f_1357_2]) ).
cnf(f_1357_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5273),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5273),U_5275),U_5274)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5273),U_5275),hAPP(c_Groups_Ouminus__class_Ouminus(U_5273),U_5274))
| U_5274 = c_Groups_Ozero__class_Ozero(U_5273)
| ~ class_Rings_Odivision__ring(U_5273) ),
inference(clausify,[status(thm)],[f_1357_3]) ).
fof(f_1358_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).
fof(f_1358_2,plain,
! [U_5277,U_5276] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),c_Groups_Osgn__class_Osgn(U_5276,U_5277)),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),U_5277),c_Groups_Ozero__class_Ozero(U_5276))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),U_5277),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),c_Groups_Osgn__class_Osgn(U_5276,U_5277)),c_Groups_Ozero__class_Ozero(U_5276))) ) )
| ~ class_Rings_Olinordered__idom(U_5276) ),
inference(variable_rename,[status(thm)],[f_1358_1]) ).
fof(f_1358_3,plain,
( ! [U_5276,U_5277] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),c_Groups_Osgn__class_Osgn(U_5276,U_5277)),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),U_5277),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ sP385(U_5276,U_5277) )
& ! [U_5276,U_5277] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),U_5277),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),c_Groups_Osgn__class_Osgn(U_5276,U_5277)),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ sP385(U_5276,U_5277) )
& ! [U_5276,U_5277] :
( sP385(U_5276,U_5277)
| ~ class_Rings_Olinordered__idom(U_5276) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP385])],[f_1358_2]) ).
cnf(f_1358_4,plain,
( sP385(U_5276,U_5277)
| ~ class_Rings_Olinordered__idom(U_5276) ),
inference(clausify,[status(thm)],[f_1358_3]) ).
cnf(f_1358_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),U_5277),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),c_Groups_Osgn__class_Osgn(U_5276,U_5277)),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ sP385(U_5276,U_5277) ),
inference(clausify,[status(thm)],[f_1358_3]) ).
cnf(f_1358_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),c_Groups_Osgn__class_Osgn(U_5276,U_5277)),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5276),U_5277),c_Groups_Ozero__class_Ozero(U_5276)))
| ~ sP385(U_5276,U_5277) ),
inference(clausify,[status(thm)],[f_1358_3]) ).
fof(f_1359_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).
fof(f_1359_2,plain,
! [U_5279,U_5278] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),c_Groups_Osgn__class_Osgn(U_5278,U_5279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),U_5279)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),U_5279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),c_Groups_Osgn__class_Osgn(U_5278,U_5279))) ) )
| ~ class_Rings_Olinordered__idom(U_5278) ),
inference(variable_rename,[status(thm)],[f_1359_1]) ).
fof(f_1359_3,plain,
( ! [U_5279,U_5278] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),c_Groups_Osgn__class_Osgn(U_5278,U_5279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),U_5279))
| ~ sP386(U_5279,U_5278) )
& ! [U_5279,U_5278] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),U_5279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),c_Groups_Osgn__class_Osgn(U_5278,U_5279)))
| ~ sP386(U_5279,U_5278) )
& ! [U_5279,U_5278] :
( sP386(U_5279,U_5278)
| ~ class_Rings_Olinordered__idom(U_5278) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP386])],[f_1359_2]) ).
cnf(f_1359_4,plain,
( sP386(U_5279,U_5278)
| ~ class_Rings_Olinordered__idom(U_5278) ),
inference(clausify,[status(thm)],[f_1359_3]) ).
cnf(f_1359_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),U_5279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),c_Groups_Osgn__class_Osgn(U_5278,U_5279)))
| ~ sP386(U_5279,U_5278) ),
inference(clausify,[status(thm)],[f_1359_3]) ).
cnf(f_1359_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),c_Groups_Osgn__class_Osgn(U_5278,U_5279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5278),c_Groups_Ozero__class_Ozero(U_5278)),U_5279))
| ~ sP386(U_5279,U_5278) ),
inference(clausify,[status(thm)],[f_1359_3]) ).
fof(f_1360_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff]) ).
fof(f_1360_2,plain,
! [U_5283,U_5282,U_5281,U_5280] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5280,U_5281)),c_Sum__Type_OPlus(U_5280,U_5281,U_5282,U_5283)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5281),U_5283))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5280),U_5282)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5281),U_5283))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_5280),U_5282)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5280,U_5281)),c_Sum__Type_OPlus(U_5280,U_5281,U_5282,U_5283))) ) ),
inference(variable_rename,[status(thm)],[f_1360_1]) ).
fof(f_1360_3,plain,
( ! [U_5291,U_5289,U_5287,U_5285] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5285,U_5287)),c_Sum__Type_OPlus(U_5285,U_5287,U_5289,U_5291)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5287),U_5291))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5285),U_5289)) )
& ! [U_5290,U_5288,U_5286,U_5284] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5286),U_5290))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_5284),U_5288)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5284,U_5286)),c_Sum__Type_OPlus(U_5284,U_5286,U_5288,U_5290))) ) ),
inference(miniscope,[status(thm)],[f_1360_2]) ).
fof(f_1360_4,plain,
( ! [U_5284,U_5290,U_5286,U_5288] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5286),U_5290))
| ~ sP387(U_5284,U_5290,U_5286,U_5288) )
& ! [U_5284,U_5290,U_5286,U_5288] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5284),U_5288))
| ~ sP387(U_5284,U_5290,U_5286,U_5288) )
& ! [U_5285,U_5291,U_5287,U_5289] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5285,U_5287)),c_Sum__Type_OPlus(U_5285,U_5287,U_5289,U_5291)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5287),U_5291))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5285),U_5289)) )
& ! [U_5284,U_5290,U_5286,U_5288] :
( sP387(U_5284,U_5290,U_5286,U_5288)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5284,U_5286)),c_Sum__Type_OPlus(U_5284,U_5286,U_5288,U_5290))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP387])],[f_1360_3]) ).
cnf(f_1360_5,plain,
( sP387(U_5284,U_5290,U_5286,U_5288)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5284,U_5286)),c_Sum__Type_OPlus(U_5284,U_5286,U_5288,U_5290))) ),
inference(clausify,[status(thm)],[f_1360_4]) ).
cnf(f_1360_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5285,U_5287)),c_Sum__Type_OPlus(U_5285,U_5287,U_5289,U_5291)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5287),U_5291))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5285),U_5289)) ),
inference(clausify,[status(thm)],[f_1360_4]) ).
cnf(f_1360_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5284),U_5288))
| ~ sP387(U_5284,U_5290,U_5286,U_5288) ),
inference(clausify,[status(thm)],[f_1360_4]) ).
cnf(f_1360_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5286),U_5290))
| ~ sP387(U_5284,U_5290,U_5286,U_5288) ),
inference(clausify,[status(thm)],[f_1360_4]) ).
fof(f_1361_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus]) ).
fof(f_1361_2,plain,
! [U_5295,U_5294,U_5293,U_5292] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5292,U_5294)),c_Sum__Type_OPlus(U_5292,U_5294,U_5293,U_5295)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5294),U_5295))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5292),U_5293)) ),
inference(variable_rename,[status(thm)],[f_1361_1]) ).
fof(f_1361_3,plain,
! [U_5293,U_5294,U_5292,U_5295] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5292,U_5294)),c_Sum__Type_OPlus(U_5292,U_5294,U_5293,U_5295)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5294),U_5295))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5292),U_5293)) ),
inference(definitional_conversion,[status(esa)],[f_1361_2]) ).
cnf(f_1361_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5292,U_5294)),c_Sum__Type_OPlus(U_5292,U_5294,U_5293,U_5295)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5294),U_5295))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5292),U_5293)) ),
inference(clausify,[status(thm)],[f_1361_3]) ).
fof(f_1362_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J]) ).
fof(f_1362_2,plain,
! [U_5299,U_5298,U_5297,U_5296] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5296),U_5298))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5296,U_5297)),c_Sum__Type_OPlus(U_5296,U_5297,U_5298,U_5299))) ),
inference(variable_rename,[status(thm)],[f_1362_1]) ).
fof(f_1362_3,plain,
! [U_5296,U_5297,U_5298,U_5299] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5296),U_5298))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5296,U_5297)),c_Sum__Type_OPlus(U_5296,U_5297,U_5298,U_5299))) ),
inference(definitional_conversion,[status(esa)],[f_1362_2]) ).
cnf(f_1362_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5296),U_5298))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5296,U_5297)),c_Sum__Type_OPlus(U_5296,U_5297,U_5298,U_5299))) ),
inference(clausify,[status(thm)],[f_1362_3]) ).
fof(f_1363_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J]) ).
fof(f_1363_2,plain,
! [U_5303,U_5302,U_5301,U_5300] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5301),U_5303))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5300,U_5301)),c_Sum__Type_OPlus(U_5300,U_5301,U_5302,U_5303))) ),
inference(variable_rename,[status(thm)],[f_1363_1]) ).
fof(f_1363_3,plain,
! [U_5303,U_5302,U_5301] :
( ! [U_5300] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5300,U_5301)),c_Sum__Type_OPlus(U_5300,U_5301,U_5302,U_5303)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5301),U_5303)) ),
inference(miniscope,[status(thm)],[f_1363_2]) ).
fof(f_1363_4,plain,
! [U_5300,U_5301,U_5302,U_5303] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5300,U_5301)),c_Sum__Type_OPlus(U_5300,U_5301,U_5302,U_5303)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5301),U_5303)) ),
inference(definitional_conversion,[status(esa)],[f_1363_3]) ).
cnf(f_1363_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5300,U_5301)),c_Sum__Type_OPlus(U_5300,U_5301,U_5302,U_5303)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_5301),U_5303)) ),
inference(clausify,[status(thm)],[f_1363_4]) ).
fof(f_1364_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__pos]) ).
fof(f_1364_2,plain,
! [U_5305,U_5304] :
( c_Groups_Osgn__class_Osgn(U_5304,U_5305) = c_Groups_Oone__class_Oone(U_5304)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5304),c_Groups_Ozero__class_Ozero(U_5304)),U_5305))
| ~ class_Rings_Olinordered__idom(U_5304) ),
inference(variable_rename,[status(thm)],[f_1364_1]) ).
fof(f_1364_3,plain,
! [U_5304,U_5305] :
( c_Groups_Osgn__class_Osgn(U_5304,U_5305) = c_Groups_Oone__class_Oone(U_5304)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5304),c_Groups_Ozero__class_Ozero(U_5304)),U_5305))
| ~ class_Rings_Olinordered__idom(U_5304) ),
inference(definitional_conversion,[status(esa)],[f_1364_2]) ).
cnf(f_1364_4,plain,
( c_Groups_Osgn__class_Osgn(U_5304,U_5305) = c_Groups_Oone__class_Oone(U_5304)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5304),c_Groups_Ozero__class_Ozero(U_5304)),U_5305))
| ~ class_Rings_Olinordered__idom(U_5304) ),
inference(clausify,[status(thm)],[f_1364_3]) ).
fof(f_1365_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| c_Groups_Osgn__class_Osgn(T_b,V_a_2) != c_Groups_Oone__class_Oone(T_b) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__pos]) ).
fof(f_1365_2,plain,
! [U_5307,U_5306] :
( ( ( c_Groups_Osgn__class_Osgn(U_5306,U_5307) = c_Groups_Oone__class_Oone(U_5306)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5306),c_Groups_Ozero__class_Ozero(U_5306)),U_5307)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5306),c_Groups_Ozero__class_Ozero(U_5306)),U_5307))
| c_Groups_Osgn__class_Osgn(U_5306,U_5307) != c_Groups_Oone__class_Oone(U_5306) ) )
| ~ class_Rings_Olinordered__idom(U_5306) ),
inference(variable_rename,[status(thm)],[f_1365_1]) ).
fof(f_1365_3,plain,
( ! [U_5306,U_5307] :
( c_Groups_Osgn__class_Osgn(U_5306,U_5307) = c_Groups_Oone__class_Oone(U_5306)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5306),c_Groups_Ozero__class_Ozero(U_5306)),U_5307))
| ~ sP388(U_5306,U_5307) )
& ! [U_5306,U_5307] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5306),c_Groups_Ozero__class_Ozero(U_5306)),U_5307))
| c_Groups_Osgn__class_Osgn(U_5306,U_5307) != c_Groups_Oone__class_Oone(U_5306)
| ~ sP388(U_5306,U_5307) )
& ! [U_5306,U_5307] :
( sP388(U_5306,U_5307)
| ~ class_Rings_Olinordered__idom(U_5306) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP388])],[f_1365_2]) ).
cnf(f_1365_4,plain,
( sP388(U_5306,U_5307)
| ~ class_Rings_Olinordered__idom(U_5306) ),
inference(clausify,[status(thm)],[f_1365_3]) ).
cnf(f_1365_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5306),c_Groups_Ozero__class_Ozero(U_5306)),U_5307))
| c_Groups_Osgn__class_Osgn(U_5306,U_5307) != c_Groups_Oone__class_Oone(U_5306)
| ~ sP388(U_5306,U_5307) ),
inference(clausify,[status(thm)],[f_1365_3]) ).
cnf(f_1365_6,plain,
( c_Groups_Osgn__class_Osgn(U_5306,U_5307) = c_Groups_Oone__class_Oone(U_5306)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5306),c_Groups_Ozero__class_Ozero(U_5306)),U_5307))
| ~ sP388(U_5306,U_5307) ),
inference(clausify,[status(thm)],[f_1365_3]) ).
fof(f_1366_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Plus]) ).
fof(f_1366_2,plain,
! [U_5311,U_5310,U_5309,U_5308] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5308,U_5310)),c_Sum__Type_OPlus(U_5308,U_5310,U_5309,U_5311)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5308),U_5309)),hAPP(c_Finite__Set_Ocard(U_5310),U_5311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5310),U_5311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5308),U_5309)) ),
inference(variable_rename,[status(thm)],[f_1366_1]) ).
fof(f_1366_3,plain,
! [U_5308,U_5309,U_5310,U_5311] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5308,U_5310)),c_Sum__Type_OPlus(U_5308,U_5310,U_5309,U_5311)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5308),U_5309)),hAPP(c_Finite__Set_Ocard(U_5310),U_5311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5310),U_5311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5308),U_5309)) ),
inference(definitional_conversion,[status(esa)],[f_1366_2]) ).
cnf(f_1366_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_5308,U_5310)),c_Sum__Type_OPlus(U_5308,U_5310,U_5309,U_5311)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5308),U_5309)),hAPP(c_Finite__Set_Ocard(U_5310),U_5311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5310),U_5311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5308),U_5309)) ),
inference(clausify,[status(thm)],[f_1366_3]) ).
fof(f_1367_1,plain,
! [V_x,T_a] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) )
& ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) ) )
| V_x = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a)
| V_x != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Osgn__if(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__if]) ).
fof(f_1367_2,plain,
! [U_5313,U_5312] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5312),c_Groups_Oone__class_Oone(U_5312))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5312),c_Groups_Ozero__class_Ozero(U_5312)),U_5313)) )
& ( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = c_Groups_Oone__class_Oone(U_5312)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5312),c_Groups_Ozero__class_Ozero(U_5312)),U_5313)) ) )
| U_5313 = c_Groups_Ozero__class_Ozero(U_5312) )
& ( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = c_Groups_Ozero__class_Ozero(U_5312)
| U_5313 != c_Groups_Ozero__class_Ozero(U_5312) ) )
| ~ class_Groups_Osgn__if(U_5312) ),
inference(variable_rename,[status(thm)],[f_1367_1]) ).
fof(f_1367_3,plain,
( ! [U_5313,U_5312] :
( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5312),c_Groups_Oone__class_Oone(U_5312))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5312),c_Groups_Ozero__class_Ozero(U_5312)),U_5313))
| ~ sP389(U_5313,U_5312) )
& ! [U_5313,U_5312] :
( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = c_Groups_Oone__class_Oone(U_5312)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5312),c_Groups_Ozero__class_Ozero(U_5312)),U_5313))
| ~ sP389(U_5313,U_5312) )
& ! [U_5313,U_5312] :
( sP389(U_5313,U_5312)
| U_5313 = c_Groups_Ozero__class_Ozero(U_5312)
| ~ sP390(U_5313,U_5312) )
& ! [U_5313,U_5312] :
( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = c_Groups_Ozero__class_Ozero(U_5312)
| U_5313 != c_Groups_Ozero__class_Ozero(U_5312)
| ~ sP390(U_5313,U_5312) )
& ! [U_5313,U_5312] :
( sP390(U_5313,U_5312)
| ~ class_Groups_Osgn__if(U_5312) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP389,sP390])],[f_1367_2]) ).
cnf(f_1367_4,plain,
( sP390(U_5313,U_5312)
| ~ class_Groups_Osgn__if(U_5312) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
cnf(f_1367_5,plain,
( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = c_Groups_Ozero__class_Ozero(U_5312)
| U_5313 != c_Groups_Ozero__class_Ozero(U_5312)
| ~ sP390(U_5313,U_5312) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
cnf(f_1367_6,plain,
( sP389(U_5313,U_5312)
| U_5313 = c_Groups_Ozero__class_Ozero(U_5312)
| ~ sP390(U_5313,U_5312) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
cnf(f_1367_7,plain,
( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = c_Groups_Oone__class_Oone(U_5312)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5312),c_Groups_Ozero__class_Ozero(U_5312)),U_5313))
| ~ sP389(U_5313,U_5312) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
cnf(f_1367_8,plain,
( c_Groups_Osgn__class_Osgn(U_5312,U_5313) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5312),c_Groups_Oone__class_Oone(U_5312))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5312),c_Groups_Ozero__class_Ozero(U_5312)),U_5313))
| ~ sP389(U_5313,U_5312) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
fof(f_1368_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__neg]) ).
fof(f_1368_2,plain,
! [U_5315,U_5314] :
( c_Groups_Osgn__class_Osgn(U_5314,U_5315) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5314),c_Groups_Oone__class_Oone(U_5314))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5314),U_5315),c_Groups_Ozero__class_Ozero(U_5314)))
| ~ class_Rings_Olinordered__idom(U_5314) ),
inference(variable_rename,[status(thm)],[f_1368_1]) ).
fof(f_1368_3,plain,
! [U_5315,U_5314] :
( c_Groups_Osgn__class_Osgn(U_5314,U_5315) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5314),c_Groups_Oone__class_Oone(U_5314))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5314),U_5315),c_Groups_Ozero__class_Ozero(U_5314)))
| ~ class_Rings_Olinordered__idom(U_5314) ),
inference(definitional_conversion,[status(esa)],[f_1368_2]) ).
cnf(f_1368_4,plain,
( c_Groups_Osgn__class_Osgn(U_5314,U_5315) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5314),c_Groups_Oone__class_Oone(U_5314))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5314),U_5315),c_Groups_Ozero__class_Ozero(U_5314)))
| ~ class_Rings_Olinordered__idom(U_5314) ),
inference(clausify,[status(thm)],[f_1368_3]) ).
fof(f_1369_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg]) ).
fof(f_1369_2,plain,
! [U_5319,U_5318,U_5317,U_5316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5316),U_5319),U_5317)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5316),U_5319),U_5318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5316),c_Groups_Ozero__class_Ozero(U_5316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5316),U_5317),U_5318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),U_5319),c_Groups_Ozero__class_Ozero(U_5316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),U_5317),U_5318))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5316) ),
inference(variable_rename,[status(thm)],[f_1369_1]) ).
fof(f_1369_3,plain,
! [U_5317,U_5318,U_5316,U_5319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5316),U_5319),U_5317)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5316),U_5319),U_5318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5316),c_Groups_Ozero__class_Ozero(U_5316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5316),U_5317),U_5318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),U_5319),c_Groups_Ozero__class_Ozero(U_5316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),U_5317),U_5318))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5316) ),
inference(definitional_conversion,[status(esa)],[f_1369_2]) ).
cnf(f_1369_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5316),U_5319),U_5317)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5316),U_5319),U_5318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5316),c_Groups_Ozero__class_Ozero(U_5316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5316),U_5317),U_5318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),U_5319),c_Groups_Ozero__class_Ozero(U_5316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5316),U_5317),U_5318))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5316) ),
inference(clausify,[status(thm)],[f_1369_3]) ).
fof(f_1370_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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)))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__left__mono]) ).
fof(f_1370_2,plain,
! [U_5323,U_5322,U_5321,U_5320] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5320),U_5323),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5320),U_5323),U_5321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5320),c_Groups_Ozero__class_Ozero(U_5320)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5320),U_5322),U_5321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),c_Groups_Ozero__class_Ozero(U_5320)),U_5323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),U_5321),U_5322))
| ~ class_Fields_Olinordered__field(U_5320) ),
inference(variable_rename,[status(thm)],[f_1370_1]) ).
fof(f_1370_3,plain,
! [U_5320,U_5321,U_5322,U_5323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5320),U_5323),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5320),U_5323),U_5321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5320),c_Groups_Ozero__class_Ozero(U_5320)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5320),U_5322),U_5321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),c_Groups_Ozero__class_Ozero(U_5320)),U_5323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),U_5321),U_5322))
| ~ class_Fields_Olinordered__field(U_5320) ),
inference(definitional_conversion,[status(esa)],[f_1370_2]) ).
cnf(f_1370_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5320),U_5323),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5320),U_5323),U_5321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5320),c_Groups_Ozero__class_Ozero(U_5320)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5320),U_5322),U_5321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),c_Groups_Ozero__class_Ozero(U_5320)),U_5323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5320),U_5321),U_5322))
| ~ class_Fields_Olinordered__field(U_5320) ),
inference(clausify,[status(thm)],[f_1370_3]) ).
fof(f_1371_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).
fof(f_1371_2,plain,
! [U_5327,U_5326,U_5325,U_5324] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5324),U_5326),U_5325)),U_5327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5324),U_5327),U_5325)),U_5326)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5324),U_5327),U_5325)),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5324),U_5326),U_5325)),U_5327)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5324),U_5325),c_Groups_Ozero__class_Ozero(U_5324)))
| ~ class_Fields_Olinordered__field(U_5324) ),
inference(variable_rename,[status(thm)],[f_1371_1]) ).
fof(f_1371_3,plain,
( ! [U_5325,U_5324,U_5326,U_5327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5324),U_5326),U_5325)),U_5327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5324),U_5327),U_5325)),U_5326))
| ~ sP391(U_5325,U_5324,U_5326,U_5327) )
& ! [U_5325,U_5324,U_5326,U_5327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5324),U_5327),U_5325)),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5324),U_5326),U_5325)),U_5327))
| ~ sP391(U_5325,U_5324,U_5326,U_5327) )
& ! [U_5325,U_5324,U_5326,U_5327] :
( sP391(U_5325,U_5324,U_5326,U_5327)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5324),U_5325),c_Groups_Ozero__class_Ozero(U_5324)))
| ~ class_Fields_Olinordered__field(U_5324) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP391])],[f_1371_2]) ).
cnf(f_1371_4,plain,
( sP391(U_5325,U_5324,U_5326,U_5327)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5324),U_5325),c_Groups_Ozero__class_Ozero(U_5324)))
| ~ class_Fields_Olinordered__field(U_5324) ),
inference(clausify,[status(thm)],[f_1371_3]) ).
cnf(f_1371_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5324),U_5327),U_5325)),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5324),U_5326),U_5325)),U_5327))
| ~ sP391(U_5325,U_5324,U_5326,U_5327) ),
inference(clausify,[status(thm)],[f_1371_3]) ).
cnf(f_1371_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5324),U_5326),U_5325)),U_5327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5324),U_5327),U_5325)),U_5326))
| ~ sP391(U_5325,U_5324,U_5326,U_5327) ),
inference(clausify,[status(thm)],[f_1371_3]) ).
fof(f_1372_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( 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_ca_2)))
| ~ 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_ca_2))) )
& ( 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_ca_2)))
| ~ 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_ca_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).
fof(f_1372_2,plain,
! [U_5331,U_5330,U_5329,U_5328] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5330),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5328),U_5331),U_5329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5328),U_5330),U_5329))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5328),U_5330),U_5329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5330),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5328),U_5331),U_5329))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5328),U_5329),c_Groups_Ozero__class_Ozero(U_5328)))
| ~ class_Fields_Olinordered__field(U_5328) ),
inference(variable_rename,[status(thm)],[f_1372_1]) ).
fof(f_1372_3,plain,
( ! [U_5329,U_5330,U_5328,U_5331] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5330),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5328),U_5331),U_5329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5328),U_5330),U_5329)))
| ~ sP392(U_5329,U_5330,U_5328,U_5331) )
& ! [U_5329,U_5330,U_5328,U_5331] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5328),U_5330),U_5329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5330),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5328),U_5331),U_5329)))
| ~ sP392(U_5329,U_5330,U_5328,U_5331) )
& ! [U_5329,U_5330,U_5328,U_5331] :
( sP392(U_5329,U_5330,U_5328,U_5331)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5328),U_5329),c_Groups_Ozero__class_Ozero(U_5328)))
| ~ class_Fields_Olinordered__field(U_5328) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP392])],[f_1372_2]) ).
cnf(f_1372_4,plain,
( sP392(U_5329,U_5330,U_5328,U_5331)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5328),U_5329),c_Groups_Ozero__class_Ozero(U_5328)))
| ~ class_Fields_Olinordered__field(U_5328) ),
inference(clausify,[status(thm)],[f_1372_3]) ).
cnf(f_1372_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5328),U_5330),U_5329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5330),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5328),U_5331),U_5329)))
| ~ sP392(U_5329,U_5330,U_5328,U_5331) ),
inference(clausify,[status(thm)],[f_1372_3]) ).
cnf(f_1372_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5330),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5328),U_5331),U_5329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),U_5331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5328),U_5330),U_5329)))
| ~ sP392(U_5329,U_5330,U_5328,U_5331) ),
inference(clausify,[status(thm)],[f_1372_3]) ).
fof(f_1373_1,plain,
! [V_x,V_z,V_y,T_a] :
( 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)))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos]) ).
fof(f_1373_2,plain,
! [U_5335,U_5334,U_5333,U_5332] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5332),U_5334),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5332),U_5335),U_5333)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5332),U_5334),U_5333)),U_5335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5332),c_Groups_Ozero__class_Ozero(U_5332)),U_5333))
| ~ class_Fields_Olinordered__field(U_5332) ),
inference(variable_rename,[status(thm)],[f_1373_1]) ).
fof(f_1373_3,plain,
! [U_5334,U_5333,U_5332,U_5335] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5332),U_5334),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5332),U_5335),U_5333)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5332),U_5334),U_5333)),U_5335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5332),c_Groups_Ozero__class_Ozero(U_5332)),U_5333))
| ~ class_Fields_Olinordered__field(U_5332) ),
inference(definitional_conversion,[status(esa)],[f_1373_2]) ).
cnf(f_1373_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5332),U_5334),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5332),U_5335),U_5333)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5332),U_5334),U_5333)),U_5335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5332),c_Groups_Ozero__class_Ozero(U_5332)),U_5333))
| ~ class_Fields_Olinordered__field(U_5332) ),
inference(clausify,[status(thm)],[f_1373_3]) ).
fof(f_1374_1,plain,
! [V_z,V_x,V_y,T_a] :
( 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))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le]) ).
fof(f_1374_2,plain,
! [U_5339,U_5338,U_5337,U_5336] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5336),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5336),U_5338),U_5337)),U_5339))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5336),U_5338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5336),U_5339),U_5337)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),c_Groups_Ozero__class_Ozero(U_5336)),U_5337))
| ~ class_Fields_Olinordered__field(U_5336) ),
inference(variable_rename,[status(thm)],[f_1374_1]) ).
fof(f_1374_3,plain,
! [U_5336,U_5337,U_5338,U_5339] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5336),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5336),U_5338),U_5337)),U_5339))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5336),U_5338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5336),U_5339),U_5337)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),c_Groups_Ozero__class_Ozero(U_5336)),U_5337))
| ~ class_Fields_Olinordered__field(U_5336) ),
inference(definitional_conversion,[status(esa)],[f_1374_2]) ).
cnf(f_1374_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5336),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5336),U_5338),U_5337)),U_5339))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5336),U_5338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5336),U_5339),U_5337)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),c_Groups_Ozero__class_Ozero(U_5336)),U_5337))
| ~ class_Fields_Olinordered__field(U_5336) ),
inference(clausify,[status(thm)],[f_1374_3]) ).
fof(f_1375_1,plain,
! [V_w,V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq]) ).
fof(f_1375_2,plain,
! [U_5344,U_5343,U_5342,U_5341,U_5340] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),U_5341),U_5342)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),U_5343),U_5344)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),U_5341),U_5343)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),U_5342),U_5344))
| ~ class_Fields_Ofield__inverse__zero(U_5340) ),
inference(variable_rename,[status(thm)],[f_1375_1]) ).
fof(f_1375_3,plain,
! [U_5340,U_5341,U_5342,U_5343,U_5344] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),U_5341),U_5342)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),U_5343),U_5344)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),U_5341),U_5343)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),U_5342),U_5344))
| ~ class_Fields_Ofield__inverse__zero(U_5340) ),
inference(definitional_conversion,[status(esa)],[f_1375_2]) ).
cnf(f_1375_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),U_5341),U_5342)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),U_5343),U_5344)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),U_5341),U_5343)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5340),U_5342),U_5344))
| ~ class_Fields_Ofield__inverse__zero(U_5340) ),
inference(clausify,[status(thm)],[f_1375_3]) ).
fof(f_1376_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__divide]) ).
fof(f_1376_2,plain,
! [U_5347,U_5346,U_5345] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5345),hAPP(c_Groups_Ouminus__class_Ouminus(U_5345),U_5346)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5345),U_5347)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5345),U_5346),U_5347)
| ~ class_Fields_Ofield__inverse__zero(U_5345) ),
inference(variable_rename,[status(thm)],[f_1376_1]) ).
fof(f_1376_3,plain,
! [U_5345,U_5346,U_5347] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5345),hAPP(c_Groups_Ouminus__class_Ouminus(U_5345),U_5346)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5345),U_5347)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5345),U_5346),U_5347)
| ~ class_Fields_Ofield__inverse__zero(U_5345) ),
inference(definitional_conversion,[status(esa)],[f_1376_2]) ).
cnf(f_1376_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5345),hAPP(c_Groups_Ouminus__class_Ouminus(U_5345),U_5346)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5345),U_5347)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5345),U_5346),U_5347)
| ~ class_Fields_Ofield__inverse__zero(U_5345) ),
inference(clausify,[status(thm)],[f_1376_3]) ).
fof(f_1377_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__right]) ).
fof(f_1377_2,plain,
! [U_5350,U_5349,U_5348] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5348),U_5349),U_5350)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5348),U_5349),hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),U_5350))
| ~ class_Fields_Ofield__inverse__zero(U_5348) ),
inference(variable_rename,[status(thm)],[f_1377_1]) ).
fof(f_1377_3,plain,
! [U_5348,U_5349,U_5350] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5348),U_5349),U_5350)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5348),U_5349),hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),U_5350))
| ~ class_Fields_Ofield__inverse__zero(U_5348) ),
inference(definitional_conversion,[status(esa)],[f_1377_2]) ).
cnf(f_1377_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5348),U_5349),U_5350)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5348),U_5349),hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),U_5350))
| ~ class_Fields_Ofield__inverse__zero(U_5348) ),
inference(clausify,[status(thm)],[f_1377_3]) ).
fof(f_1378_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg]) ).
fof(f_1378_2,plain,
! [U_5354,U_5353,U_5352,U_5351] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5351),U_5353),U_5354)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5351),U_5352),U_5354)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),U_5354),c_Groups_Ozero__class_Ozero(U_5351)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),U_5352),U_5353))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5351) ),
inference(variable_rename,[status(thm)],[f_1378_1]) ).
fof(f_1378_3,plain,
! [U_5351,U_5352,U_5353,U_5354] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5351),U_5353),U_5354)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5351),U_5352),U_5354)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),U_5354),c_Groups_Ozero__class_Ozero(U_5351)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),U_5352),U_5353))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5351) ),
inference(definitional_conversion,[status(esa)],[f_1378_2]) ).
cnf(f_1378_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5351),U_5353),U_5354)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5351),U_5352),U_5354)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),U_5354),c_Groups_Ozero__class_Ozero(U_5351)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),U_5352),U_5353))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5351) ),
inference(clausify,[status(thm)],[f_1378_3]) ).
fof(f_1379_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__right__mono]) ).
fof(f_1379_2,plain,
! [U_5358,U_5357,U_5356,U_5355] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5355),U_5356),U_5358)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5355),U_5357),U_5358)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),c_Groups_Ozero__class_Ozero(U_5355)),U_5358))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),U_5356),U_5357))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5355) ),
inference(variable_rename,[status(thm)],[f_1379_1]) ).
fof(f_1379_3,plain,
! [U_5355,U_5356,U_5357,U_5358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5355),U_5356),U_5358)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5355),U_5357),U_5358)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),c_Groups_Ozero__class_Ozero(U_5355)),U_5358))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),U_5356),U_5357))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5355) ),
inference(definitional_conversion,[status(esa)],[f_1379_2]) ).
cnf(f_1379_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5355),U_5356),U_5358)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5355),U_5357),U_5358)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),c_Groups_Ozero__class_Ozero(U_5355)),U_5358))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5355),U_5356),U_5357))
| ~ class_Fields_Olinordered__field__inverse__zero(U_5355) ),
inference(clausify,[status(thm)],[f_1379_3]) ).
fof(f_1380_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ 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))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff]) ).
fof(f_1380_2,plain,
! [U_5361,U_5360,U_5359] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5359),U_5360),U_5361)),c_Groups_Ozero__class_Ozero(U_5359)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5360),c_Groups_Ozero__class_Ozero(U_5359))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5361),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5360)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5361))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5360),c_Groups_Ozero__class_Ozero(U_5359))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5361),c_Groups_Ozero__class_Ozero(U_5359)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5360)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5359),U_5360),U_5361)),c_Groups_Ozero__class_Ozero(U_5359))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5359) ),
inference(variable_rename,[status(thm)],[f_1380_1]) ).
fof(f_1380_3,plain,
( ! [U_5359,U_5360,U_5361] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5360),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ sP395(U_5359,U_5360,U_5361) )
& ! [U_5359,U_5360,U_5361] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5361),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5360))
| ~ sP395(U_5359,U_5360,U_5361) )
& ! [U_5359,U_5360,U_5361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5361))
| ~ sP394(U_5359,U_5360,U_5361) )
& ! [U_5359,U_5360,U_5361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5360),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ sP394(U_5359,U_5360,U_5361) )
& ! [U_5359,U_5360,U_5361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5361),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ sP393(U_5359,U_5360,U_5361) )
& ! [U_5359,U_5360,U_5361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5360))
| ~ sP393(U_5359,U_5360,U_5361) )
& ! [U_5359,U_5360,U_5361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5359),U_5360),U_5361)),c_Groups_Ozero__class_Ozero(U_5359)))
| sP395(U_5359,U_5360,U_5361)
| ~ sP396(U_5359,U_5360,U_5361) )
& ! [U_5359,U_5360,U_5361] :
( sP394(U_5359,U_5360,U_5361)
| sP393(U_5359,U_5360,U_5361)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5359),U_5360),U_5361)),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ sP396(U_5359,U_5360,U_5361) )
& ! [U_5359,U_5360,U_5361] :
( sP396(U_5359,U_5360,U_5361)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5359) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP393,sP394,sP395,sP396])],[f_1380_2]) ).
cnf(f_1380_4,plain,
( sP396(U_5359,U_5360,U_5361)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5359) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
cnf(f_1380_5,plain,
( sP394(U_5359,U_5360,U_5361)
| sP393(U_5359,U_5360,U_5361)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5359),U_5360),U_5361)),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ sP396(U_5359,U_5360,U_5361) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
cnf(f_1380_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5359),U_5360),U_5361)),c_Groups_Ozero__class_Ozero(U_5359)))
| sP395(U_5359,U_5360,U_5361)
| ~ sP396(U_5359,U_5360,U_5361) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
cnf(f_1380_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5360))
| ~ sP393(U_5359,U_5360,U_5361) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
cnf(f_1380_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5361),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ sP393(U_5359,U_5360,U_5361) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
cnf(f_1380_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5360),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ sP394(U_5359,U_5360,U_5361) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
cnf(f_1380_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5361))
| ~ sP394(U_5359,U_5360,U_5361) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
cnf(f_1380_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5361),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5360))
| ~ sP395(U_5359,U_5360,U_5361) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
cnf(f_1380_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),c_Groups_Ozero__class_Ozero(U_5359)),U_5361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5359),U_5360),c_Groups_Ozero__class_Ozero(U_5359)))
| ~ sP395(U_5359,U_5360,U_5361) ),
inference(clausify,[status(thm)],[f_1380_3]) ).
fof(f_1381_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ 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))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff]) ).
fof(f_1381_2,plain,
! [U_5364,U_5363,U_5362] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5364),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5363),c_Groups_Ozero__class_Ozero(U_5362))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5363)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5364),c_Groups_Ozero__class_Ozero(U_5362)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5363),c_Groups_Ozero__class_Ozero(U_5362))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5364))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5363)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5362) ),
inference(variable_rename,[status(thm)],[f_1381_1]) ).
fof(f_1381_3,plain,
( ! [U_5362,U_5363,U_5364] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5364),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5363),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ sP399(U_5362,U_5363,U_5364) )
& ! [U_5362,U_5363,U_5364] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5363))
| ~ sP399(U_5362,U_5363,U_5364) )
& ! [U_5362,U_5363,U_5364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5364),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ sP398(U_5362,U_5363,U_5364) )
& ! [U_5362,U_5363,U_5364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5363),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ sP398(U_5362,U_5363,U_5364) )
& ! [U_5362,U_5363,U_5364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5364))
| ~ sP397(U_5362,U_5363,U_5364) )
& ! [U_5362,U_5363,U_5364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5363))
| ~ sP397(U_5362,U_5363,U_5364) )
& ! [U_5362,U_5363,U_5364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364)))
| sP399(U_5362,U_5363,U_5364)
| ~ sP400(U_5362,U_5363,U_5364) )
& ! [U_5362,U_5363,U_5364] :
( sP398(U_5362,U_5363,U_5364)
| sP397(U_5362,U_5363,U_5364)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364)))
| ~ sP400(U_5362,U_5363,U_5364) )
& ! [U_5362,U_5363,U_5364] :
( sP400(U_5362,U_5363,U_5364)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5362) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP397,sP398,sP399,sP400])],[f_1381_2]) ).
cnf(f_1381_4,plain,
( sP400(U_5362,U_5363,U_5364)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5362) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
cnf(f_1381_5,plain,
( sP398(U_5362,U_5363,U_5364)
| sP397(U_5362,U_5363,U_5364)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364)))
| ~ sP400(U_5362,U_5363,U_5364) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
cnf(f_1381_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364)))
| sP399(U_5362,U_5363,U_5364)
| ~ sP400(U_5362,U_5363,U_5364) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
cnf(f_1381_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5363))
| ~ sP397(U_5362,U_5363,U_5364) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
cnf(f_1381_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5364))
| ~ sP397(U_5362,U_5363,U_5364) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
cnf(f_1381_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5363),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ sP398(U_5362,U_5363,U_5364) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
cnf(f_1381_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5364),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ sP398(U_5362,U_5363,U_5364) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
cnf(f_1381_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),c_Groups_Ozero__class_Ozero(U_5362)),U_5363))
| ~ sP399(U_5362,U_5363,U_5364) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
cnf(f_1381_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5364),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5362),U_5363),c_Groups_Ozero__class_Ozero(U_5362)))
| ~ sP399(U_5362,U_5363,U_5364) ),
inference(clausify,[status(thm)],[f_1381_3]) ).
fof(f_1382_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg]) ).
fof(f_1382_2,plain,
! [U_5368,U_5367,U_5366,U_5365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5365),U_5367),U_5368)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5365),U_5366),U_5368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),U_5368),c_Groups_Ozero__class_Ozero(U_5365)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),U_5366),U_5367))
| ~ class_Fields_Olinordered__field(U_5365) ),
inference(variable_rename,[status(thm)],[f_1382_1]) ).
fof(f_1382_3,plain,
! [U_5367,U_5366,U_5365,U_5368] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5365),U_5367),U_5368)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5365),U_5366),U_5368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),U_5368),c_Groups_Ozero__class_Ozero(U_5365)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),U_5366),U_5367))
| ~ class_Fields_Olinordered__field(U_5365) ),
inference(definitional_conversion,[status(esa)],[f_1382_2]) ).
cnf(f_1382_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5365),U_5367),U_5368)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5365),U_5366),U_5368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),U_5368),c_Groups_Ozero__class_Ozero(U_5365)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5365),U_5366),U_5367))
| ~ class_Fields_Olinordered__field(U_5365) ),
inference(clausify,[status(thm)],[f_1382_3]) ).
fof(f_1383_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono]) ).
fof(f_1383_2,plain,
! [U_5372,U_5371,U_5370,U_5369] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5369),U_5370),U_5372)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5369),U_5371),U_5372)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),c_Groups_Ozero__class_Ozero(U_5369)),U_5372))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),U_5370),U_5371))
| ~ class_Fields_Olinordered__field(U_5369) ),
inference(variable_rename,[status(thm)],[f_1383_1]) ).
fof(f_1383_3,plain,
! [U_5369,U_5370,U_5371,U_5372] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5369),U_5370),U_5372)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5369),U_5371),U_5372)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),c_Groups_Ozero__class_Ozero(U_5369)),U_5372))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),U_5370),U_5371))
| ~ class_Fields_Olinordered__field(U_5369) ),
inference(definitional_conversion,[status(esa)],[f_1383_2]) ).
cnf(f_1383_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5369),U_5370),U_5372)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5369),U_5371),U_5372)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),c_Groups_Ozero__class_Ozero(U_5369)),U_5372))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5369),U_5370),U_5371))
| ~ class_Fields_Olinordered__field(U_5369) ),
inference(clausify,[status(thm)],[f_1383_3]) ).
fof(f_1384_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__neg__neg]) ).
fof(f_1384_2,plain,
! [U_5375,U_5374,U_5373] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),c_Groups_Ozero__class_Ozero(U_5373)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5373),U_5374),U_5375)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),U_5375),c_Groups_Ozero__class_Ozero(U_5373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),U_5374),c_Groups_Ozero__class_Ozero(U_5373)))
| ~ class_Fields_Olinordered__field(U_5373) ),
inference(variable_rename,[status(thm)],[f_1384_1]) ).
fof(f_1384_3,plain,
! [U_5374,U_5373,U_5375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),c_Groups_Ozero__class_Ozero(U_5373)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5373),U_5374),U_5375)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),U_5375),c_Groups_Ozero__class_Ozero(U_5373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),U_5374),c_Groups_Ozero__class_Ozero(U_5373)))
| ~ class_Fields_Olinordered__field(U_5373) ),
inference(definitional_conversion,[status(esa)],[f_1384_2]) ).
cnf(f_1384_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),c_Groups_Ozero__class_Ozero(U_5373)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5373),U_5374),U_5375)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),U_5375),c_Groups_Ozero__class_Ozero(U_5373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5373),U_5374),c_Groups_Ozero__class_Ozero(U_5373)))
| ~ class_Fields_Olinordered__field(U_5373) ),
inference(clausify,[status(thm)],[f_1384_3]) ).
fof(f_1385_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__neg__pos]) ).
fof(f_1385_2,plain,
! [U_5378,U_5377,U_5376] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5376),U_5377),U_5378)),c_Groups_Ozero__class_Ozero(U_5376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),c_Groups_Ozero__class_Ozero(U_5376)),U_5378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),U_5377),c_Groups_Ozero__class_Ozero(U_5376)))
| ~ class_Fields_Olinordered__field(U_5376) ),
inference(variable_rename,[status(thm)],[f_1385_1]) ).
fof(f_1385_3,plain,
! [U_5376,U_5377,U_5378] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5376),U_5377),U_5378)),c_Groups_Ozero__class_Ozero(U_5376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),c_Groups_Ozero__class_Ozero(U_5376)),U_5378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),U_5377),c_Groups_Ozero__class_Ozero(U_5376)))
| ~ class_Fields_Olinordered__field(U_5376) ),
inference(definitional_conversion,[status(esa)],[f_1385_2]) ).
cnf(f_1385_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5376),U_5377),U_5378)),c_Groups_Ozero__class_Ozero(U_5376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),c_Groups_Ozero__class_Ozero(U_5376)),U_5378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5376),U_5377),c_Groups_Ozero__class_Ozero(U_5376)))
| ~ class_Fields_Olinordered__field(U_5376) ),
inference(clausify,[status(thm)],[f_1385_3]) ).
fof(f_1386_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__pos__neg]) ).
fof(f_1386_2,plain,
! [U_5381,U_5380,U_5379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5379),U_5380),U_5381)),c_Groups_Ozero__class_Ozero(U_5379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),U_5381),c_Groups_Ozero__class_Ozero(U_5379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),c_Groups_Ozero__class_Ozero(U_5379)),U_5380))
| ~ class_Fields_Olinordered__field(U_5379) ),
inference(variable_rename,[status(thm)],[f_1386_1]) ).
fof(f_1386_3,plain,
! [U_5379,U_5380,U_5381] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5379),U_5380),U_5381)),c_Groups_Ozero__class_Ozero(U_5379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),U_5381),c_Groups_Ozero__class_Ozero(U_5379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),c_Groups_Ozero__class_Ozero(U_5379)),U_5380))
| ~ class_Fields_Olinordered__field(U_5379) ),
inference(definitional_conversion,[status(esa)],[f_1386_2]) ).
cnf(f_1386_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5379),U_5380),U_5381)),c_Groups_Ozero__class_Ozero(U_5379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),U_5381),c_Groups_Ozero__class_Ozero(U_5379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5379),c_Groups_Ozero__class_Ozero(U_5379)),U_5380))
| ~ class_Fields_Olinordered__field(U_5379) ),
inference(clausify,[status(thm)],[f_1386_3]) ).
fof(f_1387_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__pos__pos]) ).
fof(f_1387_2,plain,
! [U_5384,U_5383,U_5382] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5382),U_5383),U_5384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),U_5384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),U_5383))
| ~ class_Fields_Olinordered__field(U_5382) ),
inference(variable_rename,[status(thm)],[f_1387_1]) ).
fof(f_1387_3,plain,
! [U_5383,U_5382,U_5384] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5382),U_5383),U_5384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),U_5384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),U_5383))
| ~ class_Fields_Olinordered__field(U_5382) ),
inference(definitional_conversion,[status(esa)],[f_1387_2]) ).
cnf(f_1387_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5382),U_5383),U_5384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),U_5384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5382),c_Groups_Ozero__class_Ozero(U_5382)),U_5383))
| ~ class_Fields_Olinordered__field(U_5382) ),
inference(clausify,[status(thm)],[f_1387_3]) ).
fof(f_1388_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ 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))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff]) ).
fof(f_1388_2,plain,
! [U_5387,U_5386,U_5385] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5385),U_5386),U_5387)),c_Groups_Ozero__class_Ozero(U_5385)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5386),c_Groups_Ozero__class_Ozero(U_5385))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5387),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5386)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5387))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5386),c_Groups_Ozero__class_Ozero(U_5385))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5387),c_Groups_Ozero__class_Ozero(U_5385)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5386)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5385),U_5386),U_5387)),c_Groups_Ozero__class_Ozero(U_5385))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5385) ),
inference(variable_rename,[status(thm)],[f_1388_1]) ).
fof(f_1388_3,plain,
( ! [U_5385,U_5386,U_5387] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5386),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ sP403(U_5385,U_5386,U_5387) )
& ! [U_5385,U_5386,U_5387] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5387),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5386))
| ~ sP403(U_5385,U_5386,U_5387) )
& ! [U_5385,U_5386,U_5387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5387))
| ~ sP402(U_5385,U_5386,U_5387) )
& ! [U_5385,U_5386,U_5387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5386),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ sP402(U_5385,U_5386,U_5387) )
& ! [U_5385,U_5386,U_5387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5387),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ sP401(U_5385,U_5386,U_5387) )
& ! [U_5385,U_5386,U_5387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5386))
| ~ sP401(U_5385,U_5386,U_5387) )
& ! [U_5385,U_5386,U_5387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5385),U_5386),U_5387)),c_Groups_Ozero__class_Ozero(U_5385)))
| sP403(U_5385,U_5386,U_5387)
| ~ sP404(U_5385,U_5386,U_5387) )
& ! [U_5385,U_5386,U_5387] :
( sP402(U_5385,U_5386,U_5387)
| sP401(U_5385,U_5386,U_5387)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5385),U_5386),U_5387)),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ sP404(U_5385,U_5386,U_5387) )
& ! [U_5385,U_5386,U_5387] :
( sP404(U_5385,U_5386,U_5387)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5385) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP401,sP402,sP403,sP404])],[f_1388_2]) ).
cnf(f_1388_4,plain,
( sP404(U_5385,U_5386,U_5387)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5385) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
cnf(f_1388_5,plain,
( sP402(U_5385,U_5386,U_5387)
| sP401(U_5385,U_5386,U_5387)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5385),U_5386),U_5387)),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ sP404(U_5385,U_5386,U_5387) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
cnf(f_1388_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5385),U_5386),U_5387)),c_Groups_Ozero__class_Ozero(U_5385)))
| sP403(U_5385,U_5386,U_5387)
| ~ sP404(U_5385,U_5386,U_5387) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
cnf(f_1388_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5386))
| ~ sP401(U_5385,U_5386,U_5387) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
cnf(f_1388_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5387),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ sP401(U_5385,U_5386,U_5387) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
cnf(f_1388_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5386),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ sP402(U_5385,U_5386,U_5387) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
cnf(f_1388_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5387))
| ~ sP402(U_5385,U_5386,U_5387) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
cnf(f_1388_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5387),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5386))
| ~ sP403(U_5385,U_5386,U_5387) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
cnf(f_1388_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),c_Groups_Ozero__class_Ozero(U_5385)),U_5387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5385),U_5386),c_Groups_Ozero__class_Ozero(U_5385)))
| ~ sP403(U_5385,U_5386,U_5387) ),
inference(clausify,[status(thm)],[f_1388_3]) ).
fof(f_1389_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ 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))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff]) ).
fof(f_1389_2,plain,
! [U_5390,U_5389,U_5388] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5388),U_5389),U_5390)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5390),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5389),c_Groups_Ozero__class_Ozero(U_5388))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5389)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5390),c_Groups_Ozero__class_Ozero(U_5388)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5389),c_Groups_Ozero__class_Ozero(U_5388))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5390))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5389)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5388),U_5389),U_5390))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5388) ),
inference(variable_rename,[status(thm)],[f_1389_1]) ).
fof(f_1389_3,plain,
( ! [U_5389,U_5388,U_5390] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5390),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5389),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ sP407(U_5389,U_5388,U_5390) )
& ! [U_5389,U_5388,U_5390] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5389))
| ~ sP407(U_5389,U_5388,U_5390) )
& ! [U_5389,U_5388,U_5390] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5390),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ sP406(U_5389,U_5388,U_5390) )
& ! [U_5389,U_5388,U_5390] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5389),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ sP406(U_5389,U_5388,U_5390) )
& ! [U_5389,U_5388,U_5390] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5390))
| ~ sP405(U_5389,U_5388,U_5390) )
& ! [U_5389,U_5388,U_5390] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5389))
| ~ sP405(U_5389,U_5388,U_5390) )
& ! [U_5389,U_5388,U_5390] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5388),U_5389),U_5390)))
| sP407(U_5389,U_5388,U_5390)
| ~ sP408(U_5389,U_5388,U_5390) )
& ! [U_5389,U_5388,U_5390] :
( sP406(U_5389,U_5388,U_5390)
| sP405(U_5389,U_5388,U_5390)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5388),U_5389),U_5390)))
| ~ sP408(U_5389,U_5388,U_5390) )
& ! [U_5389,U_5388,U_5390] :
( sP408(U_5389,U_5388,U_5390)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5388) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP405,sP406,sP407,sP408])],[f_1389_2]) ).
cnf(f_1389_4,plain,
( sP408(U_5389,U_5388,U_5390)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5388) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
cnf(f_1389_5,plain,
( sP406(U_5389,U_5388,U_5390)
| sP405(U_5389,U_5388,U_5390)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5388),U_5389),U_5390)))
| ~ sP408(U_5389,U_5388,U_5390) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
cnf(f_1389_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5388),U_5389),U_5390)))
| sP407(U_5389,U_5388,U_5390)
| ~ sP408(U_5389,U_5388,U_5390) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
cnf(f_1389_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5389))
| ~ sP405(U_5389,U_5388,U_5390) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
cnf(f_1389_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5390))
| ~ sP405(U_5389,U_5388,U_5390) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
cnf(f_1389_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5389),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ sP406(U_5389,U_5388,U_5390) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
cnf(f_1389_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5390),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ sP406(U_5389,U_5388,U_5390) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
cnf(f_1389_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),c_Groups_Ozero__class_Ozero(U_5388)),U_5389))
| ~ sP407(U_5389,U_5388,U_5390) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
cnf(f_1389_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5390),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5388),U_5389),c_Groups_Ozero__class_Ozero(U_5388)))
| ~ sP407(U_5389,U_5388,U_5390) ),
inference(clausify,[status(thm)],[f_1389_3]) ).
fof(f_1390_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) != V_b_2
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) ) )
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).
fof(f_1390_2,plain,
! [U_5394,U_5393,U_5392,U_5391] :
( ( ( U_5392 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5391),U_5393),U_5394)
| ( U_5392 != c_Groups_Ozero__class_Ozero(U_5391)
& U_5394 = c_Groups_Ozero__class_Ozero(U_5391) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5391),U_5392),U_5394) != U_5393
& U_5394 != c_Groups_Ozero__class_Ozero(U_5391) ) )
& ( ( ( U_5392 = c_Groups_Ozero__class_Ozero(U_5391)
| U_5394 != c_Groups_Ozero__class_Ozero(U_5391) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5391),U_5392),U_5394) = U_5393
| U_5394 = c_Groups_Ozero__class_Ozero(U_5391) ) )
| U_5392 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5391),U_5393),U_5394) ) )
| ~ class_Fields_Ofield__inverse__zero(U_5391) ),
inference(variable_rename,[status(thm)],[f_1390_1]) ).
fof(f_1390_3,plain,
( ! [U_5394,U_5392,U_5391] :
( U_5392 != c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP411(U_5394,U_5392,U_5391) )
& ! [U_5394,U_5392,U_5391] :
( U_5394 = c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP411(U_5394,U_5392,U_5391) )
& ! [U_5393,U_5394,U_5392,U_5391] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5391),U_5392),U_5394) != U_5393
| ~ sP410(U_5393,U_5394,U_5392,U_5391) )
& ! [U_5393,U_5394,U_5392,U_5391] :
( U_5394 != c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP410(U_5393,U_5394,U_5392,U_5391) )
& ! [U_5393,U_5394,U_5392,U_5391] :
( U_5392 = c_Groups_Ozero__class_Ozero(U_5391)
| U_5394 != c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP409(U_5393,U_5394,U_5392,U_5391) )
& ! [U_5393,U_5394,U_5392,U_5391] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5391),U_5392),U_5394) = U_5393
| U_5394 = c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP409(U_5393,U_5394,U_5392,U_5391) )
& ! [U_5393,U_5394,U_5392,U_5391] :
( U_5392 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5391),U_5393),U_5394)
| sP411(U_5394,U_5392,U_5391)
| sP410(U_5393,U_5394,U_5392,U_5391)
| ~ sP412(U_5393,U_5394,U_5392,U_5391) )
& ! [U_5393,U_5394,U_5392,U_5391] :
( sP409(U_5393,U_5394,U_5392,U_5391)
| U_5392 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5391),U_5393),U_5394)
| ~ sP412(U_5393,U_5394,U_5392,U_5391) )
& ! [U_5393,U_5394,U_5392,U_5391] :
( sP412(U_5393,U_5394,U_5392,U_5391)
| ~ class_Fields_Ofield__inverse__zero(U_5391) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP409,sP410,sP411,sP412])],[f_1390_2]) ).
cnf(f_1390_4,plain,
( sP412(U_5393,U_5394,U_5392,U_5391)
| ~ class_Fields_Ofield__inverse__zero(U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
cnf(f_1390_5,plain,
( sP409(U_5393,U_5394,U_5392,U_5391)
| U_5392 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5391),U_5393),U_5394)
| ~ sP412(U_5393,U_5394,U_5392,U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
cnf(f_1390_6,plain,
( U_5392 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5391),U_5393),U_5394)
| sP411(U_5394,U_5392,U_5391)
| sP410(U_5393,U_5394,U_5392,U_5391)
| ~ sP412(U_5393,U_5394,U_5392,U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
cnf(f_1390_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5391),U_5392),U_5394) = U_5393
| U_5394 = c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP409(U_5393,U_5394,U_5392,U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
cnf(f_1390_8,plain,
( U_5392 = c_Groups_Ozero__class_Ozero(U_5391)
| U_5394 != c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP409(U_5393,U_5394,U_5392,U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
cnf(f_1390_9,plain,
( U_5394 != c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP410(U_5393,U_5394,U_5392,U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
cnf(f_1390_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5391),U_5392),U_5394) != U_5393
| ~ sP410(U_5393,U_5394,U_5392,U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
cnf(f_1390_11,plain,
( U_5394 = c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP411(U_5394,U_5392,U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
cnf(f_1390_12,plain,
( U_5392 != c_Groups_Ozero__class_Ozero(U_5391)
| ~ sP411(U_5394,U_5392,U_5391) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
fof(f_1391_1,plain,
! [V_a_2,V_ca_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) != V_a_2 ) )
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).
fof(f_1391_2,plain,
! [U_5398,U_5397,U_5396,U_5395] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5395),U_5396),U_5397) = U_5398
| ( U_5398 != c_Groups_Ozero__class_Ozero(U_5395)
& U_5397 = c_Groups_Ozero__class_Ozero(U_5395) )
| ( U_5396 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5395),U_5398),U_5397)
& U_5397 != c_Groups_Ozero__class_Ozero(U_5395) ) )
& ( ( ( U_5398 = c_Groups_Ozero__class_Ozero(U_5395)
| U_5397 != c_Groups_Ozero__class_Ozero(U_5395) )
& ( U_5396 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5395),U_5398),U_5397)
| U_5397 = c_Groups_Ozero__class_Ozero(U_5395) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5395),U_5396),U_5397) != U_5398 ) )
| ~ class_Fields_Ofield__inverse__zero(U_5395) ),
inference(variable_rename,[status(thm)],[f_1391_1]) ).
fof(f_1391_3,plain,
( ! [U_5398,U_5397,U_5395] :
( U_5398 != c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP415(U_5398,U_5397,U_5395) )
& ! [U_5398,U_5397,U_5395] :
( U_5397 = c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP415(U_5398,U_5397,U_5395) )
& ! [U_5398,U_5397,U_5396,U_5395] :
( U_5396 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5395),U_5398),U_5397)
| ~ sP414(U_5398,U_5397,U_5396,U_5395) )
& ! [U_5398,U_5397,U_5396,U_5395] :
( U_5397 != c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP414(U_5398,U_5397,U_5396,U_5395) )
& ! [U_5398,U_5397,U_5396,U_5395] :
( U_5398 = c_Groups_Ozero__class_Ozero(U_5395)
| U_5397 != c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP413(U_5398,U_5397,U_5396,U_5395) )
& ! [U_5398,U_5397,U_5396,U_5395] :
( U_5396 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5395),U_5398),U_5397)
| U_5397 = c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP413(U_5398,U_5397,U_5396,U_5395) )
& ! [U_5398,U_5397,U_5396,U_5395] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5395),U_5396),U_5397) = U_5398
| sP415(U_5398,U_5397,U_5395)
| sP414(U_5398,U_5397,U_5396,U_5395)
| ~ sP416(U_5398,U_5397,U_5396,U_5395) )
& ! [U_5398,U_5397,U_5396,U_5395] :
( sP413(U_5398,U_5397,U_5396,U_5395)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5395),U_5396),U_5397) != U_5398
| ~ sP416(U_5398,U_5397,U_5396,U_5395) )
& ! [U_5398,U_5397,U_5396,U_5395] :
( sP416(U_5398,U_5397,U_5396,U_5395)
| ~ class_Fields_Ofield__inverse__zero(U_5395) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP413,sP414,sP415,sP416])],[f_1391_2]) ).
cnf(f_1391_4,plain,
( sP416(U_5398,U_5397,U_5396,U_5395)
| ~ class_Fields_Ofield__inverse__zero(U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
cnf(f_1391_5,plain,
( sP413(U_5398,U_5397,U_5396,U_5395)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5395),U_5396),U_5397) != U_5398
| ~ sP416(U_5398,U_5397,U_5396,U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
cnf(f_1391_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5395),U_5396),U_5397) = U_5398
| sP415(U_5398,U_5397,U_5395)
| sP414(U_5398,U_5397,U_5396,U_5395)
| ~ sP416(U_5398,U_5397,U_5396,U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
cnf(f_1391_7,plain,
( U_5396 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5395),U_5398),U_5397)
| U_5397 = c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP413(U_5398,U_5397,U_5396,U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
cnf(f_1391_8,plain,
( U_5398 = c_Groups_Ozero__class_Ozero(U_5395)
| U_5397 != c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP413(U_5398,U_5397,U_5396,U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
cnf(f_1391_9,plain,
( U_5397 != c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP414(U_5398,U_5397,U_5396,U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
cnf(f_1391_10,plain,
( U_5396 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5395),U_5398),U_5397)
| ~ sP414(U_5398,U_5397,U_5396,U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
cnf(f_1391_11,plain,
( U_5397 = c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP415(U_5398,U_5397,U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
cnf(f_1391_12,plain,
( U_5398 != c_Groups_Ozero__class_Ozero(U_5395)
| ~ sP415(U_5398,U_5397,U_5395) ),
inference(clausify,[status(thm)],[f_1391_3]) ).
fof(f_1392_1,plain,
! [V_b,V_a,V_c,T_a] :
( 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)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right]) ).
fof(f_1392_2,plain,
! [U_5402,U_5401,U_5400,U_5399] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5399),U_5401),U_5400)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5399),U_5402),U_5400)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5399),U_5401),U_5402)
| U_5400 = c_Groups_Ozero__class_Ozero(U_5399)
| ~ class_Fields_Ofield__inverse__zero(U_5399) ),
inference(variable_rename,[status(thm)],[f_1392_1]) ).
fof(f_1392_3,plain,
! [U_5400,U_5399,U_5402,U_5401] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5399),U_5401),U_5400)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5399),U_5402),U_5400)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5399),U_5401),U_5402)
| U_5400 = c_Groups_Ozero__class_Ozero(U_5399)
| ~ class_Fields_Ofield__inverse__zero(U_5399) ),
inference(definitional_conversion,[status(esa)],[f_1392_2]) ).
cnf(f_1392_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5399),U_5401),U_5400)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5399),U_5402),U_5400)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5399),U_5401),U_5402)
| U_5400 = c_Groups_Ozero__class_Ozero(U_5399)
| ~ class_Fields_Ofield__inverse__zero(U_5399) ),
inference(clausify,[status(thm)],[f_1392_3]) ).
fof(f_1393_1,plain,
! [V_b,V_a,V_c,T_a] :
( 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)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left]) ).
fof(f_1393_2,plain,
! [U_5406,U_5405,U_5404,U_5403] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5403),U_5404),U_5405)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5403),U_5404),U_5406)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5403),U_5405),U_5406)
| U_5404 = c_Groups_Ozero__class_Ozero(U_5403)
| ~ class_Fields_Ofield__inverse__zero(U_5403) ),
inference(variable_rename,[status(thm)],[f_1393_1]) ).
fof(f_1393_3,plain,
! [U_5403,U_5404,U_5405,U_5406] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5403),U_5404),U_5405)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5403),U_5404),U_5406)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5403),U_5405),U_5406)
| U_5404 = c_Groups_Ozero__class_Ozero(U_5403)
| ~ class_Fields_Ofield__inverse__zero(U_5403) ),
inference(definitional_conversion,[status(esa)],[f_1393_2]) ).
cnf(f_1393_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5403),U_5404),U_5405)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5403),U_5404),U_5406)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5403),U_5405),U_5406)
| U_5404 = c_Groups_Ozero__class_Ozero(U_5403)
| ~ class_Fields_Ofield__inverse__zero(U_5403) ),
inference(clausify,[status(thm)],[f_1393_3]) ).
fof(f_1394_1,plain,
! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
( ( ( 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)
| 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) )
& ( 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)
| 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) ) )
| V_z_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Fields_Ofield(T_b) ),
inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).
fof(f_1394_2,plain,
! [U_5411,U_5410,U_5409,U_5408,U_5407] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5410),U_5408) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5411),U_5409)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5410),U_5409) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5411),U_5408) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5410),U_5409) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5411),U_5408)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5410),U_5408) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5411),U_5409) ) )
| U_5409 = c_Groups_Ozero__class_Ozero(U_5407)
| U_5408 = c_Groups_Ozero__class_Ozero(U_5407)
| ~ class_Fields_Ofield(U_5407) ),
inference(variable_rename,[status(thm)],[f_1394_1]) ).
fof(f_1394_3,plain,
( ! [U_5407,U_5408,U_5409,U_5410,U_5411] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5410),U_5408) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5411),U_5409)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5410),U_5409) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5411),U_5408)
| ~ sP417(U_5407,U_5408,U_5409,U_5410,U_5411) )
& ! [U_5407,U_5408,U_5409,U_5410,U_5411] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5410),U_5409) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5411),U_5408)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5410),U_5408) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5411),U_5409)
| ~ sP417(U_5407,U_5408,U_5409,U_5410,U_5411) )
& ! [U_5407,U_5408,U_5409,U_5410,U_5411] :
( sP417(U_5407,U_5408,U_5409,U_5410,U_5411)
| U_5409 = c_Groups_Ozero__class_Ozero(U_5407)
| U_5408 = c_Groups_Ozero__class_Ozero(U_5407)
| ~ class_Fields_Ofield(U_5407) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP417])],[f_1394_2]) ).
cnf(f_1394_4,plain,
( sP417(U_5407,U_5408,U_5409,U_5410,U_5411)
| U_5409 = c_Groups_Ozero__class_Ozero(U_5407)
| U_5408 = c_Groups_Ozero__class_Ozero(U_5407)
| ~ class_Fields_Ofield(U_5407) ),
inference(clausify,[status(thm)],[f_1394_3]) ).
cnf(f_1394_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5410),U_5409) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5411),U_5408)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5410),U_5408) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5411),U_5409)
| ~ sP417(U_5407,U_5408,U_5409,U_5410,U_5411) ),
inference(clausify,[status(thm)],[f_1394_3]) ).
cnf(f_1394_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5410),U_5408) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5411),U_5409)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5410),U_5409) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5407),U_5411),U_5408)
| ~ sP417(U_5407,U_5408,U_5409,U_5410,U_5411) ),
inference(clausify,[status(thm)],[f_1394_3]) ).
fof(f_1395_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos]) ).
fof(f_1395_2,plain,
! [U_5414,U_5413,U_5412] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5412),U_5413),U_5414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),U_5414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),U_5413))
| ~ class_Fields_Olinordered__field(U_5412) ),
inference(variable_rename,[status(thm)],[f_1395_1]) ).
fof(f_1395_3,plain,
! [U_5413,U_5412,U_5414] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5412),U_5413),U_5414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),U_5414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),U_5413))
| ~ class_Fields_Olinordered__field(U_5412) ),
inference(definitional_conversion,[status(esa)],[f_1395_2]) ).
cnf(f_1395_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5412),U_5413),U_5414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),U_5414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5412),c_Groups_Ozero__class_Ozero(U_5412)),U_5413))
| ~ class_Fields_Olinordered__field(U_5412) ),
inference(clausify,[status(thm)],[f_1395_3]) ).
fof(f_1396_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg]) ).
fof(f_1396_2,plain,
! [U_5417,U_5416,U_5415] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5415),U_5416),U_5417)),c_Groups_Ozero__class_Ozero(U_5415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5415),U_5417),c_Groups_Ozero__class_Ozero(U_5415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5415),c_Groups_Ozero__class_Ozero(U_5415)),U_5416))
| ~ class_Fields_Olinordered__field(U_5415) ),
inference(variable_rename,[status(thm)],[f_1396_1]) ).
fof(f_1396_3,plain,
! [U_5415,U_5416,U_5417] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5415),U_5416),U_5417)),c_Groups_Ozero__class_Ozero(U_5415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5415),U_5417),c_Groups_Ozero__class_Ozero(U_5415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5415),c_Groups_Ozero__class_Ozero(U_5415)),U_5416))
| ~ class_Fields_Olinordered__field(U_5415) ),
inference(definitional_conversion,[status(esa)],[f_1396_2]) ).
cnf(f_1396_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5415),U_5416),U_5417)),c_Groups_Ozero__class_Ozero(U_5415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5415),U_5417),c_Groups_Ozero__class_Ozero(U_5415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5415),c_Groups_Ozero__class_Ozero(U_5415)),U_5416))
| ~ class_Fields_Olinordered__field(U_5415) ),
inference(clausify,[status(thm)],[f_1396_3]) ).
fof(f_1397_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__less2]) ).
fof(f_1397_2,plain,
! [U_5422,U_5421,U_5420,U_5419,U_5418] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5419),U_5422)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5420),U_5421)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5421),U_5422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),c_Groups_Ozero__class_Ozero(U_5418)),U_5421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),U_5419),U_5420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),c_Groups_Ozero__class_Ozero(U_5418)),U_5419))
| ~ class_Fields_Olinordered__field(U_5418) ),
inference(variable_rename,[status(thm)],[f_1397_1]) ).
fof(f_1397_3,plain,
! [U_5418,U_5419,U_5420,U_5421,U_5422] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5419),U_5422)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5420),U_5421)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5421),U_5422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),c_Groups_Ozero__class_Ozero(U_5418)),U_5421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),U_5419),U_5420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),c_Groups_Ozero__class_Ozero(U_5418)),U_5419))
| ~ class_Fields_Olinordered__field(U_5418) ),
inference(definitional_conversion,[status(esa)],[f_1397_2]) ).
cnf(f_1397_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5419),U_5422)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5420),U_5421)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5421),U_5422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),c_Groups_Ozero__class_Ozero(U_5418)),U_5421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),U_5419),U_5420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),c_Groups_Ozero__class_Ozero(U_5418)),U_5419))
| ~ class_Fields_Olinordered__field(U_5418) ),
inference(clausify,[status(thm)],[f_1397_3]) ).
fof(f_1398_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__less]) ).
fof(f_1398_2,plain,
! [U_5427,U_5426,U_5425,U_5424,U_5423] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5423),U_5424),U_5427)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5423),U_5425),U_5426)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5423),U_5426),U_5427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),c_Groups_Ozero__class_Ozero(U_5423)),U_5426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),U_5424),U_5425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5423),c_Groups_Ozero__class_Ozero(U_5423)),U_5424))
| ~ class_Fields_Olinordered__field(U_5423) ),
inference(variable_rename,[status(thm)],[f_1398_1]) ).
fof(f_1398_3,plain,
! [U_5423,U_5424,U_5425,U_5427,U_5426] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5423),U_5424),U_5427)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5423),U_5425),U_5426)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5423),U_5426),U_5427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),c_Groups_Ozero__class_Ozero(U_5423)),U_5426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),U_5424),U_5425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5423),c_Groups_Ozero__class_Ozero(U_5423)),U_5424))
| ~ class_Fields_Olinordered__field(U_5423) ),
inference(definitional_conversion,[status(esa)],[f_1398_2]) ).
cnf(f_1398_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5423),U_5424),U_5427)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5423),U_5425),U_5426)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5423),U_5426),U_5427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),c_Groups_Ozero__class_Ozero(U_5423)),U_5426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5423),U_5424),U_5425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5423),c_Groups_Ozero__class_Ozero(U_5423)),U_5424))
| ~ class_Fields_Olinordered__field(U_5423) ),
inference(clausify,[status(thm)],[f_1398_3]) ).
fof(f_1399_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__le]) ).
fof(f_1399_2,plain,
! [U_5432,U_5431,U_5430,U_5429,U_5428] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5428),U_5429),U_5432)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5428),U_5430),U_5431)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),U_5431),U_5432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5428),c_Groups_Ozero__class_Ozero(U_5428)),U_5431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),U_5429),U_5430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),c_Groups_Ozero__class_Ozero(U_5428)),U_5429))
| ~ class_Fields_Olinordered__field(U_5428) ),
inference(variable_rename,[status(thm)],[f_1399_1]) ).
fof(f_1399_3,plain,
! [U_5428,U_5431,U_5429,U_5430,U_5432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5428),U_5429),U_5432)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5428),U_5430),U_5431)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),U_5431),U_5432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5428),c_Groups_Ozero__class_Ozero(U_5428)),U_5431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),U_5429),U_5430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),c_Groups_Ozero__class_Ozero(U_5428)),U_5429))
| ~ class_Fields_Olinordered__field(U_5428) ),
inference(definitional_conversion,[status(esa)],[f_1399_2]) ).
cnf(f_1399_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5428),U_5429),U_5432)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5428),U_5430),U_5431)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),U_5431),U_5432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5428),c_Groups_Ozero__class_Ozero(U_5428)),U_5431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),U_5429),U_5430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),c_Groups_Ozero__class_Ozero(U_5428)),U_5429))
| ~ class_Fields_Olinordered__field(U_5428) ),
inference(clausify,[status(thm)],[f_1399_3]) ).
fof(f_1400_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos]) ).
fof(f_1400_2,plain,
! [U_5435,U_5434,U_5433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5433),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5433),U_5434),U_5435)),c_Groups_Ozero__class_Ozero(U_5433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5433),c_Groups_Ozero__class_Ozero(U_5433)),U_5435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5433),U_5434),c_Groups_Ozero__class_Ozero(U_5433)))
| ~ class_Fields_Olinordered__field(U_5433) ),
inference(variable_rename,[status(thm)],[f_1400_1]) ).
fof(f_1400_3,plain,
! [U_5435,U_5434,U_5433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5433),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5433),U_5434),U_5435)),c_Groups_Ozero__class_Ozero(U_5433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5433),c_Groups_Ozero__class_Ozero(U_5433)),U_5435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5433),U_5434),c_Groups_Ozero__class_Ozero(U_5433)))
| ~ class_Fields_Olinordered__field(U_5433) ),
inference(definitional_conversion,[status(esa)],[f_1400_2]) ).
cnf(f_1400_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5433),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5433),U_5434),U_5435)),c_Groups_Ozero__class_Ozero(U_5433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5433),c_Groups_Ozero__class_Ozero(U_5433)),U_5435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5433),U_5434),c_Groups_Ozero__class_Ozero(U_5433)))
| ~ class_Fields_Olinordered__field(U_5433) ),
inference(clausify,[status(thm)],[f_1400_3]) ).
fof(f_1401_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg]) ).
fof(f_1401_2,plain,
! [U_5438,U_5437,U_5436] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5436),c_Groups_Ozero__class_Ozero(U_5436)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5436),U_5437),U_5438)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5436),U_5438),c_Groups_Ozero__class_Ozero(U_5436)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5436),U_5437),c_Groups_Ozero__class_Ozero(U_5436)))
| ~ class_Fields_Olinordered__field(U_5436) ),
inference(variable_rename,[status(thm)],[f_1401_1]) ).
fof(f_1401_3,plain,
! [U_5436,U_5437,U_5438] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5436),c_Groups_Ozero__class_Ozero(U_5436)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5436),U_5437),U_5438)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5436),U_5438),c_Groups_Ozero__class_Ozero(U_5436)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5436),U_5437),c_Groups_Ozero__class_Ozero(U_5436)))
| ~ class_Fields_Olinordered__field(U_5436) ),
inference(definitional_conversion,[status(esa)],[f_1401_2]) ).
cnf(f_1401_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5436),c_Groups_Ozero__class_Ozero(U_5436)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5436),U_5437),U_5438)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5436),U_5438),c_Groups_Ozero__class_Ozero(U_5436)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5436),U_5437),c_Groups_Ozero__class_Ozero(U_5436)))
| ~ class_Fields_Olinordered__field(U_5436) ),
inference(clausify,[status(thm)],[f_1401_3]) ).
fof(f_1402_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg]) ).
fof(f_1402_2,plain,
! [U_5442,U_5441,U_5440,U_5439] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5439),U_5442),U_5440)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5439),U_5442),U_5441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),c_Groups_Ozero__class_Ozero(U_5439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5439),U_5440),U_5441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),U_5442),c_Groups_Ozero__class_Ozero(U_5439)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),U_5440),U_5441))
| ~ class_Fields_Olinordered__field(U_5439) ),
inference(variable_rename,[status(thm)],[f_1402_1]) ).
fof(f_1402_3,plain,
! [U_5439,U_5440,U_5441,U_5442] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5439),U_5442),U_5440)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5439),U_5442),U_5441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),c_Groups_Ozero__class_Ozero(U_5439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5439),U_5440),U_5441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),U_5442),c_Groups_Ozero__class_Ozero(U_5439)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),U_5440),U_5441))
| ~ class_Fields_Olinordered__field(U_5439) ),
inference(definitional_conversion,[status(esa)],[f_1402_2]) ).
cnf(f_1402_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5439),U_5442),U_5440)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5439),U_5442),U_5441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),c_Groups_Ozero__class_Ozero(U_5439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5439),U_5440),U_5441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),U_5442),c_Groups_Ozero__class_Ozero(U_5439)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5439),U_5440),U_5441))
| ~ class_Fields_Olinordered__field(U_5439) ),
inference(clausify,[status(thm)],[f_1402_3]) ).
fof(f_1403_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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)))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono]) ).
fof(f_1403_2,plain,
! [U_5446,U_5445,U_5444,U_5443] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5443),U_5446),U_5445)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5443),U_5446),U_5444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),c_Groups_Ozero__class_Ozero(U_5443)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5443),U_5445),U_5444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),c_Groups_Ozero__class_Ozero(U_5443)),U_5446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),U_5444),U_5445))
| ~ class_Fields_Olinordered__field(U_5443) ),
inference(variable_rename,[status(thm)],[f_1403_1]) ).
fof(f_1403_3,plain,
! [U_5444,U_5445,U_5443,U_5446] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5443),U_5446),U_5445)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5443),U_5446),U_5444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),c_Groups_Ozero__class_Ozero(U_5443)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5443),U_5445),U_5444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),c_Groups_Ozero__class_Ozero(U_5443)),U_5446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),U_5444),U_5445))
| ~ class_Fields_Olinordered__field(U_5443) ),
inference(definitional_conversion,[status(esa)],[f_1403_2]) ).
cnf(f_1403_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5443),U_5446),U_5445)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5443),U_5446),U_5444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),c_Groups_Ozero__class_Ozero(U_5443)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5443),U_5445),U_5444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),c_Groups_Ozero__class_Ozero(U_5443)),U_5446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5443),U_5444),U_5445))
| ~ class_Fields_Olinordered__field(U_5443) ),
inference(clausify,[status(thm)],[f_1403_3]) ).
fof(f_1404_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).
fof(f_1404_2,plain,
! [U_5450,U_5449,U_5448,U_5447] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5447),U_5449),U_5448)),U_5450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5447),U_5450),U_5448)),U_5449)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5447),U_5450),U_5448)),U_5449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5447),U_5449),U_5448)),U_5450)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),U_5448),c_Groups_Ozero__class_Ozero(U_5447)))
| ~ class_Fields_Olinordered__field(U_5447) ),
inference(variable_rename,[status(thm)],[f_1404_1]) ).
fof(f_1404_3,plain,
( ! [U_5448,U_5447,U_5449,U_5450] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5447),U_5449),U_5448)),U_5450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5447),U_5450),U_5448)),U_5449))
| ~ sP418(U_5448,U_5447,U_5449,U_5450) )
& ! [U_5448,U_5447,U_5449,U_5450] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5447),U_5450),U_5448)),U_5449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5447),U_5449),U_5448)),U_5450))
| ~ sP418(U_5448,U_5447,U_5449,U_5450) )
& ! [U_5448,U_5447,U_5449,U_5450] :
( sP418(U_5448,U_5447,U_5449,U_5450)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),U_5448),c_Groups_Ozero__class_Ozero(U_5447)))
| ~ class_Fields_Olinordered__field(U_5447) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP418])],[f_1404_2]) ).
cnf(f_1404_4,plain,
( sP418(U_5448,U_5447,U_5449,U_5450)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),U_5448),c_Groups_Ozero__class_Ozero(U_5447)))
| ~ class_Fields_Olinordered__field(U_5447) ),
inference(clausify,[status(thm)],[f_1404_3]) ).
cnf(f_1404_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5447),U_5450),U_5448)),U_5449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5447),U_5449),U_5448)),U_5450))
| ~ sP418(U_5448,U_5447,U_5449,U_5450) ),
inference(clausify,[status(thm)],[f_1404_3]) ).
cnf(f_1404_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5447),U_5449),U_5448)),U_5450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5447),U_5450),U_5448)),U_5449))
| ~ sP418(U_5448,U_5447,U_5449,U_5450) ),
inference(clausify,[status(thm)],[f_1404_3]) ).
fof(f_1405_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( 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_ca_2)))
| ~ 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_ca_2))) )
& ( 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_ca_2)))
| ~ 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_ca_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).
fof(f_1405_2,plain,
! [U_5454,U_5453,U_5452,U_5451] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5453),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5451),U_5454),U_5452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5451),U_5453),U_5452))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5451),U_5453),U_5452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5453),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5451),U_5454),U_5452))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5452),c_Groups_Ozero__class_Ozero(U_5451)))
| ~ class_Fields_Olinordered__field(U_5451) ),
inference(variable_rename,[status(thm)],[f_1405_1]) ).
fof(f_1405_3,plain,
( ! [U_5451,U_5454,U_5452,U_5453] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5453),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5451),U_5454),U_5452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5451),U_5453),U_5452)))
| ~ sP419(U_5451,U_5454,U_5452,U_5453) )
& ! [U_5451,U_5454,U_5452,U_5453] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5451),U_5453),U_5452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5453),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5451),U_5454),U_5452)))
| ~ sP419(U_5451,U_5454,U_5452,U_5453) )
& ! [U_5451,U_5454,U_5452,U_5453] :
( sP419(U_5451,U_5454,U_5452,U_5453)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5452),c_Groups_Ozero__class_Ozero(U_5451)))
| ~ class_Fields_Olinordered__field(U_5451) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP419])],[f_1405_2]) ).
cnf(f_1405_4,plain,
( sP419(U_5451,U_5454,U_5452,U_5453)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5452),c_Groups_Ozero__class_Ozero(U_5451)))
| ~ class_Fields_Olinordered__field(U_5451) ),
inference(clausify,[status(thm)],[f_1405_3]) ).
cnf(f_1405_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5451),U_5453),U_5452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5453),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5451),U_5454),U_5452)))
| ~ sP419(U_5451,U_5454,U_5452,U_5453) ),
inference(clausify,[status(thm)],[f_1405_3]) ).
cnf(f_1405_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5453),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5451),U_5454),U_5452)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5451),U_5454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5451),U_5453),U_5452)))
| ~ sP419(U_5451,U_5454,U_5452,U_5453) ),
inference(clausify,[status(thm)],[f_1405_3]) ).
fof(f_1406_1,plain,
! [V_x,V_z,V_y,T_a] :
( 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)))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos]) ).
fof(f_1406_2,plain,
! [U_5458,U_5457,U_5456,U_5455] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),U_5457),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5455),U_5458),U_5456)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5455),U_5457),U_5456)),U_5458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),c_Groups_Ozero__class_Ozero(U_5455)),U_5456))
| ~ class_Fields_Olinordered__field(U_5455) ),
inference(variable_rename,[status(thm)],[f_1406_1]) ).
fof(f_1406_3,plain,
! [U_5455,U_5456,U_5457,U_5458] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),U_5457),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5455),U_5458),U_5456)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5455),U_5457),U_5456)),U_5458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),c_Groups_Ozero__class_Ozero(U_5455)),U_5456))
| ~ class_Fields_Olinordered__field(U_5455) ),
inference(definitional_conversion,[status(esa)],[f_1406_2]) ).
cnf(f_1406_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),U_5457),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5455),U_5458),U_5456)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5455),U_5457),U_5456)),U_5458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5455),c_Groups_Ozero__class_Ozero(U_5455)),U_5456))
| ~ class_Fields_Olinordered__field(U_5455) ),
inference(clausify,[status(thm)],[f_1406_3]) ).
fof(f_1407_1,plain,
! [V_z,V_x,V_y,T_a] :
( 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))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less]) ).
fof(f_1407_2,plain,
! [U_5462,U_5461,U_5460,U_5459] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5459),U_5461),U_5460)),U_5462))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),U_5461),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5459),U_5462),U_5460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),c_Groups_Ozero__class_Ozero(U_5459)),U_5460))
| ~ class_Fields_Olinordered__field(U_5459) ),
inference(variable_rename,[status(thm)],[f_1407_1]) ).
fof(f_1407_3,plain,
! [U_5459,U_5460,U_5461,U_5462] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5459),U_5461),U_5460)),U_5462))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),U_5461),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5459),U_5462),U_5460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),c_Groups_Ozero__class_Ozero(U_5459)),U_5460))
| ~ class_Fields_Olinordered__field(U_5459) ),
inference(definitional_conversion,[status(esa)],[f_1407_2]) ).
cnf(f_1407_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5459),U_5461),U_5460)),U_5462))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),U_5461),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5459),U_5462),U_5460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5459),c_Groups_Ozero__class_Ozero(U_5459)),U_5460))
| ~ class_Fields_Olinordered__field(U_5459) ),
inference(clausify,[status(thm)],[f_1407_3]) ).
fof(f_1408_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
| ~ 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_ca_2))) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).
fof(f_1408_2,plain,
! [U_5466,U_5465,U_5464,U_5463] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5463),U_5465),U_5464)),U_5466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),U_5465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5463),U_5466),U_5464))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),U_5465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5463),U_5466),U_5464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5463),U_5465),U_5464)),U_5466)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),c_Groups_Ozero__class_Ozero(U_5463)),U_5464))
| ~ class_Fields_Olinordered__field(U_5463) ),
inference(variable_rename,[status(thm)],[f_1408_1]) ).
fof(f_1408_3,plain,
( ! [U_5463,U_5464,U_5465,U_5466] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5463),U_5465),U_5464)),U_5466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),U_5465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5463),U_5466),U_5464)))
| ~ sP420(U_5463,U_5464,U_5465,U_5466) )
& ! [U_5463,U_5464,U_5465,U_5466] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),U_5465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5463),U_5466),U_5464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5463),U_5465),U_5464)),U_5466))
| ~ sP420(U_5463,U_5464,U_5465,U_5466) )
& ! [U_5463,U_5464,U_5465,U_5466] :
( sP420(U_5463,U_5464,U_5465,U_5466)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),c_Groups_Ozero__class_Ozero(U_5463)),U_5464))
| ~ class_Fields_Olinordered__field(U_5463) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP420])],[f_1408_2]) ).
cnf(f_1408_4,plain,
( sP420(U_5463,U_5464,U_5465,U_5466)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),c_Groups_Ozero__class_Ozero(U_5463)),U_5464))
| ~ class_Fields_Olinordered__field(U_5463) ),
inference(clausify,[status(thm)],[f_1408_3]) ).
cnf(f_1408_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),U_5465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5463),U_5466),U_5464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5463),U_5465),U_5464)),U_5466))
| ~ sP420(U_5463,U_5464,U_5465,U_5466) ),
inference(clausify,[status(thm)],[f_1408_3]) ).
cnf(f_1408_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5463),U_5465),U_5464)),U_5466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5463),U_5465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5463),U_5466),U_5464)))
| ~ sP420(U_5463,U_5464,U_5465,U_5466) ),
inference(clausify,[status(thm)],[f_1408_3]) ).
fof(f_1409_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
| ~ 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_ca_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).
fof(f_1409_2,plain,
! [U_5470,U_5469,U_5468,U_5467] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),U_5469),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5467),U_5470),U_5468)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5467),U_5469),U_5468)),U_5470)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5467),U_5469),U_5468)),U_5470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),U_5469),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5467),U_5470),U_5468))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),c_Groups_Ozero__class_Ozero(U_5467)),U_5468))
| ~ class_Fields_Olinordered__field(U_5467) ),
inference(variable_rename,[status(thm)],[f_1409_1]) ).
fof(f_1409_3,plain,
( ! [U_5468,U_5467,U_5469,U_5470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),U_5469),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5467),U_5470),U_5468)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5467),U_5469),U_5468)),U_5470))
| ~ sP421(U_5468,U_5467,U_5469,U_5470) )
& ! [U_5468,U_5467,U_5469,U_5470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5467),U_5469),U_5468)),U_5470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),U_5469),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5467),U_5470),U_5468)))
| ~ sP421(U_5468,U_5467,U_5469,U_5470) )
& ! [U_5468,U_5467,U_5469,U_5470] :
( sP421(U_5468,U_5467,U_5469,U_5470)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),c_Groups_Ozero__class_Ozero(U_5467)),U_5468))
| ~ class_Fields_Olinordered__field(U_5467) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP421])],[f_1409_2]) ).
cnf(f_1409_4,plain,
( sP421(U_5468,U_5467,U_5469,U_5470)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),c_Groups_Ozero__class_Ozero(U_5467)),U_5468))
| ~ class_Fields_Olinordered__field(U_5467) ),
inference(clausify,[status(thm)],[f_1409_3]) ).
cnf(f_1409_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5467),U_5469),U_5468)),U_5470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),U_5469),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5467),U_5470),U_5468)))
| ~ sP421(U_5468,U_5467,U_5469,U_5470) ),
inference(clausify,[status(thm)],[f_1409_3]) ).
cnf(f_1409_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),U_5469),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5467),U_5470),U_5468)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5467),U_5469),U_5468)),U_5470))
| ~ sP421(U_5468,U_5467,U_5469,U_5470) ),
inference(clausify,[status(thm)],[f_1409_3]) ).
fof(f_1410_1,plain,
! [V_a_2,V_ca_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ( ~ 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_ca_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).
fof(f_1410_2,plain,
! [U_5474,U_5473,U_5472,U_5471] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5471),U_5472),U_5473)),U_5474))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5474))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)),U_5472))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5474))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)),U_5472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5471),U_5472),U_5473)),U_5474)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5471) ),
inference(variable_rename,[status(thm)],[f_1410_1]) ).
fof(f_1410_3,plain,
( ! [U_5471,U_5473,U_5474] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5474))
| ~ sP426(U_5471,U_5473,U_5474) )
& ! [U_5471,U_5473,U_5474] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471)))
| ~ sP426(U_5471,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)),U_5472))
| ~ sP425(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471)))
| ~ sP425(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( sP426(U_5471,U_5473,U_5474)
| sP425(U_5471,U_5472,U_5473,U_5474)
| ~ sP427(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473))
| ~ sP427(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)))
| ~ sP424(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473))
| ~ sP424(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5474))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471)))
| ~ sP422(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)),U_5472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471)))
| ~ sP422(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( sP422(U_5471,U_5472,U_5473,U_5474)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473))
| ~ sP423(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473))
| ~ sP423(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5471),U_5472),U_5473)),U_5474))
| sP427(U_5471,U_5472,U_5473,U_5474)
| sP424(U_5471,U_5472,U_5473,U_5474)
| ~ sP428(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( sP423(U_5471,U_5472,U_5473,U_5474)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5471),U_5472),U_5473)),U_5474))
| ~ sP428(U_5471,U_5472,U_5473,U_5474) )
& ! [U_5471,U_5472,U_5473,U_5474] :
( sP428(U_5471,U_5472,U_5473,U_5474)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5471) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP422,sP423,sP424,sP425,sP426,sP427,sP428])],[f_1410_2]) ).
cnf(f_1410_4,plain,
( sP428(U_5471,U_5472,U_5473,U_5474)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5471) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_5,plain,
( sP423(U_5471,U_5472,U_5473,U_5474)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5471),U_5472),U_5473)),U_5474))
| ~ sP428(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5471),U_5472),U_5473)),U_5474))
| sP427(U_5471,U_5472,U_5473,U_5474)
| sP424(U_5471,U_5472,U_5473,U_5474)
| ~ sP428(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473))
| ~ sP423(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_8,plain,
( sP422(U_5471,U_5472,U_5473,U_5474)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473))
| ~ sP423(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)),U_5472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471)))
| ~ sP422(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5474))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471)))
| ~ sP422(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473))
| ~ sP424(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)))
| ~ sP424(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5473))
| ~ sP427(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_14,plain,
( sP426(U_5471,U_5473,U_5474)
| sP425(U_5471,U_5472,U_5473,U_5474)
| ~ sP427(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471)))
| ~ sP425(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5471),U_5474),U_5473)),U_5472))
| ~ sP425(U_5471,U_5472,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),U_5473),c_Groups_Ozero__class_Ozero(U_5471)))
| ~ sP426(U_5471,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
cnf(f_1410_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5471),c_Groups_Ozero__class_Ozero(U_5471)),U_5474))
| ~ sP426(U_5471,U_5473,U_5474) ),
inference(clausify,[status(thm)],[f_1410_3]) ).
fof(f_1411_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( 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_ca_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ 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_ca_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
| ~ 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_ca_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).
fof(f_1411_2,plain,
! [U_5478,U_5477,U_5476,U_5475] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5475),U_5477),U_5478)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),c_Groups_Ozero__class_Ozero(U_5475)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)),U_5477))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),c_Groups_Ozero__class_Ozero(U_5475)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)),U_5477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5475),U_5477),U_5478))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5475) ),
inference(variable_rename,[status(thm)],[f_1411_1]) ).
fof(f_1411_3,plain,
( ! [U_5478,U_5476,U_5475] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP433(U_5478,U_5476,U_5475) )
& ! [U_5478,U_5476,U_5475] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP433(U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)))
| ~ sP432(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP432(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( sP433(U_5478,U_5476,U_5475)
| sP432(U_5477,U_5478,U_5476,U_5475)
| ~ sP434(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478))
| ~ sP434(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)),U_5477))
| ~ sP431(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478))
| ~ sP431(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),c_Groups_Ozero__class_Ozero(U_5475)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP429(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP429(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( sP429(U_5477,U_5478,U_5476,U_5475)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478))
| ~ sP430(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)),U_5477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478))
| ~ sP430(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5475),U_5477),U_5478)))
| sP434(U_5477,U_5478,U_5476,U_5475)
| sP431(U_5477,U_5478,U_5476,U_5475)
| ~ sP435(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( sP430(U_5477,U_5478,U_5476,U_5475)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5475),U_5477),U_5478)))
| ~ sP435(U_5477,U_5478,U_5476,U_5475) )
& ! [U_5477,U_5478,U_5476,U_5475] :
( sP435(U_5477,U_5478,U_5476,U_5475)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5475) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP429,sP430,sP431,sP432,sP433,sP434,sP435])],[f_1411_2]) ).
cnf(f_1411_4,plain,
( sP435(U_5477,U_5478,U_5476,U_5475)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_5,plain,
( sP430(U_5477,U_5478,U_5476,U_5475)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5475),U_5477),U_5478)))
| ~ sP435(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5475),U_5477),U_5478)))
| sP434(U_5477,U_5478,U_5476,U_5475)
| sP431(U_5477,U_5478,U_5476,U_5475)
| ~ sP435(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)),U_5477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478))
| ~ sP430(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_8,plain,
( sP429(U_5477,U_5478,U_5476,U_5475)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478))
| ~ sP430(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP429(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),c_Groups_Ozero__class_Ozero(U_5475)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP429(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478))
| ~ sP431(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)),U_5477))
| ~ sP431(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5478))
| ~ sP434(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_14,plain,
( sP433(U_5478,U_5476,U_5475)
| sP432(U_5477,U_5478,U_5476,U_5475)
| ~ sP434(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP432(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5478)))
| ~ sP432(U_5477,U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5478),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP433(U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
cnf(f_1411_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5475),U_5476),c_Groups_Ozero__class_Ozero(U_5475)))
| ~ sP433(U_5478,U_5476,U_5475) ),
inference(clausify,[status(thm)],[f_1411_3]) ).
fof(f_1412_1,plain,
! [V_x,V_z,V_y,T_a] :
( 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)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__num__frac]) ).
fof(f_1412_2,plain,
! [U_5482,U_5481,U_5480,U_5479] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5479),U_5481),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5479),U_5482),U_5480)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5479),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5479),U_5482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5479),U_5481),U_5480))),U_5480)
| U_5480 = c_Groups_Ozero__class_Ozero(U_5479)
| ~ class_Fields_Ofield__inverse__zero(U_5479) ),
inference(variable_rename,[status(thm)],[f_1412_1]) ).
fof(f_1412_3,plain,
! [U_5480,U_5482,U_5479,U_5481] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5479),U_5481),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5479),U_5482),U_5480)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5479),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5479),U_5482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5479),U_5481),U_5480))),U_5480)
| U_5480 = c_Groups_Ozero__class_Ozero(U_5479)
| ~ class_Fields_Ofield__inverse__zero(U_5479) ),
inference(definitional_conversion,[status(esa)],[f_1412_2]) ).
cnf(f_1412_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5479),U_5481),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5479),U_5482),U_5480)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5479),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5479),U_5482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5479),U_5481),U_5480))),U_5480)
| U_5480 = c_Groups_Ozero__class_Ozero(U_5479)
| ~ class_Fields_Ofield__inverse__zero(U_5479) ),
inference(clausify,[status(thm)],[f_1412_3]) ).
fof(f_1413_1,plain,
! [V_y,V_x,V_z,T_a] :
( 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)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff]) ).
fof(f_1413_2,plain,
! [U_5486,U_5485,U_5484,U_5483] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5483),U_5485),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5483),U_5486),U_5484)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5483),U_5484),U_5485)),U_5486)),U_5484)
| U_5484 = c_Groups_Ozero__class_Ozero(U_5483)
| ~ class_Fields_Ofield(U_5483) ),
inference(variable_rename,[status(thm)],[f_1413_1]) ).
fof(f_1413_3,plain,
! [U_5485,U_5484,U_5486,U_5483] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5483),U_5485),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5483),U_5486),U_5484)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5483),U_5484),U_5485)),U_5486)),U_5484)
| U_5484 = c_Groups_Ozero__class_Ozero(U_5483)
| ~ class_Fields_Ofield(U_5483) ),
inference(definitional_conversion,[status(esa)],[f_1413_2]) ).
cnf(f_1413_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5483),U_5485),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5483),U_5486),U_5484)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5483),U_5484),U_5485)),U_5486)),U_5484)
| U_5484 = c_Groups_Ozero__class_Ozero(U_5483)
| ~ class_Fields_Ofield(U_5483) ),
inference(clausify,[status(thm)],[f_1413_3]) ).
fof(f_1414_1,plain,
! [V_z,V_x,V_y,T_a] :
( 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)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__frac__num]) ).
fof(f_1414_2,plain,
! [U_5490,U_5489,U_5488,U_5487] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5487),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5487),U_5489),U_5488)),U_5490) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5487),U_5489),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5487),U_5490),U_5488))),U_5488)
| U_5488 = c_Groups_Ozero__class_Ozero(U_5487)
| ~ class_Fields_Ofield__inverse__zero(U_5487) ),
inference(variable_rename,[status(thm)],[f_1414_1]) ).
fof(f_1414_3,plain,
! [U_5487,U_5488,U_5489,U_5490] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5487),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5487),U_5489),U_5488)),U_5490) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5487),U_5489),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5487),U_5490),U_5488))),U_5488)
| U_5488 = c_Groups_Ozero__class_Ozero(U_5487)
| ~ class_Fields_Ofield__inverse__zero(U_5487) ),
inference(definitional_conversion,[status(esa)],[f_1414_2]) ).
cnf(f_1414_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5487),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5487),U_5489),U_5488)),U_5490) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5487),U_5489),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5487),U_5490),U_5488))),U_5488)
| U_5488 = c_Groups_Ozero__class_Ozero(U_5487)
| ~ class_Fields_Ofield__inverse__zero(U_5487) ),
inference(clausify,[status(thm)],[f_1414_3]) ).
fof(f_1415_1,plain,
! [V_y,V_x,V_z,T_a] :
( 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)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff]) ).
fof(f_1415_2,plain,
! [U_5494,U_5493,U_5492,U_5491] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5491),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),U_5492)),U_5494) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5491),U_5493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5491),U_5492),U_5494))),U_5492)
| U_5492 = c_Groups_Ozero__class_Ozero(U_5491)
| ~ class_Fields_Ofield(U_5491) ),
inference(variable_rename,[status(thm)],[f_1415_1]) ).
fof(f_1415_3,plain,
! [U_5491,U_5492,U_5493,U_5494] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5491),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),U_5492)),U_5494) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5491),U_5493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5491),U_5492),U_5494))),U_5492)
| U_5492 = c_Groups_Ozero__class_Ozero(U_5491)
| ~ class_Fields_Ofield(U_5491) ),
inference(definitional_conversion,[status(esa)],[f_1415_2]) ).
cnf(f_1415_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5491),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),U_5492)),U_5494) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5491),U_5493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5491),U_5492),U_5494))),U_5492)
| U_5492 = c_Groups_Ozero__class_Ozero(U_5491)
| ~ class_Fields_Ofield(U_5491) ),
inference(clausify,[status(thm)],[f_1415_3]) ).
fof(f_1416_1,plain,
! [V_w,V_x,V_z,V_y,T_a] :
( 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))
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__frac__eq]) ).
fof(f_1416_2,plain,
! [U_5499,U_5498,U_5497,U_5496,U_5495] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5495),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),U_5498),U_5496)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),U_5499),U_5497)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5498),U_5497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5499),U_5496))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5496),U_5497))
| U_5497 = c_Groups_Ozero__class_Ozero(U_5495)
| U_5496 = c_Groups_Ozero__class_Ozero(U_5495)
| ~ class_Fields_Ofield(U_5495) ),
inference(variable_rename,[status(thm)],[f_1416_1]) ).
fof(f_1416_3,plain,
! [U_5495,U_5496,U_5497,U_5498,U_5499] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5495),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),U_5498),U_5496)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),U_5499),U_5497)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5498),U_5497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5499),U_5496))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5496),U_5497))
| U_5497 = c_Groups_Ozero__class_Ozero(U_5495)
| U_5496 = c_Groups_Ozero__class_Ozero(U_5495)
| ~ class_Fields_Ofield(U_5495) ),
inference(definitional_conversion,[status(esa)],[f_1416_2]) ).
cnf(f_1416_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5495),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),U_5498),U_5496)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),U_5499),U_5497)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5495),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5498),U_5497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5499),U_5496))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5495),U_5496),U_5497))
| U_5497 = c_Groups_Ozero__class_Ozero(U_5495)
| U_5496 = c_Groups_Ozero__class_Ozero(U_5495)
| ~ class_Fields_Ofield(U_5495) ),
inference(clausify,[status(thm)],[f_1416_3]) ).
fof(f_1417_1,plain,
! [V_w,V_x,V_z,V_y,T_a] :
( 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))
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__frac__eq]) ).
fof(f_1417_2,plain,
! [U_5504,U_5503,U_5502,U_5501,U_5500] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5500),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),U_5503),U_5501)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),U_5504),U_5502)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5500),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5503),U_5502)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5504),U_5501))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5501),U_5502))
| U_5502 = c_Groups_Ozero__class_Ozero(U_5500)
| U_5501 = c_Groups_Ozero__class_Ozero(U_5500)
| ~ class_Fields_Ofield(U_5500) ),
inference(variable_rename,[status(thm)],[f_1417_1]) ).
fof(f_1417_3,plain,
! [U_5500,U_5501,U_5502,U_5503,U_5504] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5500),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),U_5503),U_5501)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),U_5504),U_5502)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5500),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5503),U_5502)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5504),U_5501))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5501),U_5502))
| U_5502 = c_Groups_Ozero__class_Ozero(U_5500)
| U_5501 = c_Groups_Ozero__class_Ozero(U_5500)
| ~ class_Fields_Ofield(U_5500) ),
inference(definitional_conversion,[status(esa)],[f_1417_2]) ).
cnf(f_1417_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5500),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),U_5503),U_5501)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),U_5504),U_5502)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5500),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5500),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5503),U_5502)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5504),U_5501))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5500),U_5501),U_5502))
| U_5502 = c_Groups_Ozero__class_Ozero(U_5500)
| U_5501 = c_Groups_Ozero__class_Ozero(U_5500)
| ~ class_Fields_Ofield(U_5500) ),
inference(clausify,[status(thm)],[f_1417_3]) ).
fof(f_1418_1,plain,
! [V_y,V_x,V_z,T_a] :
( 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)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff]) ).
fof(f_1418_2,plain,
! [U_5508,U_5507,U_5506,U_5505] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5505),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5505),U_5507),U_5506)),U_5508) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5505),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5505),U_5507),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5505),U_5506),U_5508))),U_5506)
| U_5506 = c_Groups_Ozero__class_Ozero(U_5505)
| ~ class_Fields_Ofield(U_5505) ),
inference(variable_rename,[status(thm)],[f_1418_1]) ).
fof(f_1418_3,plain,
! [U_5505,U_5506,U_5507,U_5508] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5505),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5505),U_5507),U_5506)),U_5508) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5505),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5505),U_5507),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5505),U_5506),U_5508))),U_5506)
| U_5506 = c_Groups_Ozero__class_Ozero(U_5505)
| ~ class_Fields_Ofield(U_5505) ),
inference(definitional_conversion,[status(esa)],[f_1418_2]) ).
cnf(f_1418_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5505),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5505),U_5507),U_5506)),U_5508) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5505),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5505),U_5507),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5505),U_5506),U_5508))),U_5506)
| U_5506 = c_Groups_Ozero__class_Ozero(U_5505)
| ~ class_Fields_Ofield(U_5505) ),
inference(clausify,[status(thm)],[f_1418_3]) ).
fof(f_1419_1,plain,
! [V_y,V_x,V_z,T_a] :
( 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)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff]) ).
fof(f_1419_2,plain,
! [U_5512,U_5511,U_5510,U_5509] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5509),U_5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),U_5512),U_5510)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5509),U_5510),U_5511)),U_5512)),U_5510)
| U_5510 = c_Groups_Ozero__class_Ozero(U_5509)
| ~ class_Fields_Ofield(U_5509) ),
inference(variable_rename,[status(thm)],[f_1419_1]) ).
fof(f_1419_3,plain,
! [U_5509,U_5510,U_5511,U_5512] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5509),U_5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),U_5512),U_5510)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5509),U_5510),U_5511)),U_5512)),U_5510)
| U_5510 = c_Groups_Ozero__class_Ozero(U_5509)
| ~ class_Fields_Ofield(U_5509) ),
inference(definitional_conversion,[status(esa)],[f_1419_2]) ).
cnf(f_1419_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5509),U_5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),U_5512),U_5510)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5509),U_5510),U_5511)),U_5512)),U_5510)
| U_5510 = c_Groups_Ozero__class_Ozero(U_5509)
| ~ class_Fields_Ofield(U_5509) ),
inference(clausify,[status(thm)],[f_1419_3]) ).
fof(f_1420_1,plain,
! [V_b,V_a,T_a] :
( 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)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__half__sum]) ).
fof(f_1420_2,plain,
! [U_5515,U_5514,U_5513] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5513),U_5514),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5513),U_5514),U_5515)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5513),c_Groups_Oone__class_Oone(U_5513)),c_Groups_Oone__class_Oone(U_5513)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5513),U_5514),U_5515))
| ~ class_Fields_Olinordered__field(U_5513) ),
inference(variable_rename,[status(thm)],[f_1420_1]) ).
fof(f_1420_3,plain,
! [U_5513,U_5514,U_5515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5513),U_5514),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5513),U_5514),U_5515)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5513),c_Groups_Oone__class_Oone(U_5513)),c_Groups_Oone__class_Oone(U_5513)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5513),U_5514),U_5515))
| ~ class_Fields_Olinordered__field(U_5513) ),
inference(definitional_conversion,[status(esa)],[f_1420_2]) ).
cnf(f_1420_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5513),U_5514),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5513),U_5514),U_5515)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5513),c_Groups_Oone__class_Oone(U_5513)),c_Groups_Oone__class_Oone(U_5513)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5513),U_5514),U_5515))
| ~ class_Fields_Olinordered__field(U_5513) ),
inference(clausify,[status(thm)],[f_1420_3]) ).
fof(f_1421_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_gt__half__sum]) ).
fof(f_1421_2,plain,
! [U_5518,U_5517,U_5516] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5516),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),U_5517),U_5518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),c_Groups_Oone__class_Oone(U_5516)),c_Groups_Oone__class_Oone(U_5516)))),U_5518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5516),U_5517),U_5518))
| ~ class_Fields_Olinordered__field(U_5516) ),
inference(variable_rename,[status(thm)],[f_1421_1]) ).
fof(f_1421_3,plain,
! [U_5516,U_5517,U_5518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5516),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),U_5517),U_5518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),c_Groups_Oone__class_Oone(U_5516)),c_Groups_Oone__class_Oone(U_5516)))),U_5518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5516),U_5517),U_5518))
| ~ class_Fields_Olinordered__field(U_5516) ),
inference(definitional_conversion,[status(esa)],[f_1421_2]) ).
cnf(f_1421_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5516),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),U_5517),U_5518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),c_Groups_Oone__class_Oone(U_5516)),c_Groups_Oone__class_Oone(U_5516)))),U_5518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5516),U_5517),U_5518))
| ~ class_Fields_Olinordered__field(U_5516) ),
inference(clausify,[status(thm)],[f_1421_3]) ).
fof(f_1422_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( ( ( 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_ca_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ 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_ca_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
| ~ 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_ca_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).
fof(f_1422_2,plain,
! [U_5522,U_5521,U_5520,U_5519] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),U_5521),U_5522)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),c_Groups_Ozero__class_Ozero(U_5519)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)),U_5521))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),c_Groups_Ozero__class_Ozero(U_5519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)),U_5521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),U_5521),U_5522))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5519) ),
inference(variable_rename,[status(thm)],[f_1422_1]) ).
fof(f_1422_3,plain,
( ! [U_5519,U_5520,U_5522] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP440(U_5519,U_5520,U_5522) )
& ! [U_5519,U_5520,U_5522] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP440(U_5519,U_5520,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)))
| ~ sP439(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP439(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( sP440(U_5519,U_5520,U_5522)
| sP439(U_5519,U_5520,U_5521,U_5522)
| ~ sP441(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522))
| ~ sP441(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)),U_5521))
| ~ sP438(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522))
| ~ sP438(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),c_Groups_Ozero__class_Ozero(U_5519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP436(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP436(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( sP436(U_5519,U_5520,U_5521,U_5522)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522))
| ~ sP437(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)),U_5521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522))
| ~ sP437(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),U_5521),U_5522)))
| sP441(U_5519,U_5520,U_5521,U_5522)
| sP438(U_5519,U_5520,U_5521,U_5522)
| ~ sP442(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( sP437(U_5519,U_5520,U_5521,U_5522)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),U_5521),U_5522)))
| ~ sP442(U_5519,U_5520,U_5521,U_5522) )
& ! [U_5519,U_5520,U_5521,U_5522] :
( sP442(U_5519,U_5520,U_5521,U_5522)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5519) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP436,sP437,sP438,sP439,sP440,sP441,sP442])],[f_1422_2]) ).
cnf(f_1422_4,plain,
( sP442(U_5519,U_5520,U_5521,U_5522)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5519) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_5,plain,
( sP437(U_5519,U_5520,U_5521,U_5522)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),U_5521),U_5522)))
| ~ sP442(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),U_5521),U_5522)))
| sP441(U_5519,U_5520,U_5521,U_5522)
| sP438(U_5519,U_5520,U_5521,U_5522)
| ~ sP442(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)),U_5521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522))
| ~ sP437(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_8,plain,
( sP436(U_5519,U_5520,U_5521,U_5522)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522))
| ~ sP437(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP436(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),c_Groups_Ozero__class_Ozero(U_5519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP436(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522))
| ~ sP438(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)),U_5521))
| ~ sP438(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5522))
| ~ sP441(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_14,plain,
( sP440(U_5519,U_5520,U_5522)
| sP439(U_5519,U_5520,U_5521,U_5522)
| ~ sP441(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP439(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5519),U_5520),U_5522)))
| ~ sP439(U_5519,U_5520,U_5521,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),U_5522),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP440(U_5519,U_5520,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5519),U_5520),c_Groups_Ozero__class_Ozero(U_5519)))
| ~ sP440(U_5519,U_5520,U_5522) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
fof(f_1423_1,plain,
! [V_a_2,V_ca_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ( ~ 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_ca_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).
fof(f_1423_2,plain,
! [U_5526,U_5525,U_5524,U_5523] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5523),U_5524),U_5525)),U_5526))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5526))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)),U_5524))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),U_5524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5526))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)),U_5524))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),U_5524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5523),U_5524),U_5525)),U_5526)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5523) ),
inference(variable_rename,[status(thm)],[f_1423_1]) ).
fof(f_1423_3,plain,
( ! [U_5526,U_5525,U_5523] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5526))
| ~ sP447(U_5526,U_5525,U_5523) )
& ! [U_5526,U_5525,U_5523] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523)))
| ~ sP447(U_5526,U_5525,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)),U_5524))
| ~ sP446(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523)))
| ~ sP446(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( sP447(U_5526,U_5525,U_5523)
| sP446(U_5526,U_5525,U_5524,U_5523)
| ~ sP448(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525))
| ~ sP448(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),U_5524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)))
| ~ sP445(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525))
| ~ sP445(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5526))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523)))
| ~ sP443(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)),U_5524))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523)))
| ~ sP443(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( sP443(U_5526,U_5525,U_5524,U_5523)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525))
| ~ sP444(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),U_5524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525))
| ~ sP444(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5523),U_5524),U_5525)),U_5526))
| sP448(U_5526,U_5525,U_5524,U_5523)
| sP445(U_5526,U_5525,U_5524,U_5523)
| ~ sP449(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( sP444(U_5526,U_5525,U_5524,U_5523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5523),U_5524),U_5525)),U_5526))
| ~ sP449(U_5526,U_5525,U_5524,U_5523) )
& ! [U_5526,U_5525,U_5524,U_5523] :
( sP449(U_5526,U_5525,U_5524,U_5523)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5523) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP443,sP444,sP445,sP446,sP447,sP448,sP449])],[f_1423_2]) ).
cnf(f_1423_4,plain,
( sP449(U_5526,U_5525,U_5524,U_5523)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_5,plain,
( sP444(U_5526,U_5525,U_5524,U_5523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5523),U_5524),U_5525)),U_5526))
| ~ sP449(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5523),U_5524),U_5525)),U_5526))
| sP448(U_5526,U_5525,U_5524,U_5523)
| sP445(U_5526,U_5525,U_5524,U_5523)
| ~ sP449(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),U_5524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525))
| ~ sP444(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_8,plain,
( sP443(U_5526,U_5525,U_5524,U_5523)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525))
| ~ sP444(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)),U_5524))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523)))
| ~ sP443(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5526))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523)))
| ~ sP443(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525))
| ~ sP445(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),U_5524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)))
| ~ sP445(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5525))
| ~ sP448(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_14,plain,
( sP447(U_5526,U_5525,U_5523)
| sP446(U_5526,U_5525,U_5524,U_5523)
| ~ sP448(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523)))
| ~ sP446(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5523),U_5526),U_5525)),U_5524))
| ~ sP446(U_5526,U_5525,U_5524,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5523),U_5525),c_Groups_Ozero__class_Ozero(U_5523)))
| ~ sP447(U_5526,U_5525,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5523),c_Groups_Ozero__class_Ozero(U_5523)),U_5526))
| ~ sP447(U_5526,U_5525,U_5523) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
fof(f_1424_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_b] :
( ( ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
| ~ 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_ca_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).
fof(f_1424_2,plain,
! [U_5530,U_5529,U_5528,U_5527] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5530),U_5528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5527),U_5529),U_5528)),U_5530)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5527),U_5529),U_5528)),U_5530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5530),U_5528))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5527),c_Groups_Ozero__class_Ozero(U_5527)),U_5528))
| ~ class_Fields_Olinordered__field(U_5527) ),
inference(variable_rename,[status(thm)],[f_1424_1]) ).
fof(f_1424_3,plain,
( ! [U_5527,U_5529,U_5528,U_5530] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5530),U_5528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5527),U_5529),U_5528)),U_5530))
| ~ sP450(U_5527,U_5529,U_5528,U_5530) )
& ! [U_5527,U_5529,U_5528,U_5530] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5527),U_5529),U_5528)),U_5530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5530),U_5528)))
| ~ sP450(U_5527,U_5529,U_5528,U_5530) )
& ! [U_5527,U_5529,U_5528,U_5530] :
( sP450(U_5527,U_5529,U_5528,U_5530)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5527),c_Groups_Ozero__class_Ozero(U_5527)),U_5528))
| ~ class_Fields_Olinordered__field(U_5527) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP450])],[f_1424_2]) ).
cnf(f_1424_4,plain,
( sP450(U_5527,U_5529,U_5528,U_5530)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5527),c_Groups_Ozero__class_Ozero(U_5527)),U_5528))
| ~ class_Fields_Olinordered__field(U_5527) ),
inference(clausify,[status(thm)],[f_1424_3]) ).
cnf(f_1424_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5527),U_5529),U_5528)),U_5530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5530),U_5528)))
| ~ sP450(U_5527,U_5529,U_5528,U_5530) ),
inference(clausify,[status(thm)],[f_1424_3]) ).
cnf(f_1424_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5530),U_5528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5527),U_5529),U_5528)),U_5530))
| ~ sP450(U_5527,U_5529,U_5528,U_5530) ),
inference(clausify,[status(thm)],[f_1424_3]) ).
fof(f_1425_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
| ~ 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_ca_2))) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).
fof(f_1425_2,plain,
! [U_5534,U_5533,U_5532,U_5531] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5531),U_5533),U_5532)),U_5534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),U_5533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5531),U_5534),U_5532))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),U_5533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5531),U_5534),U_5532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5531),U_5533),U_5532)),U_5534)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5531),c_Groups_Ozero__class_Ozero(U_5531)),U_5532))
| ~ class_Fields_Olinordered__field(U_5531) ),
inference(variable_rename,[status(thm)],[f_1425_1]) ).
fof(f_1425_3,plain,
( ! [U_5531,U_5533,U_5532,U_5534] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5531),U_5533),U_5532)),U_5534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),U_5533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5531),U_5534),U_5532)))
| ~ sP451(U_5531,U_5533,U_5532,U_5534) )
& ! [U_5531,U_5533,U_5532,U_5534] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),U_5533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5531),U_5534),U_5532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5531),U_5533),U_5532)),U_5534))
| ~ sP451(U_5531,U_5533,U_5532,U_5534) )
& ! [U_5531,U_5533,U_5532,U_5534] :
( sP451(U_5531,U_5533,U_5532,U_5534)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5531),c_Groups_Ozero__class_Ozero(U_5531)),U_5532))
| ~ class_Fields_Olinordered__field(U_5531) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP451])],[f_1425_2]) ).
cnf(f_1425_4,plain,
( sP451(U_5531,U_5533,U_5532,U_5534)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5531),c_Groups_Ozero__class_Ozero(U_5531)),U_5532))
| ~ class_Fields_Olinordered__field(U_5531) ),
inference(clausify,[status(thm)],[f_1425_3]) ).
cnf(f_1425_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),U_5533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5531),U_5534),U_5532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5531),U_5533),U_5532)),U_5534))
| ~ sP451(U_5531,U_5533,U_5532,U_5534) ),
inference(clausify,[status(thm)],[f_1425_3]) ).
cnf(f_1425_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5531),U_5533),U_5532)),U_5534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5531),U_5533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5531),U_5534),U_5532)))
| ~ sP451(U_5531,U_5533,U_5532,U_5534) ),
inference(clausify,[status(thm)],[f_1425_3]) ).
fof(f_1426_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(f_1426_2,plain,
! [U_5536,U_5535] : c_Sum__Type_OPlus(U_5535,U_5536,c_Orderings_Otop__class_Otop(tc_fun(U_5535,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5536,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_5535,U_5536),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1426_1]) ).
fof(f_1426_3,plain,
! [U_5536,U_5535] : c_Sum__Type_OPlus(U_5535,U_5536,c_Orderings_Otop__class_Otop(tc_fun(U_5535,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5536,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_5535,U_5536),tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1426_2]) ).
cnf(f_1426_4,plain,
c_Sum__Type_OPlus(U_5535,U_5536,c_Orderings_Otop__class_Otop(tc_fun(U_5535,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5536,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_5535,U_5536),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1426_3]) ).
fof(f_1427_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( 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)))
| ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
& 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))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Fields_Ofield(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un]) ).
fof(f_1427_2,plain,
! [U_5542,U_5541,U_5540,U_5539,U_5538] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),U_5540)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),U_5541))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)))
| ? [U_5537] :
( hAPP(U_5542,U_5537) = c_Groups_Ozero__class_Ozero(U_5538)
& hBOOL(hAPP(hAPP(c_member(U_5539),U_5537),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5539),U_5541))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5539),U_5540))
| ~ class_Fields_Ofield(U_5538) ),
inference(variable_rename,[status(thm)],[f_1427_1]) ).
fof(f_1427_3,plain,
! [U_5542,U_5541,U_5540,U_5539,U_5538] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),U_5540)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),U_5541))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)))
| ( hAPP(U_5542,sK132(U_5542,U_5541,U_5540,U_5539,U_5538)) = c_Groups_Ozero__class_Ozero(U_5538)
& hBOOL(hAPP(hAPP(c_member(U_5539),sK132(U_5542,U_5541,U_5540,U_5539,U_5538)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5539),U_5541))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5539),U_5540))
| ~ class_Fields_Ofield(U_5538) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_5537,sK132(U_5542,U_5541,U_5540,U_5539,U_5538))],[f_1427_2]) ).
fof(f_1427_4,plain,
( ! [U_5538,U_5539,U_5540,U_5541,U_5542] :
( hAPP(U_5542,sK132(U_5542,U_5541,U_5540,U_5539,U_5538)) = c_Groups_Ozero__class_Ozero(U_5538)
| ~ sP452(U_5538,U_5539,U_5540,U_5541,U_5542) )
& ! [U_5538,U_5539,U_5540,U_5541,U_5542] :
( hBOOL(hAPP(hAPP(c_member(U_5539),sK132(U_5542,U_5541,U_5540,U_5539,U_5538)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)))
| ~ sP452(U_5538,U_5539,U_5540,U_5541,U_5542) )
& ! [U_5538,U_5539,U_5540,U_5541,U_5542] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),U_5540)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),U_5541))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)))
| sP452(U_5538,U_5539,U_5540,U_5541,U_5542)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5539),U_5541))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5539),U_5540))
| ~ class_Fields_Ofield(U_5538) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP452])],[f_1427_3]) ).
cnf(f_1427_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),U_5540)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),U_5541))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5539,U_5538),U_5542),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)))
| sP452(U_5538,U_5539,U_5540,U_5541,U_5542)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5539),U_5541))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5539),U_5540))
| ~ class_Fields_Ofield(U_5538) ),
inference(clausify,[status(thm)],[f_1427_4]) ).
cnf(f_1427_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5539),sK132(U_5542,U_5541,U_5540,U_5539,U_5538)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5539,tc_HOL_Obool)),U_5540),U_5541)))
| ~ sP452(U_5538,U_5539,U_5540,U_5541,U_5542) ),
inference(clausify,[status(thm)],[f_1427_4]) ).
cnf(f_1427_7,plain,
( hAPP(U_5542,sK132(U_5542,U_5541,U_5540,U_5539,U_5538)) = c_Groups_Ozero__class_Ozero(U_5538)
| ~ sP452(U_5538,U_5539,U_5540,U_5541,U_5542) ),
inference(clausify,[status(thm)],[f_1427_4]) ).
fof(f_1428_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( 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))
| V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
| 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv]) ).
fof(f_1428_2,plain,
! [U_5546,U_5545,U_5544,U_5543] :
( ( c_Sum__Type_OPlus(U_5543,U_5544,U_5545,U_5546) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5543,U_5544),tc_HOL_Obool))
| U_5546 != c_Orderings_Obot__class_Obot(tc_fun(U_5544,tc_HOL_Obool))
| U_5545 != c_Orderings_Obot__class_Obot(tc_fun(U_5543,tc_HOL_Obool)) )
& ( ( U_5546 = c_Orderings_Obot__class_Obot(tc_fun(U_5544,tc_HOL_Obool))
& U_5545 = c_Orderings_Obot__class_Obot(tc_fun(U_5543,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(U_5543,U_5544,U_5545,U_5546) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5543,U_5544),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1428_1]) ).
fof(f_1428_3,plain,
( ! [U_5554,U_5552,U_5550,U_5548] :
( c_Sum__Type_OPlus(U_5548,U_5550,U_5552,U_5554) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5548,U_5550),tc_HOL_Obool))
| U_5554 != c_Orderings_Obot__class_Obot(tc_fun(U_5550,tc_HOL_Obool))
| U_5552 != c_Orderings_Obot__class_Obot(tc_fun(U_5548,tc_HOL_Obool)) )
& ! [U_5553,U_5551,U_5549,U_5547] :
( ( U_5553 = c_Orderings_Obot__class_Obot(tc_fun(U_5549,tc_HOL_Obool))
& U_5551 = c_Orderings_Obot__class_Obot(tc_fun(U_5547,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(U_5547,U_5549,U_5551,U_5553) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5547,U_5549),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1428_2]) ).
fof(f_1428_4,plain,
( ! [U_5547,U_5549,U_5551,U_5553] :
( U_5553 = c_Orderings_Obot__class_Obot(tc_fun(U_5549,tc_HOL_Obool))
| ~ sP453(U_5547,U_5549,U_5551,U_5553) )
& ! [U_5547,U_5549,U_5551,U_5553] :
( U_5551 = c_Orderings_Obot__class_Obot(tc_fun(U_5547,tc_HOL_Obool))
| ~ sP453(U_5547,U_5549,U_5551,U_5553) )
& ! [U_5552,U_5554,U_5548,U_5550] :
( c_Sum__Type_OPlus(U_5548,U_5550,U_5552,U_5554) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5548,U_5550),tc_HOL_Obool))
| U_5554 != c_Orderings_Obot__class_Obot(tc_fun(U_5550,tc_HOL_Obool))
| U_5552 != c_Orderings_Obot__class_Obot(tc_fun(U_5548,tc_HOL_Obool)) )
& ! [U_5547,U_5549,U_5551,U_5553] :
( sP453(U_5547,U_5549,U_5551,U_5553)
| c_Sum__Type_OPlus(U_5547,U_5549,U_5551,U_5553) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5547,U_5549),tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP453])],[f_1428_3]) ).
cnf(f_1428_5,plain,
( sP453(U_5547,U_5549,U_5551,U_5553)
| c_Sum__Type_OPlus(U_5547,U_5549,U_5551,U_5553) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5547,U_5549),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1428_4]) ).
cnf(f_1428_6,plain,
( c_Sum__Type_OPlus(U_5548,U_5550,U_5552,U_5554) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5548,U_5550),tc_HOL_Obool))
| U_5554 != c_Orderings_Obot__class_Obot(tc_fun(U_5550,tc_HOL_Obool))
| U_5552 != c_Orderings_Obot__class_Obot(tc_fun(U_5548,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1428_4]) ).
cnf(f_1428_7,plain,
( U_5551 = c_Orderings_Obot__class_Obot(tc_fun(U_5547,tc_HOL_Obool))
| ~ sP453(U_5547,U_5549,U_5551,U_5553) ),
inference(clausify,[status(thm)],[f_1428_4]) ).
cnf(f_1428_8,plain,
( U_5553 = c_Orderings_Obot__class_Obot(tc_fun(U_5549,tc_HOL_Obool))
| ~ sP453(U_5547,U_5549,U_5551,U_5553) ),
inference(clausify,[status(thm)],[f_1428_4]) ).
fof(f_1429_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ? [B_z] :
( ~ 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))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__le__mult__one__interval]) ).
fof(f_1429_2,plain,
! [U_5558,U_5557,U_5556] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5556),U_5557),U_5558))
| ? [U_5555] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5556),U_5555),U_5557)),U_5558))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5556),U_5555),c_Groups_Oone__class_Oone(U_5556)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5556),c_Groups_Ozero__class_Ozero(U_5556)),U_5555)) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5556) ),
inference(variable_rename,[status(thm)],[f_1429_1]) ).
fof(f_1429_3,plain,
! [U_5558,U_5557,U_5556] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5556),U_5557),U_5558))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5556),sK133(U_5558,U_5557,U_5556)),U_5557)),U_5558))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5556),sK133(U_5558,U_5557,U_5556)),c_Groups_Oone__class_Oone(U_5556)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5556),c_Groups_Ozero__class_Ozero(U_5556)),sK133(U_5558,U_5557,U_5556))) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_5556) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_5555,sK133(U_5558,U_5557,U_5556))],[f_1429_2]) ).
fof(f_1429_4,plain,
( ! [U_5556,U_5557,U_5558] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5556),sK133(U_5558,U_5557,U_5556)),U_5557)),U_5558))
| ~ sP454(U_5556,U_5557,U_5558) )
& ! [U_5556,U_5557,U_5558] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5556),sK133(U_5558,U_5557,U_5556)),c_Groups_Oone__class_Oone(U_5556)))
| ~ sP454(U_5556,U_5557,U_5558) )
& ! [U_5556,U_5557,U_5558] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5556),c_Groups_Ozero__class_Ozero(U_5556)),sK133(U_5558,U_5557,U_5556)))
| ~ sP454(U_5556,U_5557,U_5558) )
& ! [U_5556,U_5557,U_5558] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5556),U_5557),U_5558))
| sP454(U_5556,U_5557,U_5558)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5556) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP454])],[f_1429_3]) ).
cnf(f_1429_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5556),U_5557),U_5558))
| sP454(U_5556,U_5557,U_5558)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5556) ),
inference(clausify,[status(thm)],[f_1429_4]) ).
cnf(f_1429_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5556),c_Groups_Ozero__class_Ozero(U_5556)),sK133(U_5558,U_5557,U_5556)))
| ~ sP454(U_5556,U_5557,U_5558) ),
inference(clausify,[status(thm)],[f_1429_4]) ).
cnf(f_1429_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5556),sK133(U_5558,U_5557,U_5556)),c_Groups_Oone__class_Oone(U_5556)))
| ~ sP454(U_5556,U_5557,U_5558) ),
inference(clausify,[status(thm)],[f_1429_4]) ).
cnf(f_1429_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5556),sK133(U_5558,U_5557,U_5556)),U_5557)),U_5558))
| ~ sP454(U_5556,U_5557,U_5558) ),
inference(clausify,[status(thm)],[f_1429_4]) ).
fof(f_1430_1,plain,
! [V_f_2,V_S_2,T_b] :
( 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)))
| ? [B_x] :
( ~ 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)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat]) ).
fof(f_1430_2,plain,
! [U_5562,U_5561,U_5560] :
( 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(U_5560,tc_Nat_Onat),U_5562),U_5561)))
| ? [U_5559] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5562,U_5559)))
& hBOOL(hAPP(hAPP(c_member(U_5560),U_5559),U_5561)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5560),U_5561)) ),
inference(variable_rename,[status(thm)],[f_1430_1]) ).
fof(f_1430_3,plain,
! [U_5562,U_5561,U_5560] :
( 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(U_5560,tc_Nat_Onat),U_5562),U_5561)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5562,sK134(U_5562,U_5561,U_5560))))
& hBOOL(hAPP(hAPP(c_member(U_5560),sK134(U_5562,U_5561,U_5560)),U_5561)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5560),U_5561)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_5559,sK134(U_5562,U_5561,U_5560))],[f_1430_2]) ).
fof(f_1430_4,plain,
( ! [U_5561,U_5560,U_5562] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5562,sK134(U_5562,U_5561,U_5560))))
| ~ sP455(U_5561,U_5560,U_5562) )
& ! [U_5561,U_5560,U_5562] :
( hBOOL(hAPP(hAPP(c_member(U_5560),sK134(U_5562,U_5561,U_5560)),U_5561))
| ~ sP455(U_5561,U_5560,U_5562) )
& ! [U_5561,U_5560,U_5562] :
( 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(U_5560,tc_Nat_Onat),U_5562),U_5561)))
| sP455(U_5561,U_5560,U_5562)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5560),U_5561)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP455])],[f_1430_3]) ).
cnf(f_1430_5,plain,
( 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(U_5560,tc_Nat_Onat),U_5562),U_5561)))
| sP455(U_5561,U_5560,U_5562)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5560),U_5561)) ),
inference(clausify,[status(thm)],[f_1430_4]) ).
cnf(f_1430_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5560),sK134(U_5562,U_5561,U_5560)),U_5561))
| ~ sP455(U_5561,U_5560,U_5562) ),
inference(clausify,[status(thm)],[f_1430_4]) ).
cnf(f_1430_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5562,sK134(U_5562,U_5561,U_5560))))
| ~ sP455(U_5561,U_5560,U_5562) ),
inference(clausify,[status(thm)],[f_1430_4]) ).
fof(f_1431_1,plain,
! [V_n_2,V_A_2,V_f_2,T_b] :
( ? [B_x] :
( 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)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| 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) ),
inference(fof_nnf,[status(thm)],[fact_setsum__SucD]) ).
fof(f_1431_2,plain,
! [U_5567,U_5566,U_5565,U_5564] :
( ? [U_5563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5565,U_5563)))
& hBOOL(hAPP(hAPP(c_member(U_5564),U_5563),U_5566)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5564,tc_Nat_Onat),U_5565),U_5566) != hAPP(c_Nat_OSuc,U_5567) ),
inference(variable_rename,[status(thm)],[f_1431_1]) ).
fof(f_1431_3,plain,
! [U_5567,U_5566,U_5565,U_5564] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5565,sK135(U_5567,U_5566,U_5565,U_5564))))
& hBOOL(hAPP(hAPP(c_member(U_5564),sK135(U_5567,U_5566,U_5565,U_5564)),U_5566)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5564,tc_Nat_Onat),U_5565),U_5566) != hAPP(c_Nat_OSuc,U_5567) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_5563,sK135(U_5567,U_5566,U_5565,U_5564))],[f_1431_2]) ).
fof(f_1431_4,plain,
( ! [U_5564,U_5565,U_5566,U_5567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5565,sK135(U_5567,U_5566,U_5565,U_5564))))
| ~ sP456(U_5564,U_5565,U_5566,U_5567) )
& ! [U_5564,U_5565,U_5566,U_5567] :
( hBOOL(hAPP(hAPP(c_member(U_5564),sK135(U_5567,U_5566,U_5565,U_5564)),U_5566))
| ~ sP456(U_5564,U_5565,U_5566,U_5567) )
& ! [U_5564,U_5565,U_5566,U_5567] :
( sP456(U_5564,U_5565,U_5566,U_5567)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5564,tc_Nat_Onat),U_5565),U_5566) != hAPP(c_Nat_OSuc,U_5567) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP456])],[f_1431_3]) ).
cnf(f_1431_5,plain,
( sP456(U_5564,U_5565,U_5566,U_5567)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5564,tc_Nat_Onat),U_5565),U_5566) != hAPP(c_Nat_OSuc,U_5567) ),
inference(clausify,[status(thm)],[f_1431_4]) ).
cnf(f_1431_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5564),sK135(U_5567,U_5566,U_5565,U_5564)),U_5566))
| ~ sP456(U_5564,U_5565,U_5566,U_5567) ),
inference(clausify,[status(thm)],[f_1431_4]) ).
cnf(f_1431_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5565,sK135(U_5567,U_5566,U_5565,U_5564))))
| ~ sP456(U_5564,U_5565,U_5566,U_5567) ),
inference(clausify,[status(thm)],[f_1431_4]) ).
fof(f_1432_1,plain,
! [V_k_2,V_C_2,T_b] :
( 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))
| ? [B_c1] :
( ? [B_c2] :
( 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))
& B_c1 != B_c2
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) )
| ? [B_c] :
( hAPP(c_Finite__Set_Ocard(T_b),B_c) != V_k_2
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__partition]) ).
fof(f_1432_2,plain,
! [U_5573,U_5572,U_5571] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5573),hAPP(c_Finite__Set_Ocard(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) = hAPP(c_Finite__Set_Ocard(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572))
| ? [U_5570] :
( ? [U_5569] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5571,tc_HOL_Obool)),U_5570),U_5569) != c_Orderings_Obot__class_Obot(tc_fun(U_5571,tc_HOL_Obool))
& U_5570 != U_5569
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),U_5569),U_5572)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),U_5570),U_5572)) )
| ? [U_5568] :
( hAPP(c_Finite__Set_Ocard(U_5571),U_5568) != U_5573
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),U_5568),U_5572)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) ),
inference(variable_rename,[status(thm)],[f_1432_1]) ).
fof(f_1432_3,plain,
! [U_5573,U_5572,U_5571] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5573),hAPP(c_Finite__Set_Ocard(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) = hAPP(c_Finite__Set_Ocard(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572))
| ? [U_5570] :
( ? [U_5569] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5571,tc_HOL_Obool)),U_5570),U_5569) != c_Orderings_Obot__class_Obot(tc_fun(U_5571,tc_HOL_Obool))
& U_5570 != U_5569
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),U_5569),U_5572)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),U_5570),U_5572)) )
| ( hAPP(c_Finite__Set_Ocard(U_5571),sK136(U_5573,U_5572,U_5571)) != U_5573
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK136(U_5573,U_5572,U_5571)),U_5572)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_5568,sK136(U_5573,U_5572,U_5571))],[f_1432_2]) ).
fof(f_1432_4,plain,
! [U_5573,U_5572,U_5571] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5573),hAPP(c_Finite__Set_Ocard(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) = hAPP(c_Finite__Set_Ocard(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572))
| ( ? [U_5569] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5571,tc_HOL_Obool)),sK137(U_5573,U_5572,U_5571)),U_5569) != c_Orderings_Obot__class_Obot(tc_fun(U_5571,tc_HOL_Obool))
& sK137(U_5573,U_5572,U_5571) != U_5569
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),U_5569),U_5572)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK137(U_5573,U_5572,U_5571)),U_5572)) )
| ( hAPP(c_Finite__Set_Ocard(U_5571),sK136(U_5573,U_5572,U_5571)) != U_5573
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK136(U_5573,U_5572,U_5571)),U_5572)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_5570,sK137(U_5573,U_5572,U_5571))],[f_1432_3]) ).
fof(f_1432_5,plain,
! [U_5573,U_5572,U_5571] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5573),hAPP(c_Finite__Set_Ocard(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) = hAPP(c_Finite__Set_Ocard(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5571,tc_HOL_Obool)),sK137(U_5573,U_5572,U_5571)),sK138(U_5573,U_5572,U_5571)) != c_Orderings_Obot__class_Obot(tc_fun(U_5571,tc_HOL_Obool))
& sK137(U_5573,U_5572,U_5571) != sK138(U_5573,U_5572,U_5571)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK138(U_5573,U_5572,U_5571)),U_5572))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK137(U_5573,U_5572,U_5571)),U_5572)) )
| ( hAPP(c_Finite__Set_Ocard(U_5571),sK136(U_5573,U_5572,U_5571)) != U_5573
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK136(U_5573,U_5572,U_5571)),U_5572)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_5569,sK138(U_5573,U_5572,U_5571))],[f_1432_4]) ).
fof(f_1432_6,plain,
( ! [U_5571,U_5572,U_5573] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5571,tc_HOL_Obool)),sK137(U_5573,U_5572,U_5571)),sK138(U_5573,U_5572,U_5571)) != c_Orderings_Obot__class_Obot(tc_fun(U_5571,tc_HOL_Obool))
| ~ sP458(U_5571,U_5572,U_5573) )
& ! [U_5571,U_5572,U_5573] :
( sK137(U_5573,U_5572,U_5571) != sK138(U_5573,U_5572,U_5571)
| ~ sP458(U_5571,U_5572,U_5573) )
& ! [U_5571,U_5572,U_5573] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK138(U_5573,U_5572,U_5571)),U_5572))
| ~ sP458(U_5571,U_5572,U_5573) )
& ! [U_5571,U_5572,U_5573] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK137(U_5573,U_5572,U_5571)),U_5572))
| ~ sP458(U_5571,U_5572,U_5573) )
& ! [U_5571,U_5572,U_5573] :
( hAPP(c_Finite__Set_Ocard(U_5571),sK136(U_5573,U_5572,U_5571)) != U_5573
| ~ sP457(U_5571,U_5572,U_5573) )
& ! [U_5571,U_5572,U_5573] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK136(U_5573,U_5572,U_5571)),U_5572))
| ~ sP457(U_5571,U_5572,U_5573) )
& ! [U_5571,U_5572,U_5573] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5573),hAPP(c_Finite__Set_Ocard(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) = hAPP(c_Finite__Set_Ocard(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572))
| sP458(U_5571,U_5572,U_5573)
| sP457(U_5571,U_5572,U_5573)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP457,sP458])],[f_1432_5]) ).
cnf(f_1432_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5573),hAPP(c_Finite__Set_Ocard(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) = hAPP(c_Finite__Set_Ocard(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572))
| sP458(U_5571,U_5572,U_5573)
| sP457(U_5571,U_5572,U_5573)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5571),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5571,tc_HOL_Obool),U_5572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5571,tc_HOL_Obool)),U_5572)) ),
inference(clausify,[status(thm)],[f_1432_6]) ).
cnf(f_1432_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK136(U_5573,U_5572,U_5571)),U_5572))
| ~ sP457(U_5571,U_5572,U_5573) ),
inference(clausify,[status(thm)],[f_1432_6]) ).
cnf(f_1432_9,plain,
( hAPP(c_Finite__Set_Ocard(U_5571),sK136(U_5573,U_5572,U_5571)) != U_5573
| ~ sP457(U_5571,U_5572,U_5573) ),
inference(clausify,[status(thm)],[f_1432_6]) ).
cnf(f_1432_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK137(U_5573,U_5572,U_5571)),U_5572))
| ~ sP458(U_5571,U_5572,U_5573) ),
inference(clausify,[status(thm)],[f_1432_6]) ).
cnf(f_1432_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_5571,tc_HOL_Obool)),sK138(U_5573,U_5572,U_5571)),U_5572))
| ~ sP458(U_5571,U_5572,U_5573) ),
inference(clausify,[status(thm)],[f_1432_6]) ).
cnf(f_1432_12,plain,
( sK137(U_5573,U_5572,U_5571) != sK138(U_5573,U_5572,U_5571)
| ~ sP458(U_5571,U_5572,U_5573) ),
inference(clausify,[status(thm)],[f_1432_6]) ).
cnf(f_1432_13,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5571,tc_HOL_Obool)),sK137(U_5573,U_5572,U_5571)),sK138(U_5573,U_5572,U_5571)) != c_Orderings_Obot__class_Obot(tc_fun(U_5571,tc_HOL_Obool))
| ~ sP458(U_5571,U_5572,U_5573) ),
inference(clausify,[status(thm)],[f_1432_6]) ).
fof(f_1433_1,plain,
! [V_f_2,V_S_2,T_b,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) = c_Groups_Oone__class_Oone(T_c)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__1]) ).
fof(f_1433_2,plain,
! [U_5578,U_5577,U_5576,U_5575] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5575,U_5576,c_Groups_Otimes__class_Otimes(U_5575)),U_5578),c_Groups_Oone__class_Oone(U_5575)),U_5577) = c_Groups_Oone__class_Oone(U_5575)
| ? [U_5574] :
( hAPP(U_5578,U_5574) != c_Groups_Oone__class_Oone(U_5575)
& hBOOL(hAPP(hAPP(c_member(U_5576),U_5574),U_5577)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5576),U_5577))
| ~ class_Groups_Ocomm__monoid__mult(U_5575) ),
inference(variable_rename,[status(thm)],[f_1433_1]) ).
fof(f_1433_3,plain,
! [U_5578,U_5577,U_5576,U_5575] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5575,U_5576,c_Groups_Otimes__class_Otimes(U_5575)),U_5578),c_Groups_Oone__class_Oone(U_5575)),U_5577) = c_Groups_Oone__class_Oone(U_5575)
| ( hAPP(U_5578,sK139(U_5578,U_5577,U_5576,U_5575)) != c_Groups_Oone__class_Oone(U_5575)
& hBOOL(hAPP(hAPP(c_member(U_5576),sK139(U_5578,U_5577,U_5576,U_5575)),U_5577)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5576),U_5577))
| ~ class_Groups_Ocomm__monoid__mult(U_5575) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_5574,sK139(U_5578,U_5577,U_5576,U_5575))],[f_1433_2]) ).
fof(f_1433_4,plain,
( ! [U_5576,U_5577,U_5575,U_5578] :
( hAPP(U_5578,sK139(U_5578,U_5577,U_5576,U_5575)) != c_Groups_Oone__class_Oone(U_5575)
| ~ sP459(U_5576,U_5577,U_5575,U_5578) )
& ! [U_5576,U_5577,U_5575,U_5578] :
( hBOOL(hAPP(hAPP(c_member(U_5576),sK139(U_5578,U_5577,U_5576,U_5575)),U_5577))
| ~ sP459(U_5576,U_5577,U_5575,U_5578) )
& ! [U_5576,U_5577,U_5575,U_5578] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5575,U_5576,c_Groups_Otimes__class_Otimes(U_5575)),U_5578),c_Groups_Oone__class_Oone(U_5575)),U_5577) = c_Groups_Oone__class_Oone(U_5575)
| sP459(U_5576,U_5577,U_5575,U_5578)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5576),U_5577))
| ~ class_Groups_Ocomm__monoid__mult(U_5575) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP459])],[f_1433_3]) ).
cnf(f_1433_5,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5575,U_5576,c_Groups_Otimes__class_Otimes(U_5575)),U_5578),c_Groups_Oone__class_Oone(U_5575)),U_5577) = c_Groups_Oone__class_Oone(U_5575)
| sP459(U_5576,U_5577,U_5575,U_5578)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5576),U_5577))
| ~ class_Groups_Ocomm__monoid__mult(U_5575) ),
inference(clausify,[status(thm)],[f_1433_4]) ).
cnf(f_1433_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5576),sK139(U_5578,U_5577,U_5576,U_5575)),U_5577))
| ~ sP459(U_5576,U_5577,U_5575,U_5578) ),
inference(clausify,[status(thm)],[f_1433_4]) ).
cnf(f_1433_7,plain,
( hAPP(U_5578,sK139(U_5578,U_5577,U_5576,U_5575)) != c_Groups_Oone__class_Oone(U_5575)
| ~ sP459(U_5576,U_5577,U_5575,U_5578) ),
inference(clausify,[status(thm)],[f_1433_4]) ).
fof(f_1434_1,plain,
! [V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oneutral]) ).
fof(f_1434_2,plain,
! [U_5581,U_5580] :
( hAPP(c_Finite__Set_Ocard(U_5580),U_5581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [U_5579] : hBOOL(hAPP(hAPP(c_member(U_5580),U_5579),U_5581)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5580),U_5581)) ),
inference(variable_rename,[status(thm)],[f_1434_1]) ).
fof(f_1434_3,plain,
! [U_5581,U_5580] :
( hAPP(c_Finite__Set_Ocard(U_5580),U_5581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_5580),sK140(U_5581,U_5580)),U_5581)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5580),U_5581)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_5579,sK140(U_5581,U_5580))],[f_1434_2]) ).
fof(f_1434_4,plain,
( ! [U_5580,U_5581] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP460(U_5580,U_5581) )
& ! [U_5580,U_5581] :
( hBOOL(hAPP(hAPP(c_member(U_5580),sK140(U_5581,U_5580)),U_5581))
| ~ sP460(U_5580,U_5581) )
& ! [U_5580,U_5581] :
( hAPP(c_Finite__Set_Ocard(U_5580),U_5581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP460(U_5580,U_5581)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5580),U_5581)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP460])],[f_1434_3]) ).
cnf(f_1434_5,plain,
( hAPP(c_Finite__Set_Ocard(U_5580),U_5581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP460(U_5580,U_5581)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5580),U_5581)) ),
inference(clausify,[status(thm)],[f_1434_4]) ).
cnf(f_1434_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5580),sK140(U_5581,U_5580)),U_5581))
| ~ sP460(U_5580,U_5581) ),
inference(clausify,[status(thm)],[f_1434_4]) ).
cnf(f_1434_7,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP460(U_5580,U_5581) ),
inference(clausify,[status(thm)],[f_1434_4]) ).
fof(f_1435_1,plain,
! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
( 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)
| ? [B_x] :
( hAPP(V_g_2,B_x) != hAPP(V_h_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__cong]) ).
fof(f_1435_2,plain,
! [U_5588,U_5587,U_5586,U_5585,U_5584,U_5583] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5583,U_5584,c_Groups_Otimes__class_Otimes(U_5583)),U_5586),U_5588),U_5585) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5583,U_5584,c_Groups_Otimes__class_Otimes(U_5583)),U_5587),U_5588),U_5585)
| ? [U_5582] :
( hAPP(U_5586,U_5582) != hAPP(U_5587,U_5582)
& hBOOL(hAPP(hAPP(c_member(U_5584),U_5582),U_5585)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5584),U_5585))
| ~ class_Groups_Oab__semigroup__mult(U_5583) ),
inference(variable_rename,[status(thm)],[f_1435_1]) ).
fof(f_1435_3,plain,
! [U_5588,U_5587,U_5586,U_5585,U_5584,U_5583] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5583,U_5584,c_Groups_Otimes__class_Otimes(U_5583)),U_5586),U_5588),U_5585) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5583,U_5584,c_Groups_Otimes__class_Otimes(U_5583)),U_5587),U_5588),U_5585)
| ( hAPP(U_5586,sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583)) != hAPP(U_5587,sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583))
& hBOOL(hAPP(hAPP(c_member(U_5584),sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583)),U_5585)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5584),U_5585))
| ~ class_Groups_Oab__semigroup__mult(U_5583) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_5582,sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583))],[f_1435_2]) ).
fof(f_1435_4,plain,
( ! [U_5583,U_5584,U_5585,U_5586,U_5587,U_5588] :
( hAPP(U_5586,sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583)) != hAPP(U_5587,sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583))
| ~ sP461(U_5583,U_5584,U_5585,U_5586,U_5587,U_5588) )
& ! [U_5583,U_5584,U_5585,U_5586,U_5587,U_5588] :
( hBOOL(hAPP(hAPP(c_member(U_5584),sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583)),U_5585))
| ~ sP461(U_5583,U_5584,U_5585,U_5586,U_5587,U_5588) )
& ! [U_5583,U_5584,U_5585,U_5586,U_5587,U_5588] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5583,U_5584,c_Groups_Otimes__class_Otimes(U_5583)),U_5586),U_5588),U_5585) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5583,U_5584,c_Groups_Otimes__class_Otimes(U_5583)),U_5587),U_5588),U_5585)
| sP461(U_5583,U_5584,U_5585,U_5586,U_5587,U_5588)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5584),U_5585))
| ~ class_Groups_Oab__semigroup__mult(U_5583) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP461])],[f_1435_3]) ).
cnf(f_1435_5,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5583,U_5584,c_Groups_Otimes__class_Otimes(U_5583)),U_5586),U_5588),U_5585) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5583,U_5584,c_Groups_Otimes__class_Otimes(U_5583)),U_5587),U_5588),U_5585)
| sP461(U_5583,U_5584,U_5585,U_5586,U_5587,U_5588)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5584),U_5585))
| ~ class_Groups_Oab__semigroup__mult(U_5583) ),
inference(clausify,[status(thm)],[f_1435_4]) ).
cnf(f_1435_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5584),sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583)),U_5585))
| ~ sP461(U_5583,U_5584,U_5585,U_5586,U_5587,U_5588) ),
inference(clausify,[status(thm)],[f_1435_4]) ).
cnf(f_1435_7,plain,
( hAPP(U_5586,sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583)) != hAPP(U_5587,sK141(U_5588,U_5587,U_5586,U_5585,U_5584,U_5583))
| ~ sP461(U_5583,U_5584,U_5585,U_5586,U_5587,U_5588) ),
inference(clausify,[status(thm)],[f_1435_4]) ).
fof(f_1436_1,plain,
! [V_v] :
( 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_expand__Suc]) ).
fof(f_1436_2,plain,
! [U_5589] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5589) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5589)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ 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),U_5589))) ),
inference(variable_rename,[status(thm)],[f_1436_1]) ).
fof(f_1436_3,plain,
! [U_5589] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5589) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5589)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ 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),U_5589))) ),
inference(definitional_conversion,[status(esa)],[f_1436_2]) ).
cnf(f_1436_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5589) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5589)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ 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),U_5589))) ),
inference(clausify,[status(thm)],[f_1436_3]) ).
fof(f_1437_1,plain,
! [V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Pow]) ).
fof(f_1437_2,plain,
! [U_5591,U_5590] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_5590,tc_HOL_Obool)),hAPP(c_Set_OPow(U_5590),U_5591)) = 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(U_5590),U_5591))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5590),U_5591)) ),
inference(variable_rename,[status(thm)],[f_1437_1]) ).
fof(f_1437_3,plain,
! [U_5590,U_5591] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_5590,tc_HOL_Obool)),hAPP(c_Set_OPow(U_5590),U_5591)) = 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(U_5590),U_5591))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5590),U_5591)) ),
inference(definitional_conversion,[status(esa)],[f_1437_2]) ).
cnf(f_1437_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(U_5590,tc_HOL_Obool)),hAPP(c_Set_OPow(U_5590),U_5591)) = 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(U_5590),U_5591))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5590),U_5591)) ),
inference(clausify,[status(thm)],[f_1437_3]) ).
fof(f_1438_1,plain,
! [V_y_2,V_x_2,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)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
| ~ class_Int_Oring__char__0(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).
fof(f_1438_2,plain,
! [U_5594,U_5593,U_5592] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5593) = hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5594)
| U_5593 != U_5594 )
& ( U_5593 = U_5594
| hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5593) != hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5594) ) )
| ~ class_Int_Oring__char__0(U_5592)
| ~ class_Int_Onumber__ring(U_5592) ),
inference(variable_rename,[status(thm)],[f_1438_1]) ).
fof(f_1438_3,plain,
( ! [U_5592,U_5593,U_5594] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5593) = hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5594)
| U_5593 != U_5594
| ~ sP462(U_5592,U_5593,U_5594) )
& ! [U_5592,U_5593,U_5594] :
( U_5593 = U_5594
| hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5593) != hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5594)
| ~ sP462(U_5592,U_5593,U_5594) )
& ! [U_5592,U_5593,U_5594] :
( sP462(U_5592,U_5593,U_5594)
| ~ class_Int_Oring__char__0(U_5592)
| ~ class_Int_Onumber__ring(U_5592) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP462])],[f_1438_2]) ).
cnf(f_1438_4,plain,
( sP462(U_5592,U_5593,U_5594)
| ~ class_Int_Oring__char__0(U_5592)
| ~ class_Int_Onumber__ring(U_5592) ),
inference(clausify,[status(thm)],[f_1438_3]) ).
cnf(f_1438_5,plain,
( U_5593 = U_5594
| hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5593) != hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5594)
| ~ sP462(U_5592,U_5593,U_5594) ),
inference(clausify,[status(thm)],[f_1438_3]) ).
cnf(f_1438_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5593) = hAPP(c_Int_Onumber__class_Onumber__of(U_5592),U_5594)
| U_5593 != U_5594
| ~ sP462(U_5592,U_5593,U_5594) ),
inference(clausify,[status(thm)],[f_1438_3]) ).
fof(f_1439_1,plain,
! [V_x_2,V_w_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
| V_x_2 != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) )
& ( V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != V_x_2 ) )
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).
fof(f_1439_2,plain,
! [U_5597,U_5596,U_5595] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596) = U_5597
| U_5597 != hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596) )
& ( U_5597 = hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596) != U_5597 ) )
| ~ class_Int_Onumber(U_5595) ),
inference(variable_rename,[status(thm)],[f_1439_1]) ).
fof(f_1439_3,plain,
( ! [U_5596,U_5597,U_5595] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596) = U_5597
| U_5597 != hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596)
| ~ sP463(U_5596,U_5597,U_5595) )
& ! [U_5596,U_5597,U_5595] :
( U_5597 = hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596) != U_5597
| ~ sP463(U_5596,U_5597,U_5595) )
& ! [U_5596,U_5597,U_5595] :
( sP463(U_5596,U_5597,U_5595)
| ~ class_Int_Onumber(U_5595) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP463])],[f_1439_2]) ).
cnf(f_1439_4,plain,
( sP463(U_5596,U_5597,U_5595)
| ~ class_Int_Onumber(U_5595) ),
inference(clausify,[status(thm)],[f_1439_3]) ).
cnf(f_1439_5,plain,
( U_5597 = hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596) != U_5597
| ~ sP463(U_5596,U_5597,U_5595) ),
inference(clausify,[status(thm)],[f_1439_3]) ).
cnf(f_1439_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596) = U_5597
| U_5597 != hAPP(c_Int_Onumber__class_Onumber__of(U_5595),U_5596)
| ~ sP463(U_5596,U_5597,U_5595) ),
inference(clausify,[status(thm)],[f_1439_3]) ).
fof(f_1440_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).
fof(f_1440_2,plain,
! [U_5600,U_5599,U_5598] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5598),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5599)),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5599),U_5600)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5599),U_5600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5598),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5599)),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5600))) ) )
| ~ class_Rings_Olinordered__idom(U_5598)
| ~ class_Int_Onumber__ring(U_5598) ),
inference(variable_rename,[status(thm)],[f_1440_1]) ).
fof(f_1440_3,plain,
( ! [U_5598,U_5600,U_5599] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5598),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5599)),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5599),U_5600))
| ~ sP464(U_5598,U_5600,U_5599) )
& ! [U_5598,U_5600,U_5599] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5599),U_5600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5598),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5599)),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5600)))
| ~ sP464(U_5598,U_5600,U_5599) )
& ! [U_5598,U_5600,U_5599] :
( sP464(U_5598,U_5600,U_5599)
| ~ class_Rings_Olinordered__idom(U_5598)
| ~ class_Int_Onumber__ring(U_5598) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP464])],[f_1440_2]) ).
cnf(f_1440_4,plain,
( sP464(U_5598,U_5600,U_5599)
| ~ class_Rings_Olinordered__idom(U_5598)
| ~ class_Int_Onumber__ring(U_5598) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
cnf(f_1440_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5599),U_5600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5598),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5599)),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5600)))
| ~ sP464(U_5598,U_5600,U_5599) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
cnf(f_1440_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5598),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5599)),hAPP(c_Int_Onumber__class_Onumber__of(U_5598),U_5600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5599),U_5600))
| ~ sP464(U_5598,U_5600,U_5599) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
fof(f_1441_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).
fof(f_1441_2,plain,
! [U_5603,U_5602,U_5601] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5602)),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5602),U_5603)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5602),U_5603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5602)),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5603))) ) )
| ~ class_Rings_Olinordered__idom(U_5601)
| ~ class_Int_Onumber__ring(U_5601) ),
inference(variable_rename,[status(thm)],[f_1441_1]) ).
fof(f_1441_3,plain,
( ! [U_5602,U_5603,U_5601] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5602)),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5602),U_5603))
| ~ sP465(U_5602,U_5603,U_5601) )
& ! [U_5602,U_5603,U_5601] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5602),U_5603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5602)),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5603)))
| ~ sP465(U_5602,U_5603,U_5601) )
& ! [U_5602,U_5603,U_5601] :
( sP465(U_5602,U_5603,U_5601)
| ~ class_Rings_Olinordered__idom(U_5601)
| ~ class_Int_Onumber__ring(U_5601) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP465])],[f_1441_2]) ).
cnf(f_1441_4,plain,
( sP465(U_5602,U_5603,U_5601)
| ~ class_Rings_Olinordered__idom(U_5601)
| ~ class_Int_Onumber__ring(U_5601) ),
inference(clausify,[status(thm)],[f_1441_3]) ).
cnf(f_1441_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5602),U_5603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5602)),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5603)))
| ~ sP465(U_5602,U_5603,U_5601) ),
inference(clausify,[status(thm)],[f_1441_3]) ).
cnf(f_1441_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5602)),hAPP(c_Int_Onumber__class_Onumber__of(U_5601),U_5603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5602),U_5603))
| ~ sP465(U_5602,U_5603,U_5601) ),
inference(clausify,[status(thm)],[f_1441_3]) ).
fof(f_1442_1,plain,
! [V_q,V_y,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_1442_2,plain,
! [U_5607,U_5606,U_5605,U_5604] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5604),U_5605),U_5606)),U_5607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5604),hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),U_5605),U_5607)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),U_5606),U_5607))
| ~ class_Rings_Ocomm__semiring__1(U_5604) ),
inference(variable_rename,[status(thm)],[f_1442_1]) ).
fof(f_1442_3,plain,
! [U_5605,U_5604,U_5606,U_5607] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5604),U_5605),U_5606)),U_5607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5604),hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),U_5605),U_5607)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),U_5606),U_5607))
| ~ class_Rings_Ocomm__semiring__1(U_5604) ),
inference(definitional_conversion,[status(esa)],[f_1442_2]) ).
cnf(f_1442_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5604),U_5605),U_5606)),U_5607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5604),hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),U_5605),U_5607)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5604),U_5606),U_5607))
| ~ class_Rings_Ocomm__semiring__1(U_5604) ),
inference(clausify,[status(thm)],[f_1442_3]) ).
fof(f_1443_1,plain,
! [V_w,V_v,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)) = 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__add]) ).
fof(f_1443_2,plain,
! [U_5610,U_5609,U_5608] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5608),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5609),U_5610)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5608),hAPP(c_Int_Onumber__class_Onumber__of(U_5608),U_5609)),hAPP(c_Int_Onumber__class_Onumber__of(U_5608),U_5610))
| ~ class_Int_Onumber__ring(U_5608) ),
inference(variable_rename,[status(thm)],[f_1443_1]) ).
fof(f_1443_3,plain,
! [U_5608,U_5609,U_5610] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5608),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5609),U_5610)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5608),hAPP(c_Int_Onumber__class_Onumber__of(U_5608),U_5609)),hAPP(c_Int_Onumber__class_Onumber__of(U_5608),U_5610))
| ~ class_Int_Onumber__ring(U_5608) ),
inference(definitional_conversion,[status(esa)],[f_1443_2]) ).
cnf(f_1443_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5608),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5609),U_5610)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5608),hAPP(c_Int_Onumber__class_Onumber__of(U_5608),U_5609)),hAPP(c_Int_Onumber__class_Onumber__of(U_5608),U_5610))
| ~ class_Int_Onumber__ring(U_5608) ),
inference(clausify,[status(thm)],[f_1443_3]) ).
fof(f_1444_1,plain,
! [V_w,V_v,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__eq]) ).
fof(f_1444_2,plain,
! [U_5613,U_5612,U_5611] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5612)),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5612),U_5613))
| ~ class_Int_Onumber__ring(U_5611) ),
inference(variable_rename,[status(thm)],[f_1444_1]) ).
fof(f_1444_3,plain,
! [U_5611,U_5612,U_5613] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5612)),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5612),U_5613))
| ~ class_Int_Onumber__ring(U_5611) ),
inference(definitional_conversion,[status(esa)],[f_1444_2]) ).
cnf(f_1444_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5612)),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5612),U_5613))
| ~ class_Int_Onumber__ring(U_5611) ),
inference(clausify,[status(thm)],[f_1444_3]) ).
fof(f_1445_1,plain,
! [V_z,V_w,V_v,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__left]) ).
fof(f_1445_2,plain,
! [U_5617,U_5616,U_5615,U_5614] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5616)),U_5617)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5615),U_5616))),U_5617)
| ~ class_Int_Onumber__ring(U_5614) ),
inference(variable_rename,[status(thm)],[f_1445_1]) ).
fof(f_1445_3,plain,
! [U_5614,U_5615,U_5616,U_5617] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5616)),U_5617)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5615),U_5616))),U_5617)
| ~ class_Int_Onumber__ring(U_5614) ),
inference(definitional_conversion,[status(esa)],[f_1445_2]) ).
cnf(f_1445_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5616)),U_5617)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5615),U_5616))),U_5617)
| ~ class_Int_Onumber__ring(U_5614) ),
inference(clausify,[status(thm)],[f_1445_3]) ).
fof(f_1446_1,plain,
! [V_w,V_v,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)) = 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__mult]) ).
fof(f_1446_2,plain,
! [U_5620,U_5619,U_5618] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5619),U_5620)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5619)),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5620))
| ~ class_Int_Onumber__ring(U_5618) ),
inference(variable_rename,[status(thm)],[f_1446_1]) ).
fof(f_1446_3,plain,
! [U_5618,U_5619,U_5620] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5619),U_5620)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5619)),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5620))
| ~ class_Int_Onumber__ring(U_5618) ),
inference(definitional_conversion,[status(esa)],[f_1446_2]) ).
cnf(f_1446_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5619),U_5620)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5619)),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5620))
| ~ class_Int_Onumber__ring(U_5618) ),
inference(clausify,[status(thm)],[f_1446_3]) ).
fof(f_1447_1,plain,
! [V_w,V_v,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J]) ).
fof(f_1447_2,plain,
! [U_5623,U_5622,U_5621] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5621),hAPP(c_Int_Onumber__class_Onumber__of(U_5621),U_5622)),hAPP(c_Int_Onumber__class_Onumber__of(U_5621),U_5623)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5622),U_5623))
| ~ class_Int_Onumber__ring(U_5621) ),
inference(variable_rename,[status(thm)],[f_1447_1]) ).
fof(f_1447_3,plain,
! [U_5621,U_5622,U_5623] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5621),hAPP(c_Int_Onumber__class_Onumber__of(U_5621),U_5622)),hAPP(c_Int_Onumber__class_Onumber__of(U_5621),U_5623)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5622),U_5623))
| ~ class_Int_Onumber__ring(U_5621) ),
inference(definitional_conversion,[status(esa)],[f_1447_2]) ).
cnf(f_1447_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5621),hAPP(c_Int_Onumber__class_Onumber__of(U_5621),U_5622)),hAPP(c_Int_Onumber__class_Onumber__of(U_5621),U_5623)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5622),U_5623))
| ~ class_Int_Onumber__ring(U_5621) ),
inference(clausify,[status(thm)],[f_1447_3]) ).
fof(f_1448_1,plain,
! [V_z,V_w,V_v,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__number__of__left]) ).
fof(f_1448_2,plain,
! [U_5627,U_5626,U_5625,U_5624] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),U_5625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),U_5626)),U_5627)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5625),U_5626))),U_5627)
| ~ class_Int_Onumber__ring(U_5624) ),
inference(variable_rename,[status(thm)],[f_1448_1]) ).
fof(f_1448_3,plain,
! [U_5626,U_5624,U_5625,U_5627] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),U_5625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),U_5626)),U_5627)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5625),U_5626))),U_5627)
| ~ class_Int_Onumber__ring(U_5624) ),
inference(definitional_conversion,[status(esa)],[f_1448_2]) ).
cnf(f_1448_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),U_5625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),U_5626)),U_5627)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),hAPP(c_Int_Onumber__class_Onumber__of(U_5624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5625),U_5626))),U_5627)
| ~ class_Int_Onumber__ring(U_5624) ),
inference(clausify,[status(thm)],[f_1448_3]) ).
fof(f_1449_1,plain,
! [V_w,V_v,T_a] :
( 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)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq]) ).
fof(f_1449_2,plain,
! [U_5630,U_5629,U_5628] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5628),hAPP(c_Int_Onumber__class_Onumber__of(U_5628),U_5629)),hAPP(c_Int_Onumber__class_Onumber__of(U_5628),U_5630)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5629),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5630)))
| ~ class_Int_Onumber__ring(U_5628) ),
inference(variable_rename,[status(thm)],[f_1449_1]) ).
fof(f_1449_3,plain,
! [U_5628,U_5629,U_5630] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5628),hAPP(c_Int_Onumber__class_Onumber__of(U_5628),U_5629)),hAPP(c_Int_Onumber__class_Onumber__of(U_5628),U_5630)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5629),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5630)))
| ~ class_Int_Onumber__ring(U_5628) ),
inference(definitional_conversion,[status(esa)],[f_1449_2]) ).
cnf(f_1449_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5628),hAPP(c_Int_Onumber__class_Onumber__of(U_5628),U_5629)),hAPP(c_Int_Onumber__class_Onumber__of(U_5628),U_5630)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5629),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5630)))
| ~ class_Int_Onumber__ring(U_5628) ),
inference(clausify,[status(thm)],[f_1449_3]) ).
fof(f_1450_1,plain,
! [V_w,V_v,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__diff]) ).
fof(f_1450_2,plain,
! [U_5633,U_5632,U_5631] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5632),U_5633)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5631),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),U_5632)),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),U_5633))
| ~ class_Int_Onumber__ring(U_5631) ),
inference(variable_rename,[status(thm)],[f_1450_1]) ).
fof(f_1450_3,plain,
! [U_5631,U_5632,U_5633] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5632),U_5633)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5631),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),U_5632)),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),U_5633))
| ~ class_Int_Onumber__ring(U_5631) ),
inference(definitional_conversion,[status(esa)],[f_1450_2]) ).
cnf(f_1450_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5632),U_5633)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5631),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),U_5632)),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),U_5633))
| ~ class_Int_Onumber__ring(U_5631) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
fof(f_1451_1,plain,
! [V_w,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__minus]) ).
fof(f_1451_2,plain,
! [U_5635,U_5634] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5634),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5635)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5634),hAPP(c_Int_Onumber__class_Onumber__of(U_5634),U_5635))
| ~ class_Int_Onumber__ring(U_5634) ),
inference(variable_rename,[status(thm)],[f_1451_1]) ).
fof(f_1451_3,plain,
! [U_5634,U_5635] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5634),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5635)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5634),hAPP(c_Int_Onumber__class_Onumber__of(U_5634),U_5635))
| ~ class_Int_Onumber__ring(U_5634) ),
inference(definitional_conversion,[status(esa)],[f_1451_2]) ).
cnf(f_1451_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5634),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5635)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5634),hAPP(c_Int_Onumber__class_Onumber__of(U_5634),U_5635))
| ~ class_Int_Onumber__ring(U_5634) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
fof(f_1452_1,plain,
! [V_w,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J]) ).
fof(f_1452_2,plain,
! [U_5637,U_5636] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5636),hAPP(c_Int_Onumber__class_Onumber__of(U_5636),U_5637)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5636),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5637))
| ~ class_Int_Onumber__ring(U_5636) ),
inference(variable_rename,[status(thm)],[f_1452_1]) ).
fof(f_1452_3,plain,
! [U_5636,U_5637] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5636),hAPP(c_Int_Onumber__class_Onumber__of(U_5636),U_5637)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5636),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5637))
| ~ class_Int_Onumber__ring(U_5636) ),
inference(definitional_conversion,[status(esa)],[f_1452_2]) ).
cnf(f_1452_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5636),hAPP(c_Int_Onumber__class_Onumber__of(U_5636),U_5637)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5636),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5637))
| ~ class_Int_Onumber__ring(U_5636) ),
inference(clausify,[status(thm)],[f_1452_3]) ).
fof(f_1453_1,plain,
! [V_q,V_p,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(f_1453_2,plain,
! [U_5641,U_5640,U_5639,U_5638] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),U_5639),U_5640)),U_5641) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),U_5639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5640),U_5641))
| ~ class_Rings_Ocomm__semiring__1(U_5638) ),
inference(variable_rename,[status(thm)],[f_1453_1]) ).
fof(f_1453_3,plain,
! [U_5638,U_5639,U_5640,U_5641] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),U_5639),U_5640)),U_5641) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),U_5639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5640),U_5641))
| ~ class_Rings_Ocomm__semiring__1(U_5638) ),
inference(definitional_conversion,[status(esa)],[f_1453_2]) ).
cnf(f_1453_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),U_5639),U_5640)),U_5641) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5638),U_5639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5640),U_5641))
| ~ class_Rings_Ocomm__semiring__1(U_5638) ),
inference(clausify,[status(thm)],[f_1453_3]) ).
fof(f_1454_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_1454_2,plain,
! [U_5643,U_5642] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5642),U_5643),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5643
| ~ class_Rings_Ocomm__semiring__1(U_5642) ),
inference(variable_rename,[status(thm)],[f_1454_1]) ).
fof(f_1454_3,plain,
! [U_5643,U_5642] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5642),U_5643),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5643
| ~ class_Rings_Ocomm__semiring__1(U_5642) ),
inference(definitional_conversion,[status(esa)],[f_1454_2]) ).
cnf(f_1454_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5642),U_5643),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5643
| ~ class_Rings_Ocomm__semiring__1(U_5642) ),
inference(clausify,[status(thm)],[f_1454_3]) ).
fof(f_1455_1,plain,
! [V_w_2,V_v_2,T_b] :
( ( ( 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)))
| 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))) )
& ( ~ 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)))
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(f_1455_2,plain,
! [U_5646,U_5645,U_5644] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646))) ) )
| ~ class_Orderings_Olinorder(U_5644)
| ~ class_Int_Onumber(U_5644) ),
inference(variable_rename,[status(thm)],[f_1455_1]) ).
fof(f_1455_3,plain,
( ! [U_5644,U_5645,U_5646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)))
| ~ sP466(U_5644,U_5645,U_5646) )
& ! [U_5644,U_5645,U_5646] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)))
| ~ sP466(U_5644,U_5645,U_5646) )
& ! [U_5644,U_5645,U_5646] :
( sP466(U_5644,U_5645,U_5646)
| ~ class_Orderings_Olinorder(U_5644)
| ~ class_Int_Onumber(U_5644) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP466])],[f_1455_2]) ).
cnf(f_1455_4,plain,
( sP466(U_5644,U_5645,U_5646)
| ~ class_Orderings_Olinorder(U_5644)
| ~ class_Int_Onumber(U_5644) ),
inference(clausify,[status(thm)],[f_1455_3]) ).
cnf(f_1455_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)))
| ~ sP466(U_5644,U_5645,U_5646) ),
inference(clausify,[status(thm)],[f_1455_3]) ).
cnf(f_1455_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5644),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5646)),hAPP(c_Int_Onumber__class_Onumber__of(U_5644),U_5645)))
| ~ sP466(U_5644,U_5645,U_5646) ),
inference(clausify,[status(thm)],[f_1455_3]) ).
fof(f_1456_1,plain,
! [V_v,V_b,V_a,T_b] :
( 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)))
| ~ class_Rings_Osemiring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of]) ).
fof(f_1456_2,plain,
! [U_5650,U_5649,U_5648,U_5647] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5647),U_5648),U_5649)),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5648),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5649),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650)))
| ~ class_Rings_Osemiring(U_5647)
| ~ class_Int_Onumber(U_5647) ),
inference(variable_rename,[status(thm)],[f_1456_1]) ).
fof(f_1456_3,plain,
! [U_5648,U_5647,U_5649,U_5650] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5647),U_5648),U_5649)),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5648),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5649),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650)))
| ~ class_Rings_Osemiring(U_5647)
| ~ class_Int_Onumber(U_5647) ),
inference(definitional_conversion,[status(esa)],[f_1456_2]) ).
cnf(f_1456_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5647),U_5648),U_5649)),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5648),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5649),hAPP(c_Int_Onumber__class_Onumber__of(U_5647),U_5650)))
| ~ class_Rings_Osemiring(U_5647)
| ~ class_Int_Onumber(U_5647) ),
inference(clausify,[status(thm)],[f_1456_3]) ).
fof(f_1457_1,plain,
! [V_c,V_b,V_v,T_b] :
( 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))
| ~ class_Rings_Osemiring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of]) ).
fof(f_1457_2,plain,
! [U_5654,U_5653,U_5652,U_5651] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5651),U_5653),U_5654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),U_5653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),U_5654))
| ~ class_Rings_Osemiring(U_5651)
| ~ class_Int_Onumber(U_5651) ),
inference(variable_rename,[status(thm)],[f_1457_1]) ).
fof(f_1457_3,plain,
! [U_5652,U_5651,U_5653,U_5654] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5651),U_5653),U_5654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),U_5653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),U_5654))
| ~ class_Rings_Osemiring(U_5651)
| ~ class_Int_Onumber(U_5651) ),
inference(definitional_conversion,[status(esa)],[f_1457_2]) ).
cnf(f_1457_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5651),U_5653),U_5654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),U_5653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),hAPP(c_Int_Onumber__class_Onumber__of(U_5651),U_5652)),U_5654))
| ~ class_Rings_Osemiring(U_5651)
| ~ class_Int_Onumber(U_5651) ),
inference(clausify,[status(thm)],[f_1457_3]) ).
fof(f_1458_1,plain,
! [V_q,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J]) ).
fof(f_1458_2,plain,
! [U_5657,U_5656,U_5655] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5655),U_5656),hAPP(c_Nat_OSuc,U_5657)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5656),hAPP(hAPP(c_Power_Opower__class_Opower(U_5655),U_5656),U_5657))
| ~ class_Rings_Ocomm__semiring__1(U_5655) ),
inference(variable_rename,[status(thm)],[f_1458_1]) ).
fof(f_1458_3,plain,
! [U_5656,U_5657,U_5655] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5655),U_5656),hAPP(c_Nat_OSuc,U_5657)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5656),hAPP(hAPP(c_Power_Opower__class_Opower(U_5655),U_5656),U_5657))
| ~ class_Rings_Ocomm__semiring__1(U_5655) ),
inference(definitional_conversion,[status(esa)],[f_1458_2]) ).
cnf(f_1458_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5655),U_5656),hAPP(c_Nat_OSuc,U_5657)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5656),hAPP(hAPP(c_Power_Opower__class_Opower(U_5655),U_5656),U_5657))
| ~ class_Rings_Ocomm__semiring__1(U_5655) ),
inference(clausify,[status(thm)],[f_1458_3]) ).
fof(f_1459_1,plain,
! [V_q,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J]) ).
fof(f_1459_2,plain,
! [U_5660,U_5659,U_5658] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5658),U_5659),hAPP(hAPP(c_Power_Opower__class_Opower(U_5658),U_5659),U_5660)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5658),U_5659),hAPP(c_Nat_OSuc,U_5660))
| ~ class_Rings_Ocomm__semiring__1(U_5658) ),
inference(variable_rename,[status(thm)],[f_1459_1]) ).
fof(f_1459_3,plain,
! [U_5658,U_5659,U_5660] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5658),U_5659),hAPP(hAPP(c_Power_Opower__class_Opower(U_5658),U_5659),U_5660)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5658),U_5659),hAPP(c_Nat_OSuc,U_5660))
| ~ class_Rings_Ocomm__semiring__1(U_5658) ),
inference(definitional_conversion,[status(esa)],[f_1459_2]) ).
cnf(f_1459_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5658),U_5659),hAPP(hAPP(c_Power_Opower__class_Opower(U_5658),U_5659),U_5660)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5658),U_5659),hAPP(c_Nat_OSuc,U_5660))
| ~ class_Rings_Ocomm__semiring__1(U_5658) ),
inference(clausify,[status(thm)],[f_1459_3]) ).
fof(f_1460_1,plain,
! [V_q,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J]) ).
fof(f_1460_2,plain,
! [U_5663,U_5662,U_5661] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5661),hAPP(hAPP(c_Power_Opower__class_Opower(U_5661),U_5662),U_5663)),U_5662) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5661),U_5662),hAPP(c_Nat_OSuc,U_5663))
| ~ class_Rings_Ocomm__semiring__1(U_5661) ),
inference(variable_rename,[status(thm)],[f_1460_1]) ).
fof(f_1460_3,plain,
! [U_5661,U_5662,U_5663] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5661),hAPP(hAPP(c_Power_Opower__class_Opower(U_5661),U_5662),U_5663)),U_5662) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5661),U_5662),hAPP(c_Nat_OSuc,U_5663))
| ~ class_Rings_Ocomm__semiring__1(U_5661) ),
inference(definitional_conversion,[status(esa)],[f_1460_2]) ).
cnf(f_1460_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5661),hAPP(hAPP(c_Power_Opower__class_Opower(U_5661),U_5662),U_5663)),U_5662) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5661),U_5662),hAPP(c_Nat_OSuc,U_5663))
| ~ class_Rings_Ocomm__semiring__1(U_5661) ),
inference(clausify,[status(thm)],[f_1460_3]) ).
fof(f_1461_1,plain,
! [V_c,V_w,V_v,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1]) ).
fof(f_1461_2,plain,
! [U_5667,U_5666,U_5665,U_5664] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),U_5665)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),U_5666)),U_5667)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5665),U_5666))),U_5667)
| ~ class_Int_Onumber__ring(U_5664) ),
inference(variable_rename,[status(thm)],[f_1461_1]) ).
fof(f_1461_3,plain,
! [U_5664,U_5665,U_5666,U_5667] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),U_5665)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),U_5666)),U_5667)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5665),U_5666))),U_5667)
| ~ class_Int_Onumber__ring(U_5664) ),
inference(definitional_conversion,[status(esa)],[f_1461_2]) ).
cnf(f_1461_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),U_5665)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),U_5666)),U_5667)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5664),hAPP(c_Int_Onumber__class_Onumber__of(U_5664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5665),U_5666))),U_5667)
| ~ class_Int_Onumber__ring(U_5664) ),
inference(clausify,[status(thm)],[f_1461_3]) ).
fof(f_1462_1,plain,
! [V_w,V_c,V_v,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2]) ).
fof(f_1462_2,plain,
! [U_5671,U_5670,U_5669,U_5668] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),U_5669)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5668),U_5670),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),U_5671))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5669),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5671)))),U_5670)
| ~ class_Int_Onumber__ring(U_5668) ),
inference(variable_rename,[status(thm)],[f_1462_1]) ).
fof(f_1462_3,plain,
! [U_5668,U_5669,U_5670,U_5671] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),U_5669)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5668),U_5670),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),U_5671))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5669),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5671)))),U_5670)
| ~ class_Int_Onumber__ring(U_5668) ),
inference(definitional_conversion,[status(esa)],[f_1462_2]) ).
cnf(f_1462_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),U_5669)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5668),U_5670),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),U_5671))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5669),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5671)))),U_5670)
| ~ class_Int_Onumber__ring(U_5668) ),
inference(clausify,[status(thm)],[f_1462_3]) ).
fof(f_1463_1,plain,
! [V_c,V_b,V_v,T_b] :
( 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))
| ~ class_Rings_Oring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of]) ).
fof(f_1463_2,plain,
! [U_5675,U_5674,U_5673,U_5672] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5672),U_5674),U_5675)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),U_5674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),U_5675))
| ~ class_Rings_Oring(U_5672)
| ~ class_Int_Onumber(U_5672) ),
inference(variable_rename,[status(thm)],[f_1463_1]) ).
fof(f_1463_3,plain,
! [U_5672,U_5673,U_5674,U_5675] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5672),U_5674),U_5675)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),U_5674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),U_5675))
| ~ class_Rings_Oring(U_5672)
| ~ class_Int_Onumber(U_5672) ),
inference(definitional_conversion,[status(esa)],[f_1463_2]) ).
cnf(f_1463_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5672),U_5674),U_5675)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),U_5674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),hAPP(c_Int_Onumber__class_Onumber__of(U_5672),U_5673)),U_5675))
| ~ class_Rings_Oring(U_5672)
| ~ class_Int_Onumber(U_5672) ),
inference(clausify,[status(thm)],[f_1463_3]) ).
fof(f_1464_1,plain,
! [V_v,V_b,V_a,T_b] :
( 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)))
| ~ class_Rings_Oring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of]) ).
fof(f_1464_2,plain,
! [U_5679,U_5678,U_5677,U_5676] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5676),U_5677),U_5678)),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679)))
| ~ class_Rings_Oring(U_5676)
| ~ class_Int_Onumber(U_5676) ),
inference(variable_rename,[status(thm)],[f_1464_1]) ).
fof(f_1464_3,plain,
! [U_5676,U_5677,U_5678,U_5679] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5676),U_5677),U_5678)),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679)))
| ~ class_Rings_Oring(U_5676)
| ~ class_Int_Onumber(U_5676) ),
inference(definitional_conversion,[status(esa)],[f_1464_2]) ).
cnf(f_1464_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5676),U_5677),U_5678)),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5676),U_5679)))
| ~ class_Rings_Oring(U_5676)
| ~ class_Int_Onumber(U_5676) ),
inference(clausify,[status(thm)],[f_1464_3]) ).
fof(f_1465_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_1465_2,plain,
! [U_5681,U_5680] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5680),U_5681),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_5680)
| ~ class_Rings_Ocomm__semiring__1(U_5680) ),
inference(variable_rename,[status(thm)],[f_1465_1]) ).
fof(f_1465_3,plain,
! [U_5681,U_5680] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5680),U_5681),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_5680)
| ~ class_Rings_Ocomm__semiring__1(U_5680) ),
inference(definitional_conversion,[status(esa)],[f_1465_2]) ).
cnf(f_1465_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5680),U_5681),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_5680)
| ~ class_Rings_Ocomm__semiring__1(U_5680) ),
inference(clausify,[status(thm)],[f_1465_3]) ).
fof(f_1466_1,plain,
! [V_q,V_p,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_1466_2,plain,
! [U_5685,U_5684,U_5683,U_5682] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5682),hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),U_5684)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),U_5685)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5684),U_5685))
| ~ class_Rings_Ocomm__semiring__1(U_5682) ),
inference(variable_rename,[status(thm)],[f_1466_1]) ).
fof(f_1466_3,plain,
! [U_5682,U_5683,U_5684,U_5685] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5682),hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),U_5684)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),U_5685)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5684),U_5685))
| ~ class_Rings_Ocomm__semiring__1(U_5682) ),
inference(definitional_conversion,[status(esa)],[f_1466_2]) ).
cnf(f_1466_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5682),hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),U_5684)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),U_5685)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5682),U_5683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5684),U_5685))
| ~ class_Rings_Ocomm__semiring__1(U_5682) ),
inference(clausify,[status(thm)],[f_1466_3]) ).
fof(f_1467_1,plain,
! [V_z,V_w,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult]) ).
fof(f_1467_2,plain,
! [U_5688,U_5687,U_5686] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5686),hAPP(c_Groups_Ouminus__class_Ouminus(U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5686),U_5687))),U_5688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5687))),U_5688)
| ~ class_Int_Onumber__ring(U_5686) ),
inference(variable_rename,[status(thm)],[f_1467_1]) ).
fof(f_1467_3,plain,
! [U_5686,U_5687,U_5688] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5686),hAPP(c_Groups_Ouminus__class_Ouminus(U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5686),U_5687))),U_5688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5687))),U_5688)
| ~ class_Int_Onumber__ring(U_5686) ),
inference(definitional_conversion,[status(esa)],[f_1467_2]) ).
cnf(f_1467_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5686),hAPP(c_Groups_Ouminus__class_Ouminus(U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5686),U_5687))),U_5688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5687))),U_5688)
| ~ class_Int_Onumber__ring(U_5686) ),
inference(clausify,[status(thm)],[f_1467_3]) ).
fof(f_1468_1,plain,
! [V_n_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__power]) ).
fof(f_1468_2,plain,
! [U_5691,U_5690,U_5689] :
( hBOOL(hAPP(hAPP(c_member(U_5689),hAPP(hAPP(c_Power_Opower__class_Opower(U_5689),U_5690),U_5691)),c_Int_Oring__1__class_OInts(U_5689)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5689),U_5690),c_Int_Oring__1__class_OInts(U_5689)))
| ~ class_Rings_Oring__1(U_5689) ),
inference(variable_rename,[status(thm)],[f_1468_1]) ).
fof(f_1468_3,plain,
! [U_5689,U_5690,U_5691] :
( hBOOL(hAPP(hAPP(c_member(U_5689),hAPP(hAPP(c_Power_Opower__class_Opower(U_5689),U_5690),U_5691)),c_Int_Oring__1__class_OInts(U_5689)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5689),U_5690),c_Int_Oring__1__class_OInts(U_5689)))
| ~ class_Rings_Oring__1(U_5689) ),
inference(definitional_conversion,[status(esa)],[f_1468_2]) ).
cnf(f_1468_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5689),hAPP(hAPP(c_Power_Opower__class_Opower(U_5689),U_5690),U_5691)),c_Int_Oring__1__class_OInts(U_5689)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5689),U_5690),c_Int_Oring__1__class_OInts(U_5689)))
| ~ class_Rings_Oring__1(U_5689) ),
inference(clausify,[status(thm)],[f_1468_3]) ).
fof(f_1469_1,plain,
! [V_w_2,T_b] :
( 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)))
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__number__of]) ).
fof(f_1469_2,plain,
! [U_5693,U_5692] :
( hBOOL(hAPP(hAPP(c_member(U_5692),hAPP(c_Int_Onumber__class_Onumber__of(U_5692),U_5693)),c_Int_Oring__1__class_OInts(U_5692)))
| ~ class_Int_Onumber__ring(U_5692) ),
inference(variable_rename,[status(thm)],[f_1469_1]) ).
fof(f_1469_3,plain,
! [U_5692,U_5693] :
( hBOOL(hAPP(hAPP(c_member(U_5692),hAPP(c_Int_Onumber__class_Onumber__of(U_5692),U_5693)),c_Int_Oring__1__class_OInts(U_5692)))
| ~ class_Int_Onumber__ring(U_5692) ),
inference(definitional_conversion,[status(esa)],[f_1469_2]) ).
cnf(f_1469_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5692),hAPP(c_Int_Onumber__class_Onumber__of(U_5692),U_5693)),c_Int_Oring__1__class_OInts(U_5692)))
| ~ class_Int_Onumber__ring(U_5692) ),
inference(clausify,[status(thm)],[f_1469_3]) ).
fof(f_1470_1,plain,
! [V_w_2,V_b_2,V_a_2,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))
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(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
& hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(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
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(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)) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1]) ).
fof(f_1470_2,plain,
! [U_5697,U_5696,U_5695,U_5694] :
( ( ( U_5695 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5694),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697))
| ( U_5695 != c_Groups_Ozero__class_Ozero(U_5694)
& hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) = c_Groups_Ozero__class_Ozero(U_5694) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5694),U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697)) != U_5696
& hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) != c_Groups_Ozero__class_Ozero(U_5694) ) )
& ( ( ( U_5695 = c_Groups_Ozero__class_Ozero(U_5694)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) != c_Groups_Ozero__class_Ozero(U_5694) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5694),U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697)) = U_5696
| hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) = c_Groups_Ozero__class_Ozero(U_5694) ) )
| U_5695 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5694),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697)) ) )
| ~ class_Int_Onumber(U_5694)
| ~ class_Fields_Ofield__inverse__zero(U_5694) ),
inference(variable_rename,[status(thm)],[f_1470_1]) ).
fof(f_1470_3,plain,
( ! [U_5694,U_5695,U_5697] :
( U_5695 != c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP469(U_5694,U_5695,U_5697) )
& ! [U_5694,U_5695,U_5697] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) = c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP469(U_5694,U_5695,U_5697) )
& ! [U_5694,U_5695,U_5696,U_5697] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5694),U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697)) != U_5696
| ~ sP468(U_5694,U_5695,U_5696,U_5697) )
& ! [U_5694,U_5695,U_5696,U_5697] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) != c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP468(U_5694,U_5695,U_5696,U_5697) )
& ! [U_5694,U_5695,U_5696,U_5697] :
( U_5695 = c_Groups_Ozero__class_Ozero(U_5694)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) != c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP467(U_5694,U_5695,U_5696,U_5697) )
& ! [U_5694,U_5695,U_5696,U_5697] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5694),U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697)) = U_5696
| hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) = c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP467(U_5694,U_5695,U_5696,U_5697) )
& ! [U_5694,U_5695,U_5696,U_5697] :
( U_5695 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5694),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697))
| sP469(U_5694,U_5695,U_5697)
| sP468(U_5694,U_5695,U_5696,U_5697)
| ~ sP470(U_5694,U_5695,U_5696,U_5697) )
& ! [U_5694,U_5695,U_5696,U_5697] :
( sP467(U_5694,U_5695,U_5696,U_5697)
| U_5695 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5694),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697))
| ~ sP470(U_5694,U_5695,U_5696,U_5697) )
& ! [U_5694,U_5695,U_5696,U_5697] :
( sP470(U_5694,U_5695,U_5696,U_5697)
| ~ class_Int_Onumber(U_5694)
| ~ class_Fields_Ofield__inverse__zero(U_5694) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP467,sP468,sP469,sP470])],[f_1470_2]) ).
cnf(f_1470_4,plain,
( sP470(U_5694,U_5695,U_5696,U_5697)
| ~ class_Int_Onumber(U_5694)
| ~ class_Fields_Ofield__inverse__zero(U_5694) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
cnf(f_1470_5,plain,
( sP467(U_5694,U_5695,U_5696,U_5697)
| U_5695 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5694),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697))
| ~ sP470(U_5694,U_5695,U_5696,U_5697) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
cnf(f_1470_6,plain,
( U_5695 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5694),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697))
| sP469(U_5694,U_5695,U_5697)
| sP468(U_5694,U_5695,U_5696,U_5697)
| ~ sP470(U_5694,U_5695,U_5696,U_5697) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
cnf(f_1470_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5694),U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697)) = U_5696
| hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) = c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP467(U_5694,U_5695,U_5696,U_5697) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
cnf(f_1470_8,plain,
( U_5695 = c_Groups_Ozero__class_Ozero(U_5694)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) != c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP467(U_5694,U_5695,U_5696,U_5697) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
cnf(f_1470_9,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) != c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP468(U_5694,U_5695,U_5696,U_5697) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
cnf(f_1470_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5694),U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697)) != U_5696
| ~ sP468(U_5694,U_5695,U_5696,U_5697) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
cnf(f_1470_11,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5694),U_5697) = c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP469(U_5694,U_5695,U_5697) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
cnf(f_1470_12,plain,
( U_5695 != c_Groups_Ozero__class_Ozero(U_5694)
| ~ sP469(U_5694,U_5695,U_5697) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
fof(f_1471_1,plain,
! [V_ca_2,V_b_2,V_w_2,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_ca_2)
| ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
& V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) != V_b_2
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_b_2
| V_ca_2 = c_Groups_Ozero__class_Ozero(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_ca_2) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).
fof(f_1471_2,plain,
! [U_5701,U_5700,U_5699,U_5698] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5698),U_5700),U_5701)
| ( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) != c_Groups_Ozero__class_Ozero(U_5698)
& U_5701 = c_Groups_Ozero__class_Ozero(U_5698) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699)),U_5701) != U_5700
& U_5701 != c_Groups_Ozero__class_Ozero(U_5698) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) = c_Groups_Ozero__class_Ozero(U_5698)
| U_5701 != c_Groups_Ozero__class_Ozero(U_5698) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699)),U_5701) = U_5700
| U_5701 = c_Groups_Ozero__class_Ozero(U_5698) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5698),U_5700),U_5701) ) )
| ~ class_Int_Onumber(U_5698)
| ~ class_Fields_Ofield__inverse__zero(U_5698) ),
inference(variable_rename,[status(thm)],[f_1471_1]) ).
fof(f_1471_3,plain,
( ! [U_5699,U_5698,U_5701] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) != c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP473(U_5699,U_5698,U_5701) )
& ! [U_5699,U_5698,U_5701] :
( U_5701 = c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP473(U_5699,U_5698,U_5701) )
& ! [U_5699,U_5698,U_5700,U_5701] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699)),U_5701) != U_5700
| ~ sP472(U_5699,U_5698,U_5700,U_5701) )
& ! [U_5699,U_5698,U_5700,U_5701] :
( U_5701 != c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP472(U_5699,U_5698,U_5700,U_5701) )
& ! [U_5699,U_5698,U_5700,U_5701] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) = c_Groups_Ozero__class_Ozero(U_5698)
| U_5701 != c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP471(U_5699,U_5698,U_5700,U_5701) )
& ! [U_5699,U_5698,U_5700,U_5701] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699)),U_5701) = U_5700
| U_5701 = c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP471(U_5699,U_5698,U_5700,U_5701) )
& ! [U_5699,U_5698,U_5700,U_5701] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5698),U_5700),U_5701)
| sP473(U_5699,U_5698,U_5701)
| sP472(U_5699,U_5698,U_5700,U_5701)
| ~ sP474(U_5699,U_5698,U_5700,U_5701) )
& ! [U_5699,U_5698,U_5700,U_5701] :
( sP471(U_5699,U_5698,U_5700,U_5701)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5698),U_5700),U_5701)
| ~ sP474(U_5699,U_5698,U_5700,U_5701) )
& ! [U_5699,U_5698,U_5700,U_5701] :
( sP474(U_5699,U_5698,U_5700,U_5701)
| ~ class_Int_Onumber(U_5698)
| ~ class_Fields_Ofield__inverse__zero(U_5698) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP471,sP472,sP473,sP474])],[f_1471_2]) ).
cnf(f_1471_4,plain,
( sP474(U_5699,U_5698,U_5700,U_5701)
| ~ class_Int_Onumber(U_5698)
| ~ class_Fields_Ofield__inverse__zero(U_5698) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
cnf(f_1471_5,plain,
( sP471(U_5699,U_5698,U_5700,U_5701)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5698),U_5700),U_5701)
| ~ sP474(U_5699,U_5698,U_5700,U_5701) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
cnf(f_1471_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5698),U_5700),U_5701)
| sP473(U_5699,U_5698,U_5701)
| sP472(U_5699,U_5698,U_5700,U_5701)
| ~ sP474(U_5699,U_5698,U_5700,U_5701) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
cnf(f_1471_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699)),U_5701) = U_5700
| U_5701 = c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP471(U_5699,U_5698,U_5700,U_5701) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
cnf(f_1471_8,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) = c_Groups_Ozero__class_Ozero(U_5698)
| U_5701 != c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP471(U_5699,U_5698,U_5700,U_5701) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
cnf(f_1471_9,plain,
( U_5701 != c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP472(U_5699,U_5698,U_5700,U_5701) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
cnf(f_1471_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699)),U_5701) != U_5700
| ~ sP472(U_5699,U_5698,U_5700,U_5701) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
cnf(f_1471_11,plain,
( U_5701 = c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP473(U_5699,U_5698,U_5701) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
cnf(f_1471_12,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5698),U_5699) != c_Groups_Ozero__class_Ozero(U_5698)
| ~ sP473(U_5699,U_5698,U_5701) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
fof(f_1472_1,plain,
! [V_w_2,V_ca_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
| ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
& V_ca_2 = c_Groups_Ozero__class_Ozero(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_ca_2)
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_ca_2 != c_Groups_Ozero__class_Ozero(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_ca_2)
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).
fof(f_1472_2,plain,
! [U_5705,U_5704,U_5703,U_5702] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5702),U_5703),U_5704) = hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)
| ( hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705) != c_Groups_Ozero__class_Ozero(U_5702)
& U_5704 = c_Groups_Ozero__class_Ozero(U_5702) )
| ( U_5703 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5702),hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)),U_5704)
& U_5704 != c_Groups_Ozero__class_Ozero(U_5702) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705) = c_Groups_Ozero__class_Ozero(U_5702)
| U_5704 != c_Groups_Ozero__class_Ozero(U_5702) )
& ( U_5703 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5702),hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)),U_5704)
| U_5704 = c_Groups_Ozero__class_Ozero(U_5702) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5702),U_5703),U_5704) != hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705) ) )
| ~ class_Int_Onumber(U_5702)
| ~ class_Fields_Ofield__inverse__zero(U_5702) ),
inference(variable_rename,[status(thm)],[f_1472_1]) ).
fof(f_1472_3,plain,
( ! [U_5704,U_5705,U_5702] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705) != c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP477(U_5704,U_5705,U_5702) )
& ! [U_5704,U_5705,U_5702] :
( U_5704 = c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP477(U_5704,U_5705,U_5702) )
& ! [U_5703,U_5704,U_5705,U_5702] :
( U_5703 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5702),hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)),U_5704)
| ~ sP476(U_5703,U_5704,U_5705,U_5702) )
& ! [U_5703,U_5704,U_5705,U_5702] :
( U_5704 != c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP476(U_5703,U_5704,U_5705,U_5702) )
& ! [U_5703,U_5704,U_5705,U_5702] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705) = c_Groups_Ozero__class_Ozero(U_5702)
| U_5704 != c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP475(U_5703,U_5704,U_5705,U_5702) )
& ! [U_5703,U_5704,U_5705,U_5702] :
( U_5703 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5702),hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)),U_5704)
| U_5704 = c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP475(U_5703,U_5704,U_5705,U_5702) )
& ! [U_5703,U_5704,U_5705,U_5702] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5702),U_5703),U_5704) = hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)
| sP477(U_5704,U_5705,U_5702)
| sP476(U_5703,U_5704,U_5705,U_5702)
| ~ sP478(U_5703,U_5704,U_5705,U_5702) )
& ! [U_5703,U_5704,U_5705,U_5702] :
( sP475(U_5703,U_5704,U_5705,U_5702)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5702),U_5703),U_5704) != hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)
| ~ sP478(U_5703,U_5704,U_5705,U_5702) )
& ! [U_5703,U_5704,U_5705,U_5702] :
( sP478(U_5703,U_5704,U_5705,U_5702)
| ~ class_Int_Onumber(U_5702)
| ~ class_Fields_Ofield__inverse__zero(U_5702) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP475,sP476,sP477,sP478])],[f_1472_2]) ).
cnf(f_1472_4,plain,
( sP478(U_5703,U_5704,U_5705,U_5702)
| ~ class_Int_Onumber(U_5702)
| ~ class_Fields_Ofield__inverse__zero(U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_5,plain,
( sP475(U_5703,U_5704,U_5705,U_5702)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5702),U_5703),U_5704) != hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)
| ~ sP478(U_5703,U_5704,U_5705,U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5702),U_5703),U_5704) = hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)
| sP477(U_5704,U_5705,U_5702)
| sP476(U_5703,U_5704,U_5705,U_5702)
| ~ sP478(U_5703,U_5704,U_5705,U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_7,plain,
( U_5703 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5702),hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)),U_5704)
| U_5704 = c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP475(U_5703,U_5704,U_5705,U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_8,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705) = c_Groups_Ozero__class_Ozero(U_5702)
| U_5704 != c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP475(U_5703,U_5704,U_5705,U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_9,plain,
( U_5704 != c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP476(U_5703,U_5704,U_5705,U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_10,plain,
( U_5703 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5702),hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705)),U_5704)
| ~ sP476(U_5703,U_5704,U_5705,U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_11,plain,
( U_5704 = c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP477(U_5704,U_5705,U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_12,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5702),U_5705) != c_Groups_Ozero__class_Ozero(U_5702)
| ~ sP477(U_5704,U_5705,U_5702) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
fof(f_1473_1,plain,
! [V_a_2,V_w_2,V_b_2,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
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(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))
& hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(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))
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(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 ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1]) ).
fof(f_1473_2,plain,
! [U_5709,U_5708,U_5707,U_5706] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5706),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708)) = U_5709
| ( U_5709 != c_Groups_Ozero__class_Ozero(U_5706)
& hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) = c_Groups_Ozero__class_Ozero(U_5706) )
| ( U_5707 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708))
& hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) != c_Groups_Ozero__class_Ozero(U_5706) ) )
& ( ( ( U_5709 = c_Groups_Ozero__class_Ozero(U_5706)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) != c_Groups_Ozero__class_Ozero(U_5706) )
& ( U_5707 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) = c_Groups_Ozero__class_Ozero(U_5706) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5706),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708)) != U_5709 ) )
| ~ class_Int_Onumber(U_5706)
| ~ class_Fields_Ofield__inverse__zero(U_5706) ),
inference(variable_rename,[status(thm)],[f_1473_1]) ).
fof(f_1473_3,plain,
( ! [U_5708,U_5709,U_5706] :
( U_5709 != c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP481(U_5708,U_5709,U_5706) )
& ! [U_5708,U_5709,U_5706] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) = c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP481(U_5708,U_5709,U_5706) )
& ! [U_5708,U_5709,U_5706,U_5707] :
( U_5707 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708))
| ~ sP480(U_5708,U_5709,U_5706,U_5707) )
& ! [U_5708,U_5709,U_5706,U_5707] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) != c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP480(U_5708,U_5709,U_5706,U_5707) )
& ! [U_5708,U_5709,U_5706,U_5707] :
( U_5709 = c_Groups_Ozero__class_Ozero(U_5706)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) != c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP479(U_5708,U_5709,U_5706,U_5707) )
& ! [U_5708,U_5709,U_5706,U_5707] :
( U_5707 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) = c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP479(U_5708,U_5709,U_5706,U_5707) )
& ! [U_5708,U_5709,U_5706,U_5707] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5706),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708)) = U_5709
| sP481(U_5708,U_5709,U_5706)
| sP480(U_5708,U_5709,U_5706,U_5707)
| ~ sP482(U_5708,U_5709,U_5706,U_5707) )
& ! [U_5708,U_5709,U_5706,U_5707] :
( sP479(U_5708,U_5709,U_5706,U_5707)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5706),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708)) != U_5709
| ~ sP482(U_5708,U_5709,U_5706,U_5707) )
& ! [U_5708,U_5709,U_5706,U_5707] :
( sP482(U_5708,U_5709,U_5706,U_5707)
| ~ class_Int_Onumber(U_5706)
| ~ class_Fields_Ofield__inverse__zero(U_5706) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP479,sP480,sP481,sP482])],[f_1473_2]) ).
cnf(f_1473_4,plain,
( sP482(U_5708,U_5709,U_5706,U_5707)
| ~ class_Int_Onumber(U_5706)
| ~ class_Fields_Ofield__inverse__zero(U_5706) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_5,plain,
( sP479(U_5708,U_5709,U_5706,U_5707)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5706),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708)) != U_5709
| ~ sP482(U_5708,U_5709,U_5706,U_5707) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5706),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708)) = U_5709
| sP481(U_5708,U_5709,U_5706)
| sP480(U_5708,U_5709,U_5706,U_5707)
| ~ sP482(U_5708,U_5709,U_5706,U_5707) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_7,plain,
( U_5707 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) = c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP479(U_5708,U_5709,U_5706,U_5707) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_8,plain,
( U_5709 = c_Groups_Ozero__class_Ozero(U_5706)
| hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) != c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP479(U_5708,U_5709,U_5706,U_5707) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_9,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) != c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP480(U_5708,U_5709,U_5706,U_5707) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_10,plain,
( U_5707 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708))
| ~ sP480(U_5708,U_5709,U_5706,U_5707) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_11,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5706),U_5708) = c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP481(U_5708,U_5709,U_5706) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_12,plain,
( U_5709 != c_Groups_Ozero__class_Ozero(U_5706)
| ~ sP481(U_5708,U_5709,U_5706) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
fof(f_1474_1,plain,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( ( 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))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ 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))) )
| ( ~ 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))))
& 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))) ) )
& ~ 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))) )
| ( ~ 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))
& 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))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| 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))) )
& ( 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))))
| ~ 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))) ) )
| 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))) )
& ( 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))
| ~ 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))) ) )
| ~ 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)))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of1]) ).
fof(f_1474_2,plain,
! [U_5713,U_5712,U_5711,U_5710] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5710),U_5712),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),c_Groups_Ozero__class_Ozero(U_5710)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))),U_5712))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),c_Groups_Ozero__class_Ozero(U_5710)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))),U_5712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5710),U_5712),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))) ) )
| ~ class_Int_Onumber(U_5710)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5710) ),
inference(variable_rename,[status(thm)],[f_1474_1]) ).
fof(f_1474_3,plain,
( ! [U_5711,U_5710,U_5713] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP487(U_5711,U_5710,U_5713) )
& ! [U_5711,U_5710,U_5713] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP487(U_5711,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| ~ sP486(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP486(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( sP487(U_5711,U_5710,U_5713)
| sP486(U_5711,U_5712,U_5710,U_5713)
| ~ sP488(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))
| ~ sP488(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))),U_5712))
| ~ sP485(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))
| ~ sP485(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),c_Groups_Ozero__class_Ozero(U_5710)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP483(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP483(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( sP483(U_5711,U_5712,U_5710,U_5713)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))
| ~ sP484(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))),U_5712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))
| ~ sP484(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5710),U_5712),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| sP488(U_5711,U_5712,U_5710,U_5713)
| sP485(U_5711,U_5712,U_5710,U_5713)
| ~ sP489(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( sP484(U_5711,U_5712,U_5710,U_5713)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5710),U_5712),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| ~ sP489(U_5711,U_5712,U_5710,U_5713) )
& ! [U_5711,U_5712,U_5710,U_5713] :
( sP489(U_5711,U_5712,U_5710,U_5713)
| ~ class_Int_Onumber(U_5710)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5710) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP483,sP484,sP485,sP486,sP487,sP488,sP489])],[f_1474_2]) ).
cnf(f_1474_4,plain,
( sP489(U_5711,U_5712,U_5710,U_5713)
| ~ class_Int_Onumber(U_5710)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5710) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_5,plain,
( sP484(U_5711,U_5712,U_5710,U_5713)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5710),U_5712),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| ~ sP489(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5710),U_5712),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| sP488(U_5711,U_5712,U_5710,U_5713)
| sP485(U_5711,U_5712,U_5710,U_5713)
| ~ sP489(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))),U_5712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))
| ~ sP484(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_8,plain,
( sP483(U_5711,U_5712,U_5710,U_5713)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))
| ~ sP484(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP483(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),c_Groups_Ozero__class_Ozero(U_5710)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP483(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))
| ~ sP485(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))),U_5712))
| ~ sP485(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),c_Groups_Ozero__class_Ozero(U_5710)),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)))
| ~ sP488(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_14,plain,
( sP487(U_5711,U_5710,U_5713)
| sP486(U_5711,U_5712,U_5710,U_5713)
| ~ sP488(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP486(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5710),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713))))
| ~ sP486(U_5711,U_5712,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),hAPP(c_Int_Onumber__class_Onumber__of(U_5710),U_5713)),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP487(U_5711,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5710),U_5711),c_Groups_Ozero__class_Ozero(U_5710)))
| ~ sP487(U_5711,U_5710,U_5713) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
fof(f_1475_1,plain,
! [V_ca_2,V_b_2,V_w_2,T_b] :
( ( ( 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_ca_2)))
| ( ( ( ~ 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)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ 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_ca_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ( ~ 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_ca_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
& ( ( ( ( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
& ( 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_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
| ~ 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_ca_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(f_1475_2,plain,
! [U_5717,U_5716,U_5715,U_5714] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5714),U_5716),U_5717)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),c_Groups_Ozero__class_Ozero(U_5714)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)),U_5716))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),c_Groups_Ozero__class_Ozero(U_5714)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)),U_5716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5714),U_5716),U_5717))) ) )
| ~ class_Int_Onumber(U_5714)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5714) ),
inference(variable_rename,[status(thm)],[f_1475_1]) ).
fof(f_1475_3,plain,
( ! [U_5715,U_5717,U_5714] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP494(U_5715,U_5717,U_5714) )
& ! [U_5715,U_5717,U_5714] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP494(U_5715,U_5717,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)))
| ~ sP493(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP493(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( sP494(U_5715,U_5717,U_5714)
| sP493(U_5715,U_5717,U_5716,U_5714)
| ~ sP495(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717))
| ~ sP495(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)),U_5716))
| ~ sP492(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717))
| ~ sP492(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),c_Groups_Ozero__class_Ozero(U_5714)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP490(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP490(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( sP490(U_5715,U_5717,U_5716,U_5714)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717))
| ~ sP491(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)),U_5716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717))
| ~ sP491(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5714),U_5716),U_5717)))
| sP495(U_5715,U_5717,U_5716,U_5714)
| sP492(U_5715,U_5717,U_5716,U_5714)
| ~ sP496(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( sP491(U_5715,U_5717,U_5716,U_5714)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5714),U_5716),U_5717)))
| ~ sP496(U_5715,U_5717,U_5716,U_5714) )
& ! [U_5715,U_5717,U_5716,U_5714] :
( sP496(U_5715,U_5717,U_5716,U_5714)
| ~ class_Int_Onumber(U_5714)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5714) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP490,sP491,sP492,sP493,sP494,sP495,sP496])],[f_1475_2]) ).
cnf(f_1475_4,plain,
( sP496(U_5715,U_5717,U_5716,U_5714)
| ~ class_Int_Onumber(U_5714)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_5,plain,
( sP491(U_5715,U_5717,U_5716,U_5714)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5714),U_5716),U_5717)))
| ~ sP496(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5714),U_5716),U_5717)))
| sP495(U_5715,U_5717,U_5716,U_5714)
| sP492(U_5715,U_5717,U_5716,U_5714)
| ~ sP496(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)),U_5716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717))
| ~ sP491(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_8,plain,
( sP490(U_5715,U_5717,U_5716,U_5714)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717))
| ~ sP491(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP490(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),c_Groups_Ozero__class_Ozero(U_5714)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP490(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717))
| ~ sP492(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)),U_5716))
| ~ sP492(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),c_Groups_Ozero__class_Ozero(U_5714)),U_5717))
| ~ sP495(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_14,plain,
( sP494(U_5715,U_5717,U_5714)
| sP493(U_5715,U_5717,U_5716,U_5714)
| ~ sP495(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP493(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),U_5717)))
| ~ sP493(U_5715,U_5717,U_5716,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),U_5717),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP494(U_5715,U_5717,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5714),hAPP(c_Int_Onumber__class_Onumber__of(U_5714),U_5715)),c_Groups_Ozero__class_Ozero(U_5714)))
| ~ sP494(U_5715,U_5717,U_5714) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
fof(f_1476_1,plain,
! [V_w_2,V_ca_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| ( ( ( ~ 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)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ 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_ca_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ( ~ 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_ca_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
& ( ( ( ( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( 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_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(f_1476_2,plain,
! [U_5721,U_5720,U_5719,U_5718] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),U_5720)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)),U_5719))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)),U_5719))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),U_5720)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721))) ) )
| ~ class_Int_Onumber(U_5718)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5718) ),
inference(variable_rename,[status(thm)],[f_1476_1]) ).
fof(f_1476_3,plain,
( ! [U_5720,U_5721,U_5718] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| ~ sP501(U_5720,U_5721,U_5718) )
& ! [U_5720,U_5721,U_5718] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718)))
| ~ sP501(U_5720,U_5721,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)),U_5719))
| ~ sP500(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718)))
| ~ sP500(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( sP501(U_5720,U_5721,U_5718)
| sP500(U_5720,U_5721,U_5719,U_5718)
| ~ sP502(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720))
| ~ sP502(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)))
| ~ sP499(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720))
| ~ sP499(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718)))
| ~ sP497(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)),U_5719))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718)))
| ~ sP497(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( sP497(U_5720,U_5721,U_5719,U_5718)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720))
| ~ sP498(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720))
| ~ sP498(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),U_5720)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| sP502(U_5720,U_5721,U_5719,U_5718)
| sP499(U_5720,U_5721,U_5719,U_5718)
| ~ sP503(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( sP498(U_5720,U_5721,U_5719,U_5718)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),U_5720)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| ~ sP503(U_5720,U_5721,U_5719,U_5718) )
& ! [U_5720,U_5721,U_5719,U_5718] :
( sP503(U_5720,U_5721,U_5719,U_5718)
| ~ class_Int_Onumber(U_5718)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5718) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP497,sP498,sP499,sP500,sP501,sP502,sP503])],[f_1476_2]) ).
cnf(f_1476_4,plain,
( sP503(U_5720,U_5721,U_5719,U_5718)
| ~ class_Int_Onumber(U_5718)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_5,plain,
( sP498(U_5720,U_5721,U_5719,U_5718)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),U_5720)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| ~ sP503(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),U_5720)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| sP502(U_5720,U_5721,U_5719,U_5718)
| sP499(U_5720,U_5721,U_5719,U_5718)
| ~ sP503(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720))
| ~ sP498(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_8,plain,
( sP497(U_5720,U_5721,U_5719,U_5718)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720))
| ~ sP498(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)),U_5719))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718)))
| ~ sP497(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718)))
| ~ sP497(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720))
| ~ sP499(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)))
| ~ sP499(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5720))
| ~ sP502(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_14,plain,
( sP501(U_5720,U_5721,U_5718)
| sP500(U_5720,U_5721,U_5719,U_5718)
| ~ sP502(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718)))
| ~ sP500(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)),U_5720)),U_5719))
| ~ sP500(U_5720,U_5721,U_5719,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),U_5720),c_Groups_Ozero__class_Ozero(U_5718)))
| ~ sP501(U_5720,U_5721,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),U_5721)))
| ~ sP501(U_5720,U_5721,U_5718) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
fof(f_1477_1,plain,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( ( 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))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ 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))) )
| ( ~ 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))
& 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))) ) )
& ~ 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))) )
| ( ~ 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))))
& 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))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| 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))) )
& ( 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))
| ~ 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))) ) )
| 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))) )
& ( 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))))
| ~ 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))) ) )
| ~ 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)) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of1]) ).
fof(f_1477_2,plain,
! [U_5725,U_5724,U_5723,U_5722] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5723),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5725))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5723))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5723),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5725)) ) )
| ~ class_Int_Onumber(U_5722)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5722) ),
inference(variable_rename,[status(thm)],[f_1477_1]) ).
fof(f_1477_3,plain,
( ! [U_5725,U_5722,U_5724] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
| ~ sP508(U_5725,U_5722,U_5724) )
& ! [U_5725,U_5722,U_5724] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722)))
| ~ sP508(U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5723))
| ~ sP507(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722)))
| ~ sP507(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( sP508(U_5725,U_5722,U_5724)
| sP507(U_5723,U_5725,U_5722,U_5724)
| ~ sP509(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)))
| ~ sP509(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))))
| ~ sP506(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)))
| ~ sP506(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722)))
| ~ sP504(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722)))
| ~ sP504(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( sP504(U_5723,U_5725,U_5722,U_5724)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)))
| ~ sP505(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)))
| ~ sP505(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5723),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5725))
| sP509(U_5723,U_5725,U_5722,U_5724)
| sP506(U_5723,U_5725,U_5722,U_5724)
| ~ sP510(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( sP505(U_5723,U_5725,U_5722,U_5724)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5723),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5725))
| ~ sP510(U_5723,U_5725,U_5722,U_5724) )
& ! [U_5723,U_5725,U_5722,U_5724] :
( sP510(U_5723,U_5725,U_5722,U_5724)
| ~ class_Int_Onumber(U_5722)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5722) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP504,sP505,sP506,sP507,sP508,sP509,sP510])],[f_1477_2]) ).
cnf(f_1477_4,plain,
( sP510(U_5723,U_5725,U_5722,U_5724)
| ~ class_Int_Onumber(U_5722)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5722) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_5,plain,
( sP505(U_5723,U_5725,U_5722,U_5724)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5723),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5725))
| ~ sP510(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5723),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5725))
| sP509(U_5723,U_5725,U_5722,U_5724)
| sP506(U_5723,U_5725,U_5722,U_5724)
| ~ sP510(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)))
| ~ sP505(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_8,plain,
( sP504(U_5723,U_5725,U_5722,U_5724)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)))
| ~ sP505(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722)))
| ~ sP504(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722)))
| ~ sP504(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)))
| ~ sP506(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))))
| ~ sP506(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)))
| ~ sP509(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_14,plain,
( sP508(U_5725,U_5722,U_5724)
| sP507(U_5723,U_5725,U_5722,U_5724)
| ~ sP509(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722)))
| ~ sP507(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5725),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724))),U_5723))
| ~ sP507(U_5723,U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),hAPP(c_Int_Onumber__class_Onumber__of(U_5722),U_5724)),c_Groups_Ozero__class_Ozero(U_5722)))
| ~ sP508(U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
| ~ sP508(U_5725,U_5722,U_5724) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
fof(f_1478_1,plain,
! [V_p,V_m] :
( ( 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))))
| V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__if]) ).
fof(f_1478_2,plain,
! [U_5727,U_5726] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5727),U_5726) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5727),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5726),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_5726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5727),U_5726) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5726 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1478_1]) ).
fof(f_1478_3,plain,
( ! [U_5731,U_5729] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5731),U_5729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5731),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5729),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_5729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5730,U_5728] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5730),U_5728) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5728 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1478_2]) ).
fof(f_1478_4,plain,
( ! [U_5729,U_5731] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5731),U_5729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5731),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5729),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_5729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5728,U_5730] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5730),U_5728) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5728 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1478_3]) ).
cnf(f_1478_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5730),U_5728) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5728 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1478_4]) ).
cnf(f_1478_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5731),U_5729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5731),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5729),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_5729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1478_4]) ).
fof(f_1479_1,plain,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( ( 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))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ 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))) )
| ( ~ 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))
& 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))) ) )
& ~ 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))) )
| ( ~ 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))))
& 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))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| 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))) )
& ( 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))
| ~ 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))) ) )
| 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))) )
& ( 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))))
| ~ 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))) ) )
| ~ 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)) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of1]) ).
fof(f_1479_2,plain,
! [U_5735,U_5734,U_5733,U_5732] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5732),U_5733),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5735))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),U_5735))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5733))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),U_5733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),U_5735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),U_5733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5732),U_5733),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5735)) ) )
| ~ class_Int_Onumber(U_5732)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5732) ),
inference(variable_rename,[status(thm)],[f_1479_1]) ).
fof(f_1479_3,plain,
( ! [U_5732,U_5734,U_5735] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),U_5735))
| ~ sP515(U_5732,U_5734,U_5735) )
& ! [U_5732,U_5734,U_5735] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732)))
| ~ sP515(U_5732,U_5734,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5733))
| ~ sP514(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732)))
| ~ sP514(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( sP515(U_5732,U_5734,U_5735)
| sP514(U_5732,U_5734,U_5733,U_5735)
| ~ sP516(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)))
| ~ sP516(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),U_5733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))))
| ~ sP513(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)))
| ~ sP513(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),U_5735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732)))
| ~ sP511(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732)))
| ~ sP511(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( sP511(U_5732,U_5734,U_5733,U_5735)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)))
| ~ sP512(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),U_5733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)))
| ~ sP512(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5732),U_5733),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5735))
| sP516(U_5732,U_5734,U_5733,U_5735)
| sP513(U_5732,U_5734,U_5733,U_5735)
| ~ sP517(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( sP512(U_5732,U_5734,U_5733,U_5735)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5732),U_5733),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5735))
| ~ sP517(U_5732,U_5734,U_5733,U_5735) )
& ! [U_5732,U_5734,U_5733,U_5735] :
( sP517(U_5732,U_5734,U_5733,U_5735)
| ~ class_Int_Onumber(U_5732)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5732) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP511,sP512,sP513,sP514,sP515,sP516,sP517])],[f_1479_2]) ).
cnf(f_1479_4,plain,
( sP517(U_5732,U_5734,U_5733,U_5735)
| ~ class_Int_Onumber(U_5732)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5732) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_5,plain,
( sP512(U_5732,U_5734,U_5733,U_5735)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5732),U_5733),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5735))
| ~ sP517(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5732),U_5733),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5735))
| sP516(U_5732,U_5734,U_5733,U_5735)
| sP513(U_5732,U_5734,U_5733,U_5735)
| ~ sP517(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),U_5733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)))
| ~ sP512(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_8,plain,
( sP511(U_5732,U_5734,U_5733,U_5735)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)))
| ~ sP512(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732)))
| ~ sP511(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),U_5735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732)))
| ~ sP511(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)))
| ~ sP513(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),U_5733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))))
| ~ sP513(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)))
| ~ sP516(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_14,plain,
( sP515(U_5732,U_5734,U_5735)
| sP514(U_5732,U_5734,U_5733,U_5735)
| ~ sP516(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732)))
| ~ sP514(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5732),U_5735),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734))),U_5733))
| ~ sP514(U_5732,U_5734,U_5733,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5732),hAPP(c_Int_Onumber__class_Onumber__of(U_5732),U_5734)),c_Groups_Ozero__class_Ozero(U_5732)))
| ~ sP515(U_5732,U_5734,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5732),c_Groups_Ozero__class_Ozero(U_5732)),U_5735))
| ~ sP515(U_5732,U_5734,U_5735) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
fof(f_1480_1,plain,
! [V_w_2,V_ca_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| ( ( ( ~ 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)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ 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_ca_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ( ~ 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_ca_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
& ( ( ( ( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( 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_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(f_1480_2,plain,
! [U_5739,U_5738,U_5737,U_5736] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5736),U_5737),U_5738)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)),U_5737))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),U_5737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)),U_5737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),U_5737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5736),U_5737),U_5738)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739))) ) )
| ~ class_Int_Onumber(U_5736)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5736) ),
inference(variable_rename,[status(thm)],[f_1480_1]) ).
fof(f_1480_3,plain,
( ! [U_5739,U_5738,U_5736] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| ~ sP522(U_5739,U_5738,U_5736) )
& ! [U_5739,U_5738,U_5736] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736)))
| ~ sP522(U_5739,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)),U_5737))
| ~ sP521(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736)))
| ~ sP521(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( sP522(U_5739,U_5738,U_5736)
| sP521(U_5739,U_5737,U_5738,U_5736)
| ~ sP523(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738))
| ~ sP523(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),U_5737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)))
| ~ sP520(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738))
| ~ sP520(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736)))
| ~ sP518(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)),U_5737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736)))
| ~ sP518(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( sP518(U_5739,U_5737,U_5738,U_5736)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738))
| ~ sP519(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),U_5737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738))
| ~ sP519(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5736),U_5737),U_5738)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| sP523(U_5739,U_5737,U_5738,U_5736)
| sP520(U_5739,U_5737,U_5738,U_5736)
| ~ sP524(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( sP519(U_5739,U_5737,U_5738,U_5736)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5736),U_5737),U_5738)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| ~ sP524(U_5739,U_5737,U_5738,U_5736) )
& ! [U_5739,U_5737,U_5738,U_5736] :
( sP524(U_5739,U_5737,U_5738,U_5736)
| ~ class_Int_Onumber(U_5736)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5736) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP518,sP519,sP520,sP521,sP522,sP523,sP524])],[f_1480_2]) ).
cnf(f_1480_4,plain,
( sP524(U_5739,U_5737,U_5738,U_5736)
| ~ class_Int_Onumber(U_5736)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_5,plain,
( sP519(U_5739,U_5737,U_5738,U_5736)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5736),U_5737),U_5738)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| ~ sP524(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5736),U_5737),U_5738)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| sP523(U_5739,U_5737,U_5738,U_5736)
| sP520(U_5739,U_5737,U_5738,U_5736)
| ~ sP524(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),U_5737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738))
| ~ sP519(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_8,plain,
( sP518(U_5739,U_5737,U_5738,U_5736)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738))
| ~ sP519(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)),U_5737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736)))
| ~ sP518(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736)))
| ~ sP518(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738))
| ~ sP520(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),U_5737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)))
| ~ sP520(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),U_5738))
| ~ sP523(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_14,plain,
( sP522(U_5739,U_5738,U_5736)
| sP521(U_5739,U_5737,U_5738,U_5736)
| ~ sP523(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736)))
| ~ sP521(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)),U_5738)),U_5737))
| ~ sP521(U_5739,U_5737,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5736),U_5738),c_Groups_Ozero__class_Ozero(U_5736)))
| ~ sP522(U_5739,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5736),c_Groups_Ozero__class_Ozero(U_5736)),hAPP(c_Int_Onumber__class_Onumber__of(U_5736),U_5739)))
| ~ sP522(U_5739,U_5738,U_5736) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
fof(f_1481_1,plain,
! [V_ca_2,V_b_2,V_w_2,T_b] :
( ( ( 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_ca_2)))
| ( ( ( ~ 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)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ 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_ca_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
| ( ~ 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_ca_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
& ( ( ( ( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( 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_ca_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) )
& ( 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_ca_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
| ~ 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_ca_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(f_1481_2,plain,
! [U_5743,U_5742,U_5741,U_5740] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5740),U_5742),U_5743)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),c_Groups_Ozero__class_Ozero(U_5740)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),U_5742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)),U_5742))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),c_Groups_Ozero__class_Ozero(U_5740)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),U_5742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)),U_5742))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5740),U_5742),U_5743))) ) )
| ~ class_Int_Onumber(U_5740)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5740) ),
inference(variable_rename,[status(thm)],[f_1481_1]) ).
fof(f_1481_3,plain,
( ! [U_5743,U_5740,U_5741] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP529(U_5743,U_5740,U_5741) )
& ! [U_5743,U_5740,U_5741] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP529(U_5743,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),U_5742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)))
| ~ sP528(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP528(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( sP529(U_5743,U_5740,U_5741)
| sP528(U_5743,U_5742,U_5740,U_5741)
| ~ sP530(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743))
| ~ sP530(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)),U_5742))
| ~ sP527(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743))
| ~ sP527(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),c_Groups_Ozero__class_Ozero(U_5740)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP525(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),U_5742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP525(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( sP525(U_5743,U_5742,U_5740,U_5741)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743))
| ~ sP526(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)),U_5742))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743))
| ~ sP526(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5740),U_5742),U_5743)))
| sP530(U_5743,U_5742,U_5740,U_5741)
| sP527(U_5743,U_5742,U_5740,U_5741)
| ~ sP531(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( sP526(U_5743,U_5742,U_5740,U_5741)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5740),U_5742),U_5743)))
| ~ sP531(U_5743,U_5742,U_5740,U_5741) )
& ! [U_5743,U_5742,U_5740,U_5741] :
( sP531(U_5743,U_5742,U_5740,U_5741)
| ~ class_Int_Onumber(U_5740)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5740) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP525,sP526,sP527,sP528,sP529,sP530,sP531])],[f_1481_2]) ).
cnf(f_1481_4,plain,
( sP531(U_5743,U_5742,U_5740,U_5741)
| ~ class_Int_Onumber(U_5740)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5740) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_5,plain,
( sP526(U_5743,U_5742,U_5740,U_5741)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5740),U_5742),U_5743)))
| ~ sP531(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5740),U_5742),U_5743)))
| sP530(U_5743,U_5742,U_5740,U_5741)
| sP527(U_5743,U_5742,U_5740,U_5741)
| ~ sP531(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)),U_5742))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743))
| ~ sP526(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_8,plain,
( sP525(U_5743,U_5742,U_5740,U_5741)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743))
| ~ sP526(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),U_5742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP525(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),c_Groups_Ozero__class_Ozero(U_5740)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP525(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743))
| ~ sP527(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)),U_5742))
| ~ sP527(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),c_Groups_Ozero__class_Ozero(U_5740)),U_5743))
| ~ sP530(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_14,plain,
( sP529(U_5743,U_5740,U_5741)
| sP528(U_5743,U_5742,U_5740,U_5741)
| ~ sP530(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP528(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),U_5742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),U_5743)))
| ~ sP528(U_5743,U_5742,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5740),U_5743),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP529(U_5743,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
cnf(f_1481_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5740),hAPP(c_Int_Onumber__class_Onumber__of(U_5740),U_5741)),c_Groups_Ozero__class_Ozero(U_5740)))
| ~ sP529(U_5743,U_5740,U_5741) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
fof(f_1482_1,plain,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( ( 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))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ 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))) )
| ( ~ 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))))
& 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))) ) )
& ~ 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))) )
| ( ~ 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))
& 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))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| 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))) )
& ( 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))))
| ~ 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))) ) )
| 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))) )
& ( 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))
| ~ 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))) ) )
| ~ 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)))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of1]) ).
fof(f_1482_2,plain,
! [U_5747,U_5746,U_5745,U_5744] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5744),U_5746),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),c_Groups_Ozero__class_Ozero(U_5744)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))),U_5746))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),c_Groups_Ozero__class_Ozero(U_5744)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))),U_5746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5744),U_5746),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))) ) )
| ~ class_Int_Onumber(U_5744)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5744) ),
inference(variable_rename,[status(thm)],[f_1482_1]) ).
fof(f_1482_3,plain,
( ! [U_5745,U_5747,U_5744] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP536(U_5745,U_5747,U_5744) )
& ! [U_5745,U_5747,U_5744] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP536(U_5745,U_5747,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| ~ sP535(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP535(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( sP536(U_5745,U_5747,U_5744)
| sP535(U_5745,U_5747,U_5746,U_5744)
| ~ sP537(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))
| ~ sP537(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))),U_5746))
| ~ sP534(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))
| ~ sP534(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),c_Groups_Ozero__class_Ozero(U_5744)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP532(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP532(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( sP532(U_5745,U_5747,U_5746,U_5744)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))
| ~ sP533(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))),U_5746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))
| ~ sP533(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5744),U_5746),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| sP537(U_5745,U_5747,U_5746,U_5744)
| sP534(U_5745,U_5747,U_5746,U_5744)
| ~ sP538(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( sP533(U_5745,U_5747,U_5746,U_5744)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5744),U_5746),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| ~ sP538(U_5745,U_5747,U_5746,U_5744) )
& ! [U_5745,U_5747,U_5746,U_5744] :
( sP538(U_5745,U_5747,U_5746,U_5744)
| ~ class_Int_Onumber(U_5744)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5744) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP532,sP533,sP534,sP535,sP536,sP537,sP538])],[f_1482_2]) ).
cnf(f_1482_4,plain,
( sP538(U_5745,U_5747,U_5746,U_5744)
| ~ class_Int_Onumber(U_5744)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_5,plain,
( sP533(U_5745,U_5747,U_5746,U_5744)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5744),U_5746),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| ~ sP538(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5744),U_5746),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| sP537(U_5745,U_5747,U_5746,U_5744)
| sP534(U_5745,U_5747,U_5746,U_5744)
| ~ sP538(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))),U_5746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))
| ~ sP533(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_8,plain,
( sP532(U_5745,U_5747,U_5746,U_5744)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))
| ~ sP533(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP532(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),c_Groups_Ozero__class_Ozero(U_5744)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP532(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))
| ~ sP534(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))),U_5746))
| ~ sP534(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),c_Groups_Ozero__class_Ozero(U_5744)),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)))
| ~ sP537(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_14,plain,
( sP536(U_5745,U_5747,U_5744)
| sP535(U_5745,U_5747,U_5746,U_5744)
| ~ sP537(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP535(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5744),U_5745),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747))))
| ~ sP535(U_5745,U_5747,U_5746,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5744),hAPP(c_Int_Onumber__class_Onumber__of(U_5744),U_5747)),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP536(U_5745,U_5747,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5744),U_5745),c_Groups_Ozero__class_Ozero(U_5744)))
| ~ sP536(U_5745,U_5747,U_5744) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
fof(f_1483_1,plain,
! [V_n,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__mono]) ).
fof(f_1483_2,plain,
! [U_5751,U_5750,U_5749,U_5748] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5748),hAPP(hAPP(c_Power_Opower__class_Opower(U_5748),U_5749),U_5751)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5748),U_5750),U_5751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5748),c_Groups_Ozero__class_Ozero(U_5748)),U_5749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5748),U_5749),U_5750))
| ~ class_Rings_Olinordered__semidom(U_5748) ),
inference(variable_rename,[status(thm)],[f_1483_1]) ).
fof(f_1483_3,plain,
! [U_5751,U_5749,U_5750,U_5748] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5748),hAPP(hAPP(c_Power_Opower__class_Opower(U_5748),U_5749),U_5751)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5748),U_5750),U_5751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5748),c_Groups_Ozero__class_Ozero(U_5748)),U_5749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5748),U_5749),U_5750))
| ~ class_Rings_Olinordered__semidom(U_5748) ),
inference(definitional_conversion,[status(esa)],[f_1483_2]) ).
cnf(f_1483_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5748),hAPP(hAPP(c_Power_Opower__class_Opower(U_5748),U_5749),U_5751)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5748),U_5750),U_5751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5748),c_Groups_Ozero__class_Ozero(U_5748)),U_5749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5748),U_5749),U_5750))
| ~ class_Rings_Olinordered__semidom(U_5748) ),
inference(clausify,[status(thm)],[f_1483_3]) ).
fof(f_1484_1,plain,
! [V_m,V_n,V_a,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__diff]) ).
fof(f_1484_2,plain,
! [U_5755,U_5754,U_5753,U_5752] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5755),U_5754)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5752),hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),U_5755)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),U_5754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5754),U_5755))
| U_5753 = c_Groups_Ozero__class_Ozero(U_5752)
| ~ class_Fields_Ofield(U_5752) ),
inference(variable_rename,[status(thm)],[f_1484_1]) ).
fof(f_1484_3,plain,
! [U_5752,U_5755,U_5753,U_5754] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5755),U_5754)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5752),hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),U_5755)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),U_5754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5754),U_5755))
| U_5753 = c_Groups_Ozero__class_Ozero(U_5752)
| ~ class_Fields_Ofield(U_5752) ),
inference(definitional_conversion,[status(esa)],[f_1484_2]) ).
cnf(f_1484_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5755),U_5754)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5752),hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),U_5755)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5752),U_5753),U_5754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5754),U_5755))
| U_5753 = c_Groups_Ozero__class_Ozero(U_5752)
| ~ class_Fields_Ofield(U_5752) ),
inference(clausify,[status(thm)],[f_1484_3]) ).
fof(f_1485_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__less__power]) ).
fof(f_1485_2,plain,
! [U_5758,U_5757,U_5756] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5756),c_Groups_Oone__class_Oone(U_5756)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5756),U_5757),U_5758)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5756),c_Groups_Oone__class_Oone(U_5756)),U_5757))
| ~ class_Rings_Olinordered__semidom(U_5756) ),
inference(variable_rename,[status(thm)],[f_1485_1]) ).
fof(f_1485_3,plain,
! [U_5757,U_5756,U_5758] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5756),c_Groups_Oone__class_Oone(U_5756)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5756),U_5757),U_5758)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5756),c_Groups_Oone__class_Oone(U_5756)),U_5757))
| ~ class_Rings_Olinordered__semidom(U_5756) ),
inference(definitional_conversion,[status(esa)],[f_1485_2]) ).
cnf(f_1485_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5756),c_Groups_Oone__class_Oone(U_5756)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5756),U_5757),U_5758)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5756),c_Groups_Oone__class_Oone(U_5756)),U_5757))
| ~ class_Rings_Olinordered__semidom(U_5756) ),
inference(clausify,[status(thm)],[f_1485_3]) ).
fof(f_1486_1,plain,
! [V_n,V_m,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp]) ).
fof(f_1486_2,plain,
! [U_5762,U_5761,U_5760,U_5759] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5761),U_5762))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5759),hAPP(hAPP(c_Power_Opower__class_Opower(U_5759),U_5760),U_5761)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5759),U_5760),U_5762)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5759),c_Groups_Oone__class_Oone(U_5759)),U_5760))
| ~ class_Rings_Olinordered__semidom(U_5759) ),
inference(variable_rename,[status(thm)],[f_1486_1]) ).
fof(f_1486_3,plain,
! [U_5759,U_5760,U_5761,U_5762] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5761),U_5762))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5759),hAPP(hAPP(c_Power_Opower__class_Opower(U_5759),U_5760),U_5761)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5759),U_5760),U_5762)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5759),c_Groups_Oone__class_Oone(U_5759)),U_5760))
| ~ class_Rings_Olinordered__semidom(U_5759) ),
inference(definitional_conversion,[status(esa)],[f_1486_2]) ).
cnf(f_1486_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5761),U_5762))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5759),hAPP(hAPP(c_Power_Opower__class_Opower(U_5759),U_5760),U_5761)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5759),U_5760),U_5762)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5759),c_Groups_Oone__class_Oone(U_5759)),U_5760))
| ~ class_Rings_Olinordered__semidom(U_5759) ),
inference(clausify,[status(thm)],[f_1486_3]) ).
fof(f_1487_1,plain,
! [V_y_2,V_x_2,V_b_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).
fof(f_1487_2,plain,
! [U_5766,U_5765,U_5764,U_5763] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5763),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5765)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5766)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5765),U_5766)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5765),U_5766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5763),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5765)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5766))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5763),c_Groups_Oone__class_Oone(U_5763)),U_5764))
| ~ class_Rings_Olinordered__semidom(U_5763) ),
inference(variable_rename,[status(thm)],[f_1487_1]) ).
fof(f_1487_3,plain,
( ! [U_5765,U_5764,U_5766,U_5763] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5763),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5765)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5766)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5765),U_5766))
| ~ sP539(U_5765,U_5764,U_5766,U_5763) )
& ! [U_5765,U_5764,U_5766,U_5763] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5765),U_5766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5763),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5765)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5766)))
| ~ sP539(U_5765,U_5764,U_5766,U_5763) )
& ! [U_5765,U_5764,U_5766,U_5763] :
( sP539(U_5765,U_5764,U_5766,U_5763)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5763),c_Groups_Oone__class_Oone(U_5763)),U_5764))
| ~ class_Rings_Olinordered__semidom(U_5763) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP539])],[f_1487_2]) ).
cnf(f_1487_4,plain,
( sP539(U_5765,U_5764,U_5766,U_5763)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5763),c_Groups_Oone__class_Oone(U_5763)),U_5764))
| ~ class_Rings_Olinordered__semidom(U_5763) ),
inference(clausify,[status(thm)],[f_1487_3]) ).
cnf(f_1487_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5765),U_5766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5763),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5765)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5766)))
| ~ sP539(U_5765,U_5764,U_5766,U_5763) ),
inference(clausify,[status(thm)],[f_1487_3]) ).
cnf(f_1487_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5763),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5765)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5763),U_5764),U_5766)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5765),U_5766))
| ~ sP539(U_5765,U_5764,U_5766,U_5763) ),
inference(clausify,[status(thm)],[f_1487_3]) ).
fof(f_1488_1,plain,
! [V_a,V_N,V_n,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__decreasing]) ).
fof(f_1488_2,plain,
! [U_5770,U_5769,U_5768,U_5767] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),hAPP(hAPP(c_Power_Opower__class_Opower(U_5767),U_5770),U_5769)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5767),U_5770),U_5768)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),U_5770),c_Groups_Oone__class_Oone(U_5767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),c_Groups_Ozero__class_Ozero(U_5767)),U_5770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5768),U_5769))
| ~ class_Rings_Olinordered__semidom(U_5767) ),
inference(variable_rename,[status(thm)],[f_1488_1]) ).
fof(f_1488_3,plain,
! [U_5768,U_5769,U_5770,U_5767] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),hAPP(hAPP(c_Power_Opower__class_Opower(U_5767),U_5770),U_5769)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5767),U_5770),U_5768)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),U_5770),c_Groups_Oone__class_Oone(U_5767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),c_Groups_Ozero__class_Ozero(U_5767)),U_5770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5768),U_5769))
| ~ class_Rings_Olinordered__semidom(U_5767) ),
inference(definitional_conversion,[status(esa)],[f_1488_2]) ).
cnf(f_1488_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),hAPP(hAPP(c_Power_Opower__class_Opower(U_5767),U_5770),U_5769)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5767),U_5770),U_5768)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),U_5770),c_Groups_Oone__class_Oone(U_5767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5767),c_Groups_Ozero__class_Ozero(U_5767)),U_5770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5768),U_5769))
| ~ class_Rings_Olinordered__semidom(U_5767) ),
inference(clausify,[status(thm)],[f_1488_3]) ).
fof(f_1489_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I6_J]) ).
fof(f_1489_2,plain,
! [U_5772,U_5771] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5771)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5771),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5772))),
inference(variable_rename,[status(thm)],[f_1489_1]) ).
fof(f_1489_3,plain,
! [U_5772,U_5771] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5771)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5771),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5772))),
inference(definitional_conversion,[status(esa)],[f_1489_2]) ).
cnf(f_1489_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5771)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5771),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5772))),
inference(clausify,[status(thm)],[f_1489_3]) ).
fof(f_1490_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_plus__numeral__code_I9_J]) ).
fof(f_1490_2,plain,
! [U_5774,U_5773] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5773)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5774)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5773),U_5774)),
inference(variable_rename,[status(thm)],[f_1490_1]) ).
fof(f_1490_3,plain,
! [U_5773,U_5774] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5773)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5774)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5773),U_5774)),
inference(definitional_conversion,[status(esa)],[f_1490_2]) ).
cnf(f_1490_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5773)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5774)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5773),U_5774)),
inference(clausify,[status(thm)],[f_1490_3]) ).
fof(f_1491_1,plain,
! [V_l_2,V_k_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code]) ).
fof(f_1491_2,plain,
! [U_5776,U_5775] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5775)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5776)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5775),U_5776)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5775),U_5776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5775)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5776))) ) ),
inference(variable_rename,[status(thm)],[f_1491_1]) ).
fof(f_1491_3,plain,
( ! [U_5780,U_5778] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5778)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5780)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5778),U_5780)) )
& ! [U_5779,U_5777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5777),U_5779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5779))) ) ),
inference(miniscope,[status(thm)],[f_1491_2]) ).
fof(f_1491_4,plain,
( ! [U_5778,U_5780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5778)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5780)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5778),U_5780)) )
& ! [U_5779,U_5777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5777),U_5779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5779))) ) ),
inference(definitional_conversion,[status(esa)],[f_1491_3]) ).
cnf(f_1491_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5777),U_5779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5779))) ),
inference(clausify,[status(thm)],[f_1491_4]) ).
cnf(f_1491_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5778)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5780)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5778),U_5780)) ),
inference(clausify,[status(thm)],[f_1491_4]) ).
fof(f_1492_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_times__numeral__code_I5_J]) ).
fof(f_1492_2,plain,
! [U_5782,U_5781] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5781)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5782)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5781),U_5782)),
inference(variable_rename,[status(thm)],[f_1492_1]) ).
fof(f_1492_3,plain,
! [U_5781,U_5782] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5781)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5782)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5781),U_5782)),
inference(definitional_conversion,[status(esa)],[f_1492_2]) ).
cnf(f_1492_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5781)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5782)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5781),U_5782)),
inference(clausify,[status(thm)],[f_1492_3]) ).
fof(f_1493_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I5_J]) ).
fof(f_1493_2,plain,
! [U_5783] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5783)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5783)),
inference(variable_rename,[status(thm)],[f_1493_1]) ).
fof(f_1493_3,plain,
! [U_5783] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5783)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5783)),
inference(definitional_conversion,[status(esa)],[f_1493_2]) ).
cnf(f_1493_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5783)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5783)),
inference(clausify,[status(thm)],[f_1493_3]) ).
fof(f_1494_1,plain,
! [V_l_2,V_k_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code]) ).
fof(f_1494_2,plain,
! [U_5785,U_5784] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5784)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5785)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5784),U_5785)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5784),U_5785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5784)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5785))) ) ),
inference(variable_rename,[status(thm)],[f_1494_1]) ).
fof(f_1494_3,plain,
( ! [U_5789,U_5787] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5787)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5787),U_5789)) )
& ! [U_5788,U_5786] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5786),U_5788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5786)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5788))) ) ),
inference(miniscope,[status(thm)],[f_1494_2]) ).
fof(f_1494_4,plain,
( ! [U_5787,U_5789] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5787)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5787),U_5789)) )
& ! [U_5788,U_5786] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5786),U_5788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5786)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5788))) ) ),
inference(definitional_conversion,[status(esa)],[f_1494_3]) ).
cnf(f_1494_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5786),U_5788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5786)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5788))) ),
inference(clausify,[status(thm)],[f_1494_4]) ).
cnf(f_1494_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5787)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5787),U_5789)) ),
inference(clausify,[status(thm)],[f_1494_4]) ).
fof(f_1495_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).
fof(f_1495_2,plain,
! [U_5791,U_5790] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_5790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5791),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_5790,U_5791),
inference(variable_rename,[status(thm)],[f_1495_1]) ).
fof(f_1495_3,plain,
! [U_5791,U_5790] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_5790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5791),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_5790,U_5791),
inference(definitional_conversion,[status(esa)],[f_1495_2]) ).
cnf(f_1495_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_5790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5791),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_5790,U_5791),
inference(clausify,[status(thm)],[f_1495_3]) ).
fof(f_1496_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).
fof(f_1496_2,plain,
! [U_5793,U_5792] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5792),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5793) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_5792,U_5793),
inference(variable_rename,[status(thm)],[f_1496_1]) ).
fof(f_1496_3,plain,
! [U_5792,U_5793] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5792),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5793) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_5792,U_5793),
inference(definitional_conversion,[status(esa)],[f_1496_2]) ).
cnf(f_1496_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5792),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5793) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_5792,U_5793),
inference(clausify,[status(thm)],[f_1496_3]) ).
fof(f_1497_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).
fof(f_1497_2,plain,
! [U_5795,U_5794] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5794),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5795) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_5794,U_5795),
inference(variable_rename,[status(thm)],[f_1497_1]) ).
fof(f_1497_3,plain,
! [U_5794,U_5795] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5794),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5795) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_5794,U_5795),
inference(definitional_conversion,[status(esa)],[f_1497_2]) ).
cnf(f_1497_4,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5794),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5795) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_5794,U_5795),
inference(clausify,[status(thm)],[f_1497_3]) ).
fof(f_1498_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
inference(fof_nnf,[status(thm)],[fact_zmult__1]) ).
fof(f_1498_2,plain,
! [U_5796] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5796) = U_5796,
inference(variable_rename,[status(thm)],[f_1498_1]) ).
fof(f_1498_3,plain,
! [U_5796] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5796) = U_5796,
inference(definitional_conversion,[status(esa)],[f_1498_2]) ).
cnf(f_1498_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5796) = U_5796,
inference(clausify,[status(thm)],[f_1498_3]) ).
fof(f_1499_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zmult__1__right]) ).
fof(f_1499_2,plain,
! [U_5797] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5797),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_5797,
inference(variable_rename,[status(thm)],[f_1499_1]) ).
fof(f_1499_3,plain,
! [U_5797] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5797),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_5797,
inference(definitional_conversion,[status(esa)],[f_1499_2]) ).
cnf(f_1499_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5797),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_5797,
inference(clausify,[status(thm)],[f_1499_3]) ).
fof(f_1500_1,plain,
! [V_z_2,V_w_2] :
( ( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).
fof(f_1500_2,plain,
! [U_5799,U_5798] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5798),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5799),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5798),U_5799)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5798),U_5799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5798),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5799),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1500_1]) ).
fof(f_1500_3,plain,
( ! [U_5803,U_5801] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5801),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5803),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5801),U_5803)) )
& ! [U_5802,U_5800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5800),U_5802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5800),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5802),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1500_2]) ).
fof(f_1500_4,plain,
( ! [U_5801,U_5803] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5801),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5803),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5801),U_5803)) )
& ! [U_5802,U_5800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5800),U_5802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5800),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5802),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(definitional_conversion,[status(esa)],[f_1500_3]) ).
cnf(f_1500_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5800),U_5802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5800),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5802),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
cnf(f_1500_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5801),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5803),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5801),U_5803)) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
fof(f_1501_1,plain,
! [V_z_2,V_w_2] :
( ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).
fof(f_1501_2,plain,
! [U_5805,U_5804] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5804),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5805))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5804),U_5805)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5804),U_5805))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5804),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5805)) ) ),
inference(variable_rename,[status(thm)],[f_1501_1]) ).
fof(f_1501_3,plain,
( ! [U_5809,U_5807] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5807),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5807),U_5809)) )
& ! [U_5808,U_5806] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5806),U_5808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5806),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5808)) ) ),
inference(miniscope,[status(thm)],[f_1501_2]) ).
fof(f_1501_4,plain,
( ! [U_5807,U_5809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5807),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5807),U_5809)) )
& ! [U_5808,U_5806] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5806),U_5808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5806),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5808)) ) ),
inference(definitional_conversion,[status(esa)],[f_1501_3]) ).
cnf(f_1501_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5806),U_5808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5806),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5808)) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
cnf(f_1501_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5807),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5807),U_5809)) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
fof(f_1502_1,plain,
! [V_z,V_w] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).
fof(f_1502_2,plain,
! [U_5811,U_5810] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5810),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5810),U_5811)) ),
inference(variable_rename,[status(thm)],[f_1502_1]) ).
fof(f_1502_3,plain,
! [U_5811,U_5810] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5810),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5810),U_5811)) ),
inference(definitional_conversion,[status(esa)],[f_1502_2]) ).
cnf(f_1502_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5810),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5810),U_5811)) ),
inference(clausify,[status(thm)],[f_1502_3]) ).
fof(f_1503_1,plain,
! [V_z_2,V_w_2] :
( ( 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))))
| ( V_w_2 != V_z_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) )
& ( V_w_2 = V_z_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).
fof(f_1503_2,plain,
! [U_5813,U_5812] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5812),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5813),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_5812 != U_5813
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5812),U_5813)) ) )
& ( U_5812 = U_5813
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5812),U_5813))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5812),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5813),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1503_1]) ).
fof(f_1503_3,plain,
( ! [U_5817,U_5815] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5817),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_5815 != U_5817
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5815),U_5817)) ) )
& ! [U_5816,U_5814] :
( U_5814 = U_5816
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5814),U_5816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5816),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1503_2]) ).
fof(f_1503_4,plain,
( ! [U_5817,U_5815] :
( U_5815 != U_5817
| ~ sP540(U_5817,U_5815) )
& ! [U_5817,U_5815] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5815),U_5817))
| ~ sP540(U_5817,U_5815) )
& ! [U_5817,U_5815] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5817),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| sP540(U_5817,U_5815) )
& ! [U_5816,U_5814] :
( U_5814 = U_5816
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5814),U_5816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5816),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP540])],[f_1503_3]) ).
cnf(f_1503_5,plain,
( U_5814 = U_5816
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5814),U_5816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5816),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1503_4]) ).
cnf(f_1503_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5817),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| sP540(U_5817,U_5815) ),
inference(clausify,[status(thm)],[f_1503_4]) ).
cnf(f_1503_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5815),U_5817))
| ~ sP540(U_5817,U_5815) ),
inference(clausify,[status(thm)],[f_1503_4]) ).
cnf(f_1503_8,plain,
( U_5815 != U_5817
| ~ sP540(U_5817,U_5815) ),
inference(clausify,[status(thm)],[f_1503_4]) ).
fof(f_1504_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zadd__left__mono]) ).
fof(f_1504_2,plain,
! [U_5820,U_5819,U_5818] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5820),U_5818)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5820),U_5819)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5818),U_5819)) ),
inference(variable_rename,[status(thm)],[f_1504_1]) ).
fof(f_1504_3,plain,
! [U_5819,U_5818,U_5820] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5820),U_5818)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5820),U_5819)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5818),U_5819)) ),
inference(definitional_conversion,[status(esa)],[f_1504_2]) ).
cnf(f_1504_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5820),U_5818)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5820),U_5819)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5818),U_5819)) ),
inference(clausify,[status(thm)],[f_1504_3]) ).
fof(f_1505_1,plain,
! [V_z,V_z_H,V_w,V_w_H] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) ),
inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).
fof(f_1505_2,plain,
! [U_5824,U_5823,U_5822,U_5821] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5821),U_5823)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5822),U_5824)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5823),U_5824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5821),U_5822)) ),
inference(variable_rename,[status(thm)],[f_1505_1]) ).
fof(f_1505_3,plain,
! [U_5822,U_5821,U_5823,U_5824] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5821),U_5823)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5822),U_5824)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5823),U_5824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5821),U_5822)) ),
inference(definitional_conversion,[status(esa)],[f_1505_2]) ).
cnf(f_1505_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5821),U_5823)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5822),U_5824)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5823),U_5824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5821),U_5822)) ),
inference(clausify,[status(thm)],[f_1505_3]) ).
fof(f_1506_1,plain,
! [V_w_2,V_z_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
| V_z_2 = V_w_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) )
& ( ( V_z_2 != V_w_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__le]) ).
fof(f_1506_2,plain,
! [U_5826,U_5825] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5825),U_5826))
| U_5825 = U_5826
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5825),U_5826)) )
& ( ( U_5825 != U_5826
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5825),U_5826)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5825),U_5826)) ) ),
inference(variable_rename,[status(thm)],[f_1506_1]) ).
fof(f_1506_3,plain,
( ! [U_5830,U_5828] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5828),U_5830))
| U_5828 = U_5830
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5828),U_5830)) )
& ! [U_5829,U_5827] :
( ( U_5827 != U_5829
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5827),U_5829)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5827),U_5829)) ) ),
inference(miniscope,[status(thm)],[f_1506_2]) ).
fof(f_1506_4,plain,
( ! [U_5829,U_5827] :
( U_5827 != U_5829
| ~ sP541(U_5829,U_5827) )
& ! [U_5829,U_5827] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5827),U_5829))
| ~ sP541(U_5829,U_5827) )
& ! [U_5830,U_5828] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5828),U_5830))
| U_5828 = U_5830
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5828),U_5830)) )
& ! [U_5829,U_5827] :
( sP541(U_5829,U_5827)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5827),U_5829)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP541])],[f_1506_3]) ).
cnf(f_1506_5,plain,
( sP541(U_5829,U_5827)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5827),U_5829)) ),
inference(clausify,[status(thm)],[f_1506_4]) ).
cnf(f_1506_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5828),U_5830))
| U_5828 = U_5830
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5828),U_5830)) ),
inference(clausify,[status(thm)],[f_1506_4]) ).
cnf(f_1506_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5827),U_5829))
| ~ sP541(U_5829,U_5827) ),
inference(clausify,[status(thm)],[f_1506_4]) ).
cnf(f_1506_8,plain,
( U_5827 != U_5829
| ~ sP541(U_5829,U_5827) ),
inference(clausify,[status(thm)],[f_1506_4]) ).
fof(f_1507_1,plain,
! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)),
inference(fof_nnf,[status(thm)],[fact_zle__refl]) ).
fof(f_1507_2,plain,
! [U_5831] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5831),U_5831)),
inference(variable_rename,[status(thm)],[f_1507_1]) ).
fof(f_1507_3,plain,
! [U_5831] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5831),U_5831)),
inference(definitional_conversion,[status(esa)],[f_1507_2]) ).
cnf(f_1507_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5831),U_5831)),
inference(clausify,[status(thm)],[f_1507_3]) ).
fof(f_1508_1,plain,
! [V_w,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
inference(fof_nnf,[status(thm)],[fact_zle__linear]) ).
fof(f_1508_2,plain,
! [U_5833,U_5832] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5833),U_5832))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5832),U_5833)) ),
inference(variable_rename,[status(thm)],[f_1508_1]) ).
fof(f_1508_3,plain,
! [U_5833,U_5832] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5833),U_5832))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5832),U_5833)) ),
inference(definitional_conversion,[status(esa)],[f_1508_2]) ).
cnf(f_1508_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5833),U_5832))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5832),U_5833)) ),
inference(clausify,[status(thm)],[f_1508_3]) ).
fof(f_1509_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zle__trans]) ).
fof(f_1509_2,plain,
! [U_5836,U_5835,U_5834] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5834),U_5836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5835),U_5836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5834),U_5835)) ),
inference(variable_rename,[status(thm)],[f_1509_1]) ).
fof(f_1509_3,plain,
! [U_5835,U_5834,U_5836] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5834),U_5836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5835),U_5836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5834),U_5835)) ),
inference(definitional_conversion,[status(esa)],[f_1509_2]) ).
cnf(f_1509_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5834),U_5836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5835),U_5836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5834),U_5835)) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
fof(f_1510_1,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
inference(fof_nnf,[status(thm)],[fact_zle__antisym]) ).
fof(f_1510_2,plain,
! [U_5838,U_5837] :
( U_5837 = U_5838
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5838),U_5837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5837),U_5838)) ),
inference(variable_rename,[status(thm)],[f_1510_1]) ).
fof(f_1510_3,plain,
! [U_5838,U_5837] :
( U_5837 = U_5838
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5838),U_5837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5837),U_5838)) ),
inference(definitional_conversion,[status(esa)],[f_1510_2]) ).
cnf(f_1510_4,plain,
( U_5837 = U_5838
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5838),U_5837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5837),U_5838)) ),
inference(clausify,[status(thm)],[f_1510_3]) ).
fof(f_1511_1,plain,
! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zminus__zminus]) ).
fof(f_1511_2,plain,
! [U_5839] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5839)) = U_5839,
inference(variable_rename,[status(thm)],[f_1511_1]) ).
fof(f_1511_3,plain,
! [U_5839] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5839)) = U_5839,
inference(definitional_conversion,[status(esa)],[f_1511_2]) ).
cnf(f_1511_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5839)) = U_5839,
inference(clausify,[status(thm)],[f_1511_3]) ).
fof(f_1512_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmult__zminus]) ).
fof(f_1512_2,plain,
! [U_5841,U_5840] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5840)),U_5841) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5840),U_5841)),
inference(variable_rename,[status(thm)],[f_1512_1]) ).
fof(f_1512_3,plain,
! [U_5840,U_5841] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5840)),U_5841) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5840),U_5841)),
inference(definitional_conversion,[status(esa)],[f_1512_2]) ).
cnf(f_1512_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5840)),U_5841) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5840),U_5841)),
inference(clausify,[status(thm)],[f_1512_3]) ).
fof(f_1513_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zmult__commute]) ).
fof(f_1513_2,plain,
! [U_5843,U_5842] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5842),U_5843) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5843),U_5842),
inference(variable_rename,[status(thm)],[f_1513_1]) ).
fof(f_1513_3,plain,
! [U_5842,U_5843] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5842),U_5843) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5843),U_5842),
inference(definitional_conversion,[status(esa)],[f_1513_2]) ).
cnf(f_1513_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5842),U_5843) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5843),U_5842),
inference(clausify,[status(thm)],[f_1513_3]) ).
fof(f_1514_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmult__assoc]) ).
fof(f_1514_2,plain,
! [U_5846,U_5845,U_5844] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5844),U_5845)),U_5846) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5845),U_5846)),
inference(variable_rename,[status(thm)],[f_1514_1]) ).
fof(f_1514_3,plain,
! [U_5844,U_5845,U_5846] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5844),U_5845)),U_5846) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5845),U_5846)),
inference(definitional_conversion,[status(esa)],[f_1514_2]) ).
cnf(f_1514_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5844),U_5845)),U_5846) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5845),U_5846)),
inference(clausify,[status(thm)],[f_1514_3]) ).
fof(f_1515_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_zless__linear]) ).
fof(f_1515_2,plain,
! [U_5848,U_5847] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5848),U_5847))
| U_5847 = U_5848
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5847),U_5848)) ),
inference(variable_rename,[status(thm)],[f_1515_1]) ).
fof(f_1515_3,plain,
! [U_5847,U_5848] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5848),U_5847))
| U_5847 = U_5848
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5847),U_5848)) ),
inference(definitional_conversion,[status(esa)],[f_1515_2]) ).
cnf(f_1515_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5848),U_5847))
| U_5847 = U_5848
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5847),U_5848)) ),
inference(clausify,[status(thm)],[f_1515_3]) ).
fof(f_1516_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono]) ).
fof(f_1516_2,plain,
! [U_5851,U_5850,U_5849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5849),U_5851)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5850),U_5851)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5849),U_5850)) ),
inference(variable_rename,[status(thm)],[f_1516_1]) ).
fof(f_1516_3,plain,
! [U_5849,U_5850,U_5851] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5849),U_5851)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5850),U_5851)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5849),U_5850)) ),
inference(definitional_conversion,[status(esa)],[f_1516_2]) ).
cnf(f_1516_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5849),U_5851)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5850),U_5851)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5849),U_5850)) ),
inference(clausify,[status(thm)],[f_1516_3]) ).
fof(f_1517_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zadd__commute]) ).
fof(f_1517_2,plain,
! [U_5853,U_5852] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5852),U_5853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5853),U_5852),
inference(variable_rename,[status(thm)],[f_1517_1]) ).
fof(f_1517_3,plain,
! [U_5852,U_5853] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5852),U_5853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5853),U_5852),
inference(definitional_conversion,[status(esa)],[f_1517_2]) ).
cnf(f_1517_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5852),U_5853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5853),U_5852),
inference(clausify,[status(thm)],[f_1517_3]) ).
fof(f_1518_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zadd__left__commute]) ).
fof(f_1518_2,plain,
! [U_5856,U_5855,U_5854] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5854),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5855),U_5856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5854),U_5856)),
inference(variable_rename,[status(thm)],[f_1518_1]) ).
fof(f_1518_3,plain,
! [U_5854,U_5855,U_5856] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5854),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5855),U_5856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5854),U_5856)),
inference(definitional_conversion,[status(esa)],[f_1518_2]) ).
cnf(f_1518_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5854),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5855),U_5856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5854),U_5856)),
inference(clausify,[status(thm)],[f_1518_3]) ).
fof(f_1519_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zadd__assoc]) ).
fof(f_1519_2,plain,
! [U_5859,U_5858,U_5857] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5857),U_5858)),U_5859) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5857),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5858),U_5859)),
inference(variable_rename,[status(thm)],[f_1519_1]) ).
fof(f_1519_3,plain,
! [U_5857,U_5858,U_5859] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5857),U_5858)),U_5859) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5857),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5858),U_5859)),
inference(definitional_conversion,[status(esa)],[f_1519_2]) ).
cnf(f_1519_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5857),U_5858)),U_5859) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5857),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5858),U_5859)),
inference(clausify,[status(thm)],[f_1519_3]) ).
fof(f_1520_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(f_1520_2,plain,
! [U_5862,U_5861,U_5860] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5860),U_5861)),U_5862) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5860),U_5862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5861),U_5862)),
inference(variable_rename,[status(thm)],[f_1520_1]) ).
fof(f_1520_3,plain,
! [U_5860,U_5861,U_5862] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5860),U_5861)),U_5862) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5860),U_5862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5861),U_5862)),
inference(definitional_conversion,[status(esa)],[f_1520_2]) ).
cnf(f_1520_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5860),U_5861)),U_5862) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5860),U_5862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5861),U_5862)),
inference(clausify,[status(thm)],[f_1520_3]) ).
fof(f_1521_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(f_1521_2,plain,
! [U_5865,U_5864,U_5863] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5864),U_5865)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),U_5864)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),U_5865)),
inference(variable_rename,[status(thm)],[f_1521_1]) ).
fof(f_1521_3,plain,
! [U_5863,U_5864,U_5865] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5864),U_5865)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),U_5864)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),U_5865)),
inference(definitional_conversion,[status(esa)],[f_1521_2]) ).
cnf(f_1521_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5864),U_5865)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),U_5864)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5863),U_5865)),
inference(clausify,[status(thm)],[f_1521_3]) ).
fof(f_1522_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(f_1522_2,plain,
! [U_5867,U_5866] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5866),U_5867)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5866)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5867)),
inference(variable_rename,[status(thm)],[f_1522_1]) ).
fof(f_1522_3,plain,
! [U_5866,U_5867] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5866),U_5867)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5866)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5867)),
inference(definitional_conversion,[status(esa)],[f_1522_2]) ).
cnf(f_1522_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5866),U_5867)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5866)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5867)),
inference(clausify,[status(thm)],[f_1522_3]) ).
fof(f_1523_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(f_1523_2,plain,
! [U_5869,U_5868] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5868),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5868),U_5869),
inference(variable_rename,[status(thm)],[f_1523_1]) ).
fof(f_1523_3,plain,
! [U_5868,U_5869] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5868),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5868),U_5869),
inference(definitional_conversion,[status(esa)],[f_1523_2]) ).
cnf(f_1523_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5868),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5868),U_5869),
inference(clausify,[status(thm)],[f_1523_3]) ).
fof(f_1524_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__int__def]) ).
fof(f_1524_2,plain,
! [U_5871,U_5870] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5870),U_5871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5870),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5871)),
inference(variable_rename,[status(thm)],[f_1524_1]) ).
fof(f_1524_3,plain,
! [U_5870,U_5871] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5870),U_5871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5870),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5871)),
inference(definitional_conversion,[status(esa)],[f_1524_2]) ).
cnf(f_1524_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5870),U_5871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5870),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5871)),
inference(clausify,[status(thm)],[f_1524_3]) ).
fof(f_1525_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(f_1525_2,plain,
! [U_5874,U_5873,U_5872] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5873),U_5874)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),U_5873)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),U_5874)),
inference(variable_rename,[status(thm)],[f_1525_1]) ).
fof(f_1525_3,plain,
! [U_5872,U_5873,U_5874] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5873),U_5874)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),U_5873)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),U_5874)),
inference(definitional_conversion,[status(esa)],[f_1525_2]) ).
cnf(f_1525_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5873),U_5874)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),U_5873)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5872),U_5874)),
inference(clausify,[status(thm)],[f_1525_3]) ).
fof(f_1526_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib]) ).
fof(f_1526_2,plain,
! [U_5877,U_5876,U_5875] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5875),U_5876)),U_5877) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5875),U_5877)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5876),U_5877)),
inference(variable_rename,[status(thm)],[f_1526_1]) ).
fof(f_1526_3,plain,
! [U_5875,U_5876,U_5877] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5875),U_5876)),U_5877) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5875),U_5877)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5876),U_5877)),
inference(definitional_conversion,[status(esa)],[f_1526_2]) ).
cnf(f_1526_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5875),U_5876)),U_5877) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5875),U_5877)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5876),U_5877)),
inference(clausify,[status(thm)],[f_1526_3]) ).
fof(f_1527_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) != c_Groups_Ozero__class_Ozero(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)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_equal__int__def]) ).
fof(f_1527_2,plain,
! [U_5879,U_5878] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_5878),U_5879))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5878),U_5879) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5878),U_5879) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_5878),U_5879)) ) ),
inference(variable_rename,[status(thm)],[f_1527_1]) ).
fof(f_1527_3,plain,
( ! [U_5883,U_5881] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_5881),U_5883))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5881),U_5883) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_5882,U_5880] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5880),U_5882) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_5880),U_5882)) ) ),
inference(miniscope,[status(thm)],[f_1527_2]) ).
fof(f_1527_4,plain,
( ! [U_5881,U_5883] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_5881),U_5883))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5881),U_5883) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_5882,U_5880] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5880),U_5882) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_5880),U_5882)) ) ),
inference(definitional_conversion,[status(esa)],[f_1527_3]) ).
cnf(f_1527_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5880),U_5882) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_5880),U_5882)) ),
inference(clausify,[status(thm)],[f_1527_4]) ).
cnf(f_1527_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_5881),U_5883))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5881),U_5883) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1527_4]) ).
fof(f_1528_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).
fof(f_1528_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_1528_1]) ).
cnf(f_1528_3,plain,
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),
inference(clausify,[status(thm)],[f_1528_2]) ).
fof(f_1529_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2]) ).
fof(f_1529_2,plain,
! [U_5886,U_5885,U_5884] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5886),U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5886),U_5885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5884),U_5885)) ),
inference(variable_rename,[status(thm)],[f_1529_1]) ).
fof(f_1529_3,plain,
! [U_5884,U_5885,U_5886] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5886),U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5886),U_5885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5884),U_5885)) ),
inference(definitional_conversion,[status(esa)],[f_1529_2]) ).
cnf(f_1529_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5886),U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5886),U_5885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5884),U_5885)) ),
inference(clausify,[status(thm)],[f_1529_3]) ).
fof(f_1530_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__bin__lemma]) ).
fof(f_1530_2,plain,
! [U_5888,U_5887] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5887),U_5888))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5887),U_5888)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5887),U_5888)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5887),U_5888)) ) ),
inference(variable_rename,[status(thm)],[f_1530_1]) ).
fof(f_1530_3,plain,
( ! [U_5892,U_5890] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5890),U_5892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5890),U_5892)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5891,U_5889] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5889),U_5891)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5889),U_5891)) ) ),
inference(miniscope,[status(thm)],[f_1530_2]) ).
fof(f_1530_4,plain,
( ! [U_5890,U_5892] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5890),U_5892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5890),U_5892)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5891,U_5889] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5889),U_5891)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5889),U_5891)) ) ),
inference(definitional_conversion,[status(esa)],[f_1530_3]) ).
cnf(f_1530_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5889),U_5891)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5889),U_5891)) ),
inference(clausify,[status(thm)],[f_1530_4]) ).
cnf(f_1530_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5890),U_5892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5890),U_5892)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1530_4]) ).
fof(f_1531_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
inference(fof_nnf,[status(thm)],[fact_zadd__0]) ).
fof(f_1531_2,plain,
! [U_5893] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5893) = U_5893,
inference(variable_rename,[status(thm)],[f_1531_1]) ).
fof(f_1531_3,plain,
! [U_5893] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5893) = U_5893,
inference(definitional_conversion,[status(esa)],[f_1531_2]) ).
cnf(f_1531_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5893) = U_5893,
inference(clausify,[status(thm)],[f_1531_3]) ).
fof(f_1532_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zadd__0__right]) ).
fof(f_1532_2,plain,
! [U_5894] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_5894,
inference(variable_rename,[status(thm)],[f_1532_1]) ).
fof(f_1532_3,plain,
! [U_5894] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_5894,
inference(definitional_conversion,[status(esa)],[f_1532_2]) ).
cnf(f_1532_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_5894,
inference(clausify,[status(thm)],[f_1532_3]) ).
fof(f_1533_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(f_1533_2,plain,
! [U_5895] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5895)),U_5895) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1533_1]) ).
fof(f_1533_3,plain,
! [U_5895] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5895)),U_5895) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1533_2]) ).
cnf(f_1533_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5895)),U_5895) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1533_3]) ).
fof(f_1534_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_odd__nonzero]) ).
fof(f_1534_2,plain,
! [U_5896] : 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)),U_5896)),U_5896) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1534_1]) ).
fof(f_1534_3,plain,
! [U_5896] : 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)),U_5896)),U_5896) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1534_2]) ).
cnf(f_1534_4,plain,
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)),U_5896)),U_5896) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1534_3]) ).
fof(f_1535_1,plain,
! [V_z_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).
fof(f_1535_2,plain,
! [U_5897] :
( ( 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)),U_5897)),U_5897)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5897),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5897),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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)),U_5897)),U_5897)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1535_1]) ).
fof(f_1535_3,plain,
( ! [U_5899] :
( 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)),U_5899)),U_5899)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5899),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5898] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5898),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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)),U_5898)),U_5898)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1535_2]) ).
fof(f_1535_4,plain,
( ! [U_5899] :
( 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)),U_5899)),U_5899)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5899),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5898] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5898),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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)),U_5898)),U_5898)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_1535_3]) ).
cnf(f_1535_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5898),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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)),U_5898)),U_5898)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1535_4]) ).
cnf(f_1535_6,plain,
( 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)),U_5899)),U_5899)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5899),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1535_4]) ).
fof(f_1536_1,plain,
! [V_z] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__0__less]) ).
fof(f_1536_2,plain,
! [U_5900] :
( 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)),U_5900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5900)) ),
inference(variable_rename,[status(thm)],[f_1536_1]) ).
fof(f_1536_3,plain,
! [U_5900] :
( 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)),U_5900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5900)) ),
inference(definitional_conversion,[status(esa)],[f_1536_2]) ).
cnf(f_1536_4,plain,
( 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)),U_5900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5900)) ),
inference(clausify,[status(thm)],[f_1536_3]) ).
fof(f_1537_1,plain,
! [V_z_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).
fof(f_1537_2,plain,
! [U_5901] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5901)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5901)) ) ),
inference(variable_rename,[status(thm)],[f_1537_1]) ).
fof(f_1537_3,plain,
( ! [U_5903] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5903)) )
& ! [U_5902] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5902)) ) ),
inference(miniscope,[status(thm)],[f_1537_2]) ).
fof(f_1537_4,plain,
( ! [U_5903] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5903)) )
& ! [U_5902] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5902)) ) ),
inference(definitional_conversion,[status(esa)],[f_1537_3]) ).
cnf(f_1537_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5902)) ),
inference(clausify,[status(thm)],[f_1537_4]) ).
cnf(f_1537_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5903)) ),
inference(clausify,[status(thm)],[f_1537_4]) ).
fof(f_1538_1,plain,
! [V_z_2,V_w_2] :
( ( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq]) ).
fof(f_1538_2,plain,
! [U_5905,U_5904] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5904),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5905),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5904),U_5905)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5904),U_5905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5904),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5905),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1538_1]) ).
fof(f_1538_3,plain,
( ! [U_5909,U_5907] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5907),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5909),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5907),U_5909)) )
& ! [U_5908,U_5906] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5906),U_5908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5908),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1538_2]) ).
fof(f_1538_4,plain,
( ! [U_5907,U_5909] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5907),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5909),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5907),U_5909)) )
& ! [U_5908,U_5906] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5906),U_5908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5908),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(definitional_conversion,[status(esa)],[f_1538_3]) ).
cnf(f_1538_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5906),U_5908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5908),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1538_4]) ).
cnf(f_1538_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5907),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5909),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5907),U_5909)) ),
inference(clausify,[status(thm)],[f_1538_4]) ).
fof(f_1539_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).
fof(f_1539_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1539_1]) ).
cnf(f_1539_3,plain,
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))),
inference(clausify,[status(thm)],[f_1539_2]) ).
fof(f_1540_1,plain,
! [V_n_2,V_m_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff]) ).
fof(f_1540_2,plain,
! [U_5911,U_5910] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5910),U_5911) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_5911 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_5910 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_5911 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_5910 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5910),U_5911) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5910)) ),
inference(variable_rename,[status(thm)],[f_1540_1]) ).
fof(f_1540_3,plain,
( ! [U_5910,U_5911] :
( U_5911 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP542(U_5910,U_5911) )
& ! [U_5910,U_5911] :
( U_5910 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP542(U_5910,U_5911) )
& ! [U_5910,U_5911] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5910),U_5911) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_5911 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_5910 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP543(U_5910,U_5911) )
& ! [U_5910,U_5911] :
( sP542(U_5910,U_5911)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5910),U_5911) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP543(U_5910,U_5911) )
& ! [U_5910,U_5911] :
( sP543(U_5910,U_5911)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5910)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP542,sP543])],[f_1540_2]) ).
cnf(f_1540_4,plain,
( sP543(U_5910,U_5911)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5910)) ),
inference(clausify,[status(thm)],[f_1540_3]) ).
cnf(f_1540_5,plain,
( sP542(U_5910,U_5911)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5910),U_5911) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP543(U_5910,U_5911) ),
inference(clausify,[status(thm)],[f_1540_3]) ).
cnf(f_1540_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5910),U_5911) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_5911 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_5910 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP543(U_5910,U_5911) ),
inference(clausify,[status(thm)],[f_1540_3]) ).
cnf(f_1540_7,plain,
( U_5910 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP542(U_5910,U_5911) ),
inference(clausify,[status(thm)],[f_1540_3]) ).
cnf(f_1540_8,plain,
( U_5911 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP542(U_5910,U_5911) ),
inference(clausify,[status(thm)],[f_1540_3]) ).
fof(f_1541_1,plain,
! [V_i] :
( ( ( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) ) )
| V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zsgn__def]) ).
fof(f_1541_2,plain,
! [U_5912] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5912) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5912)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5912) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5912)) ) )
| U_5912 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5912) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5912 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1541_1]) ).
fof(f_1541_3,plain,
( ! [U_5914] :
( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5914) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5914)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5914) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5914)) ) )
| U_5914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_5913] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5913) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5913 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1541_2]) ).
fof(f_1541_4,plain,
( ! [U_5914] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5914) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5914))
| ~ sP544(U_5914) )
& ! [U_5914] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5914) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5914))
| ~ sP544(U_5914) )
& ! [U_5914] :
( sP544(U_5914)
| U_5914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_5913] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5913) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5913 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP544])],[f_1541_3]) ).
cnf(f_1541_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5913) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5913 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1541_4]) ).
cnf(f_1541_6,plain,
( sP544(U_5914)
| U_5914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1541_4]) ).
cnf(f_1541_7,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5914) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5914))
| ~ sP544(U_5914) ),
inference(clausify,[status(thm)],[f_1541_4]) ).
cnf(f_1541_8,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_5914) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5914))
| ~ sP544(U_5914) ),
inference(clausify,[status(thm)],[f_1541_4]) ).
fof(f_1542_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(f_1542_2,plain,
! [U_5917,U_5916,U_5915] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5916),U_5917)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),U_5916)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),U_5917)),
inference(variable_rename,[status(thm)],[f_1542_1]) ).
fof(f_1542_3,plain,
! [U_5916,U_5917,U_5915] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5916),U_5917)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),U_5916)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),U_5917)),
inference(definitional_conversion,[status(esa)],[f_1542_2]) ).
cnf(f_1542_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5916),U_5917)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),U_5916)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5915),U_5917)),
inference(clausify,[status(thm)],[f_1542_3]) ).
fof(f_1543_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zpower__zpower]) ).
fof(f_1543_2,plain,
! [U_5920,U_5919,U_5918] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5918),U_5919)),U_5920) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5919),U_5920)),
inference(variable_rename,[status(thm)],[f_1543_1]) ).
fof(f_1543_3,plain,
! [U_5918,U_5919,U_5920] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5918),U_5919)),U_5920) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5919),U_5920)),
inference(definitional_conversion,[status(esa)],[f_1543_2]) ).
cnf(f_1543_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5918),U_5919)),U_5920) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5919),U_5920)),
inference(clausify,[status(thm)],[f_1543_3]) ).
fof(f_1544_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__power__not__zero]) ).
fof(f_1544_2,plain,
! [U_5923,U_5922,U_5921] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5921),U_5922),U_5923) != c_Groups_Ozero__class_Ozero(U_5921)
| U_5922 = c_Groups_Ozero__class_Ozero(U_5921)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5921) ),
inference(variable_rename,[status(thm)],[f_1544_1]) ).
fof(f_1544_3,plain,
! [U_5921,U_5922,U_5923] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5921),U_5922),U_5923) != c_Groups_Ozero__class_Ozero(U_5921)
| U_5922 = c_Groups_Ozero__class_Ozero(U_5921)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5921) ),
inference(definitional_conversion,[status(esa)],[f_1544_2]) ).
cnf(f_1544_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5921),U_5922),U_5923) != c_Groups_Ozero__class_Ozero(U_5921)
| U_5922 = c_Groups_Ozero__class_Ozero(U_5921)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5921) ),
inference(clausify,[status(thm)],[f_1544_3]) ).
fof(f_1545_1,plain,
! [V_n,V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Ocomm__monoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mult__distrib]) ).
fof(f_1545_2,plain,
! [U_5927,U_5926,U_5925,U_5924] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5925),U_5926)),U_5927) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5925),U_5927)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),U_5927))
| ~ class_Groups_Ocomm__monoid__mult(U_5924) ),
inference(variable_rename,[status(thm)],[f_1545_1]) ).
fof(f_1545_3,plain,
! [U_5924,U_5925,U_5926,U_5927] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5925),U_5926)),U_5927) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5925),U_5927)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),U_5927))
| ~ class_Groups_Ocomm__monoid__mult(U_5924) ),
inference(definitional_conversion,[status(esa)],[f_1545_2]) ).
cnf(f_1545_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5925),U_5926)),U_5927) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5925),U_5927)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),U_5927))
| ~ class_Groups_Ocomm__monoid__mult(U_5924) ),
inference(clausify,[status(thm)],[f_1545_3]) ).
fof(f_1546_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__commutes]) ).
fof(f_1546_2,plain,
! [U_5930,U_5929,U_5928] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),hAPP(hAPP(c_Power_Opower__class_Opower(U_5928),U_5929),U_5930)),U_5929) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5929),hAPP(hAPP(c_Power_Opower__class_Opower(U_5928),U_5929),U_5930))
| ~ class_Groups_Omonoid__mult(U_5928) ),
inference(variable_rename,[status(thm)],[f_1546_1]) ).
fof(f_1546_3,plain,
! [U_5928,U_5929,U_5930] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),hAPP(hAPP(c_Power_Opower__class_Opower(U_5928),U_5929),U_5930)),U_5929) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5929),hAPP(hAPP(c_Power_Opower__class_Opower(U_5928),U_5929),U_5930))
| ~ class_Groups_Omonoid__mult(U_5928) ),
inference(definitional_conversion,[status(esa)],[f_1546_2]) ).
cnf(f_1546_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),hAPP(hAPP(c_Power_Opower__class_Opower(U_5928),U_5929),U_5930)),U_5929) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5929),hAPP(hAPP(c_Power_Opower__class_Opower(U_5928),U_5929),U_5930))
| ~ class_Groups_Omonoid__mult(U_5928) ),
inference(clausify,[status(thm)],[f_1546_3]) ).
fof(f_1547_1,plain,
! [V_n,T_a] :
( 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)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one]) ).
fof(f_1547_2,plain,
! [U_5932,U_5931] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5931),c_Groups_Oone__class_Oone(U_5931)),U_5932) = c_Groups_Oone__class_Oone(U_5931)
| ~ class_Groups_Omonoid__mult(U_5931) ),
inference(variable_rename,[status(thm)],[f_1547_1]) ).
fof(f_1547_3,plain,
! [U_5931,U_5932] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5931),c_Groups_Oone__class_Oone(U_5931)),U_5932) = c_Groups_Oone__class_Oone(U_5931)
| ~ class_Groups_Omonoid__mult(U_5931) ),
inference(definitional_conversion,[status(esa)],[f_1547_2]) ).
cnf(f_1547_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5931),c_Groups_Oone__class_Oone(U_5931)),U_5932) = c_Groups_Oone__class_Oone(U_5931)
| ~ class_Groups_Omonoid__mult(U_5931) ),
inference(clausify,[status(thm)],[f_1547_3]) ).
fof(f_1548_1,plain,
! [V_n,V_m,V_a,T_a] :
( 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)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mult]) ).
fof(f_1548_2,plain,
! [U_5936,U_5935,U_5934,U_5933] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),U_5934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5935),U_5936)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),U_5934),U_5935)),U_5936)
| ~ class_Groups_Omonoid__mult(U_5933) ),
inference(variable_rename,[status(thm)],[f_1548_1]) ).
fof(f_1548_3,plain,
! [U_5933,U_5934,U_5935,U_5936] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),U_5934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5935),U_5936)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),U_5934),U_5935)),U_5936)
| ~ class_Groups_Omonoid__mult(U_5933) ),
inference(definitional_conversion,[status(esa)],[f_1548_2]) ).
cnf(f_1548_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),U_5934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5935),U_5936)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),U_5934),U_5935)),U_5936)
| ~ class_Groups_Omonoid__mult(U_5933) ),
inference(clausify,[status(thm)],[f_1548_3]) ).
fof(f_1549_1,plain,
! [V_n,V_b,V_a,T_a] :
( 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))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__divide]) ).
fof(f_1549_2,plain,
! [U_5940,U_5939,U_5938,U_5937] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),U_5938),U_5939)),U_5940) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),U_5938),U_5940)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),U_5939),U_5940))
| ~ class_Fields_Ofield__inverse__zero(U_5937) ),
inference(variable_rename,[status(thm)],[f_1549_1]) ).
fof(f_1549_3,plain,
! [U_5937,U_5938,U_5939,U_5940] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),U_5938),U_5939)),U_5940) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),U_5938),U_5940)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),U_5939),U_5940))
| ~ class_Fields_Ofield__inverse__zero(U_5937) ),
inference(definitional_conversion,[status(esa)],[f_1549_2]) ).
cnf(f_1549_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),U_5938),U_5939)),U_5940) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),U_5938),U_5940)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5937),U_5939),U_5940))
| ~ class_Fields_Ofield__inverse__zero(U_5937) ),
inference(clausify,[status(thm)],[f_1549_3]) ).
fof(f_1550_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one__right]) ).
fof(f_1550_2,plain,
! [U_5942,U_5941] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5941),U_5942),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5942
| ~ class_Groups_Omonoid__mult(U_5941) ),
inference(variable_rename,[status(thm)],[f_1550_1]) ).
fof(f_1550_3,plain,
! [U_5942,U_5941] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5941),U_5942),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5942
| ~ class_Groups_Omonoid__mult(U_5941) ),
inference(definitional_conversion,[status(esa)],[f_1550_2]) ).
cnf(f_1550_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5941),U_5942),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5942
| ~ class_Groups_Omonoid__mult(U_5941) ),
inference(clausify,[status(thm)],[f_1550_3]) ).
fof(f_1551_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power]) ).
fof(f_1551_2,plain,
! [U_5945,U_5944,U_5943] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5943),c_Groups_Ozero__class_Ozero(U_5943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5943),U_5944),U_5945)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5943),c_Groups_Ozero__class_Ozero(U_5943)),U_5944))
| ~ class_Rings_Olinordered__semidom(U_5943) ),
inference(variable_rename,[status(thm)],[f_1551_1]) ).
fof(f_1551_3,plain,
! [U_5943,U_5944,U_5945] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5943),c_Groups_Ozero__class_Ozero(U_5943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5943),U_5944),U_5945)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5943),c_Groups_Ozero__class_Ozero(U_5943)),U_5944))
| ~ class_Rings_Olinordered__semidom(U_5943) ),
inference(definitional_conversion,[status(esa)],[f_1551_2]) ).
cnf(f_1551_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5943),c_Groups_Ozero__class_Ozero(U_5943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5943),U_5944),U_5945)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5943),c_Groups_Ozero__class_Ozero(U_5943)),U_5944))
| ~ class_Rings_Olinordered__semidom(U_5943) ),
inference(clausify,[status(thm)],[f_1551_3]) ).
fof(f_1552_1,plain,
! [V_n,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mono]) ).
fof(f_1552_2,plain,
! [U_5949,U_5948,U_5947,U_5946] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),hAPP(hAPP(c_Power_Opower__class_Opower(U_5946),U_5947),U_5949)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5946),U_5948),U_5949)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),U_5947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),U_5947),U_5948))
| ~ class_Rings_Olinordered__semidom(U_5946) ),
inference(variable_rename,[status(thm)],[f_1552_1]) ).
fof(f_1552_3,plain,
! [U_5946,U_5947,U_5948,U_5949] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),hAPP(hAPP(c_Power_Opower__class_Opower(U_5946),U_5947),U_5949)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5946),U_5948),U_5949)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),U_5947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),U_5947),U_5948))
| ~ class_Rings_Olinordered__semidom(U_5946) ),
inference(definitional_conversion,[status(esa)],[f_1552_2]) ).
cnf(f_1552_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),hAPP(hAPP(c_Power_Opower__class_Opower(U_5946),U_5947),U_5949)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5946),U_5948),U_5949)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),U_5947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),U_5947),U_5948))
| ~ class_Rings_Olinordered__semidom(U_5946) ),
inference(clausify,[status(thm)],[f_1552_3]) ).
fof(f_1553_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power]) ).
fof(f_1553_2,plain,
! [U_5952,U_5951,U_5950] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5950),U_5951),U_5952)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),U_5951))
| ~ class_Rings_Olinordered__semidom(U_5950) ),
inference(variable_rename,[status(thm)],[f_1553_1]) ).
fof(f_1553_3,plain,
! [U_5951,U_5950,U_5952] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5950),U_5951),U_5952)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),U_5951))
| ~ class_Rings_Olinordered__semidom(U_5950) ),
inference(definitional_conversion,[status(esa)],[f_1553_2]) ).
cnf(f_1553_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5950),U_5951),U_5952)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),U_5951))
| ~ class_Rings_Olinordered__semidom(U_5950) ),
inference(clausify,[status(thm)],[f_1553_3]) ).
fof(f_1554_1,plain,
! [V_n_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
| hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Ozero__neq__one(T_b)
| ~ class_Rings_Ono__zero__divisors(T_b)
| ~ class_Rings_Omult__zero(T_b)
| ~ class_Power_Opower(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).
fof(f_1554_2,plain,
! [U_5955,U_5954,U_5953] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5953),U_5954),U_5955) = c_Groups_Ozero__class_Ozero(U_5953)
| U_5955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5954 != c_Groups_Ozero__class_Ozero(U_5953) )
& ( ( U_5955 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5954 = c_Groups_Ozero__class_Ozero(U_5953) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5953),U_5954),U_5955) != c_Groups_Ozero__class_Ozero(U_5953) ) )
| ~ class_Rings_Ozero__neq__one(U_5953)
| ~ class_Rings_Ono__zero__divisors(U_5953)
| ~ class_Rings_Omult__zero(U_5953)
| ~ class_Power_Opower(U_5953) ),
inference(variable_rename,[status(thm)],[f_1554_1]) ).
fof(f_1554_3,plain,
( ! [U_5953,U_5954,U_5955] :
( U_5955 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP545(U_5953,U_5954,U_5955) )
& ! [U_5953,U_5954,U_5955] :
( U_5954 = c_Groups_Ozero__class_Ozero(U_5953)
| ~ sP545(U_5953,U_5954,U_5955) )
& ! [U_5953,U_5954,U_5955] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5953),U_5954),U_5955) = c_Groups_Ozero__class_Ozero(U_5953)
| U_5955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5954 != c_Groups_Ozero__class_Ozero(U_5953)
| ~ sP546(U_5953,U_5954,U_5955) )
& ! [U_5953,U_5954,U_5955] :
( sP545(U_5953,U_5954,U_5955)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5953),U_5954),U_5955) != c_Groups_Ozero__class_Ozero(U_5953)
| ~ sP546(U_5953,U_5954,U_5955) )
& ! [U_5953,U_5954,U_5955] :
( sP546(U_5953,U_5954,U_5955)
| ~ class_Rings_Ozero__neq__one(U_5953)
| ~ class_Rings_Ono__zero__divisors(U_5953)
| ~ class_Rings_Omult__zero(U_5953)
| ~ class_Power_Opower(U_5953) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP545,sP546])],[f_1554_2]) ).
cnf(f_1554_4,plain,
( sP546(U_5953,U_5954,U_5955)
| ~ class_Rings_Ozero__neq__one(U_5953)
| ~ class_Rings_Ono__zero__divisors(U_5953)
| ~ class_Rings_Omult__zero(U_5953)
| ~ class_Power_Opower(U_5953) ),
inference(clausify,[status(thm)],[f_1554_3]) ).
cnf(f_1554_5,plain,
( sP545(U_5953,U_5954,U_5955)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5953),U_5954),U_5955) != c_Groups_Ozero__class_Ozero(U_5953)
| ~ sP546(U_5953,U_5954,U_5955) ),
inference(clausify,[status(thm)],[f_1554_3]) ).
cnf(f_1554_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5953),U_5954),U_5955) = c_Groups_Ozero__class_Ozero(U_5953)
| U_5955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5954 != c_Groups_Ozero__class_Ozero(U_5953)
| ~ sP546(U_5953,U_5954,U_5955) ),
inference(clausify,[status(thm)],[f_1554_3]) ).
cnf(f_1554_7,plain,
( U_5954 = c_Groups_Ozero__class_Ozero(U_5953)
| ~ sP545(U_5953,U_5954,U_5955) ),
inference(clausify,[status(thm)],[f_1554_3]) ).
cnf(f_1554_8,plain,
( U_5955 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP545(U_5953,U_5954,U_5955) ),
inference(clausify,[status(thm)],[f_1554_3]) ).
fof(f_1555_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__le__power]) ).
fof(f_1555_2,plain,
! [U_5958,U_5957,U_5956] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5956),c_Groups_Oone__class_Oone(U_5956)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5956),U_5957),U_5958)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5956),c_Groups_Oone__class_Oone(U_5956)),U_5957))
| ~ class_Rings_Olinordered__semidom(U_5956) ),
inference(variable_rename,[status(thm)],[f_1555_1]) ).
fof(f_1555_3,plain,
! [U_5958,U_5957,U_5956] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5956),c_Groups_Oone__class_Oone(U_5956)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5956),U_5957),U_5958)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5956),c_Groups_Oone__class_Oone(U_5956)),U_5957))
| ~ class_Rings_Olinordered__semidom(U_5956) ),
inference(definitional_conversion,[status(esa)],[f_1555_2]) ).
cnf(f_1555_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5956),c_Groups_Oone__class_Oone(U_5956)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5956),U_5957),U_5958)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5956),c_Groups_Oone__class_Oone(U_5956)),U_5957))
| ~ class_Rings_Olinordered__semidom(U_5956) ),
inference(clausify,[status(thm)],[f_1555_3]) ).
fof(f_1556_1,plain,
! [V_n,T_a] :
( 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)
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0__Suc]) ).
fof(f_1556_2,plain,
! [U_5960,U_5959] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5959),c_Groups_Ozero__class_Ozero(U_5959)),hAPP(c_Nat_OSuc,U_5960)) = c_Groups_Ozero__class_Ozero(U_5959)
| ~ class_Rings_Osemiring__0(U_5959)
| ~ class_Power_Opower(U_5959) ),
inference(variable_rename,[status(thm)],[f_1556_1]) ).
fof(f_1556_3,plain,
! [U_5959,U_5960] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5959),c_Groups_Ozero__class_Ozero(U_5959)),hAPP(c_Nat_OSuc,U_5960)) = c_Groups_Ozero__class_Ozero(U_5959)
| ~ class_Rings_Osemiring__0(U_5959)
| ~ class_Power_Opower(U_5959) ),
inference(definitional_conversion,[status(esa)],[f_1556_2]) ).
cnf(f_1556_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5959),c_Groups_Ozero__class_Ozero(U_5959)),hAPP(c_Nat_OSuc,U_5960)) = c_Groups_Ozero__class_Ozero(U_5959)
| ~ class_Rings_Osemiring__0(U_5959)
| ~ class_Power_Opower(U_5959) ),
inference(clausify,[status(thm)],[f_1556_3]) ).
fof(f_1557_1,plain,
! [V_n_2,V_m_2,V_a_2,T_b] :
( ( ( 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)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| 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) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).
fof(f_1557_2,plain,
! [U_5964,U_5963,U_5962,U_5961] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5963) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5964)
| U_5963 != U_5964 )
& ( U_5963 = U_5964
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5963) != hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5964) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),c_Groups_Oone__class_Oone(U_5961)),U_5962))
| ~ class_Rings_Olinordered__semidom(U_5961) ),
inference(variable_rename,[status(thm)],[f_1557_1]) ).
fof(f_1557_3,plain,
( ! [U_5961,U_5962,U_5963,U_5964] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5963) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5964)
| U_5963 != U_5964
| ~ sP547(U_5961,U_5962,U_5963,U_5964) )
& ! [U_5961,U_5962,U_5963,U_5964] :
( U_5963 = U_5964
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5963) != hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5964)
| ~ sP547(U_5961,U_5962,U_5963,U_5964) )
& ! [U_5961,U_5962,U_5963,U_5964] :
( sP547(U_5961,U_5962,U_5963,U_5964)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),c_Groups_Oone__class_Oone(U_5961)),U_5962))
| ~ class_Rings_Olinordered__semidom(U_5961) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP547])],[f_1557_2]) ).
cnf(f_1557_4,plain,
( sP547(U_5961,U_5962,U_5963,U_5964)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),c_Groups_Oone__class_Oone(U_5961)),U_5962))
| ~ class_Rings_Olinordered__semidom(U_5961) ),
inference(clausify,[status(thm)],[f_1557_3]) ).
cnf(f_1557_5,plain,
( U_5963 = U_5964
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5963) != hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5964)
| ~ sP547(U_5961,U_5962,U_5963,U_5964) ),
inference(clausify,[status(thm)],[f_1557_3]) ).
cnf(f_1557_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5963) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5961),U_5962),U_5964)
| U_5963 != U_5964
| ~ sP547(U_5961,U_5962,U_5963,U_5964) ),
inference(clausify,[status(thm)],[f_1557_3]) ).
fof(f_1558_1,plain,
! [V_n,V_a,T_a] :
( 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)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc2]) ).
fof(f_1558_2,plain,
! [U_5967,U_5966,U_5965] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5965),U_5966),hAPP(c_Nat_OSuc,U_5967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5965),hAPP(hAPP(c_Power_Opower__class_Opower(U_5965),U_5966),U_5967)),U_5966)
| ~ class_Groups_Omonoid__mult(U_5965) ),
inference(variable_rename,[status(thm)],[f_1558_1]) ).
fof(f_1558_3,plain,
! [U_5966,U_5965,U_5967] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5965),U_5966),hAPP(c_Nat_OSuc,U_5967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5965),hAPP(hAPP(c_Power_Opower__class_Opower(U_5965),U_5966),U_5967)),U_5966)
| ~ class_Groups_Omonoid__mult(U_5965) ),
inference(definitional_conversion,[status(esa)],[f_1558_2]) ).
cnf(f_1558_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5965),U_5966),hAPP(c_Nat_OSuc,U_5967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5965),hAPP(hAPP(c_Power_Opower__class_Opower(U_5965),U_5966),U_5967)),U_5966)
| ~ class_Groups_Omonoid__mult(U_5965) ),
inference(clausify,[status(thm)],[f_1558_3]) ).
fof(f_1559_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc]) ).
fof(f_1559_2,plain,
! [U_5970,U_5969,U_5968] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5968),U_5969),hAPP(c_Nat_OSuc,U_5970)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5968),U_5969),hAPP(hAPP(c_Power_Opower__class_Opower(U_5968),U_5969),U_5970))
| ~ class_Power_Opower(U_5968) ),
inference(variable_rename,[status(thm)],[f_1559_1]) ).
fof(f_1559_3,plain,
! [U_5968,U_5969,U_5970] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5968),U_5969),hAPP(c_Nat_OSuc,U_5970)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5968),U_5969),hAPP(hAPP(c_Power_Opower__class_Opower(U_5968),U_5969),U_5970))
| ~ class_Power_Opower(U_5968) ),
inference(definitional_conversion,[status(esa)],[f_1559_2]) ).
cnf(f_1559_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5968),U_5969),hAPP(c_Nat_OSuc,U_5970)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5968),U_5969),hAPP(hAPP(c_Power_Opower__class_Opower(U_5968),U_5969),U_5970))
| ~ class_Power_Opower(U_5968) ),
inference(clausify,[status(thm)],[f_1559_3]) ).
fof(f_1560_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0]) ).
fof(f_1560_2,plain,
! [U_5972,U_5971] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5971),U_5972),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_5971)
| ~ class_Power_Opower(U_5971) ),
inference(variable_rename,[status(thm)],[f_1560_1]) ).
fof(f_1560_3,plain,
! [U_5971,U_5972] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5971),U_5972),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_5971)
| ~ class_Power_Opower(U_5971) ),
inference(definitional_conversion,[status(esa)],[f_1560_2]) ).
cnf(f_1560_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5971),U_5972),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_5971)
| ~ class_Power_Opower(U_5971) ),
inference(clausify,[status(thm)],[f_1560_3]) ).
fof(f_1561_1,plain,
! [V_n,V_m,V_a,T_a] :
( 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))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__add]) ).
fof(f_1561_2,plain,
! [U_5976,U_5975,U_5974,U_5973] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5975),U_5976)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5973),hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),U_5975)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),U_5976))
| ~ class_Groups_Omonoid__mult(U_5973) ),
inference(variable_rename,[status(thm)],[f_1561_1]) ).
fof(f_1561_3,plain,
! [U_5973,U_5974,U_5975,U_5976] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5975),U_5976)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5973),hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),U_5975)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),U_5976))
| ~ class_Groups_Omonoid__mult(U_5973) ),
inference(definitional_conversion,[status(esa)],[f_1561_2]) ).
cnf(f_1561_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5975),U_5976)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5973),hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),U_5975)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5973),U_5974),U_5976))
| ~ class_Groups_Omonoid__mult(U_5973) ),
inference(clausify,[status(thm)],[f_1561_3]) ).
fof(f_1562_1,plain,
! [V_n,V_a,V_b,T_a] :
( 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))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide]) ).
fof(f_1562_2,plain,
! [U_5980,U_5979,U_5978,U_5977] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),U_5979),U_5978)),U_5980) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),U_5979),U_5980)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),U_5978),U_5980))
| U_5978 = c_Groups_Ozero__class_Ozero(U_5977)
| ~ class_Fields_Ofield(U_5977) ),
inference(variable_rename,[status(thm)],[f_1562_1]) ).
fof(f_1562_3,plain,
! [U_5977,U_5978,U_5979,U_5980] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),U_5979),U_5978)),U_5980) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),U_5979),U_5980)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),U_5978),U_5980))
| U_5978 = c_Groups_Ozero__class_Ozero(U_5977)
| ~ class_Fields_Ofield(U_5977) ),
inference(definitional_conversion,[status(esa)],[f_1562_2]) ).
cnf(f_1562_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),U_5979),U_5978)),U_5980) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),U_5979),U_5980)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5977),U_5978),U_5980))
| U_5978 = c_Groups_Ozero__class_Ozero(U_5977)
| ~ class_Fields_Ofield(U_5977) ),
inference(clausify,[status(thm)],[f_1562_3]) ).
fof(f_1563_1,plain,
! [V_n,V_a,T_a] :
( 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)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one__over]) ).
fof(f_1563_2,plain,
! [U_5983,U_5982,U_5981] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),c_Groups_Oone__class_Oone(U_5981)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5981),U_5982),U_5983)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),c_Groups_Oone__class_Oone(U_5981)),U_5982)),U_5983)
| ~ class_Fields_Ofield__inverse__zero(U_5981) ),
inference(variable_rename,[status(thm)],[f_1563_1]) ).
fof(f_1563_3,plain,
! [U_5981,U_5982,U_5983] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),c_Groups_Oone__class_Oone(U_5981)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5981),U_5982),U_5983)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),c_Groups_Oone__class_Oone(U_5981)),U_5982)),U_5983)
| ~ class_Fields_Ofield__inverse__zero(U_5981) ),
inference(definitional_conversion,[status(esa)],[f_1563_2]) ).
cnf(f_1563_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),c_Groups_Oone__class_Oone(U_5981)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5981),U_5982),U_5983)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),c_Groups_Oone__class_Oone(U_5981)),U_5982)),U_5983)
| ~ class_Fields_Ofield__inverse__zero(U_5981) ),
inference(clausify,[status(thm)],[f_1563_3]) ).
fof(f_1564_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_power__Suc__0]) ).
fof(f_1564_2,plain,
! [U_5984] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5984) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_1564_1]) ).
fof(f_1564_3,plain,
! [U_5984] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5984) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_1564_2]) ).
cnf(f_1564_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5984) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1564_3]) ).
fof(f_1565_1,plain,
! [V_m_2,V_x_2] :
( ( 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))
| ( V_x_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff]) ).
fof(f_1565_2,plain,
! [U_5986,U_5985] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5985),U_5986) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_5985 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_5986 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_5985 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_5986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5985),U_5986) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1565_1]) ).
fof(f_1565_3,plain,
( ! [U_5990,U_5988] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5988),U_5990) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_5988 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_5990 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_5989,U_5987] :
( U_5987 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_5989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5987),U_5989) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1565_2]) ).
fof(f_1565_4,plain,
( ! [U_5988,U_5990] :
( U_5988 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP548(U_5988,U_5990) )
& ! [U_5988,U_5990] :
( U_5990 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP548(U_5988,U_5990) )
& ! [U_5988,U_5990] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5988),U_5990) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP548(U_5988,U_5990) )
& ! [U_5987,U_5989] :
( U_5987 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_5989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5987),U_5989) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP548])],[f_1565_3]) ).
cnf(f_1565_5,plain,
( U_5987 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_5989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5987),U_5989) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1565_4]) ).
cnf(f_1565_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5988),U_5990) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP548(U_5988,U_5990) ),
inference(clausify,[status(thm)],[f_1565_4]) ).
cnf(f_1565_7,plain,
( U_5990 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP548(U_5988,U_5990) ),
inference(clausify,[status(thm)],[f_1565_4]) ).
cnf(f_1565_8,plain,
( U_5988 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP548(U_5988,U_5990) ),
inference(clausify,[status(thm)],[f_1565_4]) ).
fof(f_1566_1,plain,
! [V_n,V_m,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) ),
inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less]) ).
fof(f_1566_2,plain,
! [U_5993,U_5992,U_5991] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5992),U_5993))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5991),U_5992)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5991),U_5993)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5991)) ),
inference(variable_rename,[status(thm)],[f_1566_1]) ).
fof(f_1566_3,plain,
! [U_5991,U_5993,U_5992] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5992),U_5993))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5991),U_5992)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5991),U_5993)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5991)) ),
inference(definitional_conversion,[status(esa)],[f_1566_2]) ).
cnf(f_1566_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5992),U_5993))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5991),U_5992)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5991),U_5993)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5991)) ),
inference(clausify,[status(thm)],[f_1566_3]) ).
fof(f_1567_1,plain,
! [V_n_2,V_x_2] :
( ( 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)))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).
fof(f_1567_2,plain,
! [U_5995,U_5994] :
( ( 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),U_5994),U_5995)))
| ( U_5995 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5994)) ) )
& ( U_5995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5994))
| ~ 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),U_5994),U_5995))) ) ),
inference(variable_rename,[status(thm)],[f_1567_1]) ).
fof(f_1567_3,plain,
( ! [U_5999,U_5997] :
( 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),U_5997),U_5999)))
| ( U_5999 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5997)) ) )
& ! [U_5998,U_5996] :
( U_5998 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5996))
| ~ 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),U_5996),U_5998))) ) ),
inference(miniscope,[status(thm)],[f_1567_2]) ).
fof(f_1567_4,plain,
( ! [U_5999,U_5997] :
( U_5999 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP549(U_5999,U_5997) )
& ! [U_5999,U_5997] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5997))
| ~ sP549(U_5999,U_5997) )
& ! [U_5999,U_5997] :
( 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),U_5997),U_5999)))
| sP549(U_5999,U_5997) )
& ! [U_5998,U_5996] :
( U_5998 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5996))
| ~ 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),U_5996),U_5998))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP549])],[f_1567_3]) ).
cnf(f_1567_5,plain,
( U_5998 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5996))
| ~ 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),U_5996),U_5998))) ),
inference(clausify,[status(thm)],[f_1567_4]) ).
cnf(f_1567_6,plain,
( 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),U_5997),U_5999)))
| sP549(U_5999,U_5997) ),
inference(clausify,[status(thm)],[f_1567_4]) ).
cnf(f_1567_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5997))
| ~ sP549(U_5999,U_5997) ),
inference(clausify,[status(thm)],[f_1567_4]) ).
cnf(f_1567_8,plain,
( U_5999 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP549(U_5999,U_5997) ),
inference(clausify,[status(thm)],[f_1567_4]) ).
fof(f_1568_1,plain,
! [V_b,V_n,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ 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)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base]) ).
fof(f_1568_2,plain,
! [U_6003,U_6002,U_6001,U_6000] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6000),U_6001),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6000),c_Groups_Ozero__class_Ozero(U_6000)),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6000),hAPP(hAPP(c_Power_Opower__class_Opower(U_6000),U_6001),U_6002)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6000),U_6003),U_6002)))
| ~ class_Rings_Olinordered__semidom(U_6000) ),
inference(variable_rename,[status(thm)],[f_1568_1]) ).
fof(f_1568_3,plain,
! [U_6000,U_6002,U_6001,U_6003] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6000),U_6001),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6000),c_Groups_Ozero__class_Ozero(U_6000)),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6000),hAPP(hAPP(c_Power_Opower__class_Opower(U_6000),U_6001),U_6002)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6000),U_6003),U_6002)))
| ~ class_Rings_Olinordered__semidom(U_6000) ),
inference(definitional_conversion,[status(esa)],[f_1568_2]) ).
cnf(f_1568_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6000),U_6001),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6000),c_Groups_Ozero__class_Ozero(U_6000)),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6000),hAPP(hAPP(c_Power_Opower__class_Opower(U_6000),U_6001),U_6002)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6000),U_6003),U_6002)))
| ~ class_Rings_Olinordered__semidom(U_6000) ),
inference(clausify,[status(thm)],[f_1568_3]) ).
fof(f_1569_1,plain,
! [V_b,V_n,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ 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))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base]) ).
fof(f_1569_2,plain,
! [U_6007,U_6006,U_6005,U_6004] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),U_6005),U_6007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),c_Groups_Ozero__class_Ozero(U_6004)),U_6007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),hAPP(hAPP(c_Power_Opower__class_Opower(U_6004),U_6005),hAPP(c_Nat_OSuc,U_6006))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6004),U_6007),hAPP(c_Nat_OSuc,U_6006))))
| ~ class_Rings_Olinordered__semidom(U_6004) ),
inference(variable_rename,[status(thm)],[f_1569_1]) ).
fof(f_1569_3,plain,
! [U_6004,U_6005,U_6006,U_6007] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),U_6005),U_6007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),c_Groups_Ozero__class_Ozero(U_6004)),U_6007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),hAPP(hAPP(c_Power_Opower__class_Opower(U_6004),U_6005),hAPP(c_Nat_OSuc,U_6006))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6004),U_6007),hAPP(c_Nat_OSuc,U_6006))))
| ~ class_Rings_Olinordered__semidom(U_6004) ),
inference(definitional_conversion,[status(esa)],[f_1569_2]) ).
cnf(f_1569_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),U_6005),U_6007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),c_Groups_Ozero__class_Ozero(U_6004)),U_6007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6004),hAPP(hAPP(c_Power_Opower__class_Opower(U_6004),U_6005),hAPP(c_Nat_OSuc,U_6006))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6004),U_6007),hAPP(c_Nat_OSuc,U_6006))))
| ~ class_Rings_Olinordered__semidom(U_6004) ),
inference(clausify,[status(thm)],[f_1569_3]) ).
fof(f_1570_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_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))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__base]) ).
fof(f_1570_2,plain,
! [U_6011,U_6010,U_6009,U_6008] :
( U_6009 = U_6011
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6008),c_Groups_Ozero__class_Ozero(U_6008)),U_6011))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6008),c_Groups_Ozero__class_Ozero(U_6008)),U_6009))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6008),U_6009),hAPP(c_Nat_OSuc,U_6010)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6008),U_6011),hAPP(c_Nat_OSuc,U_6010))
| ~ class_Rings_Olinordered__semidom(U_6008) ),
inference(variable_rename,[status(thm)],[f_1570_1]) ).
fof(f_1570_3,plain,
! [U_6008,U_6009,U_6010,U_6011] :
( U_6009 = U_6011
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6008),c_Groups_Ozero__class_Ozero(U_6008)),U_6011))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6008),c_Groups_Ozero__class_Ozero(U_6008)),U_6009))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6008),U_6009),hAPP(c_Nat_OSuc,U_6010)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6008),U_6011),hAPP(c_Nat_OSuc,U_6010))
| ~ class_Rings_Olinordered__semidom(U_6008) ),
inference(definitional_conversion,[status(esa)],[f_1570_2]) ).
cnf(f_1570_4,plain,
( U_6009 = U_6011
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6008),c_Groups_Ozero__class_Ozero(U_6008)),U_6011))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6008),c_Groups_Ozero__class_Ozero(U_6008)),U_6009))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6008),U_6009),hAPP(c_Nat_OSuc,U_6010)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6008),U_6011),hAPP(c_Nat_OSuc,U_6010))
| ~ class_Rings_Olinordered__semidom(U_6008) ),
inference(clausify,[status(thm)],[f_1570_3]) ).
fof(f_1571_1,plain,
! [V_n,V_a,T_a] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc]) ).
fof(f_1571_2,plain,
! [U_6014,U_6013,U_6012] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6012),hAPP(hAPP(c_Power_Opower__class_Opower(U_6012),U_6013),U_6014)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6012),U_6013),hAPP(hAPP(c_Power_Opower__class_Opower(U_6012),U_6013),U_6014))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6012),c_Groups_Oone__class_Oone(U_6012)),U_6013))
| ~ class_Rings_Olinordered__semidom(U_6012) ),
inference(variable_rename,[status(thm)],[f_1571_1]) ).
fof(f_1571_3,plain,
! [U_6014,U_6013,U_6012] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6012),hAPP(hAPP(c_Power_Opower__class_Opower(U_6012),U_6013),U_6014)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6012),U_6013),hAPP(hAPP(c_Power_Opower__class_Opower(U_6012),U_6013),U_6014))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6012),c_Groups_Oone__class_Oone(U_6012)),U_6013))
| ~ class_Rings_Olinordered__semidom(U_6012) ),
inference(definitional_conversion,[status(esa)],[f_1571_2]) ).
cnf(f_1571_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6012),hAPP(hAPP(c_Power_Opower__class_Opower(U_6012),U_6013),U_6014)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6012),U_6013),hAPP(hAPP(c_Power_Opower__class_Opower(U_6012),U_6013),U_6014))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6012),c_Groups_Oone__class_Oone(U_6012)),U_6013))
| ~ class_Rings_Olinordered__semidom(U_6012) ),
inference(clausify,[status(thm)],[f_1571_3]) ).
fof(f_1572_1,plain,
! [V_n,V_a,T_a] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma]) ).
fof(f_1572_2,plain,
! [U_6017,U_6016,U_6015] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6015),c_Groups_Oone__class_Oone(U_6015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6015),U_6016),hAPP(hAPP(c_Power_Opower__class_Opower(U_6015),U_6016),U_6017))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6015),c_Groups_Oone__class_Oone(U_6015)),U_6016))
| ~ class_Rings_Olinordered__semidom(U_6015) ),
inference(variable_rename,[status(thm)],[f_1572_1]) ).
fof(f_1572_3,plain,
! [U_6015,U_6016,U_6017] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6015),c_Groups_Oone__class_Oone(U_6015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6015),U_6016),hAPP(hAPP(c_Power_Opower__class_Opower(U_6015),U_6016),U_6017))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6015),c_Groups_Oone__class_Oone(U_6015)),U_6016))
| ~ class_Rings_Olinordered__semidom(U_6015) ),
inference(definitional_conversion,[status(esa)],[f_1572_2]) ).
cnf(f_1572_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6015),c_Groups_Oone__class_Oone(U_6015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6015),U_6016),hAPP(hAPP(c_Power_Opower__class_Opower(U_6015),U_6016),U_6017))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6015),c_Groups_Oone__class_Oone(U_6015)),U_6016))
| ~ class_Rings_Olinordered__semidom(U_6015) ),
inference(clausify,[status(thm)],[f_1572_3]) ).
fof(f_1573_1,plain,
! [V_n,T_a] :
( ( ( 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)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( 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)
| V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0__left]) ).
fof(f_1573_2,plain,
! [U_6019,U_6018] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6018),c_Groups_Ozero__class_Ozero(U_6018)),U_6019) = c_Groups_Ozero__class_Ozero(U_6018)
| U_6019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6018),c_Groups_Ozero__class_Ozero(U_6018)),U_6019) = c_Groups_Oone__class_Oone(U_6018)
| U_6019 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_6018)
| ~ class_Power_Opower(U_6018) ),
inference(variable_rename,[status(thm)],[f_1573_1]) ).
fof(f_1573_3,plain,
( ! [U_6018,U_6019] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6018),c_Groups_Ozero__class_Ozero(U_6018)),U_6019) = c_Groups_Ozero__class_Ozero(U_6018)
| U_6019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP550(U_6018,U_6019) )
& ! [U_6018,U_6019] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6018),c_Groups_Ozero__class_Ozero(U_6018)),U_6019) = c_Groups_Oone__class_Oone(U_6018)
| U_6019 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP550(U_6018,U_6019) )
& ! [U_6018,U_6019] :
( sP550(U_6018,U_6019)
| ~ class_Rings_Osemiring__0(U_6018)
| ~ class_Power_Opower(U_6018) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP550])],[f_1573_2]) ).
cnf(f_1573_4,plain,
( sP550(U_6018,U_6019)
| ~ class_Rings_Osemiring__0(U_6018)
| ~ class_Power_Opower(U_6018) ),
inference(clausify,[status(thm)],[f_1573_3]) ).
cnf(f_1573_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6018),c_Groups_Ozero__class_Ozero(U_6018)),U_6019) = c_Groups_Oone__class_Oone(U_6018)
| U_6019 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP550(U_6018,U_6019) ),
inference(clausify,[status(thm)],[f_1573_3]) ).
cnf(f_1573_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6018),c_Groups_Ozero__class_Ozero(U_6018)),U_6019) = c_Groups_Ozero__class_Ozero(U_6018)
| U_6019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP550(U_6018,U_6019) ),
inference(clausify,[status(thm)],[f_1573_3]) ).
fof(f_1574_1,plain,
! [V_n,V_a,T_a] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__gt1]) ).
fof(f_1574_2,plain,
! [U_6022,U_6021,U_6020] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6020),c_Groups_Oone__class_Oone(U_6020)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6020),U_6021),hAPP(c_Nat_OSuc,U_6022))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6020),c_Groups_Oone__class_Oone(U_6020)),U_6021))
| ~ class_Rings_Olinordered__semidom(U_6020) ),
inference(variable_rename,[status(thm)],[f_1574_1]) ).
fof(f_1574_3,plain,
! [U_6021,U_6020,U_6022] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6020),c_Groups_Oone__class_Oone(U_6020)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6020),U_6021),hAPP(c_Nat_OSuc,U_6022))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6020),c_Groups_Oone__class_Oone(U_6020)),U_6021))
| ~ class_Rings_Olinordered__semidom(U_6020) ),
inference(definitional_conversion,[status(esa)],[f_1574_2]) ).
cnf(f_1574_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6020),c_Groups_Oone__class_Oone(U_6020)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6020),U_6021),hAPP(c_Nat_OSuc,U_6022))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6020),c_Groups_Oone__class_Oone(U_6020)),U_6021))
| ~ class_Rings_Olinordered__semidom(U_6020) ),
inference(clausify,[status(thm)],[f_1574_3]) ).
fof(f_1575_1,plain,
! [V_y_2,V_x_2,V_b_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).
fof(f_1575_2,plain,
! [U_6026,U_6025,U_6024,U_6023] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6025)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6025),U_6026)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6025),U_6026))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6025)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6026))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),c_Groups_Oone__class_Oone(U_6023)),U_6024))
| ~ class_Rings_Olinordered__semidom(U_6023) ),
inference(variable_rename,[status(thm)],[f_1575_1]) ).
fof(f_1575_3,plain,
( ! [U_6023,U_6024,U_6025,U_6026] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6025)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6025),U_6026))
| ~ sP551(U_6023,U_6024,U_6025,U_6026) )
& ! [U_6023,U_6024,U_6025,U_6026] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6025),U_6026))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6025)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6026)))
| ~ sP551(U_6023,U_6024,U_6025,U_6026) )
& ! [U_6023,U_6024,U_6025,U_6026] :
( sP551(U_6023,U_6024,U_6025,U_6026)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),c_Groups_Oone__class_Oone(U_6023)),U_6024))
| ~ class_Rings_Olinordered__semidom(U_6023) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP551])],[f_1575_2]) ).
cnf(f_1575_4,plain,
( sP551(U_6023,U_6024,U_6025,U_6026)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),c_Groups_Oone__class_Oone(U_6023)),U_6024))
| ~ class_Rings_Olinordered__semidom(U_6023) ),
inference(clausify,[status(thm)],[f_1575_3]) ).
cnf(f_1575_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6025),U_6026))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6025)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6026)))
| ~ sP551(U_6023,U_6024,U_6025,U_6026) ),
inference(clausify,[status(thm)],[f_1575_3]) ).
cnf(f_1575_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6023),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6025)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6023),U_6024),U_6026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6025),U_6026))
| ~ sP551(U_6023,U_6024,U_6025,U_6026) ),
inference(clausify,[status(thm)],[f_1575_3]) ).
fof(f_1576_1,plain,
! [V_n,V_m,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp]) ).
fof(f_1576_2,plain,
! [U_6030,U_6029,U_6028,U_6027] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6029),U_6030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6027),hAPP(hAPP(c_Power_Opower__class_Opower(U_6027),U_6028),U_6029)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6027),U_6028),U_6030)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6027),c_Groups_Oone__class_Oone(U_6027)),U_6028))
| ~ class_Rings_Olinordered__semidom(U_6027) ),
inference(variable_rename,[status(thm)],[f_1576_1]) ).
fof(f_1576_3,plain,
! [U_6028,U_6029,U_6027,U_6030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6029),U_6030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6027),hAPP(hAPP(c_Power_Opower__class_Opower(U_6027),U_6028),U_6029)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6027),U_6028),U_6030)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6027),c_Groups_Oone__class_Oone(U_6027)),U_6028))
| ~ class_Rings_Olinordered__semidom(U_6027) ),
inference(definitional_conversion,[status(esa)],[f_1576_2]) ).
cnf(f_1576_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6029),U_6030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6027),hAPP(hAPP(c_Power_Opower__class_Opower(U_6027),U_6028),U_6029)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6027),U_6028),U_6030)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6027),c_Groups_Oone__class_Oone(U_6027)),U_6028))
| ~ class_Rings_Olinordered__semidom(U_6027) ),
inference(clausify,[status(thm)],[f_1576_3]) ).
fof(f_1577_1,plain,
! [V_a,V_N,V_n,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing]) ).
fof(f_1577_2,plain,
! [U_6034,U_6033,U_6032,U_6031] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6031),hAPP(hAPP(c_Power_Opower__class_Opower(U_6031),U_6034),U_6032)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6031),U_6034),U_6033)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6031),c_Groups_Oone__class_Oone(U_6031)),U_6034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6032),U_6033))
| ~ class_Rings_Olinordered__semidom(U_6031) ),
inference(variable_rename,[status(thm)],[f_1577_1]) ).
fof(f_1577_3,plain,
! [U_6032,U_6031,U_6033,U_6034] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6031),hAPP(hAPP(c_Power_Opower__class_Opower(U_6031),U_6034),U_6032)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6031),U_6034),U_6033)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6031),c_Groups_Oone__class_Oone(U_6031)),U_6034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6032),U_6033))
| ~ class_Rings_Olinordered__semidom(U_6031) ),
inference(definitional_conversion,[status(esa)],[f_1577_2]) ).
cnf(f_1577_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6031),hAPP(hAPP(c_Power_Opower__class_Opower(U_6031),U_6034),U_6032)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6031),U_6034),U_6033)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6031),c_Groups_Oone__class_Oone(U_6031)),U_6034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6032),U_6033))
| ~ class_Rings_Olinordered__semidom(U_6031) ),
inference(clausify,[status(thm)],[f_1577_3]) ).
fof(f_1578_1,plain,
! [V_a,V_N,V_n,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing]) ).
fof(f_1578_2,plain,
! [U_6038,U_6037,U_6036,U_6035] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6035),hAPP(hAPP(c_Power_Opower__class_Opower(U_6035),U_6038),U_6036)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6035),U_6038),U_6037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6035),c_Groups_Oone__class_Oone(U_6035)),U_6038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6036),U_6037))
| ~ class_Rings_Olinordered__semidom(U_6035) ),
inference(variable_rename,[status(thm)],[f_1578_1]) ).
fof(f_1578_3,plain,
! [U_6035,U_6036,U_6037,U_6038] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6035),hAPP(hAPP(c_Power_Opower__class_Opower(U_6035),U_6038),U_6036)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6035),U_6038),U_6037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6035),c_Groups_Oone__class_Oone(U_6035)),U_6038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6036),U_6037))
| ~ class_Rings_Olinordered__semidom(U_6035) ),
inference(definitional_conversion,[status(esa)],[f_1578_2]) ).
cnf(f_1578_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6035),hAPP(hAPP(c_Power_Opower__class_Opower(U_6035),U_6038),U_6036)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6035),U_6038),U_6037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6035),c_Groups_Oone__class_Oone(U_6035)),U_6038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6036),U_6037))
| ~ class_Rings_Olinordered__semidom(U_6035) ),
inference(clausify,[status(thm)],[f_1578_3]) ).
fof(f_1579_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__minus]) ).
fof(f_1579_2,plain,
! [U_6041,U_6040,U_6039] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(U_6039),U_6040)),U_6041) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6039),hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(U_6039),c_Groups_Oone__class_Oone(U_6039))),U_6041)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),U_6040),U_6041))
| ~ class_Rings_Oring__1(U_6039) ),
inference(variable_rename,[status(thm)],[f_1579_1]) ).
fof(f_1579_3,plain,
! [U_6039,U_6040,U_6041] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(U_6039),U_6040)),U_6041) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6039),hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(U_6039),c_Groups_Oone__class_Oone(U_6039))),U_6041)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),U_6040),U_6041))
| ~ class_Rings_Oring__1(U_6039) ),
inference(definitional_conversion,[status(esa)],[f_1579_2]) ).
cnf(f_1579_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(U_6039),U_6040)),U_6041) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6039),hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(U_6039),c_Groups_Oone__class_Oone(U_6039))),U_6041)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6039),U_6040),U_6041))
| ~ class_Rings_Oring__1(U_6039) ),
inference(clausify,[status(thm)],[f_1579_3]) ).
fof(f_1580_1,plain,
! [V_n,V_i] :
( 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)))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_nat__one__le__power]) ).
fof(f_1580_2,plain,
! [U_6043,U_6042] :
( 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),U_6042),U_6043)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6042)) ),
inference(variable_rename,[status(thm)],[f_1580_1]) ).
fof(f_1580_3,plain,
! [U_6042,U_6043] :
( 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),U_6042),U_6043)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6042)) ),
inference(definitional_conversion,[status(esa)],[f_1580_2]) ).
cnf(f_1580_4,plain,
( 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),U_6042),U_6043)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6042)) ),
inference(clausify,[status(thm)],[f_1580_3]) ).
fof(f_1581_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less]) ).
fof(f_1581_2,plain,
! [U_6046,U_6045,U_6044] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6044),U_6045),hAPP(hAPP(c_Power_Opower__class_Opower(U_6044),U_6045),U_6046))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6044),U_6045),U_6046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),U_6045),c_Groups_Oone__class_Oone(U_6044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),c_Groups_Ozero__class_Ozero(U_6044)),U_6045))
| ~ class_Rings_Olinordered__semidom(U_6044) ),
inference(variable_rename,[status(thm)],[f_1581_1]) ).
fof(f_1581_3,plain,
! [U_6044,U_6045,U_6046] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6044),U_6045),hAPP(hAPP(c_Power_Opower__class_Opower(U_6044),U_6045),U_6046))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6044),U_6045),U_6046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),U_6045),c_Groups_Oone__class_Oone(U_6044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),c_Groups_Ozero__class_Ozero(U_6044)),U_6045))
| ~ class_Rings_Olinordered__semidom(U_6044) ),
inference(definitional_conversion,[status(esa)],[f_1581_2]) ).
cnf(f_1581_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6044),U_6045),hAPP(hAPP(c_Power_Opower__class_Opower(U_6044),U_6045),U_6046))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6044),U_6045),U_6046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),U_6045),c_Groups_Oone__class_Oone(U_6044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),c_Groups_Ozero__class_Ozero(U_6044)),U_6045))
| ~ class_Rings_Olinordered__semidom(U_6044) ),
inference(clausify,[status(thm)],[f_1581_3]) ).
fof(f_1582_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(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_b),V_n)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base]) ).
fof(f_1582_2,plain,
! [U_6050,U_6049,U_6048,U_6047] :
( U_6048 = U_6050
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6047),c_Groups_Ozero__class_Ozero(U_6047)),U_6050))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6047),c_Groups_Ozero__class_Ozero(U_6047)),U_6048))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6047),U_6048),U_6049) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6047),U_6050),U_6049)
| ~ class_Rings_Olinordered__semidom(U_6047) ),
inference(variable_rename,[status(thm)],[f_1582_1]) ).
fof(f_1582_3,plain,
! [U_6047,U_6048,U_6049,U_6050] :
( U_6048 = U_6050
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6047),c_Groups_Ozero__class_Ozero(U_6047)),U_6050))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6047),c_Groups_Ozero__class_Ozero(U_6047)),U_6048))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6047),U_6048),U_6049) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6047),U_6050),U_6049)
| ~ class_Rings_Olinordered__semidom(U_6047) ),
inference(definitional_conversion,[status(esa)],[f_1582_2]) ).
cnf(f_1582_4,plain,
( U_6048 = U_6050
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6047),c_Groups_Ozero__class_Ozero(U_6047)),U_6050))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6047),c_Groups_Ozero__class_Ozero(U_6047)),U_6048))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6047),U_6048),U_6049) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6047),U_6050),U_6049)
| ~ class_Rings_Olinordered__semidom(U_6047) ),
inference(clausify,[status(thm)],[f_1582_3]) ).
fof(f_1583_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one]) ).
fof(f_1583_2,plain,
! [U_6053,U_6052,U_6051] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),hAPP(hAPP(c_Power_Opower__class_Opower(U_6051),U_6052),hAPP(c_Nat_OSuc,U_6053))),c_Groups_Oone__class_Oone(U_6051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),U_6052),c_Groups_Oone__class_Oone(U_6051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),c_Groups_Ozero__class_Ozero(U_6051)),U_6052))
| ~ class_Rings_Olinordered__semidom(U_6051) ),
inference(variable_rename,[status(thm)],[f_1583_1]) ).
fof(f_1583_3,plain,
! [U_6051,U_6052,U_6053] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),hAPP(hAPP(c_Power_Opower__class_Opower(U_6051),U_6052),hAPP(c_Nat_OSuc,U_6053))),c_Groups_Oone__class_Oone(U_6051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),U_6052),c_Groups_Oone__class_Oone(U_6051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),c_Groups_Ozero__class_Ozero(U_6051)),U_6052))
| ~ class_Rings_Olinordered__semidom(U_6051) ),
inference(definitional_conversion,[status(esa)],[f_1583_2]) ).
cnf(f_1583_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),hAPP(hAPP(c_Power_Opower__class_Opower(U_6051),U_6052),hAPP(c_Nat_OSuc,U_6053))),c_Groups_Oone__class_Oone(U_6051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),U_6052),c_Groups_Oone__class_Oone(U_6051)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),c_Groups_Ozero__class_Ozero(U_6051)),U_6052))
| ~ class_Rings_Olinordered__semidom(U_6051) ),
inference(clausify,[status(thm)],[f_1583_3]) ).
fof(f_1584_1,plain,
! [V_a,V_N,V_n,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing]) ).
fof(f_1584_2,plain,
! [U_6057,U_6056,U_6055,U_6054] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6057),U_6056)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6057),U_6055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),U_6057),c_Groups_Oone__class_Oone(U_6054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),c_Groups_Ozero__class_Ozero(U_6054)),U_6057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6055),U_6056))
| ~ class_Rings_Olinordered__semidom(U_6054) ),
inference(variable_rename,[status(thm)],[f_1584_1]) ).
fof(f_1584_3,plain,
! [U_6054,U_6055,U_6056,U_6057] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6057),U_6056)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6057),U_6055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),U_6057),c_Groups_Oone__class_Oone(U_6054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),c_Groups_Ozero__class_Ozero(U_6054)),U_6057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6055),U_6056))
| ~ class_Rings_Olinordered__semidom(U_6054) ),
inference(definitional_conversion,[status(esa)],[f_1584_2]) ).
cnf(f_1584_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6057),U_6056)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6057),U_6055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),U_6057),c_Groups_Oone__class_Oone(U_6054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),c_Groups_Ozero__class_Ozero(U_6054)),U_6057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6055),U_6056))
| ~ class_Rings_Olinordered__semidom(U_6054) ),
inference(clausify,[status(thm)],[f_1584_3]) ).
fof(f_1585_1,plain,
! [V_q,V_r,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
| 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1]) ).
fof(f_1585_2,plain,
! [U_6060,U_6059,U_6058] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6059),U_6058))
| U_6058 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6058),U_6060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6058)) ),
inference(variable_rename,[status(thm)],[f_1585_1]) ).
fof(f_1585_3,plain,
! [U_6059,U_6058,U_6060] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6059),U_6058))
| U_6058 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6058),U_6060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6058)) ),
inference(definitional_conversion,[status(esa)],[f_1585_2]) ).
cnf(f_1585_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6059),U_6058))
| U_6058 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6058),U_6060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6058)) ),
inference(clausify,[status(thm)],[f_1585_3]) ).
fof(f_1586_1,plain,
! [V_q,V_r,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
| 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2]) ).
fof(f_1586_2,plain,
! [U_6063,U_6062,U_6061] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6063),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6062))
| U_6061 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6061),U_6063))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)) ),
inference(variable_rename,[status(thm)],[f_1586_1]) ).
fof(f_1586_3,plain,
! [U_6061,U_6063,U_6062] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6063),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6062))
| U_6061 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6061),U_6063))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)) ),
inference(definitional_conversion,[status(esa)],[f_1586_2]) ).
cnf(f_1586_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6063),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6062))
| U_6061 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6061),U_6063))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)) ),
inference(clausify,[status(thm)],[f_1586_3]) ).
fof(f_1587_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_q__pos__lemma]) ).
fof(f_1587_2,plain,
! [U_6066,U_6065,U_6064] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6064))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6066),U_6064))
| ~ 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),U_6064),U_6065)),U_6066))) ),
inference(variable_rename,[status(thm)],[f_1587_1]) ).
fof(f_1587_3,plain,
! [U_6065,U_6066,U_6064] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6064))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6066),U_6064))
| ~ 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),U_6064),U_6065)),U_6066))) ),
inference(definitional_conversion,[status(esa)],[f_1587_2]) ).
cnf(f_1587_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6064))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6066),U_6064))
| ~ 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),U_6064),U_6065)),U_6066))) ),
inference(clausify,[status(thm)],[f_1587_3]) ).
fof(f_1588_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_q__neg__lemma]) ).
fof(f_1588_2,plain,
! [U_6069,U_6068,U_6067] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6068),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6069))
| ~ 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),U_6067),U_6068)),U_6069)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1588_1]) ).
fof(f_1588_3,plain,
! [U_6068,U_6067,U_6069] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6068),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6069))
| ~ 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),U_6067),U_6068)),U_6069)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1588_2]) ).
cnf(f_1588_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6068),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6069))
| ~ 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),U_6067),U_6068)),U_6069)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1588_3]) ).
fof(f_1589_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma]) ).
fof(f_1589_2,plain,
! [U_6074,U_6073,U_6072,U_6071,U_6070] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6071),U_6073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6074),U_6070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6072),U_6070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6072))
| ~ 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),U_6070),U_6071)),U_6072)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6070),U_6073)),U_6074))) ),
inference(variable_rename,[status(thm)],[f_1589_1]) ).
fof(f_1589_3,plain,
! [U_6070,U_6071,U_6072,U_6073,U_6074] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6071),U_6073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6074),U_6070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6072),U_6070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6072))
| ~ 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),U_6070),U_6071)),U_6072)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6070),U_6073)),U_6074))) ),
inference(definitional_conversion,[status(esa)],[f_1589_2]) ).
cnf(f_1589_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6071),U_6073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6074),U_6070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6072),U_6070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6072))
| ~ 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),U_6070),U_6071)),U_6072)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6070),U_6073)),U_6074))) ),
inference(clausify,[status(thm)],[f_1589_3]) ).
fof(f_1590_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
| ~ 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)))
| 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) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma]) ).
fof(f_1590_2,plain,
! [U_6080,U_6079,U_6078,U_6077,U_6076,U_6075] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6076),U_6079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6078),U_6075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6077))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6080),U_6078))
| ~ 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),U_6078),U_6079)),U_6080)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6075),U_6076)),U_6077) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6078),U_6079)),U_6080) ),
inference(variable_rename,[status(thm)],[f_1590_1]) ).
fof(f_1590_3,plain,
! [U_6075,U_6076,U_6078,U_6077,U_6079,U_6080] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6076),U_6079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6078),U_6075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6077))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6080),U_6078))
| ~ 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),U_6078),U_6079)),U_6080)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6075),U_6076)),U_6077) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6078),U_6079)),U_6080) ),
inference(definitional_conversion,[status(esa)],[f_1590_2]) ).
cnf(f_1590_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6076),U_6079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6078),U_6075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6077))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6080),U_6078))
| ~ 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),U_6078),U_6079)),U_6080)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6075),U_6076)),U_6077) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6078),U_6079)),U_6080) ),
inference(clausify,[status(thm)],[f_1590_3]) ).
fof(f_1591_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__atLeastAtMost__int]) ).
fof(f_1591_2,plain,
! [U_6082,U_6081] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6081,U_6082))),
inference(variable_rename,[status(thm)],[f_1591_1]) ).
fof(f_1591_3,plain,
! [U_6082,U_6081] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6081,U_6082))),
inference(definitional_conversion,[status(esa)],[f_1591_2]) ).
cnf(f_1591_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6081,U_6082))),
inference(clausify,[status(thm)],[f_1591_3]) ).
fof(f_1592_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__atLeastLessThan__int]) ).
fof(f_1592_2,plain,
! [U_6084,U_6083] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6083),U_6084))),
inference(variable_rename,[status(thm)],[f_1592_1]) ).
fof(f_1592_3,plain,
! [U_6083,U_6084] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6083),U_6084))),
inference(definitional_conversion,[status(esa)],[f_1592_2]) ).
cnf(f_1592_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6083),U_6084))),
inference(clausify,[status(thm)],[f_1592_3]) ).
fof(f_1593_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).
fof(f_1593_2,plain,
! [U_6086,U_6085] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6085,U_6086))),
inference(variable_rename,[status(thm)],[f_1593_1]) ).
fof(f_1593_3,plain,
! [U_6085,U_6086] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6085,U_6086))),
inference(definitional_conversion,[status(esa)],[f_1593_2]) ).
cnf(f_1593_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6085,U_6086))),
inference(clausify,[status(thm)],[f_1593_3]) ).
fof(f_1594_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).
fof(f_1594_2,plain,
! [U_6088,U_6087] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6087,U_6088))),
inference(variable_rename,[status(thm)],[f_1594_1]) ).
fof(f_1594_3,plain,
! [U_6087,U_6088] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6087,U_6088))),
inference(definitional_conversion,[status(esa)],[f_1594_2]) ).
cnf(f_1594_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6087,U_6088))),
inference(clausify,[status(thm)],[f_1594_3]) ).
fof(f_1595_1,plain,
! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k,
inference(fof_nnf,[status(thm)],[fact_number__of__is__id]) ).
fof(f_1595_2,plain,
! [U_6089] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6089) = U_6089,
inference(variable_rename,[status(thm)],[f_1595_1]) ).
fof(f_1595_3,plain,
! [U_6089] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6089) = U_6089,
inference(definitional_conversion,[status(esa)],[f_1595_2]) ).
cnf(f_1595_4,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6089) = U_6089,
inference(clausify,[status(thm)],[f_1595_3]) ).
fof(f_1596_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__int__code]) ).
fof(f_1596_2,plain,
! [U_6091,U_6090] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6090)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6091)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6090),U_6091)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6090),U_6091))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6090)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6091))) ) ),
inference(variable_rename,[status(thm)],[f_1596_1]) ).
fof(f_1596_3,plain,
( ! [U_6095,U_6093] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6093)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6095)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6093),U_6095)) )
& ! [U_6094,U_6092] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6092),U_6094))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6092)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6094))) ) ),
inference(miniscope,[status(thm)],[f_1596_2]) ).
fof(f_1596_4,plain,
( ! [U_6093,U_6095] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6093)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6095)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6093),U_6095)) )
& ! [U_6094,U_6092] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6092),U_6094))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6092)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6094))) ) ),
inference(definitional_conversion,[status(esa)],[f_1596_3]) ).
cnf(f_1596_5,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6092),U_6094))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6092)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6094))) ),
inference(clausify,[status(thm)],[f_1596_4]) ).
cnf(f_1596_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6093)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6095)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6093),U_6095)) ),
inference(clausify,[status(thm)],[f_1596_4]) ).
fof(f_1597_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_int__0__neq__1]) ).
fof(f_1597_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1597_1]) ).
cnf(f_1597_3,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1597_2]) ).
fof(f_1598_1,plain,
! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)),
inference(fof_nnf,[status(thm)],[fact_eq__int__refl]) ).
fof(f_1598_2,plain,
! [U_6096] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6096),U_6096)),
inference(variable_rename,[status(thm)],[f_1598_1]) ).
fof(f_1598_3,plain,
! [U_6096] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6096),U_6096)),
inference(definitional_conversion,[status(esa)],[f_1598_2]) ).
cnf(f_1598_4,plain,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_6096),U_6096)),
inference(clausify,[status(thm)],[f_1598_3]) ).
fof(f_1599_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).
fof(f_1599_2,plain,
! [U_6097] : 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)),U_6097))),
inference(variable_rename,[status(thm)],[f_1599_1]) ).
fof(f_1599_3,plain,
! [U_6097] : 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)),U_6097))),
inference(definitional_conversion,[status(esa)],[f_1599_2]) ).
cnf(f_1599_4,plain,
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)),U_6097))),
inference(clausify,[status(thm)],[f_1599_3]) ).
fof(f_1600_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
| ~ 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)))
| 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) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma]) ).
fof(f_1600_2,plain,
! [U_6103,U_6102,U_6101,U_6100,U_6099,U_6098] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6102),U_6099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6101),U_6098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6103))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6100),U_6098))
| ~ 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),U_6101),U_6102)),U_6103)),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),U_6098),U_6099)),U_6100) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6101),U_6102)),U_6103) ),
inference(variable_rename,[status(thm)],[f_1600_1]) ).
fof(f_1600_3,plain,
! [U_6098,U_6100,U_6101,U_6099,U_6102,U_6103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6102),U_6099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6101),U_6098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6103))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6100),U_6098))
| ~ 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),U_6101),U_6102)),U_6103)),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),U_6098),U_6099)),U_6100) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6101),U_6102)),U_6103) ),
inference(definitional_conversion,[status(esa)],[f_1600_2]) ).
cnf(f_1600_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6102),U_6099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6101),U_6098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6103))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6100),U_6098))
| ~ 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),U_6101),U_6102)),U_6103)),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),U_6098),U_6099)),U_6100) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6101),U_6102)),U_6103) ),
inference(clausify,[status(thm)],[f_1600_3]) ).
fof(f_1601_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg]) ).
fof(f_1601_2,plain,
! [U_6108,U_6107,U_6106,U_6105,U_6104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6107),U_6105))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6104),U_6106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6104),U_6108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6108),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),U_6104),U_6105)),U_6106)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6104),U_6107)),U_6108))) ),
inference(variable_rename,[status(thm)],[f_1601_1]) ).
fof(f_1601_3,plain,
! [U_6107,U_6105,U_6106,U_6108,U_6104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6107),U_6105))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6104),U_6106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6104),U_6108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6108),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),U_6104),U_6105)),U_6106)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6104),U_6107)),U_6108))) ),
inference(definitional_conversion,[status(esa)],[f_1601_2]) ).
cnf(f_1601_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6107),U_6105))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6104),U_6106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6104),U_6108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6108),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),U_6104),U_6105)),U_6106)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6104),U_6107)),U_6108))) ),
inference(clausify,[status(thm)],[f_1601_3]) ).
fof(f_1602_1,plain,
! [V_i_2,V_j_2] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_simp__from__to]) ).
fof(f_1602_2,plain,
! [U_6110,U_6109] :
( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6110,U_6109) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_6110),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6110),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6109))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6109),U_6110)) )
& ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6110,U_6109) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6109),U_6110)) ) ),
inference(variable_rename,[status(thm)],[f_1602_1]) ).
fof(f_1602_3,plain,
( ! [U_6114,U_6112] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6114,U_6112) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_6114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6114),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6112))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6112),U_6114)) )
& ! [U_6113,U_6111] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6113,U_6111) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6111),U_6113)) ) ),
inference(miniscope,[status(thm)],[f_1602_2]) ).
fof(f_1602_4,plain,
( ! [U_6112,U_6114] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6114,U_6112) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_6114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6114),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6112))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6112),U_6114)) )
& ! [U_6113,U_6111] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6113,U_6111) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6111),U_6113)) ) ),
inference(definitional_conversion,[status(esa)],[f_1602_3]) ).
cnf(f_1602_5,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6113,U_6111) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6111),U_6113)) ),
inference(clausify,[status(thm)],[f_1602_4]) ).
cnf(f_1602_6,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6114,U_6112) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_6114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6114),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6112))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6112),U_6114)) ),
inference(clausify,[status(thm)],[f_1602_4]) ).
fof(f_1603_1,plain,
! [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),V_x),V_n)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).
fof(f_1603_2,plain,
! [U_6116,U_6115] :
( 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),U_6115),U_6116)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6115)) ),
inference(variable_rename,[status(thm)],[f_1603_1]) ).
fof(f_1603_3,plain,
! [U_6116,U_6115] :
( 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),U_6115),U_6116)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6115)) ),
inference(definitional_conversion,[status(esa)],[f_1603_2]) ).
cnf(f_1603_4,plain,
( 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),U_6115),U_6116)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6115)) ),
inference(clausify,[status(thm)],[f_1603_3]) ).
fof(f_1604_1,plain,
! [V_y,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_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).
fof(f_1604_2,plain,
! [U_6118,U_6117] :
( 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),U_6117),U_6118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6118))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6117)) ),
inference(variable_rename,[status(thm)],[f_1604_1]) ).
fof(f_1604_3,plain,
! [U_6117,U_6118] :
( 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),U_6117),U_6118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6118))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6117)) ),
inference(definitional_conversion,[status(esa)],[f_1604_2]) ).
cnf(f_1604_4,plain,
( 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),U_6117),U_6118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6118))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6117)) ),
inference(clausify,[status(thm)],[f_1604_3]) ).
fof(f_1605_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
fof(f_1605_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1605_1]) ).
cnf(f_1605_3,plain,
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))),
inference(clausify,[status(thm)],[f_1605_2]) ).
fof(f_1606_1,plain,
! [V_y,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_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_1606_2,plain,
! [U_6120,U_6119] :
( 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),U_6119),U_6120)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6119)) ),
inference(variable_rename,[status(thm)],[f_1606_1]) ).
fof(f_1606_3,plain,
! [U_6119,U_6120] :
( 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),U_6119),U_6120)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6119)) ),
inference(definitional_conversion,[status(esa)],[f_1606_2]) ).
cnf(f_1606_4,plain,
( 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),U_6119),U_6120)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6119)) ),
inference(clausify,[status(thm)],[f_1606_3]) ).
fof(f_1607_1,plain,
! [T_b] :
( 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))
| ~ class_Power_Opower(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).
fof(f_1607_2,plain,
! [U_6121] :
( c_Power_Opower__class_Opower(U_6121) = c_Power_Opower_Opower(U_6121,c_Groups_Oone__class_Oone(U_6121),c_Groups_Otimes__class_Otimes(U_6121))
| ~ class_Power_Opower(U_6121) ),
inference(variable_rename,[status(thm)],[f_1607_1]) ).
fof(f_1607_3,plain,
! [U_6121] :
( c_Power_Opower__class_Opower(U_6121) = c_Power_Opower_Opower(U_6121,c_Groups_Oone__class_Oone(U_6121),c_Groups_Otimes__class_Otimes(U_6121))
| ~ class_Power_Opower(U_6121) ),
inference(definitional_conversion,[status(esa)],[f_1607_2]) ).
cnf(f_1607_4,plain,
( c_Power_Opower__class_Opower(U_6121) = c_Power_Opower_Opower(U_6121,c_Groups_Oone__class_Oone(U_6121),c_Groups_Otimes__class_Otimes(U_6121))
| ~ class_Power_Opower(U_6121) ),
inference(clausify,[status(thm)],[f_1607_3]) ).
fof(f_1608_1,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__int]) ).
fof(f_1608_2,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_1608_1]) ).
cnf(f_1608_3,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_1608_2]) ).
fof(f_1609_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(f_1609_2,plain,
! [U_6125,U_6124,U_6123,U_6122] : hAPP(hAPP(c_Power_Opower_Opower(U_6122,U_6123,U_6124),U_6125),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6123,
inference(variable_rename,[status(thm)],[f_1609_1]) ).
fof(f_1609_3,plain,
! [U_6122,U_6123,U_6124,U_6125] : hAPP(hAPP(c_Power_Opower_Opower(U_6122,U_6123,U_6124),U_6125),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6123,
inference(definitional_conversion,[status(esa)],[f_1609_2]) ).
cnf(f_1609_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_6122,U_6123,U_6124),U_6125),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6123,
inference(clausify,[status(thm)],[f_1609_3]) ).
fof(f_1610_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(f_1610_2,plain,
! [U_6130,U_6129,U_6128,U_6127,U_6126] : hAPP(hAPP(c_Power_Opower_Opower(U_6126,U_6127,U_6128),U_6129),hAPP(c_Nat_OSuc,U_6130)) = hAPP(hAPP(U_6128,U_6129),hAPP(hAPP(c_Power_Opower_Opower(U_6126,U_6127,U_6128),U_6129),U_6130)),
inference(variable_rename,[status(thm)],[f_1610_1]) ).
fof(f_1610_3,plain,
! [U_6126,U_6127,U_6128,U_6129,U_6130] : hAPP(hAPP(c_Power_Opower_Opower(U_6126,U_6127,U_6128),U_6129),hAPP(c_Nat_OSuc,U_6130)) = hAPP(hAPP(U_6128,U_6129),hAPP(hAPP(c_Power_Opower_Opower(U_6126,U_6127,U_6128),U_6129),U_6130)),
inference(definitional_conversion,[status(esa)],[f_1610_2]) ).
cnf(f_1610_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_6126,U_6127,U_6128),U_6129),hAPP(c_Nat_OSuc,U_6130)) = hAPP(hAPP(U_6128,U_6129),hAPP(hAPP(c_Power_Opower_Opower(U_6126,U_6127,U_6128),U_6129),U_6130)),
inference(clausify,[status(thm)],[f_1610_3]) ).
fof(f_1611_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).
fof(f_1611_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1611_1]) ).
cnf(f_1611_3,plain,
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))),
inference(clausify,[status(thm)],[f_1611_2]) ).
fof(f_1612_1,plain,
! [V_A_2,V_t_2,V_D_2] :
( ! [B_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
& 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))) ) )
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_aset_I6_J]) ).
fof(f_1612_2,plain,
! [U_6136,U_6135,U_6134] :
( ! [U_6133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6133),U_6134)),U_6135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6133),U_6135))
| ? [U_6132] :
( ? [U_6131] :
( U_6133 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6131),U_6132)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6131),U_6136)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6132),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6134))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6135),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6134)) ),
inference(variable_rename,[status(thm)],[f_1612_1]) ).
fof(f_1612_3,plain,
! [U_6136,U_6135,U_6134] :
( ! [U_6133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6133),U_6134)),U_6135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6133),U_6135))
| ( ? [U_6131] :
( U_6133 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6131),sK142(U_6136,U_6135,U_6134,U_6133))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6131),U_6136)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK142(U_6136,U_6135,U_6134,U_6133)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6134))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6135),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6134)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_6132,sK142(U_6136,U_6135,U_6134,U_6133))],[f_1612_2]) ).
fof(f_1612_4,plain,
! [U_6136,U_6135,U_6134] :
( ! [U_6133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6133),U_6134)),U_6135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6133),U_6135))
| ( U_6133 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK143(U_6136,U_6135,U_6134,U_6133)),sK142(U_6136,U_6135,U_6134,U_6133))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK143(U_6136,U_6135,U_6134,U_6133)),U_6136))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK142(U_6136,U_6135,U_6134,U_6133)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6134))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6135),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6134)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_6131,sK143(U_6136,U_6135,U_6134,U_6133))],[f_1612_3]) ).
fof(f_1612_5,plain,
( ! [U_6133,U_6134,U_6135,U_6136] :
( U_6133 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK143(U_6136,U_6135,U_6134,U_6133)),sK142(U_6136,U_6135,U_6134,U_6133))
| ~ sP552(U_6133,U_6134,U_6135,U_6136) )
& ! [U_6133,U_6134,U_6135,U_6136] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK143(U_6136,U_6135,U_6134,U_6133)),U_6136))
| ~ sP552(U_6133,U_6134,U_6135,U_6136) )
& ! [U_6133,U_6134,U_6135,U_6136] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK142(U_6136,U_6135,U_6134,U_6133)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6134)))
| ~ sP552(U_6133,U_6134,U_6135,U_6136) )
& ! [U_6133,U_6134,U_6135,U_6136] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6133),U_6134)),U_6135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6133),U_6135))
| sP552(U_6133,U_6134,U_6135,U_6136)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6135),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6134)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP552])],[f_1612_4]) ).
cnf(f_1612_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6133),U_6134)),U_6135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6133),U_6135))
| sP552(U_6133,U_6134,U_6135,U_6136)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6135),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6134)) ),
inference(clausify,[status(thm)],[f_1612_5]) ).
cnf(f_1612_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK142(U_6136,U_6135,U_6134,U_6133)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6134)))
| ~ sP552(U_6133,U_6134,U_6135,U_6136) ),
inference(clausify,[status(thm)],[f_1612_5]) ).
cnf(f_1612_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK143(U_6136,U_6135,U_6134,U_6133)),U_6136))
| ~ sP552(U_6133,U_6134,U_6135,U_6136) ),
inference(clausify,[status(thm)],[f_1612_5]) ).
cnf(f_1612_9,plain,
( U_6133 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK143(U_6136,U_6135,U_6134,U_6133)),sK142(U_6136,U_6135,U_6134,U_6133))
| ~ sP552(U_6133,U_6134,U_6135,U_6136) ),
inference(clausify,[status(thm)],[f_1612_5]) ).
fof(f_1613_1,plain,
! [V_B_2,V_t_2,V_D_2] :
( ! [B_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
& 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))) ) )
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_bset_I8_J]) ).
fof(f_1613_2,plain,
! [U_6142,U_6141,U_6140] :
( ! [U_6139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6139),U_6140)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),U_6139))
| ? [U_6138] :
( ? [U_6137] :
( U_6139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6137),U_6138)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6137),U_6142)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6138),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6140))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6141),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6140)) ),
inference(variable_rename,[status(thm)],[f_1613_1]) ).
fof(f_1613_3,plain,
! [U_6142,U_6141,U_6140] :
( ! [U_6139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6139),U_6140)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),U_6139))
| ( ? [U_6137] :
( U_6139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6137),sK144(U_6142,U_6141,U_6140,U_6139))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6137),U_6142)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK144(U_6142,U_6141,U_6140,U_6139)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6140))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6141),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6140)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_6138,sK144(U_6142,U_6141,U_6140,U_6139))],[f_1613_2]) ).
fof(f_1613_4,plain,
! [U_6142,U_6141,U_6140] :
( ! [U_6139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6139),U_6140)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),U_6139))
| ( U_6139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK145(U_6142,U_6141,U_6140,U_6139)),sK144(U_6142,U_6141,U_6140,U_6139))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK145(U_6142,U_6141,U_6140,U_6139)),U_6142))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK144(U_6142,U_6141,U_6140,U_6139)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6140))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6141),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6140)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_6137,sK145(U_6142,U_6141,U_6140,U_6139))],[f_1613_3]) ).
fof(f_1613_5,plain,
( ! [U_6142,U_6139,U_6140,U_6141] :
( U_6139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK145(U_6142,U_6141,U_6140,U_6139)),sK144(U_6142,U_6141,U_6140,U_6139))
| ~ sP553(U_6142,U_6139,U_6140,U_6141) )
& ! [U_6142,U_6139,U_6140,U_6141] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK145(U_6142,U_6141,U_6140,U_6139)),U_6142))
| ~ sP553(U_6142,U_6139,U_6140,U_6141) )
& ! [U_6142,U_6139,U_6140,U_6141] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK144(U_6142,U_6141,U_6140,U_6139)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6140)))
| ~ sP553(U_6142,U_6139,U_6140,U_6141) )
& ! [U_6142,U_6139,U_6140,U_6141] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6139),U_6140)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),U_6139))
| sP553(U_6142,U_6139,U_6140,U_6141)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6141),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6140)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP553])],[f_1613_4]) ).
cnf(f_1613_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6139),U_6140)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6141),U_6139))
| sP553(U_6142,U_6139,U_6140,U_6141)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6141),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6140)) ),
inference(clausify,[status(thm)],[f_1613_5]) ).
cnf(f_1613_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK144(U_6142,U_6141,U_6140,U_6139)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6140)))
| ~ sP553(U_6142,U_6139,U_6140,U_6141) ),
inference(clausify,[status(thm)],[f_1613_5]) ).
cnf(f_1613_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK145(U_6142,U_6141,U_6140,U_6139)),U_6142))
| ~ sP553(U_6142,U_6139,U_6140,U_6141) ),
inference(clausify,[status(thm)],[f_1613_5]) ).
cnf(f_1613_9,plain,
( U_6139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK145(U_6142,U_6141,U_6140,U_6139)),sK144(U_6142,U_6141,U_6140,U_6139))
| ~ sP553(U_6142,U_6139,U_6140,U_6141) ),
inference(clausify,[status(thm)],[f_1613_5]) ).
fof(f_1614_1,plain,
! [V_t_2,V_B_2,V_D_2] :
( ! [B_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
& 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_bset_I6_J]) ).
fof(f_1614_2,plain,
! [U_6148,U_6147,U_6146] :
( ! [U_6145] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6145),U_6146)),U_6148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6145),U_6148))
| ? [U_6144] :
( ? [U_6143] :
( U_6145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6143),U_6144)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6143),U_6147)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6144),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6146))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6146)) ),
inference(variable_rename,[status(thm)],[f_1614_1]) ).
fof(f_1614_3,plain,
! [U_6148,U_6147,U_6146] :
( ! [U_6145] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6145),U_6146)),U_6148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6145),U_6148))
| ( ? [U_6143] :
( U_6145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6143),sK146(U_6148,U_6147,U_6146,U_6145))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6143),U_6147)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK146(U_6148,U_6147,U_6146,U_6145)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6146))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6146)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_6144,sK146(U_6148,U_6147,U_6146,U_6145))],[f_1614_2]) ).
fof(f_1614_4,plain,
! [U_6148,U_6147,U_6146] :
( ! [U_6145] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6145),U_6146)),U_6148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6145),U_6148))
| ( U_6145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK147(U_6148,U_6147,U_6146,U_6145)),sK146(U_6148,U_6147,U_6146,U_6145))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK147(U_6148,U_6147,U_6146,U_6145)),U_6147))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK146(U_6148,U_6147,U_6146,U_6145)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6146))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6146)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_6143,sK147(U_6148,U_6147,U_6146,U_6145))],[f_1614_3]) ).
fof(f_1614_5,plain,
( ! [U_6145,U_6148,U_6146,U_6147] :
( U_6145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK147(U_6148,U_6147,U_6146,U_6145)),sK146(U_6148,U_6147,U_6146,U_6145))
| ~ sP554(U_6145,U_6148,U_6146,U_6147) )
& ! [U_6145,U_6148,U_6146,U_6147] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK147(U_6148,U_6147,U_6146,U_6145)),U_6147))
| ~ sP554(U_6145,U_6148,U_6146,U_6147) )
& ! [U_6145,U_6148,U_6146,U_6147] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK146(U_6148,U_6147,U_6146,U_6145)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6146)))
| ~ sP554(U_6145,U_6148,U_6146,U_6147) )
& ! [U_6145,U_6148,U_6146,U_6147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6145),U_6146)),U_6148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6145),U_6148))
| sP554(U_6145,U_6148,U_6146,U_6147)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6146)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP554])],[f_1614_4]) ).
cnf(f_1614_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6145),U_6146)),U_6148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6145),U_6148))
| sP554(U_6145,U_6148,U_6146,U_6147)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6146)) ),
inference(clausify,[status(thm)],[f_1614_5]) ).
cnf(f_1614_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK146(U_6148,U_6147,U_6146,U_6145)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6146)))
| ~ sP554(U_6145,U_6148,U_6146,U_6147) ),
inference(clausify,[status(thm)],[f_1614_5]) ).
cnf(f_1614_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK147(U_6148,U_6147,U_6146,U_6145)),U_6147))
| ~ sP554(U_6145,U_6148,U_6146,U_6147) ),
inference(clausify,[status(thm)],[f_1614_5]) ).
cnf(f_1614_9,plain,
( U_6145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK147(U_6148,U_6147,U_6146,U_6145)),sK146(U_6148,U_6147,U_6146,U_6145))
| ~ sP554(U_6145,U_6148,U_6146,U_6147) ),
inference(clausify,[status(thm)],[f_1614_5]) ).
fof(f_1615_1,plain,
! [V_t_2,V_A_2,V_D_2] :
( ! [B_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
& 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_aset_I8_J]) ).
fof(f_1615_2,plain,
! [U_6154,U_6153,U_6152] :
( ! [U_6151] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6151),U_6152)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),U_6151))
| ? [U_6150] :
( ? [U_6149] :
( U_6151 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6149),U_6150)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6149),U_6153)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6150),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6152))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6152)) ),
inference(variable_rename,[status(thm)],[f_1615_1]) ).
fof(f_1615_3,plain,
! [U_6154,U_6153,U_6152] :
( ! [U_6151] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6151),U_6152)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),U_6151))
| ( ? [U_6149] :
( U_6151 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6149),sK148(U_6154,U_6153,U_6152,U_6151))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6149),U_6153)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK148(U_6154,U_6153,U_6152,U_6151)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6152))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6152)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_6150,sK148(U_6154,U_6153,U_6152,U_6151))],[f_1615_2]) ).
fof(f_1615_4,plain,
! [U_6154,U_6153,U_6152] :
( ! [U_6151] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6151),U_6152)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),U_6151))
| ( U_6151 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK149(U_6154,U_6153,U_6152,U_6151)),sK148(U_6154,U_6153,U_6152,U_6151))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK149(U_6154,U_6153,U_6152,U_6151)),U_6153))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK148(U_6154,U_6153,U_6152,U_6151)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6152))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6152)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_6149,sK149(U_6154,U_6153,U_6152,U_6151))],[f_1615_3]) ).
fof(f_1615_5,plain,
( ! [U_6153,U_6154,U_6151,U_6152] :
( U_6151 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK149(U_6154,U_6153,U_6152,U_6151)),sK148(U_6154,U_6153,U_6152,U_6151))
| ~ sP555(U_6153,U_6154,U_6151,U_6152) )
& ! [U_6153,U_6154,U_6151,U_6152] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK149(U_6154,U_6153,U_6152,U_6151)),U_6153))
| ~ sP555(U_6153,U_6154,U_6151,U_6152) )
& ! [U_6153,U_6154,U_6151,U_6152] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK148(U_6154,U_6153,U_6152,U_6151)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6152)))
| ~ sP555(U_6153,U_6154,U_6151,U_6152) )
& ! [U_6153,U_6154,U_6151,U_6152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6151),U_6152)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),U_6151))
| sP555(U_6153,U_6154,U_6151,U_6152)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6152)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP555])],[f_1615_4]) ).
cnf(f_1615_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6151),U_6152)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6154),U_6151))
| sP555(U_6153,U_6154,U_6151,U_6152)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6152)) ),
inference(clausify,[status(thm)],[f_1615_5]) ).
cnf(f_1615_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK148(U_6154,U_6153,U_6152,U_6151)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6152)))
| ~ sP555(U_6153,U_6154,U_6151,U_6152) ),
inference(clausify,[status(thm)],[f_1615_5]) ).
cnf(f_1615_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK149(U_6154,U_6153,U_6152,U_6151)),U_6153))
| ~ sP555(U_6153,U_6154,U_6151,U_6152) ),
inference(clausify,[status(thm)],[f_1615_5]) ).
cnf(f_1615_9,plain,
( U_6151 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK149(U_6154,U_6153,U_6152,U_6151)),sK148(U_6154,U_6153,U_6152,U_6151))
| ~ sP555(U_6153,U_6154,U_6151,U_6152) ),
inference(clausify,[status(thm)],[f_1615_5]) ).
fof(f_1616_1,plain,
! [V_Pa_2,V_d_2] :
( ( ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
| ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ 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))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& 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))) )
| ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) )
| ? [B_x,B_k] :
( ( ~ hBOOL(hAPP(V_Pa_2,B_x))
& 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)))) )
| ( ~ 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))))
& hBOOL(hAPP(V_Pa_2,B_x)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
inference(fof_nnf,[status(thm)],[fact_periodic__finite__ex]) ).
fof(f_1616_2,plain,
! [U_6162,U_6161] :
( ( ( ? [U_6160] : hBOOL(hAPP(U_6162,U_6160))
| ! [U_6159] :
( ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) ) )
& ( ? [U_6158] :
( hBOOL(hAPP(U_6162,U_6158))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6158),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) )
| ! [U_6157] : ~ hBOOL(hAPP(U_6162,U_6157)) ) )
| ? [U_6156,U_6155] :
( ( ~ hBOOL(hAPP(U_6162,U_6156))
& hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6155),U_6161)))) )
| ( ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6155),U_6161))))
& hBOOL(hAPP(U_6162,U_6156)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(variable_rename,[status(thm)],[f_1616_1]) ).
fof(f_1616_3,plain,
! [U_6162,U_6161] :
( ( ( ? [U_6160] : hBOOL(hAPP(U_6162,U_6160))
| ! [U_6159] :
( ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) ) )
& ( ? [U_6158] :
( hBOOL(hAPP(U_6162,U_6158))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6158),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) )
| ! [U_6157] : ~ hBOOL(hAPP(U_6162,U_6157)) ) )
| ? [U_6166] :
( ? [U_6164] : hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6166),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6164),U_6161))))
& ~ hBOOL(hAPP(U_6162,U_6166)) )
| ? [U_6165] :
( ? [U_6163] : ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6165),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6163),U_6161))))
& hBOOL(hAPP(U_6162,U_6165)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(miniscope,[status(thm)],[f_1616_2]) ).
fof(f_1616_4,plain,
! [U_6162,U_6161] :
( ( ( ? [U_6160] : hBOOL(hAPP(U_6162,U_6160))
| ! [U_6159] :
( ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) ) )
& ( ? [U_6158] :
( hBOOL(hAPP(U_6162,U_6158))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6158),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) )
| ! [U_6157] : ~ hBOOL(hAPP(U_6162,U_6157)) ) )
| ? [U_6166] :
( ? [U_6164] : hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6166),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6164),U_6161))))
& ~ hBOOL(hAPP(U_6162,U_6166)) )
| ( ? [U_6163] : ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK150(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6163),U_6161))))
& hBOOL(hAPP(U_6162,sK150(U_6162,U_6161))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_6165,sK150(U_6162,U_6161))],[f_1616_3]) ).
fof(f_1616_5,plain,
! [U_6162,U_6161] :
( ( ( ? [U_6160] : hBOOL(hAPP(U_6162,U_6160))
| ! [U_6159] :
( ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) ) )
& ( ? [U_6158] :
( hBOOL(hAPP(U_6162,U_6158))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6158),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) )
| ! [U_6157] : ~ hBOOL(hAPP(U_6162,U_6157)) ) )
| ? [U_6166] :
( ? [U_6164] : hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6166),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6164),U_6161))))
& ~ hBOOL(hAPP(U_6162,U_6166)) )
| ( ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK150(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK151(U_6162,U_6161)),U_6161))))
& hBOOL(hAPP(U_6162,sK150(U_6162,U_6161))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_6163,sK151(U_6162,U_6161))],[f_1616_4]) ).
fof(f_1616_6,plain,
! [U_6162,U_6161] :
( ( ( ? [U_6160] : hBOOL(hAPP(U_6162,U_6160))
| ! [U_6159] :
( ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) ) )
& ( ? [U_6158] :
( hBOOL(hAPP(U_6162,U_6158))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6158),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) )
| ! [U_6157] : ~ hBOOL(hAPP(U_6162,U_6157)) ) )
| ( ? [U_6164] : hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK152(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6164),U_6161))))
& ~ hBOOL(hAPP(U_6162,sK152(U_6162,U_6161))) )
| ( ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK150(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK151(U_6162,U_6161)),U_6161))))
& hBOOL(hAPP(U_6162,sK150(U_6162,U_6161))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_6166,sK152(U_6162,U_6161))],[f_1616_5]) ).
fof(f_1616_7,plain,
! [U_6162,U_6161] :
( ( ( ? [U_6160] : hBOOL(hAPP(U_6162,U_6160))
| ! [U_6159] :
( ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) ) )
& ( ? [U_6158] :
( hBOOL(hAPP(U_6162,U_6158))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6158),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) )
| ! [U_6157] : ~ hBOOL(hAPP(U_6162,U_6157)) ) )
| ( hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK152(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK153(U_6162,U_6161)),U_6161))))
& ~ hBOOL(hAPP(U_6162,sK152(U_6162,U_6161))) )
| ( ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK150(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK151(U_6162,U_6161)),U_6161))))
& hBOOL(hAPP(U_6162,sK150(U_6162,U_6161))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_6164,sK153(U_6162,U_6161))],[f_1616_6]) ).
fof(f_1616_8,plain,
! [U_6162,U_6161] :
( ( ( ? [U_6160] : hBOOL(hAPP(U_6162,U_6160))
| ! [U_6159] :
( ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) ) )
& ( ( hBOOL(hAPP(U_6162,sK154(U_6162,U_6161)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_6162,U_6161)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) )
| ! [U_6157] : ~ hBOOL(hAPP(U_6162,U_6157)) ) )
| ( hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK152(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK153(U_6162,U_6161)),U_6161))))
& ~ hBOOL(hAPP(U_6162,sK152(U_6162,U_6161))) )
| ( ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK150(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK151(U_6162,U_6161)),U_6161))))
& hBOOL(hAPP(U_6162,sK150(U_6162,U_6161))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_6158,sK154(U_6162,U_6161))],[f_1616_7]) ).
fof(f_1616_9,plain,
! [U_6162,U_6161] :
( ( ( hBOOL(hAPP(U_6162,sK155(U_6162,U_6161)))
| ! [U_6159] :
( ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) ) )
& ( ( hBOOL(hAPP(U_6162,sK154(U_6162,U_6161)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_6162,U_6161)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161))) )
| ! [U_6157] : ~ hBOOL(hAPP(U_6162,U_6157)) ) )
| ( hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK152(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK153(U_6162,U_6161)),U_6161))))
& ~ hBOOL(hAPP(U_6162,sK152(U_6162,U_6161))) )
| ( ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK150(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK151(U_6162,U_6161)),U_6161))))
& hBOOL(hAPP(U_6162,sK150(U_6162,U_6161))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_6160,sK155(U_6162,U_6161))],[f_1616_8]) ).
fof(f_1616_10,plain,
( ! [U_6161,U_6162] :
( hBOOL(hAPP(U_6162,sK154(U_6162,U_6161)))
| ~ sP558(U_6161,U_6162) )
& ! [U_6161,U_6162] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_6162,U_6161)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161)))
| ~ sP558(U_6161,U_6162) )
& ! [U_6157,U_6159,U_6161,U_6162] :
( hBOOL(hAPP(U_6162,sK155(U_6162,U_6161)))
| ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161)))
| ~ sP559(U_6157,U_6159,U_6161,U_6162) )
& ! [U_6157,U_6159,U_6161,U_6162] :
( sP558(U_6161,U_6162)
| ~ hBOOL(hAPP(U_6162,U_6157))
| ~ sP559(U_6157,U_6159,U_6161,U_6162) )
& ! [U_6161,U_6162] :
( hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK152(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK153(U_6162,U_6161)),U_6161))))
| ~ sP557(U_6161,U_6162) )
& ! [U_6161,U_6162] :
( ~ hBOOL(hAPP(U_6162,sK152(U_6162,U_6161)))
| ~ sP557(U_6161,U_6162) )
& ! [U_6161,U_6162] :
( ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK150(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK151(U_6162,U_6161)),U_6161))))
| ~ sP556(U_6161,U_6162) )
& ! [U_6161,U_6162] :
( hBOOL(hAPP(U_6162,sK150(U_6162,U_6161)))
| ~ sP556(U_6161,U_6162) )
& ! [U_6157,U_6159,U_6161,U_6162] :
( sP559(U_6157,U_6159,U_6161,U_6162)
| sP557(U_6161,U_6162)
| sP556(U_6161,U_6162)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP556,sP557,sP558,sP559])],[f_1616_9]) ).
cnf(f_1616_11,plain,
( sP559(U_6157,U_6159,U_6161,U_6162)
| sP557(U_6161,U_6162)
| sP556(U_6161,U_6162)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
cnf(f_1616_12,plain,
( hBOOL(hAPP(U_6162,sK150(U_6162,U_6161)))
| ~ sP556(U_6161,U_6162) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
cnf(f_1616_13,plain,
( ~ hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK150(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK151(U_6162,U_6161)),U_6161))))
| ~ sP556(U_6161,U_6162) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
cnf(f_1616_14,plain,
( ~ hBOOL(hAPP(U_6162,sK152(U_6162,U_6161)))
| ~ sP557(U_6161,U_6162) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
cnf(f_1616_15,plain,
( hBOOL(hAPP(U_6162,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK152(U_6162,U_6161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK153(U_6162,U_6161)),U_6161))))
| ~ sP557(U_6161,U_6162) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
cnf(f_1616_16,plain,
( sP558(U_6161,U_6162)
| ~ hBOOL(hAPP(U_6162,U_6157))
| ~ sP559(U_6157,U_6159,U_6161,U_6162) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
cnf(f_1616_17,plain,
( hBOOL(hAPP(U_6162,sK155(U_6162,U_6161)))
| ~ hBOOL(hAPP(U_6162,U_6159))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6159),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161)))
| ~ sP559(U_6157,U_6159,U_6161,U_6162) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
cnf(f_1616_18,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_6162,U_6161)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6161)))
| ~ sP558(U_6161,U_6162) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
cnf(f_1616_19,plain,
( hBOOL(hAPP(U_6162,sK154(U_6162,U_6161)))
| ~ sP558(U_6161,U_6162) ),
inference(clausify,[status(thm)],[f_1616_10]) ).
fof(f_1617_1,plain,
! [V_A_2,V_t_2,V_D_2] :
( ! [B_x] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2
| B_x = V_t_2
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
& 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_aset_I4_J]) ).
fof(f_1617_2,plain,
! [U_6172,U_6171,U_6170] :
( ! [U_6169] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6169),U_6170) != U_6171
| U_6169 = U_6171
| ? [U_6168] :
( ? [U_6167] :
( U_6169 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6167),U_6168)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6167),U_6172)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6168),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6170))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6171),U_6172))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6170)) ),
inference(variable_rename,[status(thm)],[f_1617_1]) ).
fof(f_1617_3,plain,
! [U_6172,U_6171,U_6170] :
( ! [U_6169] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6169),U_6170) != U_6171
| U_6169 = U_6171
| ( ? [U_6167] :
( U_6169 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6167),sK156(U_6172,U_6171,U_6170,U_6169))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6167),U_6172)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_6172,U_6171,U_6170,U_6169)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6170))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6171),U_6172))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6170)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_6168,sK156(U_6172,U_6171,U_6170,U_6169))],[f_1617_2]) ).
fof(f_1617_4,plain,
! [U_6172,U_6171,U_6170] :
( ! [U_6169] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6169),U_6170) != U_6171
| U_6169 = U_6171
| ( U_6169 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK157(U_6172,U_6171,U_6170,U_6169)),sK156(U_6172,U_6171,U_6170,U_6169))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK157(U_6172,U_6171,U_6170,U_6169)),U_6172))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_6172,U_6171,U_6170,U_6169)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6170))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6171),U_6172))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6170)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_6167,sK157(U_6172,U_6171,U_6170,U_6169))],[f_1617_3]) ).
fof(f_1617_5,plain,
( ! [U_6171,U_6172,U_6170,U_6169] :
( U_6169 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK157(U_6172,U_6171,U_6170,U_6169)),sK156(U_6172,U_6171,U_6170,U_6169))
| ~ sP560(U_6171,U_6172,U_6170,U_6169) )
& ! [U_6171,U_6172,U_6170,U_6169] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK157(U_6172,U_6171,U_6170,U_6169)),U_6172))
| ~ sP560(U_6171,U_6172,U_6170,U_6169) )
& ! [U_6171,U_6172,U_6170,U_6169] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_6172,U_6171,U_6170,U_6169)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6170)))
| ~ sP560(U_6171,U_6172,U_6170,U_6169) )
& ! [U_6171,U_6172,U_6170,U_6169] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6169),U_6170) != U_6171
| U_6169 = U_6171
| sP560(U_6171,U_6172,U_6170,U_6169)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6171),U_6172))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6170)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP560])],[f_1617_4]) ).
cnf(f_1617_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6169),U_6170) != U_6171
| U_6169 = U_6171
| sP560(U_6171,U_6172,U_6170,U_6169)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6171),U_6172))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6170)) ),
inference(clausify,[status(thm)],[f_1617_5]) ).
cnf(f_1617_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_6172,U_6171,U_6170,U_6169)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6170)))
| ~ sP560(U_6171,U_6172,U_6170,U_6169) ),
inference(clausify,[status(thm)],[f_1617_5]) ).
cnf(f_1617_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK157(U_6172,U_6171,U_6170,U_6169)),U_6172))
| ~ sP560(U_6171,U_6172,U_6170,U_6169) ),
inference(clausify,[status(thm)],[f_1617_5]) ).
cnf(f_1617_9,plain,
( U_6169 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK157(U_6172,U_6171,U_6170,U_6169)),sK156(U_6172,U_6171,U_6170,U_6169))
| ~ sP560(U_6171,U_6172,U_6170,U_6169) ),
inference(clausify,[status(thm)],[f_1617_5]) ).
fof(f_1618_1,plain,
! [V_B_2,V_t_2,V_D_2] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2
| ? [B_x] :
( ? [B_xa] :
( V_t_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) )
& 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))) )
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_bset_I3_J]) ).
fof(f_1618_2,plain,
! [U_6177,U_6176,U_6175] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),U_6175) = U_6176
| ? [U_6174] :
( ? [U_6173] :
( U_6176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6173),U_6174)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6173),U_6177)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6174),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6175))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6175)) ),
inference(variable_rename,[status(thm)],[f_1618_1]) ).
fof(f_1618_3,plain,
! [U_6177,U_6176,U_6175] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),U_6175) = U_6176
| ( ? [U_6173] :
( U_6176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6173),sK158(U_6177,U_6176,U_6175))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6173),U_6177)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_6177,U_6176,U_6175)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6175))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6175)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_6174,sK158(U_6177,U_6176,U_6175))],[f_1618_2]) ).
fof(f_1618_4,plain,
! [U_6177,U_6176,U_6175] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),U_6175) = U_6176
| ( U_6176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK159(U_6177,U_6176,U_6175)),sK158(U_6177,U_6176,U_6175))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK159(U_6177,U_6176,U_6175)),U_6177))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_6177,U_6176,U_6175)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6175))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6175)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_6173,sK159(U_6177,U_6176,U_6175))],[f_1618_3]) ).
fof(f_1618_5,plain,
( ! [U_6177,U_6175,U_6176] :
( U_6176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK159(U_6177,U_6176,U_6175)),sK158(U_6177,U_6176,U_6175))
| ~ sP561(U_6177,U_6175,U_6176) )
& ! [U_6177,U_6175,U_6176] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK159(U_6177,U_6176,U_6175)),U_6177))
| ~ sP561(U_6177,U_6175,U_6176) )
& ! [U_6177,U_6175,U_6176] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_6177,U_6176,U_6175)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6175)))
| ~ sP561(U_6177,U_6175,U_6176) )
& ! [U_6177,U_6175,U_6176] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),U_6175) = U_6176
| sP561(U_6177,U_6175,U_6176)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6175)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP561])],[f_1618_4]) ).
cnf(f_1618_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),U_6175) = U_6176
| sP561(U_6177,U_6175,U_6176)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6176),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6175)) ),
inference(clausify,[status(thm)],[f_1618_5]) ).
cnf(f_1618_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_6177,U_6176,U_6175)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6175)))
| ~ sP561(U_6177,U_6175,U_6176) ),
inference(clausify,[status(thm)],[f_1618_5]) ).
cnf(f_1618_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK159(U_6177,U_6176,U_6175)),U_6177))
| ~ sP561(U_6177,U_6175,U_6176) ),
inference(clausify,[status(thm)],[f_1618_5]) ).
cnf(f_1618_9,plain,
( U_6176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK159(U_6177,U_6176,U_6175)),sK158(U_6177,U_6176,U_6175))
| ~ sP561(U_6177,U_6175,U_6176) ),
inference(clausify,[status(thm)],[f_1618_5]) ).
fof(f_1619_1,plain,
! [V_A_2,V_t_2,V_D_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2
| ? [B_x] :
( ? [B_xa] :
( V_t_2 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) )
& 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))) )
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_aset_I3_J]) ).
fof(f_1619_2,plain,
! [U_6182,U_6181,U_6180] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),U_6180) = U_6181
| ? [U_6179] :
( ? [U_6178] :
( U_6181 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6178),U_6179)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6178),U_6182)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6179),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6180))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6180)) ),
inference(variable_rename,[status(thm)],[f_1619_1]) ).
fof(f_1619_3,plain,
! [U_6182,U_6181,U_6180] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),U_6180) = U_6181
| ( ? [U_6178] :
( U_6181 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6178),sK160(U_6182,U_6181,U_6180))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6178),U_6182)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_6182,U_6181,U_6180)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6180))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6180)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_6179,sK160(U_6182,U_6181,U_6180))],[f_1619_2]) ).
fof(f_1619_4,plain,
! [U_6182,U_6181,U_6180] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),U_6180) = U_6181
| ( U_6181 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK161(U_6182,U_6181,U_6180)),sK160(U_6182,U_6181,U_6180))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK161(U_6182,U_6181,U_6180)),U_6182))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_6182,U_6181,U_6180)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6180))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6180)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_6178,sK161(U_6182,U_6181,U_6180))],[f_1619_3]) ).
fof(f_1619_5,plain,
( ! [U_6182,U_6180,U_6181] :
( U_6181 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK161(U_6182,U_6181,U_6180)),sK160(U_6182,U_6181,U_6180))
| ~ sP562(U_6182,U_6180,U_6181) )
& ! [U_6182,U_6180,U_6181] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK161(U_6182,U_6181,U_6180)),U_6182))
| ~ sP562(U_6182,U_6180,U_6181) )
& ! [U_6182,U_6180,U_6181] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_6182,U_6181,U_6180)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6180)))
| ~ sP562(U_6182,U_6180,U_6181) )
& ! [U_6182,U_6180,U_6181] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),U_6180) = U_6181
| sP562(U_6182,U_6180,U_6181)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6180)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP562])],[f_1619_4]) ).
cnf(f_1619_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),U_6180) = U_6181
| sP562(U_6182,U_6180,U_6181)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6181),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6180)) ),
inference(clausify,[status(thm)],[f_1619_5]) ).
cnf(f_1619_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_6182,U_6181,U_6180)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6180)))
| ~ sP562(U_6182,U_6180,U_6181) ),
inference(clausify,[status(thm)],[f_1619_5]) ).
cnf(f_1619_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK161(U_6182,U_6181,U_6180)),U_6182))
| ~ sP562(U_6182,U_6180,U_6181) ),
inference(clausify,[status(thm)],[f_1619_5]) ).
cnf(f_1619_9,plain,
( U_6181 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK161(U_6182,U_6181,U_6180)),sK160(U_6182,U_6181,U_6180))
| ~ sP562(U_6182,U_6180,U_6181) ),
inference(clausify,[status(thm)],[f_1619_5]) ).
fof(f_1620_1,plain,
! [V_A_2,V_t_2,V_D_2] :
( ! [B_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
& 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_aset_I5_J]) ).
fof(f_1620_2,plain,
! [U_6188,U_6187,U_6186] :
( ! [U_6185] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6185),U_6186)),U_6187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6185),U_6187))
| ? [U_6184] :
( ? [U_6183] :
( U_6185 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6183),U_6184)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6183),U_6188)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6184),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6186))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6187),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6186)) ),
inference(variable_rename,[status(thm)],[f_1620_1]) ).
fof(f_1620_3,plain,
! [U_6188,U_6187,U_6186] :
( ! [U_6185] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6185),U_6186)),U_6187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6185),U_6187))
| ( ? [U_6183] :
( U_6185 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6183),sK162(U_6188,U_6187,U_6186,U_6185))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6183),U_6188)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_6188,U_6187,U_6186,U_6185)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6186))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6187),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6186)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_6184,sK162(U_6188,U_6187,U_6186,U_6185))],[f_1620_2]) ).
fof(f_1620_4,plain,
! [U_6188,U_6187,U_6186] :
( ! [U_6185] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6185),U_6186)),U_6187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6185),U_6187))
| ( U_6185 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK163(U_6188,U_6187,U_6186,U_6185)),sK162(U_6188,U_6187,U_6186,U_6185))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK163(U_6188,U_6187,U_6186,U_6185)),U_6188))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_6188,U_6187,U_6186,U_6185)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6186))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6187),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6186)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_6183,sK163(U_6188,U_6187,U_6186,U_6185))],[f_1620_3]) ).
fof(f_1620_5,plain,
( ! [U_6185,U_6187,U_6186,U_6188] :
( U_6185 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK163(U_6188,U_6187,U_6186,U_6185)),sK162(U_6188,U_6187,U_6186,U_6185))
| ~ sP563(U_6185,U_6187,U_6186,U_6188) )
& ! [U_6185,U_6187,U_6186,U_6188] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK163(U_6188,U_6187,U_6186,U_6185)),U_6188))
| ~ sP563(U_6185,U_6187,U_6186,U_6188) )
& ! [U_6185,U_6187,U_6186,U_6188] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_6188,U_6187,U_6186,U_6185)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6186)))
| ~ sP563(U_6185,U_6187,U_6186,U_6188) )
& ! [U_6185,U_6187,U_6186,U_6188] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6185),U_6186)),U_6187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6185),U_6187))
| sP563(U_6185,U_6187,U_6186,U_6188)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6187),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6186)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP563])],[f_1620_4]) ).
cnf(f_1620_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6185),U_6186)),U_6187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6185),U_6187))
| sP563(U_6185,U_6187,U_6186,U_6188)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6187),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6186)) ),
inference(clausify,[status(thm)],[f_1620_5]) ).
cnf(f_1620_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_6188,U_6187,U_6186,U_6185)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6186)))
| ~ sP563(U_6185,U_6187,U_6186,U_6188) ),
inference(clausify,[status(thm)],[f_1620_5]) ).
cnf(f_1620_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK163(U_6188,U_6187,U_6186,U_6185)),U_6188))
| ~ sP563(U_6185,U_6187,U_6186,U_6188) ),
inference(clausify,[status(thm)],[f_1620_5]) ).
cnf(f_1620_9,plain,
( U_6185 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK163(U_6188,U_6187,U_6186,U_6185)),sK162(U_6188,U_6187,U_6186,U_6185))
| ~ sP563(U_6185,U_6187,U_6186,U_6188) ),
inference(clausify,[status(thm)],[f_1620_5]) ).
fof(f_1621_1,plain,
! [V_B_2,V_t_2,V_D_2] :
( ! [B_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
& 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_bset_I7_J]) ).
fof(f_1621_2,plain,
! [U_6194,U_6193,U_6192] :
( ! [U_6191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6191),U_6192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),U_6191))
| ? [U_6190] :
( ? [U_6189] :
( U_6191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6189),U_6190)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6189),U_6194)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6190),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6192))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6193),U_6194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6192)) ),
inference(variable_rename,[status(thm)],[f_1621_1]) ).
fof(f_1621_3,plain,
! [U_6194,U_6193,U_6192] :
( ! [U_6191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6191),U_6192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),U_6191))
| ( ? [U_6189] :
( U_6191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6189),sK164(U_6194,U_6193,U_6192,U_6191))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6189),U_6194)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_6194,U_6193,U_6192,U_6191)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6192))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6193),U_6194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6192)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_6190,sK164(U_6194,U_6193,U_6192,U_6191))],[f_1621_2]) ).
fof(f_1621_4,plain,
! [U_6194,U_6193,U_6192] :
( ! [U_6191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6191),U_6192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),U_6191))
| ( U_6191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK165(U_6194,U_6193,U_6192,U_6191)),sK164(U_6194,U_6193,U_6192,U_6191))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK165(U_6194,U_6193,U_6192,U_6191)),U_6194))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_6194,U_6193,U_6192,U_6191)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6192))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6193),U_6194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6192)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_6189,sK165(U_6194,U_6193,U_6192,U_6191))],[f_1621_3]) ).
fof(f_1621_5,plain,
( ! [U_6193,U_6194,U_6191,U_6192] :
( U_6191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK165(U_6194,U_6193,U_6192,U_6191)),sK164(U_6194,U_6193,U_6192,U_6191))
| ~ sP564(U_6193,U_6194,U_6191,U_6192) )
& ! [U_6193,U_6194,U_6191,U_6192] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK165(U_6194,U_6193,U_6192,U_6191)),U_6194))
| ~ sP564(U_6193,U_6194,U_6191,U_6192) )
& ! [U_6193,U_6194,U_6191,U_6192] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_6194,U_6193,U_6192,U_6191)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6192)))
| ~ sP564(U_6193,U_6194,U_6191,U_6192) )
& ! [U_6193,U_6194,U_6191,U_6192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6191),U_6192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),U_6191))
| sP564(U_6193,U_6194,U_6191,U_6192)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6193),U_6194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6192)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP564])],[f_1621_4]) ).
cnf(f_1621_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6191),U_6192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6193),U_6191))
| sP564(U_6193,U_6194,U_6191,U_6192)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6193),U_6194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6192)) ),
inference(clausify,[status(thm)],[f_1621_5]) ).
cnf(f_1621_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_6194,U_6193,U_6192,U_6191)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6192)))
| ~ sP564(U_6193,U_6194,U_6191,U_6192) ),
inference(clausify,[status(thm)],[f_1621_5]) ).
cnf(f_1621_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK165(U_6194,U_6193,U_6192,U_6191)),U_6194))
| ~ sP564(U_6193,U_6194,U_6191,U_6192) ),
inference(clausify,[status(thm)],[f_1621_5]) ).
cnf(f_1621_9,plain,
( U_6191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK165(U_6194,U_6193,U_6192,U_6191)),sK164(U_6194,U_6193,U_6192,U_6191))
| ~ sP564(U_6193,U_6194,U_6191,U_6192) ),
inference(clausify,[status(thm)],[f_1621_5]) ).
fof(f_1622_1,plain,
! [V_B_2,V_t_2,V_D_2] :
( ! [B_x] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2
| B_x = V_t_2
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
& 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_bset_I4_J]) ).
fof(f_1622_2,plain,
! [U_6200,U_6199,U_6198] :
( ! [U_6197] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6197),U_6198) != U_6199
| U_6197 = U_6199
| ? [U_6196] :
( ? [U_6195] :
( U_6197 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6195),U_6196)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6195),U_6200)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6196),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6198))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6199),U_6200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6198)) ),
inference(variable_rename,[status(thm)],[f_1622_1]) ).
fof(f_1622_3,plain,
! [U_6200,U_6199,U_6198] :
( ! [U_6197] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6197),U_6198) != U_6199
| U_6197 = U_6199
| ( ? [U_6195] :
( U_6197 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6195),sK166(U_6200,U_6199,U_6198,U_6197))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6195),U_6200)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6200,U_6199,U_6198,U_6197)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6198))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6199),U_6200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6198)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_6196,sK166(U_6200,U_6199,U_6198,U_6197))],[f_1622_2]) ).
fof(f_1622_4,plain,
! [U_6200,U_6199,U_6198] :
( ! [U_6197] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6197),U_6198) != U_6199
| U_6197 = U_6199
| ( U_6197 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK167(U_6200,U_6199,U_6198,U_6197)),sK166(U_6200,U_6199,U_6198,U_6197))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_6200,U_6199,U_6198,U_6197)),U_6200))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6200,U_6199,U_6198,U_6197)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6198))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6199),U_6200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6198)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_6195,sK167(U_6200,U_6199,U_6198,U_6197))],[f_1622_3]) ).
fof(f_1622_5,plain,
( ! [U_6200,U_6197,U_6198,U_6199] :
( U_6197 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK167(U_6200,U_6199,U_6198,U_6197)),sK166(U_6200,U_6199,U_6198,U_6197))
| ~ sP565(U_6200,U_6197,U_6198,U_6199) )
& ! [U_6200,U_6197,U_6198,U_6199] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_6200,U_6199,U_6198,U_6197)),U_6200))
| ~ sP565(U_6200,U_6197,U_6198,U_6199) )
& ! [U_6200,U_6197,U_6198,U_6199] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6200,U_6199,U_6198,U_6197)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6198)))
| ~ sP565(U_6200,U_6197,U_6198,U_6199) )
& ! [U_6200,U_6197,U_6198,U_6199] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6197),U_6198) != U_6199
| U_6197 = U_6199
| sP565(U_6200,U_6197,U_6198,U_6199)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6199),U_6200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6198)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP565])],[f_1622_4]) ).
cnf(f_1622_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6197),U_6198) != U_6199
| U_6197 = U_6199
| sP565(U_6200,U_6197,U_6198,U_6199)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6199),U_6200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6198)) ),
inference(clausify,[status(thm)],[f_1622_5]) ).
cnf(f_1622_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6200,U_6199,U_6198,U_6197)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6198)))
| ~ sP565(U_6200,U_6197,U_6198,U_6199) ),
inference(clausify,[status(thm)],[f_1622_5]) ).
cnf(f_1622_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_6200,U_6199,U_6198,U_6197)),U_6200))
| ~ sP565(U_6200,U_6197,U_6198,U_6199) ),
inference(clausify,[status(thm)],[f_1622_5]) ).
cnf(f_1622_9,plain,
( U_6197 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK167(U_6200,U_6199,U_6198,U_6197)),sK166(U_6200,U_6199,U_6198,U_6197))
| ~ sP565(U_6200,U_6197,U_6198,U_6199) ),
inference(clausify,[status(thm)],[f_1622_5]) ).
fof(f_1623_1,plain,
! [V_t_2,V_A_2,V_D_2] :
( ! [B_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
& 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_aset_I7_J]) ).
fof(f_1623_2,plain,
! [U_6206,U_6205,U_6204] :
( ! [U_6203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6203),U_6204)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),U_6203))
| ? [U_6202] :
( ? [U_6201] :
( U_6203 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6201),U_6202)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6201),U_6205)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6202),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6204))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6204)) ),
inference(variable_rename,[status(thm)],[f_1623_1]) ).
fof(f_1623_3,plain,
! [U_6206,U_6205,U_6204] :
( ! [U_6203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6203),U_6204)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),U_6203))
| ( ? [U_6201] :
( U_6203 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6201),sK168(U_6206,U_6205,U_6204,U_6203))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6201),U_6205)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_6206,U_6205,U_6204,U_6203)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6204))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6204)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_6202,sK168(U_6206,U_6205,U_6204,U_6203))],[f_1623_2]) ).
fof(f_1623_4,plain,
! [U_6206,U_6205,U_6204] :
( ! [U_6203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6203),U_6204)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),U_6203))
| ( U_6203 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK169(U_6206,U_6205,U_6204,U_6203)),sK168(U_6206,U_6205,U_6204,U_6203))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK169(U_6206,U_6205,U_6204,U_6203)),U_6205))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_6206,U_6205,U_6204,U_6203)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6204))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6204)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_6201,sK169(U_6206,U_6205,U_6204,U_6203))],[f_1623_3]) ).
fof(f_1623_5,plain,
( ! [U_6206,U_6203,U_6204,U_6205] :
( U_6203 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK169(U_6206,U_6205,U_6204,U_6203)),sK168(U_6206,U_6205,U_6204,U_6203))
| ~ sP566(U_6206,U_6203,U_6204,U_6205) )
& ! [U_6206,U_6203,U_6204,U_6205] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK169(U_6206,U_6205,U_6204,U_6203)),U_6205))
| ~ sP566(U_6206,U_6203,U_6204,U_6205) )
& ! [U_6206,U_6203,U_6204,U_6205] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_6206,U_6205,U_6204,U_6203)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6204)))
| ~ sP566(U_6206,U_6203,U_6204,U_6205) )
& ! [U_6206,U_6203,U_6204,U_6205] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6203),U_6204)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),U_6203))
| sP566(U_6206,U_6203,U_6204,U_6205)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6204)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP566])],[f_1623_4]) ).
cnf(f_1623_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6203),U_6204)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6206),U_6203))
| sP566(U_6206,U_6203,U_6204,U_6205)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6204)) ),
inference(clausify,[status(thm)],[f_1623_5]) ).
cnf(f_1623_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_6206,U_6205,U_6204,U_6203)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6204)))
| ~ sP566(U_6206,U_6203,U_6204,U_6205) ),
inference(clausify,[status(thm)],[f_1623_5]) ).
cnf(f_1623_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK169(U_6206,U_6205,U_6204,U_6203)),U_6205))
| ~ sP566(U_6206,U_6203,U_6204,U_6205) ),
inference(clausify,[status(thm)],[f_1623_5]) ).
cnf(f_1623_9,plain,
( U_6203 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK169(U_6206,U_6205,U_6204,U_6203)),sK168(U_6206,U_6205,U_6204,U_6203))
| ~ sP566(U_6206,U_6203,U_6204,U_6205) ),
inference(clausify,[status(thm)],[f_1623_5]) ).
fof(f_1624_1,plain,
! [V_t_2,V_B_2,V_D_2] :
( ! [B_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
| ? [B_xa] :
( ? [B_xb] :
( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
& 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_bset_I5_J]) ).
fof(f_1624_2,plain,
! [U_6212,U_6211,U_6210] :
( ! [U_6209] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6209),U_6210)),U_6212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6209),U_6212))
| ? [U_6208] :
( ? [U_6207] :
( U_6209 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6207),U_6208)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6207),U_6211)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6208),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6210))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6210)) ),
inference(variable_rename,[status(thm)],[f_1624_1]) ).
fof(f_1624_3,plain,
! [U_6212,U_6211,U_6210] :
( ! [U_6209] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6209),U_6210)),U_6212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6209),U_6212))
| ( ? [U_6207] :
( U_6209 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6207),sK170(U_6212,U_6211,U_6210,U_6209))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6207),U_6211)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_6212,U_6211,U_6210,U_6209)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6210))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6210)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_6208,sK170(U_6212,U_6211,U_6210,U_6209))],[f_1624_2]) ).
fof(f_1624_4,plain,
! [U_6212,U_6211,U_6210] :
( ! [U_6209] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6209),U_6210)),U_6212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6209),U_6212))
| ( U_6209 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK171(U_6212,U_6211,U_6210,U_6209)),sK170(U_6212,U_6211,U_6210,U_6209))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_6212,U_6211,U_6210,U_6209)),U_6211))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_6212,U_6211,U_6210,U_6209)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6210))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6210)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_6207,sK171(U_6212,U_6211,U_6210,U_6209))],[f_1624_3]) ).
fof(f_1624_5,plain,
( ! [U_6212,U_6211,U_6209,U_6210] :
( U_6209 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK171(U_6212,U_6211,U_6210,U_6209)),sK170(U_6212,U_6211,U_6210,U_6209))
| ~ sP567(U_6212,U_6211,U_6209,U_6210) )
& ! [U_6212,U_6211,U_6209,U_6210] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_6212,U_6211,U_6210,U_6209)),U_6211))
| ~ sP567(U_6212,U_6211,U_6209,U_6210) )
& ! [U_6212,U_6211,U_6209,U_6210] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_6212,U_6211,U_6210,U_6209)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6210)))
| ~ sP567(U_6212,U_6211,U_6209,U_6210) )
& ! [U_6212,U_6211,U_6209,U_6210] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6209),U_6210)),U_6212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6209),U_6212))
| sP567(U_6212,U_6211,U_6209,U_6210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6210)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP567])],[f_1624_4]) ).
cnf(f_1624_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6209),U_6210)),U_6212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6209),U_6212))
| sP567(U_6212,U_6211,U_6209,U_6210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6210)) ),
inference(clausify,[status(thm)],[f_1624_5]) ).
cnf(f_1624_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_6212,U_6211,U_6210,U_6209)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6210)))
| ~ sP567(U_6212,U_6211,U_6209,U_6210) ),
inference(clausify,[status(thm)],[f_1624_5]) ).
cnf(f_1624_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_6212,U_6211,U_6210,U_6209)),U_6211))
| ~ sP567(U_6212,U_6211,U_6209,U_6210) ),
inference(clausify,[status(thm)],[f_1624_5]) ).
cnf(f_1624_9,plain,
( U_6209 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK171(U_6212,U_6211,U_6210,U_6209)),sK170(U_6212,U_6211,U_6210,U_6209))
| ~ sP567(U_6212,U_6211,U_6209,U_6210) ),
inference(clausify,[status(thm)],[f_1624_5]) ).
fof(f_1625_1,plain,
! [V_x,V_y] :
( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) )
& ( c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).
fof(f_1625_2,plain,
! [U_6214,U_6213] :
( ( c_Nat__Transfer_Otsub(U_6214,U_6213) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6213),U_6214)) )
& ( c_Nat__Transfer_Otsub(U_6214,U_6213) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6214),U_6213)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6213),U_6214)) ) ),
inference(variable_rename,[status(thm)],[f_1625_1]) ).
fof(f_1625_3,plain,
( ! [U_6218,U_6216] :
( c_Nat__Transfer_Otsub(U_6218,U_6216) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6216),U_6218)) )
& ! [U_6217,U_6215] :
( c_Nat__Transfer_Otsub(U_6217,U_6215) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6217),U_6215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6215),U_6217)) ) ),
inference(miniscope,[status(thm)],[f_1625_2]) ).
fof(f_1625_4,plain,
( ! [U_6216,U_6218] :
( c_Nat__Transfer_Otsub(U_6218,U_6216) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6216),U_6218)) )
& ! [U_6217,U_6215] :
( c_Nat__Transfer_Otsub(U_6217,U_6215) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6217),U_6215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6215),U_6217)) ) ),
inference(definitional_conversion,[status(esa)],[f_1625_3]) ).
cnf(f_1625_5,plain,
( c_Nat__Transfer_Otsub(U_6217,U_6215) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6217),U_6215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6215),U_6217)) ),
inference(clausify,[status(thm)],[f_1625_4]) ).
cnf(f_1625_6,plain,
( c_Nat__Transfer_Otsub(U_6218,U_6216) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6216),U_6218)) ),
inference(clausify,[status(thm)],[f_1625_4]) ).
fof(f_1626_1,plain,
! [V_k,V_m] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_int__power__div__base]) ).
fof(f_1626_2,plain,
! [U_6220,U_6219] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6220),U_6219)),U_6220) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6220),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6219),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6219)) ),
inference(variable_rename,[status(thm)],[f_1626_1]) ).
fof(f_1626_3,plain,
! [U_6219,U_6220] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6220),U_6219)),U_6220) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6220),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6219),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6219)) ),
inference(definitional_conversion,[status(esa)],[f_1626_2]) ).
cnf(f_1626_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6220),U_6219)),U_6220) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6220),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6219),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6219)) ),
inference(clausify,[status(thm)],[f_1626_3]) ).
fof(f_1627_1,plain,
! [V_k_2,V_Pa_2,V_d_2] :
( ! [B_x] :
( 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))))
| ~ hBOOL(hAPP(V_Pa_2,B_x)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2)))
& hBOOL(hAPP(V_Pa_2,B_x)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma]) ).
fof(f_1627_2,plain,
! [U_6225,U_6224,U_6223] :
( ! [U_6222] :
( hBOOL(hAPP(U_6224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6225),U_6223))))
| ~ hBOOL(hAPP(U_6224,U_6222)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6225))
| ? [U_6221] :
( ~ hBOOL(hAPP(U_6224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6221),U_6223)))
& hBOOL(hAPP(U_6224,U_6221)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6223)) ),
inference(variable_rename,[status(thm)],[f_1627_1]) ).
fof(f_1627_3,plain,
! [U_6225,U_6224,U_6223] :
( ! [U_6222] :
( hBOOL(hAPP(U_6224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6225),U_6223))))
| ~ hBOOL(hAPP(U_6224,U_6222)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6225))
| ( ~ hBOOL(hAPP(U_6224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK172(U_6225,U_6224,U_6223)),U_6223)))
& hBOOL(hAPP(U_6224,sK172(U_6225,U_6224,U_6223))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6223)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_6221,sK172(U_6225,U_6224,U_6223))],[f_1627_2]) ).
fof(f_1627_4,plain,
( ! [U_6223,U_6224,U_6225] :
( ~ hBOOL(hAPP(U_6224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK172(U_6225,U_6224,U_6223)),U_6223)))
| ~ sP568(U_6223,U_6224,U_6225) )
& ! [U_6223,U_6224,U_6225] :
( hBOOL(hAPP(U_6224,sK172(U_6225,U_6224,U_6223)))
| ~ sP568(U_6223,U_6224,U_6225) )
& ! [U_6222,U_6223,U_6224,U_6225] :
( hBOOL(hAPP(U_6224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6225),U_6223))))
| ~ hBOOL(hAPP(U_6224,U_6222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6225))
| sP568(U_6223,U_6224,U_6225)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6223)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP568])],[f_1627_3]) ).
cnf(f_1627_5,plain,
( hBOOL(hAPP(U_6224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6225),U_6223))))
| ~ hBOOL(hAPP(U_6224,U_6222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6225))
| sP568(U_6223,U_6224,U_6225)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6223)) ),
inference(clausify,[status(thm)],[f_1627_4]) ).
cnf(f_1627_6,plain,
( hBOOL(hAPP(U_6224,sK172(U_6225,U_6224,U_6223)))
| ~ sP568(U_6223,U_6224,U_6225) ),
inference(clausify,[status(thm)],[f_1627_4]) ).
cnf(f_1627_7,plain,
( ~ hBOOL(hAPP(U_6224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK172(U_6225,U_6224,U_6223)),U_6223)))
| ~ sP568(U_6223,U_6224,U_6225) ),
inference(clausify,[status(thm)],[f_1627_4]) ).
fof(f_1628_1,plain,
! [V_k_2,V_Pa_2,V_d_2] :
( ! [B_x] :
( 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))))
| ~ hBOOL(hAPP(V_Pa_2,B_x)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))
& hBOOL(hAPP(V_Pa_2,B_x)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).
fof(f_1628_2,plain,
! [U_6230,U_6229,U_6228] :
( ! [U_6227] :
( hBOOL(hAPP(U_6229,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6230),U_6228))))
| ~ hBOOL(hAPP(U_6229,U_6227)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6230))
| ? [U_6226] :
( ~ hBOOL(hAPP(U_6229,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6226),U_6228)))
& hBOOL(hAPP(U_6229,U_6226)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6228)) ),
inference(variable_rename,[status(thm)],[f_1628_1]) ).
fof(f_1628_3,plain,
! [U_6230,U_6229,U_6228] :
( ! [U_6227] :
( hBOOL(hAPP(U_6229,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6230),U_6228))))
| ~ hBOOL(hAPP(U_6229,U_6227)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6230))
| ( ~ hBOOL(hAPP(U_6229,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK173(U_6230,U_6229,U_6228)),U_6228)))
& hBOOL(hAPP(U_6229,sK173(U_6230,U_6229,U_6228))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6228)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_6226,sK173(U_6230,U_6229,U_6228))],[f_1628_2]) ).
fof(f_1628_4,plain,
( ! [U_6229,U_6228,U_6230] :
( ~ hBOOL(hAPP(U_6229,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK173(U_6230,U_6229,U_6228)),U_6228)))
| ~ sP569(U_6229,U_6228,U_6230) )
& ! [U_6229,U_6228,U_6230] :
( hBOOL(hAPP(U_6229,sK173(U_6230,U_6229,U_6228)))
| ~ sP569(U_6229,U_6228,U_6230) )
& ! [U_6229,U_6227,U_6228,U_6230] :
( hBOOL(hAPP(U_6229,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6230),U_6228))))
| ~ hBOOL(hAPP(U_6229,U_6227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6230))
| sP569(U_6229,U_6228,U_6230)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6228)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP569])],[f_1628_3]) ).
cnf(f_1628_5,plain,
( hBOOL(hAPP(U_6229,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6230),U_6228))))
| ~ hBOOL(hAPP(U_6229,U_6227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6230))
| sP569(U_6229,U_6228,U_6230)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6228)) ),
inference(clausify,[status(thm)],[f_1628_4]) ).
cnf(f_1628_6,plain,
( hBOOL(hAPP(U_6229,sK173(U_6230,U_6229,U_6228)))
| ~ sP569(U_6229,U_6228,U_6230) ),
inference(clausify,[status(thm)],[f_1628_4]) ).
cnf(f_1628_7,plain,
( ~ hBOOL(hAPP(U_6229,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK173(U_6230,U_6229,U_6228)),U_6228)))
| ~ sP569(U_6229,U_6228,U_6230) ),
inference(clausify,[status(thm)],[f_1628_4]) ).
fof(f_1629_1,plain,
! [V_v,T_a] :
( ( ( 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)
| 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))) )
& ( 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)
| ~ 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))) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__number__of__lemma]) ).
fof(f_1629_2,plain,
! [U_6232,U_6231] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6231),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6232)) = c_Groups_Ozero__class_Ozero(U_6231)
| 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),U_6232))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6231),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6232)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6231),U_6232)
| ~ 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),U_6232))) ) )
| ~ class_Int_Onumber__ring(U_6231) ),
inference(variable_rename,[status(thm)],[f_1629_1]) ).
fof(f_1629_3,plain,
( ! [U_6232,U_6231] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6231),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6232)) = c_Groups_Ozero__class_Ozero(U_6231)
| 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),U_6232)))
| ~ sP570(U_6232,U_6231) )
& ! [U_6232,U_6231] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6231),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6232)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6231),U_6232)
| ~ 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),U_6232)))
| ~ sP570(U_6232,U_6231) )
& ! [U_6232,U_6231] :
( sP570(U_6232,U_6231)
| ~ class_Int_Onumber__ring(U_6231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP570])],[f_1629_2]) ).
cnf(f_1629_4,plain,
( sP570(U_6232,U_6231)
| ~ class_Int_Onumber__ring(U_6231) ),
inference(clausify,[status(thm)],[f_1629_3]) ).
cnf(f_1629_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6231),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6232)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6231),U_6232)
| ~ 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),U_6232)))
| ~ sP570(U_6232,U_6231) ),
inference(clausify,[status(thm)],[f_1629_3]) ).
cnf(f_1629_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6231),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6232)) = c_Groups_Ozero__class_Ozero(U_6231)
| 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),U_6232)))
| ~ sP570(U_6232,U_6231) ),
inference(clausify,[status(thm)],[f_1629_3]) ).
fof(f_1630_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_negative__zle]) ).
fof(f_1630_2,plain,
! [U_6234,U_6233] : 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),U_6233))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6234))),
inference(variable_rename,[status(thm)],[f_1630_1]) ).
fof(f_1630_3,plain,
! [U_6233,U_6234] : 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),U_6233))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6234))),
inference(definitional_conversion,[status(esa)],[f_1630_2]) ).
cnf(f_1630_4,plain,
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),U_6233))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6234))),
inference(clausify,[status(thm)],[f_1630_3]) ).
fof(f_1631_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_negative__zless]) ).
fof(f_1631_2,plain,
! [U_6236,U_6235] : 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,U_6235)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6236))),
inference(variable_rename,[status(thm)],[f_1631_1]) ).
fof(f_1631_3,plain,
! [U_6235,U_6236] : 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,U_6235)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6236))),
inference(definitional_conversion,[status(esa)],[f_1631_2]) ).
cnf(f_1631_4,plain,
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,U_6235)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6236))),
inference(clausify,[status(thm)],[f_1631_3]) ).
fof(f_1632_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).
fof(f_1632_2,plain,
! [U_6238,U_6237] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6237),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6238)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6237),U_6238)),
inference(variable_rename,[status(thm)],[f_1632_1]) ).
fof(f_1632_3,plain,
! [U_6237,U_6238] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6237),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6238)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6237),U_6238)),
inference(definitional_conversion,[status(esa)],[f_1632_2]) ).
cnf(f_1632_4,plain,
c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6237),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6238)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6237),U_6238)),
inference(clausify,[status(thm)],[f_1632_3]) ).
fof(f_1633_1,plain,
! [V_n_2,V_m_2,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)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| 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) ) )
| ~ class_Nat_Osemiring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff]) ).
fof(f_1633_2,plain,
! [U_6241,U_6240,U_6239] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6240) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6241)
| U_6240 != U_6241 )
& ( U_6240 = U_6241
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6240) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6241) ) )
| ~ class_Nat_Osemiring__char__0(U_6239) ),
inference(variable_rename,[status(thm)],[f_1633_1]) ).
fof(f_1633_3,plain,
( ! [U_6239,U_6240,U_6241] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6240) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6241)
| U_6240 != U_6241
| ~ sP571(U_6239,U_6240,U_6241) )
& ! [U_6239,U_6240,U_6241] :
( U_6240 = U_6241
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6240) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6241)
| ~ sP571(U_6239,U_6240,U_6241) )
& ! [U_6239,U_6240,U_6241] :
( sP571(U_6239,U_6240,U_6241)
| ~ class_Nat_Osemiring__char__0(U_6239) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP571])],[f_1633_2]) ).
cnf(f_1633_4,plain,
( sP571(U_6239,U_6240,U_6241)
| ~ class_Nat_Osemiring__char__0(U_6239) ),
inference(clausify,[status(thm)],[f_1633_3]) ).
cnf(f_1633_5,plain,
( U_6240 = U_6241
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6240) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6241)
| ~ sP571(U_6239,U_6240,U_6241) ),
inference(clausify,[status(thm)],[f_1633_3]) ).
cnf(f_1633_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6240) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6239),U_6241)
| U_6240 != U_6241
| ~ sP571(U_6239,U_6240,U_6241) ),
inference(clausify,[status(thm)],[f_1633_3]) ).
fof(f_1634_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zdiv__zero]) ).
fof(f_1634_2,plain,
! [U_6242] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6242) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1634_1]) ).
fof(f_1634_3,plain,
! [U_6242] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6242) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1634_2]) ).
cnf(f_1634_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6242) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1634_3]) ).
fof(f_1635_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zdiv__zminus__zminus]) ).
fof(f_1635_2,plain,
! [U_6244,U_6243] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6243)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6244)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6243),U_6244),
inference(variable_rename,[status(thm)],[f_1635_1]) ).
fof(f_1635_3,plain,
! [U_6243,U_6244] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6243)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6244)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6243),U_6244),
inference(definitional_conversion,[status(esa)],[f_1635_2]) ).
cnf(f_1635_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6243)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6244)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6243),U_6244),
inference(clausify,[status(thm)],[f_1635_3]) ).
fof(f_1636_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2]) ).
fof(f_1636_2,plain,
! [U_6246,U_6245] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6245),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6246)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6245)),U_6246),
inference(variable_rename,[status(thm)],[f_1636_1]) ).
fof(f_1636_3,plain,
! [U_6245,U_6246] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6245),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6246)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6245)),U_6246),
inference(definitional_conversion,[status(esa)],[f_1636_2]) ).
cnf(f_1636_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6245),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6246)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6245)),U_6246),
inference(clausify,[status(thm)],[f_1636_3]) ).
fof(f_1637_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__0]) ).
fof(f_1637_2,plain,
! [U_6248,U_6247] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6247),c_Groups_Ozero__class_Ozero(U_6247)),U_6248) = c_Groups_Ozero__class_Ozero(U_6247)
| ~ class_Divides_Osemiring__div(U_6247) ),
inference(variable_rename,[status(thm)],[f_1637_1]) ).
fof(f_1637_3,plain,
! [U_6247,U_6248] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6247),c_Groups_Ozero__class_Ozero(U_6247)),U_6248) = c_Groups_Ozero__class_Ozero(U_6247)
| ~ class_Divides_Osemiring__div(U_6247) ),
inference(definitional_conversion,[status(esa)],[f_1637_2]) ).
cnf(f_1637_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6247),c_Groups_Ozero__class_Ozero(U_6247)),U_6248) = c_Groups_Ozero__class_Ozero(U_6247)
| ~ class_Divides_Osemiring__div(U_6247) ),
inference(clausify,[status(thm)],[f_1637_3]) ).
fof(f_1638_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__by__0]) ).
fof(f_1638_2,plain,
! [U_6250,U_6249] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6249),U_6250),c_Groups_Ozero__class_Ozero(U_6249)) = c_Groups_Ozero__class_Ozero(U_6249)
| ~ class_Divides_Osemiring__div(U_6249) ),
inference(variable_rename,[status(thm)],[f_1638_1]) ).
fof(f_1638_3,plain,
! [U_6249,U_6250] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6249),U_6250),c_Groups_Ozero__class_Ozero(U_6249)) = c_Groups_Ozero__class_Ozero(U_6249)
| ~ class_Divides_Osemiring__div(U_6249) ),
inference(definitional_conversion,[status(esa)],[f_1638_2]) ).
cnf(f_1638_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6249),U_6250),c_Groups_Ozero__class_Ozero(U_6249)) = c_Groups_Ozero__class_Ozero(U_6249)
| ~ class_Divides_Osemiring__div(U_6249) ),
inference(clausify,[status(thm)],[f_1638_3]) ).
fof(f_1639_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__by__1]) ).
fof(f_1639_2,plain,
! [U_6252,U_6251] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6251),U_6252),c_Groups_Oone__class_Oone(U_6251)) = U_6252
| ~ class_Divides_Osemiring__div(U_6251) ),
inference(variable_rename,[status(thm)],[f_1639_1]) ).
fof(f_1639_3,plain,
! [U_6251,U_6252] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6251),U_6252),c_Groups_Oone__class_Oone(U_6251)) = U_6252
| ~ class_Divides_Osemiring__div(U_6251) ),
inference(definitional_conversion,[status(esa)],[f_1639_2]) ).
cnf(f_1639_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6251),U_6252),c_Groups_Oone__class_Oone(U_6251)) = U_6252
| ~ class_Divides_Osemiring__div(U_6251) ),
inference(clausify,[status(thm)],[f_1639_3]) ).
fof(f_1640_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).
fof(f_1640_2,plain,
! [U_6253] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6253) = 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)),U_6253)),
inference(variable_rename,[status(thm)],[f_1640_1]) ).
fof(f_1640_3,plain,
! [U_6253] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6253) = 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)),U_6253)),
inference(definitional_conversion,[status(esa)],[f_1640_2]) ).
cnf(f_1640_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6253) = 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)),U_6253)),
inference(clausify,[status(thm)],[f_1640_3]) ).
fof(f_1641_1,plain,
! [V_A_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J]) ).
fof(f_1641_2,plain,
! [U_6255,U_6254] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6254),U_6255))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6254)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6255))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6254)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6255)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6254),U_6255)) ) ),
inference(variable_rename,[status(thm)],[f_1641_1]) ).
fof(f_1641_3,plain,
( ! [U_6259,U_6257] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6257),U_6259))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6257)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6259))) )
& ! [U_6258,U_6256] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6256)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6258)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6256),U_6258)) ) ),
inference(miniscope,[status(thm)],[f_1641_2]) ).
fof(f_1641_4,plain,
( ! [U_6257,U_6259] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6257),U_6259))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6257)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6259))) )
& ! [U_6258,U_6256] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6256)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6258)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6256),U_6258)) ) ),
inference(definitional_conversion,[status(esa)],[f_1641_3]) ).
cnf(f_1641_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6256)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6258)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6256),U_6258)) ),
inference(clausify,[status(thm)],[f_1641_4]) ).
cnf(f_1641_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6257),U_6259))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6257)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6259))) ),
inference(clausify,[status(thm)],[f_1641_4]) ).
fof(f_1642_1,plain,
! [V_B_2,V_A_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J]) ).
fof(f_1642_2,plain,
! [U_6261,U_6260] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6260),U_6261))
| ~ 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)),U_6260)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6261))) )
& ( 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)),U_6260)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6261)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6260),U_6261)) ) ),
inference(variable_rename,[status(thm)],[f_1642_1]) ).
fof(f_1642_3,plain,
( ! [U_6265,U_6263] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6263),U_6265))
| ~ 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)),U_6263)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6265))) )
& ! [U_6264,U_6262] :
( 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)),U_6262)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6264)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6262),U_6264)) ) ),
inference(miniscope,[status(thm)],[f_1642_2]) ).
fof(f_1642_4,plain,
( ! [U_6263,U_6265] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6263),U_6265))
| ~ 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)),U_6263)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6265))) )
& ! [U_6264,U_6262] :
( 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)),U_6262)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6264)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6262),U_6264)) ) ),
inference(definitional_conversion,[status(esa)],[f_1642_3]) ).
cnf(f_1642_5,plain,
( 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)),U_6262)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6264)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6262),U_6264)) ),
inference(clausify,[status(thm)],[f_1642_4]) ).
cnf(f_1642_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6263),U_6265))
| ~ 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)),U_6263)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6265))) ),
inference(clausify,[status(thm)],[f_1642_4]) ).
fof(f_1643_1,plain,
! [V_y,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_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_1643_2,plain,
! [U_6267,U_6266] :
( 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),U_6266),U_6267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6266)) ),
inference(variable_rename,[status(thm)],[f_1643_1]) ).
fof(f_1643_3,plain,
! [U_6266,U_6267] :
( 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),U_6266),U_6267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6266)) ),
inference(definitional_conversion,[status(esa)],[f_1643_2]) ).
cnf(f_1643_4,plain,
( 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),U_6266),U_6267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6266)) ),
inference(clausify,[status(thm)],[f_1643_3]) ).
fof(f_1644_1,plain,
! [V_a_2,V_b_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff]) ).
fof(f_1644_2,plain,
! [U_6269,U_6268] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6269),U_6268)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6269),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6269),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6269),U_6268)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6268)) ),
inference(variable_rename,[status(thm)],[f_1644_1]) ).
fof(f_1644_3,plain,
( ! [U_6269,U_6268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6269),U_6268)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6269),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP572(U_6269,U_6268) )
& ! [U_6269,U_6268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6269),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6269),U_6268)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP572(U_6269,U_6268) )
& ! [U_6269,U_6268] :
( sP572(U_6269,U_6268)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6268)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP572])],[f_1644_2]) ).
cnf(f_1644_4,plain,
( sP572(U_6269,U_6268)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6268)) ),
inference(clausify,[status(thm)],[f_1644_3]) ).
cnf(f_1644_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6269),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6269),U_6268)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP572(U_6269,U_6268) ),
inference(clausify,[status(thm)],[f_1644_3]) ).
cnf(f_1644_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6269),U_6268)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6269),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP572(U_6269,U_6268) ),
inference(clausify,[status(thm)],[f_1644_3]) ).
fof(f_1645_1,plain,
! [V_a_2,V_b_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff]) ).
fof(f_1645_2,plain,
! [U_6271,U_6270] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6271)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6271))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6270),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1645_1]) ).
fof(f_1645_3,plain,
( ! [U_6271,U_6270] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6271))
| ~ sP573(U_6271,U_6270) )
& ! [U_6271,U_6270] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6271))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP573(U_6271,U_6270) )
& ! [U_6271,U_6270] :
( sP573(U_6271,U_6270)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6270),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP573])],[f_1645_2]) ).
cnf(f_1645_4,plain,
( sP573(U_6271,U_6270)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6270),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1645_3]) ).
cnf(f_1645_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6271))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP573(U_6271,U_6270) ),
inference(clausify,[status(thm)],[f_1645_3]) ).
cnf(f_1645_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6271))
| ~ sP573(U_6271,U_6270) ),
inference(clausify,[status(thm)],[f_1645_3]) ).
fof(f_1646_1,plain,
! [V_b,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0]) ).
fof(f_1646_2,plain,
! [U_6273,U_6272] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6272),U_6273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6273))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6272),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1646_1]) ).
fof(f_1646_3,plain,
! [U_6273,U_6272] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6272),U_6273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6273))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6272),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1646_2]) ).
cnf(f_1646_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6272),U_6273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6273))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6272),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1646_3]) ).
fof(f_1647_1,plain,
! [V_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__self]) ).
fof(f_1647_2,plain,
! [U_6274] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6274),U_6274) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1647_1]) ).
fof(f_1647_3,plain,
! [U_6274] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6274),U_6274) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_1647_2]) ).
cnf(f_1647_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6274),U_6274) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1647_3]) ).
fof(f_1648_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_int__0]) ).
fof(f_1648_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_1648_1]) ).
cnf(f_1648_3,plain,
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),
inference(clausify,[status(thm)],[f_1648_2]) ).
fof(f_1649_1,plain,
! [V_n_2] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv]) ).
fof(f_1649_2,plain,
! [U_6275] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6275) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6275 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6275) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1649_1]) ).
fof(f_1649_3,plain,
( ! [U_6277] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6277) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6277 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6276] :
( U_6276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6276) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1649_2]) ).
fof(f_1649_4,plain,
( ! [U_6277] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6277) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6277 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6276] :
( U_6276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6276) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_1649_3]) ).
cnf(f_1649_5,plain,
( U_6276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6276) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1649_4]) ).
cnf(f_1649_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6277) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6277 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1649_4]) ).
fof(f_1650_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]) ).
fof(f_1650_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_1650_1]) ).
cnf(f_1650_3,plain,
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)),
inference(clausify,[status(thm)],[f_1650_2]) ).
fof(f_1651_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_zero__zle__int]) ).
fof(f_1651_2,plain,
! [U_6278] : 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),U_6278))),
inference(variable_rename,[status(thm)],[f_1651_1]) ).
fof(f_1651_3,plain,
! [U_6278] : 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),U_6278))),
inference(definitional_conversion,[status(esa)],[f_1651_2]) ).
cnf(f_1651_4,plain,
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),U_6278))),
inference(clausify,[status(thm)],[f_1651_3]) ).
fof(f_1652_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).
fof(f_1652_2,plain,
! [U_6279] : 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),U_6279))),
inference(variable_rename,[status(thm)],[f_1652_1]) ).
fof(f_1652_3,plain,
! [U_6279] : 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),U_6279))),
inference(definitional_conversion,[status(esa)],[f_1652_2]) ).
cnf(f_1652_4,plain,
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),U_6279))),
inference(clausify,[status(thm)],[f_1652_3]) ).
fof(f_1653_1,plain,
! [V_Pa_2] :
( ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
& ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
| ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J]) ).
fof(f_1653_2,plain,
! [U_6284] :
( ( ? [U_6283] :
( hBOOL(hAPP(U_6284,U_6283))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6283)) )
| ! [U_6282] : ~ hBOOL(hAPP(U_6284,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6282))) )
& ( ? [U_6281] : hBOOL(hAPP(U_6284,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6281)))
| ! [U_6280] :
( ~ hBOOL(hAPP(U_6284,U_6280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6280)) ) ) ),
inference(variable_rename,[status(thm)],[f_1653_1]) ).
fof(f_1653_3,plain,
( ! [U_6286] :
( ? [U_6283] :
( hBOOL(hAPP(U_6286,U_6283))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6283)) )
| ! [U_6282] : ~ hBOOL(hAPP(U_6286,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6282))) )
& ! [U_6285] :
( ? [U_6281] : hBOOL(hAPP(U_6285,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6281)))
| ! [U_6280] :
( ~ hBOOL(hAPP(U_6285,U_6280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6280)) ) ) ),
inference(miniscope,[status(thm)],[f_1653_2]) ).
fof(f_1653_4,plain,
( ! [U_6286] :
( ? [U_6283] :
( hBOOL(hAPP(U_6286,U_6283))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6283)) )
| ! [U_6282] : ~ hBOOL(hAPP(U_6286,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6282))) )
& ! [U_6285] :
( hBOOL(hAPP(U_6285,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK174(U_6285))))
| ! [U_6280] :
( ~ hBOOL(hAPP(U_6285,U_6280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6280)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_6281,sK174(U_6285))],[f_1653_3]) ).
fof(f_1653_5,plain,
( ! [U_6286] :
( ( hBOOL(hAPP(U_6286,sK175(U_6286)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK175(U_6286))) )
| ! [U_6282] : ~ hBOOL(hAPP(U_6286,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6282))) )
& ! [U_6285] :
( hBOOL(hAPP(U_6285,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK174(U_6285))))
| ! [U_6280] :
( ~ hBOOL(hAPP(U_6285,U_6280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6280)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_6283,sK175(U_6286))],[f_1653_4]) ).
fof(f_1653_6,plain,
( ! [U_6286] :
( hBOOL(hAPP(U_6286,sK175(U_6286)))
| ~ sP574(U_6286) )
& ! [U_6286] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK175(U_6286)))
| ~ sP574(U_6286) )
& ! [U_6282,U_6286] :
( sP574(U_6286)
| ~ hBOOL(hAPP(U_6286,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6282))) )
& ! [U_6280,U_6285] :
( hBOOL(hAPP(U_6285,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK174(U_6285))))
| ~ hBOOL(hAPP(U_6285,U_6280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6280)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP574])],[f_1653_5]) ).
cnf(f_1653_7,plain,
( hBOOL(hAPP(U_6285,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK174(U_6285))))
| ~ hBOOL(hAPP(U_6285,U_6280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6280)) ),
inference(clausify,[status(thm)],[f_1653_6]) ).
cnf(f_1653_8,plain,
( sP574(U_6286)
| ~ hBOOL(hAPP(U_6286,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6282))) ),
inference(clausify,[status(thm)],[f_1653_6]) ).
cnf(f_1653_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK175(U_6286)))
| ~ sP574(U_6286) ),
inference(clausify,[status(thm)],[f_1653_6]) ).
cnf(f_1653_10,plain,
( hBOOL(hAPP(U_6286,sK175(U_6286)))
| ~ sP574(U_6286) ),
inference(clausify,[status(thm)],[f_1653_6]) ).
fof(f_1654_1,plain,
! [V_Pa_2] :
( ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ? [B_x] : ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
& ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J]) ).
fof(f_1654_2,plain,
! [U_6291] :
( ( ! [U_6290] :
( hBOOL(hAPP(U_6291,U_6290))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6290)) )
| ? [U_6289] : ~ hBOOL(hAPP(U_6291,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6289))) )
& ( ! [U_6288] : hBOOL(hAPP(U_6291,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6288)))
| ? [U_6287] :
( ~ hBOOL(hAPP(U_6291,U_6287))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6287)) ) ) ),
inference(variable_rename,[status(thm)],[f_1654_1]) ).
fof(f_1654_3,plain,
( ! [U_6293] :
( ! [U_6290] :
( hBOOL(hAPP(U_6293,U_6290))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6290)) )
| ? [U_6289] : ~ hBOOL(hAPP(U_6293,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6289))) )
& ! [U_6292] :
( ! [U_6288] : hBOOL(hAPP(U_6292,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6288)))
| ? [U_6287] :
( ~ hBOOL(hAPP(U_6292,U_6287))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6287)) ) ) ),
inference(miniscope,[status(thm)],[f_1654_2]) ).
fof(f_1654_4,plain,
( ! [U_6293] :
( ! [U_6290] :
( hBOOL(hAPP(U_6293,U_6290))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6290)) )
| ? [U_6289] : ~ hBOOL(hAPP(U_6293,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6289))) )
& ! [U_6292] :
( ! [U_6288] : hBOOL(hAPP(U_6292,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6288)))
| ( ~ hBOOL(hAPP(U_6292,sK176(U_6292)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK176(U_6292))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_6287,sK176(U_6292))],[f_1654_3]) ).
fof(f_1654_5,plain,
( ! [U_6293] :
( ! [U_6290] :
( hBOOL(hAPP(U_6293,U_6290))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6290)) )
| ~ hBOOL(hAPP(U_6293,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK177(U_6293)))) )
& ! [U_6292] :
( ! [U_6288] : hBOOL(hAPP(U_6292,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6288)))
| ( ~ hBOOL(hAPP(U_6292,sK176(U_6292)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK176(U_6292))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_6289,sK177(U_6293))],[f_1654_4]) ).
fof(f_1654_6,plain,
( ! [U_6292] :
( ~ hBOOL(hAPP(U_6292,sK176(U_6292)))
| ~ sP575(U_6292) )
& ! [U_6292] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK176(U_6292)))
| ~ sP575(U_6292) )
& ! [U_6290,U_6293] :
( hBOOL(hAPP(U_6293,U_6290))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6290))
| ~ hBOOL(hAPP(U_6293,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK177(U_6293)))) )
& ! [U_6288,U_6292] :
( hBOOL(hAPP(U_6292,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6288)))
| sP575(U_6292) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP575])],[f_1654_5]) ).
cnf(f_1654_7,plain,
( hBOOL(hAPP(U_6292,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6288)))
| sP575(U_6292) ),
inference(clausify,[status(thm)],[f_1654_6]) ).
cnf(f_1654_8,plain,
( hBOOL(hAPP(U_6293,U_6290))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6290))
| ~ hBOOL(hAPP(U_6293,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK177(U_6293)))) ),
inference(clausify,[status(thm)],[f_1654_6]) ).
cnf(f_1654_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK176(U_6292)))
| ~ sP575(U_6292) ),
inference(clausify,[status(thm)],[f_1654_6]) ).
cnf(f_1654_10,plain,
( ~ hBOOL(hAPP(U_6292,sK176(U_6292)))
| ~ sP575(U_6292) ),
inference(clausify,[status(thm)],[f_1654_6]) ).
fof(f_1655_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_int__less__0__conv]) ).
fof(f_1655_2,plain,
! [U_6294] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6294)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1655_1]) ).
fof(f_1655_3,plain,
! [U_6294] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6294)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1655_2]) ).
cnf(f_1655_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6294)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1655_3]) ).
fof(f_1656_1,plain,
! [V_n_2,V_m_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__int]) ).
fof(f_1656_2,plain,
! [U_6296,U_6295] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6295)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6296)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6295),U_6296)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6295),U_6296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6295)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6296))) ) ),
inference(variable_rename,[status(thm)],[f_1656_1]) ).
fof(f_1656_3,plain,
( ! [U_6300,U_6298] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6298)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6300)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6298),U_6300)) )
& ! [U_6299,U_6297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6297),U_6299))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6297)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6299))) ) ),
inference(miniscope,[status(thm)],[f_1656_2]) ).
fof(f_1656_4,plain,
( ! [U_6298,U_6300] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6298)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6300)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6298),U_6300)) )
& ! [U_6297,U_6299] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6297),U_6299))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6297)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6299))) ) ),
inference(definitional_conversion,[status(esa)],[f_1656_3]) ).
cnf(f_1656_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6297),U_6299))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6297)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6299))) ),
inference(clausify,[status(thm)],[f_1656_4]) ).
cnf(f_1656_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6298)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6300)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6298),U_6300)) ),
inference(clausify,[status(thm)],[f_1656_4]) ).
fof(f_1657_1,plain,
! [V_y_2,V_x_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J]) ).
fof(f_1657_2,plain,
! [U_6302,U_6301] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6301)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6302)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6301),U_6302)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6301),U_6302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6301)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6302))) ) ),
inference(variable_rename,[status(thm)],[f_1657_1]) ).
fof(f_1657_3,plain,
( ! [U_6306,U_6304] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6304)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6306)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6304),U_6306)) )
& ! [U_6305,U_6303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6303),U_6305))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6303)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6305))) ) ),
inference(miniscope,[status(thm)],[f_1657_2]) ).
fof(f_1657_4,plain,
( ! [U_6304,U_6306] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6304)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6306)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6304),U_6306)) )
& ! [U_6305,U_6303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6303),U_6305))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6303)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6305))) ) ),
inference(definitional_conversion,[status(esa)],[f_1657_3]) ).
cnf(f_1657_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6303),U_6305))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6303)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6305))) ),
inference(clausify,[status(thm)],[f_1657_4]) ).
cnf(f_1657_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6304)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6306)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6304),U_6306)) ),
inference(clausify,[status(thm)],[f_1657_4]) ).
fof(f_1658_1,plain,
! [V_n_2,V_m_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__int]) ).
fof(f_1658_2,plain,
! [U_6308,U_6307] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6307)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6308)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6307),U_6308)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6307),U_6308))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6307)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6308))) ) ),
inference(variable_rename,[status(thm)],[f_1658_1]) ).
fof(f_1658_3,plain,
( ! [U_6312,U_6310] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6310)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6312)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6310),U_6312)) )
& ! [U_6311,U_6309] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6309),U_6311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6309)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6311))) ) ),
inference(miniscope,[status(thm)],[f_1658_2]) ).
fof(f_1658_4,plain,
( ! [U_6310,U_6312] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6310)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6312)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6310),U_6312)) )
& ! [U_6311,U_6309] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6309),U_6311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6309)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6311))) ) ),
inference(definitional_conversion,[status(esa)],[f_1658_3]) ).
cnf(f_1658_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6309),U_6311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6309)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6311))) ),
inference(clausify,[status(thm)],[f_1658_4]) ).
cnf(f_1658_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6310)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6312)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6310),U_6312)) ),
inference(clausify,[status(thm)],[f_1658_4]) ).
fof(f_1659_1,plain,
! [V_y_2,V_x_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J]) ).
fof(f_1659_2,plain,
! [U_6314,U_6313] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6313)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6313),U_6314)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6313),U_6314))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6313)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6314))) ) ),
inference(variable_rename,[status(thm)],[f_1659_1]) ).
fof(f_1659_3,plain,
( ! [U_6318,U_6316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6316)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6316),U_6318)) )
& ! [U_6317,U_6315] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6315),U_6317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6315)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6317))) ) ),
inference(miniscope,[status(thm)],[f_1659_2]) ).
fof(f_1659_4,plain,
( ! [U_6316,U_6318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6316)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6316),U_6318)) )
& ! [U_6315,U_6317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6315),U_6317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6315)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6317))) ) ),
inference(definitional_conversion,[status(esa)],[f_1659_3]) ).
cnf(f_1659_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6315),U_6317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6315)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6317))) ),
inference(clausify,[status(thm)],[f_1659_4]) ).
cnf(f_1659_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6316)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6316),U_6318)) ),
inference(clausify,[status(thm)],[f_1659_4]) ).
fof(f_1660_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zadd__int]) ).
fof(f_1660_2,plain,
! [U_6320,U_6319] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6319),U_6320)),
inference(variable_rename,[status(thm)],[f_1660_1]) ).
fof(f_1660_3,plain,
! [U_6320,U_6319] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6319),U_6320)),
inference(definitional_conversion,[status(esa)],[f_1660_2]) ).
cnf(f_1660_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6319),U_6320)),
inference(clausify,[status(thm)],[f_1660_3]) ).
fof(f_1661_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zadd__int__left]) ).
fof(f_1661_2,plain,
! [U_6323,U_6322,U_6321] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6322)),U_6323)) = 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),U_6321),U_6322))),U_6323),
inference(variable_rename,[status(thm)],[f_1661_1]) ).
fof(f_1661_3,plain,
! [U_6321,U_6322,U_6323] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6322)),U_6323)) = 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),U_6321),U_6322))),U_6323),
inference(definitional_conversion,[status(esa)],[f_1661_2]) ).
cnf(f_1661_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6322)),U_6323)) = 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),U_6321),U_6322))),U_6323),
inference(clausify,[status(thm)],[f_1661_3]) ).
fof(f_1662_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).
fof(f_1662_2,plain,
! [U_6325,U_6324] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6324)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6325)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6324),U_6325)),
inference(variable_rename,[status(thm)],[f_1662_1]) ).
fof(f_1662_3,plain,
! [U_6324,U_6325] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6324)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6325)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6324),U_6325)),
inference(definitional_conversion,[status(esa)],[f_1662_2]) ).
cnf(f_1662_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6324)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6325)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6324),U_6325)),
inference(clausify,[status(thm)],[f_1662_3]) ).
fof(f_1663_1,plain,
! [V_z_2,V_w_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
| ! [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)) )
& ( ? [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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__iff__zadd]) ).
fof(f_1663_2,plain,
! [U_6329,U_6328] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6328),U_6329))
| ! [U_6327] : U_6329 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6328),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6327)) )
& ( ? [U_6326] : U_6329 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6328),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6328),U_6329)) ) ),
inference(variable_rename,[status(thm)],[f_1663_1]) ).
fof(f_1663_3,plain,
( ! [U_6333,U_6331] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6331),U_6333))
| ! [U_6327] : U_6333 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6331),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6327)) )
& ! [U_6332,U_6330] :
( ? [U_6326] : U_6332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6330),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6330),U_6332)) ) ),
inference(miniscope,[status(thm)],[f_1663_2]) ).
fof(f_1663_4,plain,
( ! [U_6333,U_6331] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6331),U_6333))
| ! [U_6327] : U_6333 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6331),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6327)) )
& ! [U_6332,U_6330] :
( U_6332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6330),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK178(U_6332,U_6330)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6330),U_6332)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_6326,sK178(U_6332,U_6330))],[f_1663_3]) ).
fof(f_1663_5,plain,
( ! [U_6327,U_6331,U_6333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6331),U_6333))
| U_6333 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6331),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6327)) )
& ! [U_6332,U_6330] :
( U_6332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6330),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK178(U_6332,U_6330)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6330),U_6332)) ) ),
inference(definitional_conversion,[status(esa)],[f_1663_4]) ).
cnf(f_1663_6,plain,
( U_6332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6330),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK178(U_6332,U_6330)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6330),U_6332)) ),
inference(clausify,[status(thm)],[f_1663_5]) ).
cnf(f_1663_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6331),U_6333))
| U_6333 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6331),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6327)) ),
inference(clausify,[status(thm)],[f_1663_5]) ).
fof(f_1664_1,plain,
! [V_m,T_a] :
( 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)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat]) ).
fof(f_1664_2,plain,
! [U_6335,U_6334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6334),U_6335)))
| ~ class_Rings_Olinordered__semidom(U_6334) ),
inference(variable_rename,[status(thm)],[f_1664_1]) ).
fof(f_1664_3,plain,
! [U_6334,U_6335] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6334),U_6335)))
| ~ class_Rings_Olinordered__semidom(U_6334) ),
inference(definitional_conversion,[status(esa)],[f_1664_2]) ).
cnf(f_1664_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6334),U_6335)))
| ~ class_Rings_Olinordered__semidom(U_6334) ),
inference(clausify,[status(thm)],[f_1664_3]) ).
fof(f_1665_1,plain,
! [V_n,T_a] :
( 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)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff]) ).
fof(f_1665_2,plain,
! [U_6337,U_6336] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6336),c_Groups_Ozero__class_Ozero(U_6336)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6336),U_6337)))
| ~ class_Rings_Olinordered__semidom(U_6336) ),
inference(variable_rename,[status(thm)],[f_1665_1]) ).
fof(f_1665_3,plain,
! [U_6336,U_6337] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6336),c_Groups_Ozero__class_Ozero(U_6336)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6336),U_6337)))
| ~ class_Rings_Olinordered__semidom(U_6336) ),
inference(definitional_conversion,[status(esa)],[f_1665_2]) ).
cnf(f_1665_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6336),c_Groups_Ozero__class_Ozero(U_6336)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6336),U_6337)))
| ~ class_Rings_Olinordered__semidom(U_6336) ),
inference(clausify,[status(thm)],[f_1665_3]) ).
fof(f_1666_1,plain,
! [V_m_2,V_n_2] :
( ( 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)
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_negative__eq__positive]) ).
fof(f_1666_2,plain,
! [U_6339,U_6338] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6338)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6339)
| U_6339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6338 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_6339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6338)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6339) ) ),
inference(variable_rename,[status(thm)],[f_1666_1]) ).
fof(f_1666_3,plain,
( ! [U_6343,U_6341] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6341)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6343)
| U_6343 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6341 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6342,U_6340] :
( ( U_6342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6340 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6340)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6342) ) ),
inference(miniscope,[status(thm)],[f_1666_2]) ).
fof(f_1666_4,plain,
( ! [U_6342,U_6340] :
( U_6342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP576(U_6342,U_6340) )
& ! [U_6342,U_6340] :
( U_6340 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP576(U_6342,U_6340) )
& ! [U_6343,U_6341] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6341)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6343)
| U_6343 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6341 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6342,U_6340] :
( sP576(U_6342,U_6340)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6340)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6342) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP576])],[f_1666_3]) ).
cnf(f_1666_5,plain,
( sP576(U_6342,U_6340)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6340)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6342) ),
inference(clausify,[status(thm)],[f_1666_4]) ).
cnf(f_1666_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6341)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6343)
| U_6343 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6341 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1666_4]) ).
cnf(f_1666_7,plain,
( U_6340 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP576(U_6342,U_6340) ),
inference(clausify,[status(thm)],[f_1666_4]) ).
cnf(f_1666_8,plain,
( U_6342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP576(U_6342,U_6340) ),
inference(clausify,[status(thm)],[f_1666_4]) ).
fof(f_1667_1,plain,
! [V_m,T_a] :
( ~ 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)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__less__0__iff]) ).
fof(f_1667_2,plain,
! [U_6345,U_6344] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6344),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6344),U_6345)),c_Groups_Ozero__class_Ozero(U_6344)))
| ~ class_Rings_Olinordered__semidom(U_6344) ),
inference(variable_rename,[status(thm)],[f_1667_1]) ).
fof(f_1667_3,plain,
! [U_6344,U_6345] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6344),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6344),U_6345)),c_Groups_Ozero__class_Ozero(U_6344)))
| ~ class_Rings_Olinordered__semidom(U_6344) ),
inference(definitional_conversion,[status(esa)],[f_1667_2]) ).
cnf(f_1667_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6344),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6344),U_6345)),c_Groups_Ozero__class_Ozero(U_6344)))
| ~ class_Rings_Olinordered__semidom(U_6344) ),
inference(clausify,[status(thm)],[f_1667_3]) ).
fof(f_1668_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_not__int__zless__negative]) ).
fof(f_1668_2,plain,
! [U_6347,U_6346] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6346)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6347)))),
inference(variable_rename,[status(thm)],[f_1668_1]) ).
fof(f_1668_3,plain,
! [U_6346,U_6347] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6346)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6347)))),
inference(definitional_conversion,[status(esa)],[f_1668_2]) ).
cnf(f_1668_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6346)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6347)))),
inference(clausify,[status(thm)],[f_1668_3]) ).
fof(f_1669_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_int__mult]) ).
fof(f_1669_2,plain,
! [U_6349,U_6348] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6348),U_6349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6348)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6349)),
inference(variable_rename,[status(thm)],[f_1669_1]) ).
fof(f_1669_3,plain,
! [U_6348,U_6349] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6348),U_6349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6348)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6349)),
inference(definitional_conversion,[status(esa)],[f_1669_2]) ).
cnf(f_1669_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6348),U_6349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6348)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6349)),
inference(clausify,[status(thm)],[f_1669_3]) ).
fof(f_1670_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmult__int]) ).
fof(f_1670_2,plain,
! [U_6351,U_6350] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6350)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6351)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6350),U_6351)),
inference(variable_rename,[status(thm)],[f_1670_1]) ).
fof(f_1670_3,plain,
! [U_6350,U_6351] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6350)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6351)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6350),U_6351)),
inference(definitional_conversion,[status(esa)],[f_1670_2]) ).
cnf(f_1670_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6350)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6351)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6350),U_6351)),
inference(clausify,[status(thm)],[f_1670_3]) ).
fof(f_1671_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).
fof(f_1671_2,plain,
! [U_6353,U_6352] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6352)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6353)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6353)),
inference(variable_rename,[status(thm)],[f_1671_1]) ).
fof(f_1671_3,plain,
! [U_6352,U_6353] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6352)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6353)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6353)),
inference(definitional_conversion,[status(esa)],[f_1671_2]) ).
cnf(f_1671_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6352)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6353)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6353)),
inference(clausify,[status(thm)],[f_1671_3]) ).
fof(f_1672_1,plain,
! [T_a] :
( 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)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__0]) ).
fof(f_1672_2,plain,
! [U_6354] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6354),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_6354)
| ~ class_Rings_Osemiring__1(U_6354) ),
inference(variable_rename,[status(thm)],[f_1672_1]) ).
fof(f_1672_3,plain,
! [U_6354] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6354),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_6354)
| ~ class_Rings_Osemiring__1(U_6354) ),
inference(definitional_conversion,[status(esa)],[f_1672_2]) ).
cnf(f_1672_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6354),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_6354)
| ~ class_Rings_Osemiring__1(U_6354) ),
inference(clausify,[status(thm)],[f_1672_3]) ).
fof(f_1673_1,plain,
! [V_n,V_m,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ 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)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less]) ).
fof(f_1673_2,plain,
! [U_6357,U_6356,U_6355] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6355),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6355),U_6356)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6355),U_6357)))
| ~ class_Rings_Olinordered__semidom(U_6355) ),
inference(variable_rename,[status(thm)],[f_1673_1]) ).
fof(f_1673_3,plain,
! [U_6355,U_6356,U_6357] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6355),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6355),U_6356)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6355),U_6357)))
| ~ class_Rings_Olinordered__semidom(U_6355) ),
inference(definitional_conversion,[status(esa)],[f_1673_2]) ).
cnf(f_1673_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6355),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6355),U_6356)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6355),U_6357)))
| ~ class_Rings_Olinordered__semidom(U_6355) ),
inference(clausify,[status(thm)],[f_1673_3]) ).
fof(f_1674_1,plain,
! [V_n,V_m,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less]) ).
fof(f_1674_2,plain,
! [U_6360,U_6359,U_6358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6358),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6358),U_6359)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6358),U_6360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6359),U_6360))
| ~ class_Rings_Olinordered__semidom(U_6358) ),
inference(variable_rename,[status(thm)],[f_1674_1]) ).
fof(f_1674_3,plain,
! [U_6358,U_6359,U_6360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6358),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6358),U_6359)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6358),U_6360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6359),U_6360))
| ~ class_Rings_Olinordered__semidom(U_6358) ),
inference(definitional_conversion,[status(esa)],[f_1674_2]) ).
cnf(f_1674_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6358),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6358),U_6359)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6358),U_6360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6359),U_6360))
| ~ class_Rings_Olinordered__semidom(U_6358) ),
inference(clausify,[status(thm)],[f_1674_3]) ).
fof(f_1675_1,plain,
! [V_n_2,V_m_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff]) ).
fof(f_1675_2,plain,
! [U_6363,U_6362,U_6361] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6362)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6362),U_6363)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6362),U_6363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6362)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6363))) ) )
| ~ class_Rings_Olinordered__semidom(U_6361) ),
inference(variable_rename,[status(thm)],[f_1675_1]) ).
fof(f_1675_3,plain,
( ! [U_6363,U_6361,U_6362] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6362)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6362),U_6363))
| ~ sP577(U_6363,U_6361,U_6362) )
& ! [U_6363,U_6361,U_6362] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6362),U_6363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6362)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6363)))
| ~ sP577(U_6363,U_6361,U_6362) )
& ! [U_6363,U_6361,U_6362] :
( sP577(U_6363,U_6361,U_6362)
| ~ class_Rings_Olinordered__semidom(U_6361) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP577])],[f_1675_2]) ).
cnf(f_1675_4,plain,
( sP577(U_6363,U_6361,U_6362)
| ~ class_Rings_Olinordered__semidom(U_6361) ),
inference(clausify,[status(thm)],[f_1675_3]) ).
cnf(f_1675_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6362),U_6363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6362)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6363)))
| ~ sP577(U_6363,U_6361,U_6362) ),
inference(clausify,[status(thm)],[f_1675_3]) ).
cnf(f_1675_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6362)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6361),U_6363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6362),U_6363))
| ~ sP577(U_6363,U_6361,U_6362) ),
inference(clausify,[status(thm)],[f_1675_3]) ).
fof(f_1676_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_int__1]) ).
fof(f_1676_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_1676_1]) ).
cnf(f_1676_3,plain,
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),
inference(clausify,[status(thm)],[f_1676_2]) ).
fof(f_1677_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]) ).
fof(f_1677_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_1677_1]) ).
cnf(f_1677_3,plain,
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)),
inference(clausify,[status(thm)],[f_1677_2]) ).
fof(f_1678_1,plain,
! [V_n_2,V_m_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff]) ).
fof(f_1678_2,plain,
! [U_6366,U_6365,U_6364] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6364),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6365)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6365),U_6366)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6365),U_6366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6364),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6365)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6366))) ) )
| ~ class_Rings_Olinordered__semidom(U_6364) ),
inference(variable_rename,[status(thm)],[f_1678_1]) ).
fof(f_1678_3,plain,
( ! [U_6366,U_6364,U_6365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6364),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6365)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6365),U_6366))
| ~ sP578(U_6366,U_6364,U_6365) )
& ! [U_6366,U_6364,U_6365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6365),U_6366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6364),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6365)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6366)))
| ~ sP578(U_6366,U_6364,U_6365) )
& ! [U_6366,U_6364,U_6365] :
( sP578(U_6366,U_6364,U_6365)
| ~ class_Rings_Olinordered__semidom(U_6364) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP578])],[f_1678_2]) ).
cnf(f_1678_4,plain,
( sP578(U_6366,U_6364,U_6365)
| ~ class_Rings_Olinordered__semidom(U_6364) ),
inference(clausify,[status(thm)],[f_1678_3]) ).
cnf(f_1678_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6365),U_6366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6364),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6365)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6366)))
| ~ sP578(U_6366,U_6364,U_6365) ),
inference(clausify,[status(thm)],[f_1678_3]) ).
cnf(f_1678_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6364),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6365)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6364),U_6366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6365),U_6366))
| ~ sP578(U_6366,U_6364,U_6365) ),
inference(clausify,[status(thm)],[f_1678_3]) ).
fof(f_1679_1,plain,
! [V_n,V_m,T_a] :
( 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))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__add]) ).
fof(f_1679_2,plain,
! [U_6369,U_6368,U_6367] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6368),U_6369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6367),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),U_6368)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),U_6369))
| ~ class_Rings_Osemiring__1(U_6367) ),
inference(variable_rename,[status(thm)],[f_1679_1]) ).
fof(f_1679_3,plain,
! [U_6368,U_6367,U_6369] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6368),U_6369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6367),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),U_6368)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),U_6369))
| ~ class_Rings_Osemiring__1(U_6367) ),
inference(definitional_conversion,[status(esa)],[f_1679_2]) ).
cnf(f_1679_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6368),U_6369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6367),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),U_6368)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6367),U_6369))
| ~ class_Rings_Osemiring__1(U_6367) ),
inference(clausify,[status(thm)],[f_1679_3]) ).
fof(f_1680_1,plain,
! [V_n,V_m,T_a] :
( 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))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__mult]) ).
fof(f_1680_2,plain,
! [U_6372,U_6371,U_6370] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6371),U_6372)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6370),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),U_6371)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),U_6372))
| ~ class_Rings_Osemiring__1(U_6370) ),
inference(variable_rename,[status(thm)],[f_1680_1]) ).
fof(f_1680_3,plain,
! [U_6370,U_6371,U_6372] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6371),U_6372)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6370),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),U_6371)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),U_6372))
| ~ class_Rings_Osemiring__1(U_6370) ),
inference(definitional_conversion,[status(esa)],[f_1680_2]) ).
cnf(f_1680_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6371),U_6372)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6370),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),U_6371)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6370),U_6372))
| ~ class_Rings_Osemiring__1(U_6370) ),
inference(clausify,[status(thm)],[f_1680_3]) ).
fof(f_1681_1,plain,
! [V_b,V_a,V_c,T_a] :
( ( ( 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)
| V_c = c_Groups_Ozero__class_Ozero(T_a) )
& ( 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)
| V_c != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if]) ).
fof(f_1681_2,plain,
! [U_6376,U_6375,U_6374,U_6373] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6375)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6376)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),U_6375),U_6376)
| U_6374 = c_Groups_Ozero__class_Ozero(U_6373) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6375)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6376)) = c_Groups_Ozero__class_Ozero(U_6373)
| U_6374 != c_Groups_Ozero__class_Ozero(U_6373) ) )
| ~ class_Divides_Osemiring__div(U_6373) ),
inference(variable_rename,[status(thm)],[f_1681_1]) ).
fof(f_1681_3,plain,
( ! [U_6373,U_6374,U_6375,U_6376] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6375)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6376)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),U_6375),U_6376)
| U_6374 = c_Groups_Ozero__class_Ozero(U_6373)
| ~ sP579(U_6373,U_6374,U_6375,U_6376) )
& ! [U_6373,U_6374,U_6375,U_6376] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6375)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6376)) = c_Groups_Ozero__class_Ozero(U_6373)
| U_6374 != c_Groups_Ozero__class_Ozero(U_6373)
| ~ sP579(U_6373,U_6374,U_6375,U_6376) )
& ! [U_6373,U_6374,U_6375,U_6376] :
( sP579(U_6373,U_6374,U_6375,U_6376)
| ~ class_Divides_Osemiring__div(U_6373) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP579])],[f_1681_2]) ).
cnf(f_1681_4,plain,
( sP579(U_6373,U_6374,U_6375,U_6376)
| ~ class_Divides_Osemiring__div(U_6373) ),
inference(clausify,[status(thm)],[f_1681_3]) ).
cnf(f_1681_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6375)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6376)) = c_Groups_Ozero__class_Ozero(U_6373)
| U_6374 != c_Groups_Ozero__class_Ozero(U_6373)
| ~ sP579(U_6373,U_6374,U_6375,U_6376) ),
inference(clausify,[status(thm)],[f_1681_3]) ).
cnf(f_1681_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6375)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6373),U_6374),U_6376)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6373),U_6375),U_6376)
| U_6374 = c_Groups_Ozero__class_Ozero(U_6373)
| ~ sP579(U_6373,U_6374,U_6375,U_6376) ),
inference(clausify,[status(thm)],[f_1681_3]) ).
fof(f_1682_1,plain,
! [V_a,V_b,T_a] :
( 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
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id]) ).
fof(f_1682_2,plain,
! [U_6379,U_6378,U_6377] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6377),U_6379),U_6378)),U_6378) = U_6379
| U_6378 = c_Groups_Ozero__class_Ozero(U_6377)
| ~ class_Divides_Osemiring__div(U_6377) ),
inference(variable_rename,[status(thm)],[f_1682_1]) ).
fof(f_1682_3,plain,
! [U_6379,U_6378,U_6377] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6377),U_6379),U_6378)),U_6378) = U_6379
| U_6378 = c_Groups_Ozero__class_Ozero(U_6377)
| ~ class_Divides_Osemiring__div(U_6377) ),
inference(definitional_conversion,[status(esa)],[f_1682_2]) ).
cnf(f_1682_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6377),U_6379),U_6378)),U_6378) = U_6379
| U_6378 = c_Groups_Ozero__class_Ozero(U_6377)
| ~ class_Divides_Osemiring__div(U_6377) ),
inference(clausify,[status(thm)],[f_1682_3]) ).
fof(f_1683_1,plain,
! [V_a,V_b,T_a] :
( 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
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id]) ).
fof(f_1683_2,plain,
! [U_6382,U_6381,U_6380] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6380),U_6381),U_6382)),U_6381) = U_6382
| U_6381 = c_Groups_Ozero__class_Ozero(U_6380)
| ~ class_Divides_Osemiring__div(U_6380) ),
inference(variable_rename,[status(thm)],[f_1683_1]) ).
fof(f_1683_3,plain,
! [U_6380,U_6381,U_6382] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6380),U_6381),U_6382)),U_6381) = U_6382
| U_6381 = c_Groups_Ozero__class_Ozero(U_6380)
| ~ class_Divides_Osemiring__div(U_6380) ),
inference(definitional_conversion,[status(esa)],[f_1683_2]) ).
cnf(f_1683_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6380),U_6381),U_6382)),U_6381) = U_6382
| U_6381 = c_Groups_Ozero__class_Ozero(U_6380)
| ~ class_Divides_Osemiring__div(U_6380) ),
inference(clausify,[status(thm)],[f_1683_3]) ).
fof(f_1684_1,plain,
! [V_b,V_a,V_c,T_a] :
( 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)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__mult2]) ).
fof(f_1684_2,plain,
! [U_6386,U_6385,U_6384,U_6383] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6385),U_6384)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6384)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6383),U_6385),U_6386)
| U_6384 = c_Groups_Ozero__class_Ozero(U_6383)
| ~ class_Divides_Osemiring__div(U_6383) ),
inference(variable_rename,[status(thm)],[f_1684_1]) ).
fof(f_1684_3,plain,
! [U_6383,U_6384,U_6385,U_6386] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6385),U_6384)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6384)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6383),U_6385),U_6386)
| U_6384 = c_Groups_Ozero__class_Ozero(U_6383)
| ~ class_Divides_Osemiring__div(U_6383) ),
inference(definitional_conversion,[status(esa)],[f_1684_2]) ).
cnf(f_1684_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6385),U_6384)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6384)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6383),U_6385),U_6386)
| U_6384 = c_Groups_Ozero__class_Ozero(U_6383)
| ~ class_Divides_Osemiring__div(U_6383) ),
inference(clausify,[status(thm)],[f_1684_3]) ).
fof(f_1685_1,plain,
! [V_b,V_a,V_c,T_a] :
( 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)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__mult1]) ).
fof(f_1685_2,plain,
! [U_6390,U_6389,U_6388,U_6387] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6387),U_6388),U_6389)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6387),U_6388),U_6390)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6387),U_6389),U_6390)
| U_6388 = c_Groups_Ozero__class_Ozero(U_6387)
| ~ class_Divides_Osemiring__div(U_6387) ),
inference(variable_rename,[status(thm)],[f_1685_1]) ).
fof(f_1685_3,plain,
! [U_6387,U_6388,U_6389,U_6390] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6387),U_6388),U_6389)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6387),U_6388),U_6390)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6387),U_6389),U_6390)
| U_6388 = c_Groups_Ozero__class_Ozero(U_6387)
| ~ class_Divides_Osemiring__div(U_6387) ),
inference(definitional_conversion,[status(esa)],[f_1685_2]) ).
cnf(f_1685_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6387),U_6388),U_6389)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6387),U_6388),U_6390)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6387),U_6389),U_6390)
| U_6388 = c_Groups_Ozero__class_Ozero(U_6387)
| ~ class_Divides_Osemiring__div(U_6387) ),
inference(clausify,[status(thm)],[f_1685_3]) ).
fof(f_1686_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__self]) ).
fof(f_1686_2,plain,
! [U_6392,U_6391] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6391),U_6392),U_6392) = c_Groups_Oone__class_Oone(U_6391)
| U_6392 = c_Groups_Ozero__class_Ozero(U_6391)
| ~ class_Divides_Osemiring__div(U_6391) ),
inference(variable_rename,[status(thm)],[f_1686_1]) ).
fof(f_1686_3,plain,
! [U_6392,U_6391] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6391),U_6392),U_6392) = c_Groups_Oone__class_Oone(U_6391)
| U_6392 = c_Groups_Ozero__class_Ozero(U_6391)
| ~ class_Divides_Osemiring__div(U_6391) ),
inference(definitional_conversion,[status(esa)],[f_1686_2]) ).
cnf(f_1686_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6391),U_6392),U_6392) = c_Groups_Oone__class_Oone(U_6391)
| U_6392 = c_Groups_Ozero__class_Ozero(U_6391)
| ~ class_Divides_Osemiring__div(U_6391) ),
inference(clausify,[status(thm)],[f_1686_3]) ).
fof(f_1687_1,plain,
! [T_a] :
( 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)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__1]) ).
fof(f_1687_2,plain,
! [U_6393] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6393),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6393)
| ~ class_Rings_Osemiring__1(U_6393) ),
inference(variable_rename,[status(thm)],[f_1687_1]) ).
fof(f_1687_3,plain,
! [U_6393] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6393),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6393)
| ~ class_Rings_Osemiring__1(U_6393) ),
inference(definitional_conversion,[status(esa)],[f_1687_2]) ).
cnf(f_1687_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6393),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6393)
| ~ class_Rings_Osemiring__1(U_6393) ),
inference(clausify,[status(thm)],[f_1687_3]) ).
fof(f_1688_1,plain,
! [V_n_2,T_b] :
( 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)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__of__nat]) ).
fof(f_1688_2,plain,
! [U_6395,U_6394] :
( hBOOL(hAPP(hAPP(c_member(U_6394),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6394),U_6395)),c_Int_Oring__1__class_OInts(U_6394)))
| ~ class_Rings_Oring__1(U_6394) ),
inference(variable_rename,[status(thm)],[f_1688_1]) ).
fof(f_1688_3,plain,
! [U_6394,U_6395] :
( hBOOL(hAPP(hAPP(c_member(U_6394),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6394),U_6395)),c_Int_Oring__1__class_OInts(U_6394)))
| ~ class_Rings_Oring__1(U_6394) ),
inference(definitional_conversion,[status(esa)],[f_1688_2]) ).
cnf(f_1688_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_6394),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6394),U_6395)),c_Int_Oring__1__class_OInts(U_6394)))
| ~ class_Rings_Oring__1(U_6394) ),
inference(clausify,[status(thm)],[f_1688_3]) ).
fof(f_1689_1,plain,
! [V_n,V_m,T_a] :
( 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)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__power]) ).
fof(f_1689_2,plain,
! [U_6398,U_6397,U_6396] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6396),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6397),U_6398)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6396),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6396),U_6397)),U_6398)
| ~ class_Rings_Osemiring__1(U_6396) ),
inference(variable_rename,[status(thm)],[f_1689_1]) ).
fof(f_1689_3,plain,
! [U_6396,U_6397,U_6398] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6396),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6397),U_6398)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6396),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6396),U_6397)),U_6398)
| ~ class_Rings_Osemiring__1(U_6396) ),
inference(definitional_conversion,[status(esa)],[f_1689_2]) ).
cnf(f_1689_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6396),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6397),U_6398)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6396),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6396),U_6397)),U_6398)
| ~ class_Rings_Osemiring__1(U_6396) ),
inference(clausify,[status(thm)],[f_1689_3]) ).
fof(f_1690_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_int__power]) ).
fof(f_1690_2,plain,
! [U_6400,U_6399] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6399),U_6400)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6399)),U_6400),
inference(variable_rename,[status(thm)],[f_1690_1]) ).
fof(f_1690_3,plain,
! [U_6399,U_6400] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6399),U_6400)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6399)),U_6400),
inference(definitional_conversion,[status(esa)],[f_1690_2]) ).
cnf(f_1690_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6399),U_6400)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6399)),U_6400),
inference(clausify,[status(thm)],[f_1690_3]) ).
fof(f_1691_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zpower__int]) ).
fof(f_1691_2,plain,
! [U_6402,U_6401] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6401)),U_6402) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6401),U_6402)),
inference(variable_rename,[status(thm)],[f_1691_1]) ).
fof(f_1691_3,plain,
! [U_6401,U_6402] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6401)),U_6402) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6401),U_6402)),
inference(definitional_conversion,[status(esa)],[f_1691_2]) ).
cnf(f_1691_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6401)),U_6402) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6401),U_6402)),
inference(clausify,[status(thm)],[f_1691_3]) ).
fof(f_1692_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).
fof(f_1692_2,plain,
! [U_6404,U_6403] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6403)),U_6404) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6403),U_6404)),
inference(variable_rename,[status(thm)],[f_1692_1]) ).
fof(f_1692_3,plain,
! [U_6403,U_6404] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6403)),U_6404) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6403),U_6404)),
inference(definitional_conversion,[status(esa)],[f_1692_2]) ).
cnf(f_1692_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6403)),U_6404) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6403),U_6404)),
inference(clausify,[status(thm)],[f_1692_3]) ).
fof(f_1693_1,plain,
! [V_A_2] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J]) ).
fof(f_1693_2,plain,
! [U_6405] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6405))
| ~ 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)),U_6405))) )
& ( 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)),U_6405)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6405)) ) ),
inference(variable_rename,[status(thm)],[f_1693_1]) ).
fof(f_1693_3,plain,
( ! [U_6407] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6407))
| ~ 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)),U_6407))) )
& ! [U_6406] :
( 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)),U_6406)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6406)) ) ),
inference(miniscope,[status(thm)],[f_1693_2]) ).
fof(f_1693_4,plain,
( ! [U_6407] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6407))
| ~ 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)),U_6407))) )
& ! [U_6406] :
( 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)),U_6406)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6406)) ) ),
inference(definitional_conversion,[status(esa)],[f_1693_3]) ).
cnf(f_1693_5,plain,
( 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)),U_6406)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6406)) ),
inference(clausify,[status(thm)],[f_1693_4]) ).
cnf(f_1693_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6407))
| ~ 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)),U_6407))) ),
inference(clausify,[status(thm)],[f_1693_4]) ).
fof(f_1694_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]) ).
fof(f_1694_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1694_1]) ).
cnf(f_1694_3,plain,
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))),
inference(clausify,[status(thm)],[f_1694_2]) ).
fof(f_1695_1,plain,
! [V_k_2,V_i_2] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff]) ).
fof(f_1695_2,plain,
! [U_6409,U_6408] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6408),U_6409) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6409),U_6408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6408),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6408),U_6409))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6408)) )
& U_6409 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6409),U_6408))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6408),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6408),U_6409))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6408)) )
| U_6409 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6408),U_6409) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1695_1]) ).
fof(f_1695_3,plain,
( ! [U_6413,U_6411] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6411),U_6413) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6413),U_6411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6411),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6411),U_6413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6411)) )
& U_6413 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6412,U_6410] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6412),U_6410))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6410),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6410),U_6412))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6410)) )
| U_6412 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6410),U_6412) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1695_2]) ).
fof(f_1695_4,plain,
( ! [U_6413,U_6411] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6413),U_6411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6411),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP582(U_6413,U_6411) )
& ! [U_6413,U_6411] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6411),U_6413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6411))
| ~ sP582(U_6413,U_6411) )
& ! [U_6413,U_6411] :
( U_6413 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP582(U_6413,U_6411) )
& ! [U_6410,U_6412] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6412),U_6410))
| ~ sP581(U_6410,U_6412) )
& ! [U_6410,U_6412] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6410),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP581(U_6410,U_6412) )
& ! [U_6410,U_6412] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6410),U_6412))
| ~ sP580(U_6410,U_6412) )
& ! [U_6410,U_6412] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6410))
| ~ sP580(U_6410,U_6412) )
& ! [U_6413,U_6411] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6411),U_6413) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP582(U_6413,U_6411) )
& ! [U_6410,U_6412] :
( sP581(U_6410,U_6412)
| sP580(U_6410,U_6412)
| U_6412 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6410),U_6412) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP580,sP581,sP582])],[f_1695_3]) ).
cnf(f_1695_5,plain,
( sP581(U_6410,U_6412)
| sP580(U_6410,U_6412)
| U_6412 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6410),U_6412) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
cnf(f_1695_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6411),U_6413) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP582(U_6413,U_6411) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
cnf(f_1695_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6410))
| ~ sP580(U_6410,U_6412) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
cnf(f_1695_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6410),U_6412))
| ~ sP580(U_6410,U_6412) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
cnf(f_1695_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6410),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP581(U_6410,U_6412) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
cnf(f_1695_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6412),U_6410))
| ~ sP581(U_6410,U_6412) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
cnf(f_1695_11,plain,
( U_6413 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP582(U_6413,U_6411) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
cnf(f_1695_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6411),U_6413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6411))
| ~ sP582(U_6413,U_6411) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
cnf(f_1695_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6413),U_6411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6411),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP582(U_6413,U_6411) ),
inference(clausify,[status(thm)],[f_1695_4]) ).
fof(f_1696_1,plain,
! [V_a_2,V_b_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff]) ).
fof(f_1696_2,plain,
! [U_6415,U_6414] :
( ( ( 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),U_6415),U_6414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6415)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6415))
| ~ 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),U_6415),U_6414))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6414)) ),
inference(variable_rename,[status(thm)],[f_1696_1]) ).
fof(f_1696_3,plain,
( ! [U_6414,U_6415] :
( 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),U_6415),U_6414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6415))
| ~ sP583(U_6414,U_6415) )
& ! [U_6414,U_6415] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6415))
| ~ 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),U_6415),U_6414)))
| ~ sP583(U_6414,U_6415) )
& ! [U_6414,U_6415] :
( sP583(U_6414,U_6415)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6414)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP583])],[f_1696_2]) ).
cnf(f_1696_4,plain,
( sP583(U_6414,U_6415)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6414)) ),
inference(clausify,[status(thm)],[f_1696_3]) ).
cnf(f_1696_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6415))
| ~ 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),U_6415),U_6414)))
| ~ sP583(U_6414,U_6415) ),
inference(clausify,[status(thm)],[f_1696_3]) ).
cnf(f_1696_6,plain,
( 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),U_6415),U_6414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6415))
| ~ sP583(U_6414,U_6415) ),
inference(clausify,[status(thm)],[f_1696_3]) ).
fof(f_1697_1,plain,
! [V_i_2,V_k_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff]) ).
fof(f_1697_2,plain,
! [U_6417,U_6416] :
( ( ( 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),U_6417),U_6416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6416),U_6417)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6416),U_6417))
| ~ 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),U_6417),U_6416))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6416)) ),
inference(variable_rename,[status(thm)],[f_1697_1]) ).
fof(f_1697_3,plain,
( ! [U_6417,U_6416] :
( 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),U_6417),U_6416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6416),U_6417))
| ~ sP584(U_6417,U_6416) )
& ! [U_6417,U_6416] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6416),U_6417))
| ~ 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),U_6417),U_6416)))
| ~ sP584(U_6417,U_6416) )
& ! [U_6417,U_6416] :
( sP584(U_6417,U_6416)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6416)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP584])],[f_1697_2]) ).
cnf(f_1697_4,plain,
( sP584(U_6417,U_6416)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6416)) ),
inference(clausify,[status(thm)],[f_1697_3]) ).
cnf(f_1697_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6416),U_6417))
| ~ 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),U_6417),U_6416)))
| ~ sP584(U_6417,U_6416) ),
inference(clausify,[status(thm)],[f_1697_3]) ).
cnf(f_1697_6,plain,
( 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),U_6417),U_6416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6416),U_6417))
| ~ sP584(U_6417,U_6416) ),
inference(clausify,[status(thm)],[f_1697_3]) ).
fof(f_1698_1,plain,
! [V_b_2,V_a_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) )
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ),
inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff]) ).
fof(f_1698_2,plain,
! [U_6419,U_6418] :
( ( ( 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),U_6418),U_6419)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6419),U_6418)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6419))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6419),U_6418)) )
| ~ 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),U_6418),U_6419))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6418)) ),
inference(variable_rename,[status(thm)],[f_1698_1]) ).
fof(f_1698_3,plain,
( ! [U_6419,U_6418] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6419))
| ~ sP585(U_6419,U_6418) )
& ! [U_6419,U_6418] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6419),U_6418))
| ~ sP585(U_6419,U_6418) )
& ! [U_6419,U_6418] :
( 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),U_6418),U_6419)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6419),U_6418))
| ~ sP586(U_6419,U_6418) )
& ! [U_6419,U_6418] :
( sP585(U_6419,U_6418)
| ~ 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),U_6418),U_6419)))
| ~ sP586(U_6419,U_6418) )
& ! [U_6419,U_6418] :
( sP586(U_6419,U_6418)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6418)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP585,sP586])],[f_1698_2]) ).
cnf(f_1698_4,plain,
( sP586(U_6419,U_6418)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6418)) ),
inference(clausify,[status(thm)],[f_1698_3]) ).
cnf(f_1698_5,plain,
( sP585(U_6419,U_6418)
| ~ 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),U_6418),U_6419)))
| ~ sP586(U_6419,U_6418) ),
inference(clausify,[status(thm)],[f_1698_3]) ).
cnf(f_1698_6,plain,
( 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),U_6418),U_6419)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6419),U_6418))
| ~ sP586(U_6419,U_6418) ),
inference(clausify,[status(thm)],[f_1698_3]) ).
cnf(f_1698_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6419),U_6418))
| ~ sP585(U_6419,U_6418) ),
inference(clausify,[status(thm)],[f_1698_3]) ).
cnf(f_1698_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6419))
| ~ sP585(U_6419,U_6418) ),
inference(clausify,[status(thm)],[f_1698_3]) ).
fof(f_1699_1,plain,
! [V_b,V_b_H,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2]) ).
fof(f_1699_2,plain,
! [U_6422,U_6421,U_6420] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6420),U_6422)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6420),U_6421)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6421),U_6422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6420)) ),
inference(variable_rename,[status(thm)],[f_1699_1]) ).
fof(f_1699_3,plain,
! [U_6422,U_6420,U_6421] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6420),U_6422)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6420),U_6421)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6421),U_6422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6420)) ),
inference(definitional_conversion,[status(esa)],[f_1699_2]) ).
cnf(f_1699_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6420),U_6422)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6420),U_6421)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6421),U_6422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6420)) ),
inference(clausify,[status(thm)],[f_1699_3]) ).
fof(f_1700_1,plain,
! [V_b,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0]) ).
fof(f_1700_2,plain,
! [U_6424,U_6423] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6423),U_6424)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6424),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6423)) ),
inference(variable_rename,[status(thm)],[f_1700_1]) ).
fof(f_1700_3,plain,
! [U_6424,U_6423] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6423),U_6424)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6424),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6423)) ),
inference(definitional_conversion,[status(esa)],[f_1700_2]) ).
cnf(f_1700_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6423),U_6424)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6424),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6423)) ),
inference(clausify,[status(thm)],[f_1700_3]) ).
fof(f_1701_1,plain,
! [V_b,V_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial]) ).
fof(f_1701_2,plain,
! [U_6426,U_6425] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6425),U_6426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6425),U_6426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6425)) ),
inference(variable_rename,[status(thm)],[f_1701_1]) ).
fof(f_1701_3,plain,
! [U_6425,U_6426] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6425),U_6426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6425),U_6426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6425)) ),
inference(definitional_conversion,[status(esa)],[f_1701_2]) ).
cnf(f_1701_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6425),U_6426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6425),U_6426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6425)) ),
inference(clausify,[status(thm)],[f_1701_3]) ).
fof(f_1702_1,plain,
! [V_a_2,V_b_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff]) ).
fof(f_1702_2,plain,
! [U_6428,U_6427] :
( ( ( 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),U_6428),U_6427)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6428),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6428),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),U_6428),U_6427))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6427),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1702_1]) ).
fof(f_1702_3,plain,
( ! [U_6428,U_6427] :
( 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),U_6428),U_6427)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6428),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP587(U_6428,U_6427) )
& ! [U_6428,U_6427] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6428),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),U_6428),U_6427)))
| ~ sP587(U_6428,U_6427) )
& ! [U_6428,U_6427] :
( sP587(U_6428,U_6427)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6427),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP587])],[f_1702_2]) ).
cnf(f_1702_4,plain,
( sP587(U_6428,U_6427)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6427),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1702_3]) ).
cnf(f_1702_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6428),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),U_6428),U_6427)))
| ~ sP587(U_6428,U_6427) ),
inference(clausify,[status(thm)],[f_1702_3]) ).
cnf(f_1702_6,plain,
( 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),U_6428),U_6427)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6428),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP587(U_6428,U_6427) ),
inference(clausify,[status(thm)],[f_1702_3]) ).
fof(f_1703_1,plain,
! [V_b,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0]) ).
fof(f_1703_2,plain,
! [U_6430,U_6429] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6429),U_6430)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6429),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1703_1]) ).
fof(f_1703_3,plain,
! [U_6429,U_6430] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6429),U_6430)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6429),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1703_2]) ).
cnf(f_1703_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6429),U_6430)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6429),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1703_3]) ).
fof(f_1704_1,plain,
! [V_b,V_b_H,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg]) ).
fof(f_1704_2,plain,
! [U_6433,U_6432,U_6431] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6431),U_6432)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6431),U_6433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6432),U_6433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6431),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1704_1]) ).
fof(f_1704_3,plain,
! [U_6431,U_6432,U_6433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6431),U_6432)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6431),U_6433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6432),U_6433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6431),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1704_2]) ).
cnf(f_1704_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6431),U_6432)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6431),U_6433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6432),U_6433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6431),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1704_3]) ).
fof(f_1705_1,plain,
! [V_b,V_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial]) ).
fof(f_1705_2,plain,
! [U_6435,U_6434] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6434),U_6435) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6435),U_6434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6434),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1705_1]) ).
fof(f_1705_3,plain,
! [U_6435,U_6434] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6434),U_6435) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6435),U_6434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6434),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1705_2]) ).
cnf(f_1705_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6434),U_6435) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6435),U_6434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6434),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1705_3]) ).
fof(f_1706_1,plain,
! [V_b,V_a_H,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono1]) ).
fof(f_1706_2,plain,
! [U_6438,U_6437,U_6436] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6436),U_6438)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6437),U_6438)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6436),U_6437)) ),
inference(variable_rename,[status(thm)],[f_1706_1]) ).
fof(f_1706_3,plain,
! [U_6436,U_6437,U_6438] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6436),U_6438)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6437),U_6438)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6436),U_6437)) ),
inference(definitional_conversion,[status(esa)],[f_1706_2]) ).
cnf(f_1706_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6436),U_6438)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6437),U_6438)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6436),U_6437)) ),
inference(clausify,[status(thm)],[f_1706_3]) ).
fof(f_1707_1,plain,
! [V_b,V_a_H,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg]) ).
fof(f_1707_2,plain,
! [U_6441,U_6440,U_6439] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6440),U_6441)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6439),U_6441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6441),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6439),U_6440)) ),
inference(variable_rename,[status(thm)],[f_1707_1]) ).
fof(f_1707_3,plain,
! [U_6439,U_6440,U_6441] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6440),U_6441)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6439),U_6441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6441),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6439),U_6440)) ),
inference(definitional_conversion,[status(esa)],[f_1707_2]) ).
cnf(f_1707_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6440),U_6441)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6439),U_6441)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6441),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6439),U_6440)) ),
inference(clausify,[status(thm)],[f_1707_3]) ).
fof(f_1708_1,plain,
! [V_k,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_int__div__less__self]) ).
fof(f_1708_2,plain,
! [U_6443,U_6442] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6442),U_6443)),U_6442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6442)) ),
inference(variable_rename,[status(thm)],[f_1708_1]) ).
fof(f_1708_3,plain,
! [U_6442,U_6443] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6442),U_6443)),U_6442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6442)) ),
inference(definitional_conversion,[status(esa)],[f_1708_2]) ).
cnf(f_1708_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6442),U_6443)),U_6442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6442)) ),
inference(clausify,[status(thm)],[f_1708_3]) ).
fof(f_1709_1,plain,
! [V_b,V_a,V_c] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq]) ).
fof(f_1709_2,plain,
! [U_6446,U_6445,U_6444] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6446),U_6444)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6445),U_6446)),U_6444)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6444)) ),
inference(variable_rename,[status(thm)],[f_1709_1]) ).
fof(f_1709_3,plain,
! [U_6444,U_6445,U_6446] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6446),U_6444)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6445),U_6446)),U_6444)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6444)) ),
inference(definitional_conversion,[status(esa)],[f_1709_2]) ).
cnf(f_1709_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6446),U_6444)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6445),U_6446)),U_6444)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6444)) ),
inference(clausify,[status(thm)],[f_1709_3]) ).
fof(f_1710_1,plain,
! [V_n_2] :
( ( 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)))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_int__le__0__conv]) ).
fof(f_1710_2,plain,
! [U_6447] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6447)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6447 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6447)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1710_1]) ).
fof(f_1710_3,plain,
( ! [U_6449] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6449)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6449 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6448] :
( U_6448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6448)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1710_2]) ).
fof(f_1710_4,plain,
( ! [U_6449] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6449)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6449 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6448] :
( U_6448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6448)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_1710_3]) ).
cnf(f_1710_5,plain,
( U_6448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6448)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1710_4]) ).
cnf(f_1710_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6449)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6449 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1710_4]) ).
fof(f_1711_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_int__Suc0__eq__1]) ).
fof(f_1711_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_1711_1]) ).
cnf(f_1711_3,plain,
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),
inference(clausify,[status(thm)],[f_1711_2]) ).
fof(f_1712_1,plain,
! [V_z_2,V_w_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ! [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))) )
& ( ? [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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd]) ).
fof(f_1712_2,plain,
! [U_6453,U_6452] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6452),U_6453))
| ! [U_6451] : U_6453 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6452),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6451))) )
& ( ? [U_6450] : U_6453 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6452),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6452),U_6453)) ) ),
inference(variable_rename,[status(thm)],[f_1712_1]) ).
fof(f_1712_3,plain,
( ! [U_6457,U_6455] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6455),U_6457))
| ! [U_6451] : U_6457 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6451))) )
& ! [U_6456,U_6454] :
( ? [U_6450] : U_6456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6454),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6454),U_6456)) ) ),
inference(miniscope,[status(thm)],[f_1712_2]) ).
fof(f_1712_4,plain,
( ! [U_6457,U_6455] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6455),U_6457))
| ! [U_6451] : U_6457 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6451))) )
& ! [U_6456,U_6454] :
( U_6456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6454),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK179(U_6456,U_6454))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6454),U_6456)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_6450,sK179(U_6456,U_6454))],[f_1712_3]) ).
fof(f_1712_5,plain,
( ! [U_6451,U_6455,U_6457] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6455),U_6457))
| U_6457 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6451))) )
& ! [U_6456,U_6454] :
( U_6456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6454),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK179(U_6456,U_6454))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6454),U_6456)) ) ),
inference(definitional_conversion,[status(esa)],[f_1712_4]) ).
cnf(f_1712_6,plain,
( U_6456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6454),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK179(U_6456,U_6454))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6454),U_6456)) ),
inference(clausify,[status(thm)],[f_1712_5]) ).
cnf(f_1712_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6455),U_6457))
| U_6457 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6451))) ),
inference(clausify,[status(thm)],[f_1712_5]) ).
fof(f_1713_1,plain,
! [V_m_2,V_n_2] :
( ( 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))))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_int__zle__neg]) ).
fof(f_1713_2,plain,
! [U_6459,U_6458] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6458)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6459))))
| U_6459 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6458 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_6459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6458)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6459)))) ) ),
inference(variable_rename,[status(thm)],[f_1713_1]) ).
fof(f_1713_3,plain,
( ! [U_6463,U_6461] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6461)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6463))))
| U_6463 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6461 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6462,U_6460] :
( ( U_6462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6460)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6462)))) ) ),
inference(miniscope,[status(thm)],[f_1713_2]) ).
fof(f_1713_4,plain,
( ! [U_6460,U_6462] :
( U_6462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP588(U_6460,U_6462) )
& ! [U_6460,U_6462] :
( U_6460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP588(U_6460,U_6462) )
& ! [U_6463,U_6461] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6461)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6463))))
| U_6463 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6461 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6460,U_6462] :
( sP588(U_6460,U_6462)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6460)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6462)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP588])],[f_1713_3]) ).
cnf(f_1713_5,plain,
( sP588(U_6460,U_6462)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6460)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6462)))) ),
inference(clausify,[status(thm)],[f_1713_4]) ).
cnf(f_1713_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6461)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6463))))
| U_6463 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6461 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1713_4]) ).
cnf(f_1713_7,plain,
( U_6460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP588(U_6460,U_6462) ),
inference(clausify,[status(thm)],[f_1713_4]) ).
cnf(f_1713_8,plain,
( U_6462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP588(U_6460,U_6462) ),
inference(clausify,[status(thm)],[f_1713_4]) ).
fof(f_1714_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_int__Suc]) ).
fof(f_1714_2,plain,
! [U_6464] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6464)) = 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),U_6464)),
inference(variable_rename,[status(thm)],[f_1714_1]) ).
fof(f_1714_3,plain,
! [U_6464] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6464)) = 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),U_6464)),
inference(definitional_conversion,[status(esa)],[f_1714_2]) ).
cnf(f_1714_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6464)) = 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),U_6464)),
inference(clausify,[status(thm)],[f_1714_3]) ).
fof(f_1715_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_negative__zle__0]) ).
fof(f_1715_2,plain,
! [U_6465] : 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),U_6465))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1715_1]) ).
fof(f_1715_3,plain,
! [U_6465] : 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),U_6465))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1715_2]) ).
cnf(f_1715_4,plain,
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),U_6465))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1715_3]) ).
fof(f_1716_1,plain,
! [V_m,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_zdiff__int]) ).
fof(f_1716_2,plain,
! [U_6467,U_6466] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6467)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6466)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6467),U_6466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6466),U_6467)) ),
inference(variable_rename,[status(thm)],[f_1716_1]) ).
fof(f_1716_3,plain,
! [U_6467,U_6466] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6467)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6466)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6467),U_6466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6466),U_6467)) ),
inference(definitional_conversion,[status(esa)],[f_1716_2]) ).
cnf(f_1716_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6467)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6466)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6467),U_6466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6466),U_6467)) ),
inference(clausify,[status(thm)],[f_1716_3]) ).
fof(f_1717_1,plain,
! [V_m,T_a] :
( 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))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__Suc]) ).
fof(f_1717_2,plain,
! [U_6469,U_6468] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6468),hAPP(c_Nat_OSuc,U_6469)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6468),c_Groups_Oone__class_Oone(U_6468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6468),U_6469))
| ~ class_Rings_Osemiring__1(U_6468) ),
inference(variable_rename,[status(thm)],[f_1717_1]) ).
fof(f_1717_3,plain,
! [U_6468,U_6469] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6468),hAPP(c_Nat_OSuc,U_6469)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6468),c_Groups_Oone__class_Oone(U_6468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6468),U_6469))
| ~ class_Rings_Osemiring__1(U_6468) ),
inference(definitional_conversion,[status(esa)],[f_1717_2]) ).
cnf(f_1717_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6468),hAPP(c_Nat_OSuc,U_6469)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6468),c_Groups_Oone__class_Oone(U_6468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6468),U_6469))
| ~ class_Rings_Osemiring__1(U_6468) ),
inference(clausify,[status(thm)],[f_1717_3]) ).
fof(f_1718_1,plain,
! [V_m,V_n,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__diff]) ).
fof(f_1718_2,plain,
! [U_6472,U_6471,U_6470] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6472),U_6471)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6470),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),U_6472)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),U_6471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6471),U_6472))
| ~ class_Rings_Oring__1(U_6470) ),
inference(variable_rename,[status(thm)],[f_1718_1]) ).
fof(f_1718_3,plain,
! [U_6470,U_6471,U_6472] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6472),U_6471)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6470),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),U_6472)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),U_6471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6471),U_6472))
| ~ class_Rings_Oring__1(U_6470) ),
inference(definitional_conversion,[status(esa)],[f_1718_2]) ).
cnf(f_1718_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6472),U_6471)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6470),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),U_6472)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6470),U_6471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6471),U_6472))
| ~ class_Rings_Oring__1(U_6470) ),
inference(clausify,[status(thm)],[f_1718_3]) ).
fof(f_1719_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self2]) ).
fof(f_1719_2,plain,
! [U_6476,U_6475,U_6474,U_6473] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6473),U_6475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6473),U_6474),U_6476))),U_6474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6473),U_6476),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6473),U_6475),U_6474))
| U_6474 = c_Groups_Ozero__class_Ozero(U_6473)
| ~ class_Divides_Osemiring__div(U_6473) ),
inference(variable_rename,[status(thm)],[f_1719_1]) ).
fof(f_1719_3,plain,
! [U_6473,U_6474,U_6475,U_6476] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6473),U_6475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6473),U_6474),U_6476))),U_6474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6473),U_6476),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6473),U_6475),U_6474))
| U_6474 = c_Groups_Ozero__class_Ozero(U_6473)
| ~ class_Divides_Osemiring__div(U_6473) ),
inference(definitional_conversion,[status(esa)],[f_1719_2]) ).
cnf(f_1719_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6473),U_6475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6473),U_6474),U_6476))),U_6474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6473),U_6476),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6473),U_6475),U_6474))
| U_6474 = c_Groups_Ozero__class_Ozero(U_6473)
| ~ class_Divides_Osemiring__div(U_6473) ),
inference(clausify,[status(thm)],[f_1719_3]) ).
fof(f_1720_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self1]) ).
fof(f_1720_2,plain,
! [U_6480,U_6479,U_6478,U_6477] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6477),U_6479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6477),U_6480),U_6478))),U_6478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6477),U_6480),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6477),U_6479),U_6478))
| U_6478 = c_Groups_Ozero__class_Ozero(U_6477)
| ~ class_Divides_Osemiring__div(U_6477) ),
inference(variable_rename,[status(thm)],[f_1720_1]) ).
fof(f_1720_3,plain,
! [U_6477,U_6478,U_6479,U_6480] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6477),U_6479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6477),U_6480),U_6478))),U_6478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6477),U_6480),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6477),U_6479),U_6478))
| U_6478 = c_Groups_Ozero__class_Ozero(U_6477)
| ~ class_Divides_Osemiring__div(U_6477) ),
inference(definitional_conversion,[status(esa)],[f_1720_2]) ).
cnf(f_1720_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6477),U_6479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6477),U_6480),U_6478))),U_6478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6477),U_6480),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6477),U_6479),U_6478))
| U_6478 = c_Groups_Ozero__class_Ozero(U_6477)
| ~ class_Divides_Osemiring__div(U_6477) ),
inference(clausify,[status(thm)],[f_1720_3]) ).
fof(f_1721_1,plain,
! [V_a,V_b,T_a] :
( 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))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__add__self1]) ).
fof(f_1721_2,plain,
! [U_6483,U_6482,U_6481] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6481),U_6482),U_6483)),U_6482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6481),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6481),U_6483),U_6482)),c_Groups_Oone__class_Oone(U_6481))
| U_6482 = c_Groups_Ozero__class_Ozero(U_6481)
| ~ class_Divides_Osemiring__div(U_6481) ),
inference(variable_rename,[status(thm)],[f_1721_1]) ).
fof(f_1721_3,plain,
! [U_6481,U_6482,U_6483] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6481),U_6482),U_6483)),U_6482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6481),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6481),U_6483),U_6482)),c_Groups_Oone__class_Oone(U_6481))
| U_6482 = c_Groups_Ozero__class_Ozero(U_6481)
| ~ class_Divides_Osemiring__div(U_6481) ),
inference(definitional_conversion,[status(esa)],[f_1721_2]) ).
cnf(f_1721_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6481),U_6482),U_6483)),U_6482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6481),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6481),U_6483),U_6482)),c_Groups_Oone__class_Oone(U_6481))
| U_6482 = c_Groups_Ozero__class_Ozero(U_6481)
| ~ class_Divides_Osemiring__div(U_6481) ),
inference(clausify,[status(thm)],[f_1721_3]) ).
fof(f_1722_1,plain,
! [V_a,V_b,T_a] :
( 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))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__add__self2]) ).
fof(f_1722_2,plain,
! [U_6486,U_6485,U_6484] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6484),U_6486),U_6485)),U_6485) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6484),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6484),U_6486),U_6485)),c_Groups_Oone__class_Oone(U_6484))
| U_6485 = c_Groups_Ozero__class_Ozero(U_6484)
| ~ class_Divides_Osemiring__div(U_6484) ),
inference(variable_rename,[status(thm)],[f_1722_1]) ).
fof(f_1722_3,plain,
! [U_6484,U_6485,U_6486] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6484),U_6486),U_6485)),U_6485) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6484),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6484),U_6486),U_6485)),c_Groups_Oone__class_Oone(U_6484))
| U_6485 = c_Groups_Ozero__class_Ozero(U_6484)
| ~ class_Divides_Osemiring__div(U_6484) ),
inference(definitional_conversion,[status(esa)],[f_1722_2]) ).
cnf(f_1722_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6484),U_6486),U_6485)),U_6485) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6484),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6484),U_6486),U_6485)),c_Groups_Oone__class_Oone(U_6484))
| U_6485 = c_Groups_Ozero__class_Ozero(U_6484)
| ~ class_Divides_Osemiring__div(U_6484) ),
inference(clausify,[status(thm)],[f_1722_3]) ).
fof(f_1723_1,plain,
! [V_n_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv]) ).
fof(f_1723_2,plain,
! [U_6487] :
( ( 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),U_6487)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6487)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6487))
| ~ 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),U_6487))) ) ),
inference(variable_rename,[status(thm)],[f_1723_1]) ).
fof(f_1723_3,plain,
( ! [U_6489] :
( 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),U_6489)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6489)) )
& ! [U_6488] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6488))
| ~ 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),U_6488))) ) ),
inference(miniscope,[status(thm)],[f_1723_2]) ).
fof(f_1723_4,plain,
( ! [U_6489] :
( 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),U_6489)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6489)) )
& ! [U_6488] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6488))
| ~ 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),U_6488))) ) ),
inference(definitional_conversion,[status(esa)],[f_1723_3]) ).
cnf(f_1723_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6488))
| ~ 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),U_6488))) ),
inference(clausify,[status(thm)],[f_1723_4]) ).
cnf(f_1723_6,plain,
( 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),U_6489)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6489)) ),
inference(clausify,[status(thm)],[f_1723_4]) ).
fof(f_1724_1,plain,
! [V_k,V_j,V_i] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma]) ).
fof(f_1724_2,plain,
! [U_6492,U_6491,U_6490] :
( 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),U_6492)),U_6490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6492)),U_6491)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6490),U_6491)) ),
inference(variable_rename,[status(thm)],[f_1724_1]) ).
fof(f_1724_3,plain,
! [U_6490,U_6491,U_6492] :
( 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),U_6492)),U_6490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6492)),U_6491)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6490),U_6491)) ),
inference(definitional_conversion,[status(esa)],[f_1724_2]) ).
cnf(f_1724_4,plain,
( 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),U_6492)),U_6490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6492)),U_6491)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6490),U_6491)) ),
inference(clausify,[status(thm)],[f_1724_3]) ).
fof(f_1725_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_not__zle__0__negative]) ).
fof(f_1725_2,plain,
! [U_6493] : ~ 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,U_6493))))),
inference(variable_rename,[status(thm)],[f_1725_1]) ).
fof(f_1725_3,plain,
! [U_6493] : ~ 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,U_6493))))),
inference(definitional_conversion,[status(esa)],[f_1725_2]) ).
cnf(f_1725_4,plain,
~ 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,U_6493))))),
inference(clausify,[status(thm)],[f_1725_3]) ).
fof(f_1726_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_negative__zless__0]) ).
fof(f_1726_2,plain,
! [U_6494] : 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,U_6494)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1726_1]) ).
fof(f_1726_3,plain,
! [U_6494] : 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,U_6494)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1726_2]) ).
cnf(f_1726_4,plain,
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,U_6494)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1726_3]) ).
fof(f_1727_1,plain,
! [V_n_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff]) ).
fof(f_1727_2,plain,
! [U_6496,U_6495] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),c_Groups_Ozero__class_Ozero(U_6495)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6495),U_6496)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6496)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6496))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),c_Groups_Ozero__class_Ozero(U_6495)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6495),U_6496))) ) )
| ~ class_Rings_Olinordered__semidom(U_6495) ),
inference(variable_rename,[status(thm)],[f_1727_1]) ).
fof(f_1727_3,plain,
( ! [U_6495,U_6496] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),c_Groups_Ozero__class_Ozero(U_6495)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6495),U_6496)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6496))
| ~ sP589(U_6495,U_6496) )
& ! [U_6495,U_6496] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6496))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),c_Groups_Ozero__class_Ozero(U_6495)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6495),U_6496)))
| ~ sP589(U_6495,U_6496) )
& ! [U_6495,U_6496] :
( sP589(U_6495,U_6496)
| ~ class_Rings_Olinordered__semidom(U_6495) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP589])],[f_1727_2]) ).
cnf(f_1727_4,plain,
( sP589(U_6495,U_6496)
| ~ class_Rings_Olinordered__semidom(U_6495) ),
inference(clausify,[status(thm)],[f_1727_3]) ).
cnf(f_1727_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6496))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),c_Groups_Ozero__class_Ozero(U_6495)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6495),U_6496)))
| ~ sP589(U_6495,U_6496) ),
inference(clausify,[status(thm)],[f_1727_3]) ).
cnf(f_1727_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),c_Groups_Ozero__class_Ozero(U_6495)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6495),U_6496)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6496))
| ~ sP589(U_6495,U_6496) ),
inference(clausify,[status(thm)],[f_1727_3]) ).
fof(f_1728_1,plain,
! [V_r_1,V_y,V_b_1,V_a_1] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y
| V_b_1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
| 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) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__eq]) ).
fof(f_1728_2,plain,
! [U_6500,U_6499,U_6498,U_6497] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6497),U_6498) = U_6499
| U_6498 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6500),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6498),U_6500)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6498)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6500),U_6498))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6500)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6498)) )
| U_6497 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6498),U_6499)),U_6500) ),
inference(variable_rename,[status(thm)],[f_1728_1]) ).
fof(f_1728_3,plain,
( ! [U_6498,U_6500] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6500),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6498),U_6500))
| ~ sP591(U_6498,U_6500) )
& ! [U_6498,U_6500] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6498))
| ~ sP591(U_6498,U_6500) )
& ! [U_6498,U_6500] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6500),U_6498))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6500))
| ~ sP590(U_6498,U_6500) )
& ! [U_6498,U_6500] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6498))
| ~ sP590(U_6498,U_6500) )
& ! [U_6498,U_6497,U_6499,U_6500] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6497),U_6498) = U_6499
| U_6498 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP591(U_6498,U_6500)
| sP590(U_6498,U_6500)
| U_6497 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6498),U_6499)),U_6500) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP590,sP591])],[f_1728_2]) ).
cnf(f_1728_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6497),U_6498) = U_6499
| U_6498 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP591(U_6498,U_6500)
| sP590(U_6498,U_6500)
| U_6497 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6498),U_6499)),U_6500) ),
inference(clausify,[status(thm)],[f_1728_3]) ).
cnf(f_1728_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6498))
| ~ sP590(U_6498,U_6500) ),
inference(clausify,[status(thm)],[f_1728_3]) ).
cnf(f_1728_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6500),U_6498))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6500))
| ~ sP590(U_6498,U_6500) ),
inference(clausify,[status(thm)],[f_1728_3]) ).
cnf(f_1728_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6498))
| ~ sP591(U_6498,U_6500) ),
inference(clausify,[status(thm)],[f_1728_3]) ).
cnf(f_1728_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6500),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6498),U_6500))
| ~ sP591(U_6498,U_6500) ),
inference(clausify,[status(thm)],[f_1728_3]) ).
fof(f_1729_1,plain,
! [V_k_2,V_n_2,V_Pa_2] :
( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_Pa_2,B_i))
& ? [B_j] :
( 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_Pa_2,B_i))
& ? [B_j] :
( 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
| ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [B_i] :
( hBOOL(hAPP(V_Pa_2,B_i))
| ! [B_j] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [B_i] :
( hBOOL(hAPP(V_Pa_2,B_i))
| ! [B_j] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
& ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).
fof(f_1729_2,plain,
! [U_6511,U_6510,U_6509] :
( ( hBOOL(hAPP(U_6509,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6510),U_6511)))
| ( ? [U_6508] :
( ~ hBOOL(hAPP(U_6509,U_6508))
& ? [U_6507] :
( U_6510 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6511),U_6508)),U_6507)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6511),U_6507)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6511),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6506] :
( ~ hBOOL(hAPP(U_6509,U_6506))
& ? [U_6505] :
( U_6510 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6511),U_6506)),U_6505)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6505),U_6511))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6505)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6511)) )
| ( ~ hBOOL(hAPP(U_6509,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6511 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_6504] :
( hBOOL(hAPP(U_6509,U_6504))
| ! [U_6503] :
( U_6510 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6511),U_6504)),U_6503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6511),U_6503)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6511),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6502] :
( hBOOL(hAPP(U_6509,U_6502))
| ! [U_6501] :
( U_6510 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6511),U_6502)),U_6501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6501),U_6511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6501)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6511)) )
& ( hBOOL(hAPP(U_6509,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6511 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6509,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6510),U_6511))) ) ),
inference(variable_rename,[status(thm)],[f_1729_1]) ).
fof(f_1729_3,plain,
( ! [U_6517,U_6515,U_6513] :
( hBOOL(hAPP(U_6513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6515),U_6517)))
| ( ? [U_6508] :
( ~ hBOOL(hAPP(U_6513,U_6508))
& ? [U_6507] :
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6508)),U_6507)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),U_6507)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6506] :
( ~ hBOOL(hAPP(U_6513,U_6506))
& ? [U_6505] :
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6506)),U_6505)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6505),U_6517))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6505)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517)) )
| ( ~ hBOOL(hAPP(U_6513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6516,U_6514,U_6512] :
( ( ( ! [U_6504] :
( hBOOL(hAPP(U_6512,U_6504))
| ! [U_6503] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6504)),U_6503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),U_6503)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6502] :
( hBOOL(hAPP(U_6512,U_6502))
| ! [U_6501] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6502)),U_6501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6501),U_6516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6501)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6516)) )
& ( hBOOL(hAPP(U_6512,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6516 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6512,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6514),U_6516))) ) ),
inference(miniscope,[status(thm)],[f_1729_2]) ).
fof(f_1729_4,plain,
( ! [U_6517,U_6515,U_6513] :
( hBOOL(hAPP(U_6513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6515),U_6517)))
| ( ? [U_6508] :
( ~ hBOOL(hAPP(U_6513,U_6508))
& ? [U_6507] :
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6508)),U_6507)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),U_6507)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6513,sK180(U_6517,U_6515,U_6513)))
& ? [U_6505] :
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK180(U_6517,U_6515,U_6513))),U_6505)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6505),U_6517))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6505)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517)) )
| ( ~ hBOOL(hAPP(U_6513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6516,U_6514,U_6512] :
( ( ( ! [U_6504] :
( hBOOL(hAPP(U_6512,U_6504))
| ! [U_6503] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6504)),U_6503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),U_6503)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6502] :
( hBOOL(hAPP(U_6512,U_6502))
| ! [U_6501] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6502)),U_6501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6501),U_6516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6501)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6516)) )
& ( hBOOL(hAPP(U_6512,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6516 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6512,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6514),U_6516))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_6506,sK180(U_6517,U_6515,U_6513))],[f_1729_3]) ).
fof(f_1729_5,plain,
( ! [U_6517,U_6515,U_6513] :
( hBOOL(hAPP(U_6513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6515),U_6517)))
| ( ? [U_6508] :
( ~ hBOOL(hAPP(U_6513,U_6508))
& ? [U_6507] :
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6508)),U_6507)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),U_6507)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6513,sK180(U_6517,U_6515,U_6513)))
& U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK180(U_6517,U_6515,U_6513))),sK181(U_6517,U_6515,U_6513))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK181(U_6517,U_6515,U_6513)),U_6517))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK181(U_6517,U_6515,U_6513)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517)) )
| ( ~ hBOOL(hAPP(U_6513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6516,U_6514,U_6512] :
( ( ( ! [U_6504] :
( hBOOL(hAPP(U_6512,U_6504))
| ! [U_6503] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6504)),U_6503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),U_6503)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6502] :
( hBOOL(hAPP(U_6512,U_6502))
| ! [U_6501] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6502)),U_6501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6501),U_6516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6501)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6516)) )
& ( hBOOL(hAPP(U_6512,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6516 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6512,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6514),U_6516))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_6505,sK181(U_6517,U_6515,U_6513))],[f_1729_4]) ).
fof(f_1729_6,plain,
( ! [U_6517,U_6515,U_6513] :
( hBOOL(hAPP(U_6513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6515),U_6517)))
| ( ~ hBOOL(hAPP(U_6513,sK182(U_6517,U_6515,U_6513)))
& ? [U_6507] :
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK182(U_6517,U_6515,U_6513))),U_6507)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),U_6507)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6513,sK180(U_6517,U_6515,U_6513)))
& U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK180(U_6517,U_6515,U_6513))),sK181(U_6517,U_6515,U_6513))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK181(U_6517,U_6515,U_6513)),U_6517))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK181(U_6517,U_6515,U_6513)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517)) )
| ( ~ hBOOL(hAPP(U_6513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6516,U_6514,U_6512] :
( ( ( ! [U_6504] :
( hBOOL(hAPP(U_6512,U_6504))
| ! [U_6503] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6504)),U_6503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),U_6503)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6502] :
( hBOOL(hAPP(U_6512,U_6502))
| ! [U_6501] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6502)),U_6501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6501),U_6516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6501)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6516)) )
& ( hBOOL(hAPP(U_6512,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6516 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6512,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6514),U_6516))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_6508,sK182(U_6517,U_6515,U_6513))],[f_1729_5]) ).
fof(f_1729_7,plain,
( ! [U_6517,U_6515,U_6513] :
( hBOOL(hAPP(U_6513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6515),U_6517)))
| ( ~ hBOOL(hAPP(U_6513,sK182(U_6517,U_6515,U_6513)))
& U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK182(U_6517,U_6515,U_6513))),sK183(U_6517,U_6515,U_6513))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK183(U_6517,U_6515,U_6513)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),sK183(U_6517,U_6515,U_6513)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6513,sK180(U_6517,U_6515,U_6513)))
& U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK180(U_6517,U_6515,U_6513))),sK181(U_6517,U_6515,U_6513))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK181(U_6517,U_6515,U_6513)),U_6517))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK181(U_6517,U_6515,U_6513)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517)) )
| ( ~ hBOOL(hAPP(U_6513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6516,U_6514,U_6512] :
( ( ( ! [U_6504] :
( hBOOL(hAPP(U_6512,U_6504))
| ! [U_6503] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6504)),U_6503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),U_6503)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6502] :
( hBOOL(hAPP(U_6512,U_6502))
| ! [U_6501] :
( U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6502)),U_6501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6501),U_6516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6501)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6516)) )
& ( hBOOL(hAPP(U_6512,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6516 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6512,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6514),U_6516))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_6507,sK183(U_6517,U_6515,U_6513))],[f_1729_6]) ).
fof(f_1729_8,plain,
( ! [U_6513,U_6517,U_6515] :
( ~ hBOOL(hAPP(U_6513,sK182(U_6517,U_6515,U_6513)))
| ~ sP595(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK182(U_6517,U_6515,U_6513))),sK183(U_6517,U_6515,U_6513))
| ~ sP595(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK183(U_6517,U_6515,U_6513)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP595(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),sK183(U_6517,U_6515,U_6513)))
| ~ sP595(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP595(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( ~ hBOOL(hAPP(U_6513,sK180(U_6517,U_6515,U_6513)))
| ~ sP594(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK180(U_6517,U_6515,U_6513))),sK181(U_6517,U_6515,U_6513))
| ~ sP594(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK181(U_6517,U_6515,U_6513)),U_6517))
| ~ sP594(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK181(U_6517,U_6515,U_6513)))
| ~ sP594(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517,U_6515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517))
| ~ sP594(U_6513,U_6517,U_6515) )
& ! [U_6513,U_6517] :
( ~ hBOOL(hAPP(U_6513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP593(U_6513,U_6517) )
& ! [U_6513,U_6517] :
( U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP593(U_6513,U_6517) )
& ! [U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516] :
( hBOOL(hAPP(U_6512,U_6504))
| U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6504)),U_6503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),U_6503))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP592(U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516) )
& ! [U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516] :
( hBOOL(hAPP(U_6512,U_6502))
| U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6502)),U_6501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6501),U_6516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6501))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6516))
| ~ sP592(U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516) )
& ! [U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516] :
( hBOOL(hAPP(U_6512,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6516 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP592(U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516) )
& ! [U_6513,U_6517,U_6515] :
( hBOOL(hAPP(U_6513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6515),U_6517)))
| sP595(U_6513,U_6517,U_6515)
| sP594(U_6513,U_6517,U_6515)
| sP593(U_6513,U_6517) )
& ! [U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516] :
( sP592(U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516)
| ~ hBOOL(hAPP(U_6512,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6514),U_6516))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP592,sP593,sP594,sP595])],[f_1729_7]) ).
cnf(f_1729_9,plain,
( sP592(U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516)
| ~ hBOOL(hAPP(U_6512,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6514),U_6516))) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_10,plain,
( hBOOL(hAPP(U_6513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6515),U_6517)))
| sP595(U_6513,U_6517,U_6515)
| sP594(U_6513,U_6517,U_6515)
| sP593(U_6513,U_6517) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_11,plain,
( hBOOL(hAPP(U_6512,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6516 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP592(U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_12,plain,
( hBOOL(hAPP(U_6512,U_6502))
| U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6502)),U_6501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6501),U_6516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6501))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6516))
| ~ sP592(U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_13,plain,
( hBOOL(hAPP(U_6512,U_6504))
| U_6514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6516),U_6504)),U_6503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),U_6503))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP592(U_6504,U_6501,U_6502,U_6514,U_6503,U_6512,U_6516) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_14,plain,
( U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP593(U_6513,U_6517) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_15,plain,
( ~ hBOOL(hAPP(U_6513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP593(U_6513,U_6517) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_16,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517))
| ~ sP594(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_17,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK181(U_6517,U_6515,U_6513)))
| ~ sP594(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_18,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK181(U_6517,U_6515,U_6513)),U_6517))
| ~ sP594(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_19,plain,
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK180(U_6517,U_6515,U_6513))),sK181(U_6517,U_6515,U_6513))
| ~ sP594(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_20,plain,
( ~ hBOOL(hAPP(U_6513,sK180(U_6517,U_6515,U_6513)))
| ~ sP594(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_21,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP595(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_22,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),sK183(U_6517,U_6515,U_6513)))
| ~ sP595(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_23,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK183(U_6517,U_6515,U_6513)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP595(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_24,plain,
( U_6515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),sK182(U_6517,U_6515,U_6513))),sK183(U_6517,U_6515,U_6513))
| ~ sP595(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
cnf(f_1729_25,plain,
( ~ hBOOL(hAPP(U_6513,sK182(U_6517,U_6515,U_6513)))
| ~ sP595(U_6513,U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1729_8]) ).
fof(f_1730_1,plain,
! [V_y,V_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).
fof(f_1730_2,plain,
! [U_6519,U_6518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_6518,U_6519)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6518)) ),
inference(variable_rename,[status(thm)],[f_1730_1]) ).
fof(f_1730_3,plain,
! [U_6519,U_6518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_6518,U_6519)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6518)) ),
inference(definitional_conversion,[status(esa)],[f_1730_2]) ).
cnf(f_1730_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_6518,U_6519)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6518)) ),
inference(clausify,[status(thm)],[f_1730_3]) ).
fof(f_1731_1,plain,
! [V_y_2,V_x_2,V_Pa_2] :
( ( 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))))
| ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
| ( ~ 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))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
& ( ( ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zdiff__int__split]) ).
fof(f_1731_2,plain,
! [U_6522,U_6521,U_6520] :
( ( hBOOL(hAPP(U_6520,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6521),U_6522))))
| ( ~ hBOOL(hAPP(U_6520,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6521),U_6522)) )
| ( ~ hBOOL(hAPP(U_6520,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6521)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6522))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6522),U_6521)) ) )
& ( ( ( hBOOL(hAPP(U_6520,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6521),U_6522)) )
& ( hBOOL(hAPP(U_6520,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6521)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6522))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6522),U_6521)) ) )
| ~ hBOOL(hAPP(U_6520,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6521),U_6522)))) ) ),
inference(variable_rename,[status(thm)],[f_1731_1]) ).
fof(f_1731_3,plain,
( ! [U_6528,U_6526,U_6524] :
( hBOOL(hAPP(U_6524,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6526),U_6528))))
| ( ~ hBOOL(hAPP(U_6524,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6526),U_6528)) )
| ( ~ hBOOL(hAPP(U_6524,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6526)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6528))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6528),U_6526)) ) )
& ! [U_6527,U_6525,U_6523] :
( ( ( hBOOL(hAPP(U_6523,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6525),U_6527)) )
& ( hBOOL(hAPP(U_6523,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6525)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6527))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6527),U_6525)) ) )
| ~ hBOOL(hAPP(U_6523,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6525),U_6527)))) ) ),
inference(miniscope,[status(thm)],[f_1731_2]) ).
fof(f_1731_4,plain,
( ! [U_6528,U_6524,U_6526] :
( ~ hBOOL(hAPP(U_6524,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP598(U_6528,U_6524,U_6526) )
& ! [U_6528,U_6524,U_6526] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6526),U_6528))
| ~ sP598(U_6528,U_6524,U_6526) )
& ! [U_6528,U_6524,U_6526] :
( ~ hBOOL(hAPP(U_6524,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6526)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6528))))
| ~ sP597(U_6528,U_6524,U_6526) )
& ! [U_6528,U_6524,U_6526] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6528),U_6526))
| ~ sP597(U_6528,U_6524,U_6526) )
& ! [U_6525,U_6527,U_6523] :
( hBOOL(hAPP(U_6523,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6525),U_6527))
| ~ sP596(U_6525,U_6527,U_6523) )
& ! [U_6525,U_6527,U_6523] :
( hBOOL(hAPP(U_6523,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6525)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6527))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6527),U_6525))
| ~ sP596(U_6525,U_6527,U_6523) )
& ! [U_6528,U_6524,U_6526] :
( hBOOL(hAPP(U_6524,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6526),U_6528))))
| sP598(U_6528,U_6524,U_6526)
| sP597(U_6528,U_6524,U_6526) )
& ! [U_6525,U_6527,U_6523] :
( sP596(U_6525,U_6527,U_6523)
| ~ hBOOL(hAPP(U_6523,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6525),U_6527)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP596,sP597,sP598])],[f_1731_3]) ).
cnf(f_1731_5,plain,
( sP596(U_6525,U_6527,U_6523)
| ~ hBOOL(hAPP(U_6523,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6525),U_6527)))) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
cnf(f_1731_6,plain,
( hBOOL(hAPP(U_6524,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6526),U_6528))))
| sP598(U_6528,U_6524,U_6526)
| sP597(U_6528,U_6524,U_6526) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
cnf(f_1731_7,plain,
( hBOOL(hAPP(U_6523,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6525)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6527))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6527),U_6525))
| ~ sP596(U_6525,U_6527,U_6523) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
cnf(f_1731_8,plain,
( hBOOL(hAPP(U_6523,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6525),U_6527))
| ~ sP596(U_6525,U_6527,U_6523) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
cnf(f_1731_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6528),U_6526))
| ~ sP597(U_6528,U_6524,U_6526) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
cnf(f_1731_10,plain,
( ~ hBOOL(hAPP(U_6524,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6526)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6528))))
| ~ sP597(U_6528,U_6524,U_6526) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
cnf(f_1731_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6526),U_6528))
| ~ sP598(U_6528,U_6524,U_6526) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
cnf(f_1731_12,plain,
( ~ hBOOL(hAPP(U_6524,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP598(U_6528,U_6524,U_6526) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
fof(f_1732_1,plain,
! [V_x,V_y] :
( c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_tsub__eq]) ).
fof(f_1732_2,plain,
! [U_6530,U_6529] :
( c_Nat__Transfer_Otsub(U_6530,U_6529) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6530),U_6529)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6529),U_6530)) ),
inference(variable_rename,[status(thm)],[f_1732_1]) ).
fof(f_1732_3,plain,
! [U_6530,U_6529] :
( c_Nat__Transfer_Otsub(U_6530,U_6529) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6530),U_6529)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6529),U_6530)) ),
inference(definitional_conversion,[status(esa)],[f_1732_2]) ).
cnf(f_1732_4,plain,
( c_Nat__Transfer_Otsub(U_6530,U_6529) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6530),U_6529)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6529),U_6530)) ),
inference(clausify,[status(thm)],[f_1732_3]) ).
fof(f_1733_1,plain,
! [V_k,V_l] :
( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) )
& ( c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) ) ),
inference(fof_nnf,[status(thm)],[fact_z3div__def]) ).
fof(f_1733_2,plain,
! [U_6532,U_6531] :
( ( c_SMT_Oz3div(U_6532,U_6531) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6532),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6531)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6531)) )
& ( c_SMT_Oz3div(U_6532,U_6531) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6532),U_6531)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6531)) ) ),
inference(variable_rename,[status(thm)],[f_1733_1]) ).
fof(f_1733_3,plain,
( ! [U_6536,U_6534] :
( c_SMT_Oz3div(U_6536,U_6534) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6536),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6534)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6534)) )
& ! [U_6535,U_6533] :
( c_SMT_Oz3div(U_6535,U_6533) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6535),U_6533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6533)) ) ),
inference(miniscope,[status(thm)],[f_1733_2]) ).
fof(f_1733_4,plain,
( ! [U_6536,U_6534] :
( c_SMT_Oz3div(U_6536,U_6534) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6536),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6534)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6534)) )
& ! [U_6535,U_6533] :
( c_SMT_Oz3div(U_6535,U_6533) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6535),U_6533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6533)) ) ),
inference(definitional_conversion,[status(esa)],[f_1733_3]) ).
cnf(f_1733_5,plain,
( c_SMT_Oz3div(U_6535,U_6533) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6535),U_6533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6533)) ),
inference(clausify,[status(thm)],[f_1733_4]) ).
cnf(f_1733_6,plain,
( c_SMT_Oz3div(U_6536,U_6534) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6536),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6534)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6534)) ),
inference(clausify,[status(thm)],[f_1733_4]) ).
fof(f_1734_1,plain,
! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
( 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)))
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) )
| ~ class_Rings_Osemiring__1(T_c)
| ~ class_Groups_Oordered__ab__semigroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__bounded]) ).
fof(f_1734_2,plain,
! [U_6542,U_6541,U_6540,U_6539,U_6538] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6539,U_6538),U_6541),U_6540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6538),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6538),hAPP(c_Finite__Set_Ocard(U_6539),U_6540))),U_6542)))
| ? [U_6537] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6538),hAPP(U_6541,U_6537)),U_6542))
& hBOOL(hAPP(hAPP(c_member(U_6539),U_6537),U_6540)) )
| ~ class_Rings_Osemiring__1(U_6538)
| ~ class_Groups_Oordered__ab__semigroup__add(U_6538) ),
inference(variable_rename,[status(thm)],[f_1734_1]) ).
fof(f_1734_3,plain,
! [U_6542,U_6541,U_6540,U_6539,U_6538] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6539,U_6538),U_6541),U_6540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6538),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6538),hAPP(c_Finite__Set_Ocard(U_6539),U_6540))),U_6542)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6538),hAPP(U_6541,sK184(U_6542,U_6541,U_6540,U_6539,U_6538))),U_6542))
& hBOOL(hAPP(hAPP(c_member(U_6539),sK184(U_6542,U_6541,U_6540,U_6539,U_6538)),U_6540)) )
| ~ class_Rings_Osemiring__1(U_6538)
| ~ class_Groups_Oordered__ab__semigroup__add(U_6538) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_6537,sK184(U_6542,U_6541,U_6540,U_6539,U_6538))],[f_1734_2]) ).
fof(f_1734_4,plain,
( ! [U_6539,U_6538,U_6540,U_6541,U_6542] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6538),hAPP(U_6541,sK184(U_6542,U_6541,U_6540,U_6539,U_6538))),U_6542))
| ~ sP599(U_6539,U_6538,U_6540,U_6541,U_6542) )
& ! [U_6539,U_6538,U_6540,U_6541,U_6542] :
( hBOOL(hAPP(hAPP(c_member(U_6539),sK184(U_6542,U_6541,U_6540,U_6539,U_6538)),U_6540))
| ~ sP599(U_6539,U_6538,U_6540,U_6541,U_6542) )
& ! [U_6539,U_6538,U_6540,U_6541,U_6542] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6539,U_6538),U_6541),U_6540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6538),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6538),hAPP(c_Finite__Set_Ocard(U_6539),U_6540))),U_6542)))
| sP599(U_6539,U_6538,U_6540,U_6541,U_6542)
| ~ class_Rings_Osemiring__1(U_6538)
| ~ class_Groups_Oordered__ab__semigroup__add(U_6538) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP599])],[f_1734_3]) ).
cnf(f_1734_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6539,U_6538),U_6541),U_6540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6538),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6538),hAPP(c_Finite__Set_Ocard(U_6539),U_6540))),U_6542)))
| sP599(U_6539,U_6538,U_6540,U_6541,U_6542)
| ~ class_Rings_Osemiring__1(U_6538)
| ~ class_Groups_Oordered__ab__semigroup__add(U_6538) ),
inference(clausify,[status(thm)],[f_1734_4]) ).
cnf(f_1734_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_6539),sK184(U_6542,U_6541,U_6540,U_6539,U_6538)),U_6540))
| ~ sP599(U_6539,U_6538,U_6540,U_6541,U_6542) ),
inference(clausify,[status(thm)],[f_1734_4]) ).
cnf(f_1734_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6538),hAPP(U_6541,sK184(U_6542,U_6541,U_6540,U_6539,U_6538))),U_6542))
| ~ sP599(U_6539,U_6538,U_6540,U_6541,U_6542) ),
inference(clausify,[status(thm)],[f_1734_4]) ).
fof(f_1735_1,plain,
! [V_b,V_a] :
( 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)
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__neg__trivial]) ).
fof(f_1735_2,plain,
! [U_6544,U_6543] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6543),U_6544) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6543),U_6544)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6543)) ),
inference(variable_rename,[status(thm)],[f_1735_1]) ).
fof(f_1735_3,plain,
! [U_6543,U_6544] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6543),U_6544) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6543),U_6544)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6543)) ),
inference(definitional_conversion,[status(esa)],[f_1735_2]) ).
cnf(f_1735_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6543),U_6544) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6543),U_6544)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6543)) ),
inference(clausify,[status(thm)],[f_1735_3]) ).
fof(f_1736_1,plain,
! [V_n_2,V_Pa_2,V_k_2] :
( ( ( 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)))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))
& 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
& ( ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))
| 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_split__neg__lemma]) ).
fof(f_1736_2,plain,
! [U_6551,U_6550,U_6549] :
( ( ( hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549)))
| ? [U_6548,U_6547] :
( ~ hBOOL(hAPP(hAPP(U_6550,U_6548),U_6547))
& U_6551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),U_6548)),U_6547)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6547),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),U_6547)) ) )
& ( ! [U_6546,U_6545] :
( hBOOL(hAPP(hAPP(U_6550,U_6546),U_6545))
| U_6551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),U_6546)),U_6545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6545),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),U_6545)) )
| ~ hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1736_1]) ).
fof(f_1736_3,plain,
! [U_6551,U_6550,U_6549] :
( ( ( hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549)))
| ? [U_6547] :
( ~ hBOOL(hAPP(hAPP(U_6550,sK185(U_6551,U_6550,U_6549)),U_6547))
& U_6551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),sK185(U_6551,U_6550,U_6549))),U_6547)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6547),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),U_6547)) ) )
& ( ! [U_6546,U_6545] :
( hBOOL(hAPP(hAPP(U_6550,U_6546),U_6545))
| U_6551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),U_6546)),U_6545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6545),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),U_6545)) )
| ~ hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_6548,sK185(U_6551,U_6550,U_6549))],[f_1736_2]) ).
fof(f_1736_4,plain,
! [U_6551,U_6550,U_6549] :
( ( ( hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549)))
| ( ~ hBOOL(hAPP(hAPP(U_6550,sK185(U_6551,U_6550,U_6549)),sK186(U_6551,U_6550,U_6549)))
& U_6551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),sK185(U_6551,U_6550,U_6549))),sK186(U_6551,U_6550,U_6549))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK186(U_6551,U_6550,U_6549)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),sK186(U_6551,U_6550,U_6549))) ) )
& ( ! [U_6546,U_6545] :
( hBOOL(hAPP(hAPP(U_6550,U_6546),U_6545))
| U_6551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),U_6546)),U_6545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6545),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),U_6545)) )
| ~ hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_6547,sK186(U_6551,U_6550,U_6549))],[f_1736_3]) ).
fof(f_1736_5,plain,
( ! [U_6549,U_6550,U_6551] :
( ~ hBOOL(hAPP(hAPP(U_6550,sK185(U_6551,U_6550,U_6549)),sK186(U_6551,U_6550,U_6549)))
| ~ sP600(U_6549,U_6550,U_6551) )
& ! [U_6549,U_6550,U_6551] :
( U_6551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),sK185(U_6551,U_6550,U_6549))),sK186(U_6551,U_6550,U_6549))
| ~ sP600(U_6549,U_6550,U_6551) )
& ! [U_6549,U_6550,U_6551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK186(U_6551,U_6550,U_6549)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP600(U_6549,U_6550,U_6551) )
& ! [U_6549,U_6550,U_6551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),sK186(U_6551,U_6550,U_6549)))
| ~ sP600(U_6549,U_6550,U_6551) )
& ! [U_6545,U_6546,U_6549,U_6550,U_6551] :
( hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549)))
| sP600(U_6549,U_6550,U_6551)
| ~ sP601(U_6545,U_6546,U_6549,U_6550,U_6551) )
& ! [U_6545,U_6546,U_6549,U_6550,U_6551] :
( hBOOL(hAPP(hAPP(U_6550,U_6546),U_6545))
| U_6551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),U_6546)),U_6545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6545),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),U_6545))
| ~ hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549)))
| ~ sP601(U_6545,U_6546,U_6549,U_6550,U_6551) )
& ! [U_6545,U_6546,U_6549,U_6550,U_6551] :
( sP601(U_6545,U_6546,U_6549,U_6550,U_6551)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP600,sP601])],[f_1736_4]) ).
cnf(f_1736_6,plain,
( sP601(U_6545,U_6546,U_6549,U_6550,U_6551)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1736_5]) ).
cnf(f_1736_7,plain,
( hBOOL(hAPP(hAPP(U_6550,U_6546),U_6545))
| U_6551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),U_6546)),U_6545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6545),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),U_6545))
| ~ hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549)))
| ~ sP601(U_6545,U_6546,U_6549,U_6550,U_6551) ),
inference(clausify,[status(thm)],[f_1736_5]) ).
cnf(f_1736_8,plain,
( hBOOL(hAPP(hAPP(U_6550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6551),U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6551,U_6549)))
| sP600(U_6549,U_6550,U_6551)
| ~ sP601(U_6545,U_6546,U_6549,U_6550,U_6551) ),
inference(clausify,[status(thm)],[f_1736_5]) ).
cnf(f_1736_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6549),sK186(U_6551,U_6550,U_6549)))
| ~ sP600(U_6549,U_6550,U_6551) ),
inference(clausify,[status(thm)],[f_1736_5]) ).
cnf(f_1736_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK186(U_6551,U_6550,U_6549)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP600(U_6549,U_6550,U_6551) ),
inference(clausify,[status(thm)],[f_1736_5]) ).
cnf(f_1736_11,plain,
( U_6551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6549),sK185(U_6551,U_6550,U_6549))),sK186(U_6551,U_6550,U_6549))
| ~ sP600(U_6549,U_6550,U_6551) ),
inference(clausify,[status(thm)],[f_1736_5]) ).
cnf(f_1736_12,plain,
( ~ hBOOL(hAPP(hAPP(U_6550,sK185(U_6551,U_6550,U_6549)),sK186(U_6551,U_6550,U_6549)))
| ~ sP600(U_6549,U_6550,U_6551) ),
inference(clausify,[status(thm)],[f_1736_5]) ).
fof(f_1737_1,plain,
! [V_n_2,V_Pa_2,V_k_2] :
( ( ( 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)))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))
& 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
& ( ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))
| 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
inference(fof_nnf,[status(thm)],[fact_split__pos__lemma]) ).
fof(f_1737_2,plain,
! [U_6558,U_6557,U_6556] :
( ( ( hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556)))
| ? [U_6555,U_6554] :
( ~ hBOOL(hAPP(hAPP(U_6557,U_6555),U_6554))
& U_6558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),U_6555)),U_6554)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6554),U_6556))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6554)) ) )
& ( ! [U_6553,U_6552] :
( hBOOL(hAPP(hAPP(U_6557,U_6553),U_6552))
| U_6558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),U_6553)),U_6552)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6552),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6552)) )
| ~ hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6556)) ),
inference(variable_rename,[status(thm)],[f_1737_1]) ).
fof(f_1737_3,plain,
! [U_6558,U_6557,U_6556] :
( ( ( hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556)))
| ? [U_6554] :
( ~ hBOOL(hAPP(hAPP(U_6557,sK187(U_6558,U_6557,U_6556)),U_6554))
& U_6558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),sK187(U_6558,U_6557,U_6556))),U_6554)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6554),U_6556))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6554)) ) )
& ( ! [U_6553,U_6552] :
( hBOOL(hAPP(hAPP(U_6557,U_6553),U_6552))
| U_6558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),U_6553)),U_6552)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6552),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6552)) )
| ~ hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6556)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_6555,sK187(U_6558,U_6557,U_6556))],[f_1737_2]) ).
fof(f_1737_4,plain,
! [U_6558,U_6557,U_6556] :
( ( ( hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556)))
| ( ~ hBOOL(hAPP(hAPP(U_6557,sK187(U_6558,U_6557,U_6556)),sK188(U_6558,U_6557,U_6556)))
& U_6558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),sK187(U_6558,U_6557,U_6556))),sK188(U_6558,U_6557,U_6556))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK188(U_6558,U_6557,U_6556)),U_6556))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK188(U_6558,U_6557,U_6556))) ) )
& ( ! [U_6553,U_6552] :
( hBOOL(hAPP(hAPP(U_6557,U_6553),U_6552))
| U_6558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),U_6553)),U_6552)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6552),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6552)) )
| ~ hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6556)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_6554,sK188(U_6558,U_6557,U_6556))],[f_1737_3]) ).
fof(f_1737_5,plain,
( ! [U_6556,U_6558,U_6557] :
( ~ hBOOL(hAPP(hAPP(U_6557,sK187(U_6558,U_6557,U_6556)),sK188(U_6558,U_6557,U_6556)))
| ~ sP602(U_6556,U_6558,U_6557) )
& ! [U_6556,U_6558,U_6557] :
( U_6558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),sK187(U_6558,U_6557,U_6556))),sK188(U_6558,U_6557,U_6556))
| ~ sP602(U_6556,U_6558,U_6557) )
& ! [U_6556,U_6558,U_6557] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK188(U_6558,U_6557,U_6556)),U_6556))
| ~ sP602(U_6556,U_6558,U_6557) )
& ! [U_6556,U_6558,U_6557] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK188(U_6558,U_6557,U_6556)))
| ~ sP602(U_6556,U_6558,U_6557) )
& ! [U_6556,U_6553,U_6558,U_6552,U_6557] :
( hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556)))
| sP602(U_6556,U_6558,U_6557)
| ~ sP603(U_6556,U_6553,U_6558,U_6552,U_6557) )
& ! [U_6556,U_6553,U_6558,U_6552,U_6557] :
( hBOOL(hAPP(hAPP(U_6557,U_6553),U_6552))
| U_6558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),U_6553)),U_6552)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6552),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6552))
| ~ hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556)))
| ~ sP603(U_6556,U_6553,U_6558,U_6552,U_6557) )
& ! [U_6556,U_6553,U_6558,U_6552,U_6557] :
( sP603(U_6556,U_6553,U_6558,U_6552,U_6557)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6556)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP602,sP603])],[f_1737_4]) ).
cnf(f_1737_6,plain,
( sP603(U_6556,U_6553,U_6558,U_6552,U_6557)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6556)) ),
inference(clausify,[status(thm)],[f_1737_5]) ).
cnf(f_1737_7,plain,
( hBOOL(hAPP(hAPP(U_6557,U_6553),U_6552))
| U_6558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),U_6553)),U_6552)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6552),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6552))
| ~ hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556)))
| ~ sP603(U_6556,U_6553,U_6558,U_6552,U_6557) ),
inference(clausify,[status(thm)],[f_1737_5]) ).
cnf(f_1737_8,plain,
( hBOOL(hAPP(hAPP(U_6557,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6558),U_6556)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6558,U_6556)))
| sP602(U_6556,U_6558,U_6557)
| ~ sP603(U_6556,U_6553,U_6558,U_6552,U_6557) ),
inference(clausify,[status(thm)],[f_1737_5]) ).
cnf(f_1737_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK188(U_6558,U_6557,U_6556)))
| ~ sP602(U_6556,U_6558,U_6557) ),
inference(clausify,[status(thm)],[f_1737_5]) ).
cnf(f_1737_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK188(U_6558,U_6557,U_6556)),U_6556))
| ~ sP602(U_6556,U_6558,U_6557) ),
inference(clausify,[status(thm)],[f_1737_5]) ).
cnf(f_1737_11,plain,
( U_6558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6556),sK187(U_6558,U_6557,U_6556))),sK188(U_6558,U_6557,U_6556))
| ~ sP602(U_6556,U_6558,U_6557) ),
inference(clausify,[status(thm)],[f_1737_5]) ).
cnf(f_1737_12,plain,
( ~ hBOOL(hAPP(hAPP(U_6557,sK187(U_6558,U_6557,U_6556)),sK188(U_6558,U_6557,U_6556)))
| ~ sP602(U_6556,U_6558,U_6557) ),
inference(clausify,[status(thm)],[f_1737_5]) ).
fof(f_1738_1,plain,
! [V_v,T_a] :
( ( ( 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)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__number__of__eq]) ).
fof(f_1738_2,plain,
! [U_6560,U_6559] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6560)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6559),U_6560)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6560))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6560)) = c_Groups_Ozero__class_Ozero(U_6559)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6560))) ) )
| ~ class_Int_Onumber__ring(U_6559) ),
inference(variable_rename,[status(thm)],[f_1738_1]) ).
fof(f_1738_3,plain,
( ! [U_6560,U_6559] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6560)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6559),U_6560)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6560)))
| ~ sP604(U_6560,U_6559) )
& ! [U_6560,U_6559] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6560)) = c_Groups_Ozero__class_Ozero(U_6559)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6560)))
| ~ sP604(U_6560,U_6559) )
& ! [U_6560,U_6559] :
( sP604(U_6560,U_6559)
| ~ class_Int_Onumber__ring(U_6559) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP604])],[f_1738_2]) ).
cnf(f_1738_4,plain,
( sP604(U_6560,U_6559)
| ~ class_Int_Onumber__ring(U_6559) ),
inference(clausify,[status(thm)],[f_1738_3]) ).
cnf(f_1738_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6560)) = c_Groups_Ozero__class_Ozero(U_6559)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6560)))
| ~ sP604(U_6560,U_6559) ),
inference(clausify,[status(thm)],[f_1738_3]) ).
cnf(f_1738_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6560)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6559),U_6560)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6560)))
| ~ sP604(U_6560,U_6559) ),
inference(clausify,[status(thm)],[f_1738_3]) ).
fof(f_1739_1,plain,
! [V_B_2,V_A_2] :
( ( 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)),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) )
& ( 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)
| V_A_2 != V_B_2 ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J]) ).
fof(f_1739_2,plain,
! [U_6562,U_6561] :
( ( U_6561 = U_6562
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6561) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6562) )
& ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6561) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6562)
| U_6561 != U_6562 ) ),
inference(variable_rename,[status(thm)],[f_1739_1]) ).
fof(f_1739_3,plain,
( ! [U_6566,U_6564] :
( U_6564 = U_6566
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6564) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6566) )
& ! [U_6565,U_6563] :
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6563) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6565)
| U_6563 != U_6565 ) ),
inference(miniscope,[status(thm)],[f_1739_2]) ).
fof(f_1739_4,plain,
( ! [U_6564,U_6566] :
( U_6564 = U_6566
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6564) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6566) )
& ! [U_6563,U_6565] :
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6563) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6565)
| U_6563 != U_6565 ) ),
inference(definitional_conversion,[status(esa)],[f_1739_3]) ).
cnf(f_1739_5,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6563) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6565)
| U_6563 != U_6565 ),
inference(clausify,[status(thm)],[f_1739_4]) ).
cnf(f_1739_6,plain,
( U_6564 = U_6566
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6564) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6566) ),
inference(clausify,[status(thm)],[f_1739_4]) ).
fof(f_1740_1,plain,
! [V_y_2,V_x_2] :
( ( 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)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J]) ).
fof(f_1740_2,plain,
! [U_6568,U_6567] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6567) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6568)
| U_6567 != U_6568 )
& ( U_6567 = U_6568
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6567) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6568) ) ),
inference(variable_rename,[status(thm)],[f_1740_1]) ).
fof(f_1740_3,plain,
( ! [U_6572,U_6570] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6570) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6572)
| U_6570 != U_6572 )
& ! [U_6571,U_6569] :
( U_6569 = U_6571
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6569) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6571) ) ),
inference(miniscope,[status(thm)],[f_1740_2]) ).
fof(f_1740_4,plain,
( ! [U_6570,U_6572] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6570) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6572)
| U_6570 != U_6572 )
& ! [U_6571,U_6569] :
( U_6569 = U_6571
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6569) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6571) ) ),
inference(definitional_conversion,[status(esa)],[f_1740_3]) ).
cnf(f_1740_5,plain,
( U_6569 = U_6571
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6569) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6571) ),
inference(clausify,[status(thm)],[f_1740_4]) ).
cnf(f_1740_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6570) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6572)
| U_6570 != U_6572 ),
inference(clausify,[status(thm)],[f_1740_4]) ).
fof(f_1741_1,plain,
! [V_B_2,V_A_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J]) ).
fof(f_1741_2,plain,
! [U_6574,U_6573] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6573),U_6574))
| ~ 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)),U_6573)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6574))) )
& ( 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)),U_6573)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6574)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6573),U_6574)) ) ),
inference(variable_rename,[status(thm)],[f_1741_1]) ).
fof(f_1741_3,plain,
( ! [U_6578,U_6576] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6576),U_6578))
| ~ 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)),U_6576)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6578))) )
& ! [U_6577,U_6575] :
( 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)),U_6575)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6577)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6575),U_6577)) ) ),
inference(miniscope,[status(thm)],[f_1741_2]) ).
fof(f_1741_4,plain,
( ! [U_6576,U_6578] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6576),U_6578))
| ~ 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)),U_6576)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6578))) )
& ! [U_6575,U_6577] :
( 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)),U_6575)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6577)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6575),U_6577)) ) ),
inference(definitional_conversion,[status(esa)],[f_1741_3]) ).
cnf(f_1741_5,plain,
( 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)),U_6575)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6577)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6575),U_6577)) ),
inference(clausify,[status(thm)],[f_1741_4]) ).
cnf(f_1741_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6576),U_6578))
| ~ 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)),U_6576)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6578))) ),
inference(clausify,[status(thm)],[f_1741_4]) ).
fof(f_1742_1,plain,
! [V_n_2,V_m_2] :
( ( 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)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_int__int__eq]) ).
fof(f_1742_2,plain,
! [U_6580,U_6579] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6579) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6580)
| U_6579 != U_6580 )
& ( U_6579 = U_6580
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6579) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6580) ) ),
inference(variable_rename,[status(thm)],[f_1742_1]) ).
fof(f_1742_3,plain,
( ! [U_6584,U_6582] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6582) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6584)
| U_6582 != U_6584 )
& ! [U_6583,U_6581] :
( U_6581 = U_6583
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6581) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6583) ) ),
inference(miniscope,[status(thm)],[f_1742_2]) ).
fof(f_1742_4,plain,
( ! [U_6584,U_6582] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6582) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6584)
| U_6582 != U_6584 )
& ! [U_6583,U_6581] :
( U_6581 = U_6583
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6581) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6583) ) ),
inference(definitional_conversion,[status(esa)],[f_1742_3]) ).
cnf(f_1742_5,plain,
( U_6581 = U_6583
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6581) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6583) ),
inference(clausify,[status(thm)],[f_1742_4]) ).
cnf(f_1742_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6582) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6584)
| U_6582 != U_6584 ),
inference(clausify,[status(thm)],[f_1742_4]) ).
fof(f_1743_1,plain,
! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
inference(fof_nnf,[status(thm)],[fact_not__neg__int]) ).
fof(f_1743_2,plain,
! [U_6585] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6585))),
inference(variable_rename,[status(thm)],[f_1743_1]) ).
fof(f_1743_3,plain,
! [U_6585] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6585))),
inference(definitional_conversion,[status(esa)],[f_1743_2]) ).
cnf(f_1743_4,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6585))),
inference(clausify,[status(thm)],[f_1743_3]) ).
fof(f_1744_1,plain,
! [V_a,T_a] :
( c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__0]) ).
fof(f_1744_2,plain,
! [U_6587,U_6586] :
( c_Divides_Odiv__class_Omod(U_6586,c_Groups_Ozero__class_Ozero(U_6586),U_6587) = c_Groups_Ozero__class_Ozero(U_6586)
| ~ class_Divides_Osemiring__div(U_6586) ),
inference(variable_rename,[status(thm)],[f_1744_1]) ).
fof(f_1744_3,plain,
! [U_6586,U_6587] :
( c_Divides_Odiv__class_Omod(U_6586,c_Groups_Ozero__class_Ozero(U_6586),U_6587) = c_Groups_Ozero__class_Ozero(U_6586)
| ~ class_Divides_Osemiring__div(U_6586) ),
inference(definitional_conversion,[status(esa)],[f_1744_2]) ).
cnf(f_1744_4,plain,
( c_Divides_Odiv__class_Omod(U_6586,c_Groups_Ozero__class_Ozero(U_6586),U_6587) = c_Groups_Ozero__class_Ozero(U_6586)
| ~ class_Divides_Osemiring__div(U_6586) ),
inference(clausify,[status(thm)],[f_1744_3]) ).
fof(f_1745_1,plain,
! [V_a,T_a] :
( c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__by__0]) ).
fof(f_1745_2,plain,
! [U_6589,U_6588] :
( c_Divides_Odiv__class_Omod(U_6588,U_6589,c_Groups_Ozero__class_Ozero(U_6588)) = U_6589
| ~ class_Divides_Osemiring__div(U_6588) ),
inference(variable_rename,[status(thm)],[f_1745_1]) ).
fof(f_1745_3,plain,
! [U_6588,U_6589] :
( c_Divides_Odiv__class_Omod(U_6588,U_6589,c_Groups_Ozero__class_Ozero(U_6588)) = U_6589
| ~ class_Divides_Osemiring__div(U_6588) ),
inference(definitional_conversion,[status(esa)],[f_1745_2]) ).
cnf(f_1745_4,plain,
( c_Divides_Odiv__class_Omod(U_6588,U_6589,c_Groups_Ozero__class_Ozero(U_6588)) = U_6589
| ~ class_Divides_Osemiring__div(U_6588) ),
inference(clausify,[status(thm)],[f_1745_3]) ).
fof(f_1746_1,plain,
! [V_a,T_a] :
( c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__self]) ).
fof(f_1746_2,plain,
! [U_6591,U_6590] :
( c_Divides_Odiv__class_Omod(U_6590,U_6591,U_6591) = c_Groups_Ozero__class_Ozero(U_6590)
| ~ class_Divides_Osemiring__div(U_6590) ),
inference(variable_rename,[status(thm)],[f_1746_1]) ).
fof(f_1746_3,plain,
! [U_6590,U_6591] :
( c_Divides_Odiv__class_Omod(U_6590,U_6591,U_6591) = c_Groups_Ozero__class_Ozero(U_6590)
| ~ class_Divides_Osemiring__div(U_6590) ),
inference(definitional_conversion,[status(esa)],[f_1746_2]) ).
cnf(f_1746_4,plain,
( c_Divides_Odiv__class_Omod(U_6590,U_6591,U_6591) = c_Groups_Ozero__class_Ozero(U_6590)
| ~ class_Divides_Osemiring__div(U_6590) ),
inference(clausify,[status(thm)],[f_1746_3]) ).
fof(f_1747_1,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(fof_nnf,[status(thm)],[fact_neg__number__of__Min]) ).
fof(f_1747_2,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(definitional_conversion,[status(esa)],[f_1747_1]) ).
cnf(f_1747_3,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(clausify,[status(thm)],[f_1747_2]) ).
fof(f_1748_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zmod__minus1__right]) ).
fof(f_1748_2,plain,
! [U_6592] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6592,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1748_1]) ).
fof(f_1748_3,plain,
! [U_6592] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6592,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1748_2]) ).
cnf(f_1748_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6592,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1748_3]) ).
fof(f_1749_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial]) ).
fof(f_1749_2,plain,
! [U_6595,U_6594,U_6593] :
( c_Divides_Odiv__class_Omod(U_6593,c_Divides_Odiv__class_Omod(U_6593,U_6594,U_6595),U_6595) = c_Divides_Odiv__class_Omod(U_6593,U_6594,U_6595)
| ~ class_Divides_Osemiring__div(U_6593) ),
inference(variable_rename,[status(thm)],[f_1749_1]) ).
fof(f_1749_3,plain,
! [U_6594,U_6593,U_6595] :
( c_Divides_Odiv__class_Omod(U_6593,c_Divides_Odiv__class_Omod(U_6593,U_6594,U_6595),U_6595) = c_Divides_Odiv__class_Omod(U_6593,U_6594,U_6595)
| ~ class_Divides_Osemiring__div(U_6593) ),
inference(definitional_conversion,[status(esa)],[f_1749_2]) ).
cnf(f_1749_4,plain,
( c_Divides_Odiv__class_Omod(U_6593,c_Divides_Odiv__class_Omod(U_6593,U_6594,U_6595),U_6595) = c_Divides_Odiv__class_Omod(U_6593,U_6594,U_6595)
| ~ class_Divides_Osemiring__div(U_6593) ),
inference(clausify,[status(thm)],[f_1749_3]) ).
fof(f_1750_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__add__self2]) ).
fof(f_1750_2,plain,
! [U_6598,U_6597,U_6596] :
( c_Divides_Odiv__class_Omod(U_6596,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6596),U_6597),U_6598),U_6598) = c_Divides_Odiv__class_Omod(U_6596,U_6597,U_6598)
| ~ class_Divides_Osemiring__div(U_6596) ),
inference(variable_rename,[status(thm)],[f_1750_1]) ).
fof(f_1750_3,plain,
! [U_6596,U_6597,U_6598] :
( c_Divides_Odiv__class_Omod(U_6596,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6596),U_6597),U_6598),U_6598) = c_Divides_Odiv__class_Omod(U_6596,U_6597,U_6598)
| ~ class_Divides_Osemiring__div(U_6596) ),
inference(definitional_conversion,[status(esa)],[f_1750_2]) ).
cnf(f_1750_4,plain,
( c_Divides_Odiv__class_Omod(U_6596,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6596),U_6597),U_6598),U_6598) = c_Divides_Odiv__class_Omod(U_6596,U_6597,U_6598)
| ~ class_Divides_Osemiring__div(U_6596) ),
inference(clausify,[status(thm)],[f_1750_3]) ).
fof(f_1751_1,plain,
! [V_a,V_b,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__add__self1]) ).
fof(f_1751_2,plain,
! [U_6601,U_6600,U_6599] :
( c_Divides_Odiv__class_Omod(U_6599,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6599),U_6600),U_6601),U_6600) = c_Divides_Odiv__class_Omod(U_6599,U_6601,U_6600)
| ~ class_Divides_Osemiring__div(U_6599) ),
inference(variable_rename,[status(thm)],[f_1751_1]) ).
fof(f_1751_3,plain,
! [U_6599,U_6600,U_6601] :
( c_Divides_Odiv__class_Omod(U_6599,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6599),U_6600),U_6601),U_6600) = c_Divides_Odiv__class_Omod(U_6599,U_6601,U_6600)
| ~ class_Divides_Osemiring__div(U_6599) ),
inference(definitional_conversion,[status(esa)],[f_1751_2]) ).
cnf(f_1751_4,plain,
( c_Divides_Odiv__class_Omod(U_6599,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6599),U_6600),U_6601),U_6600) = c_Divides_Odiv__class_Omod(U_6599,U_6601,U_6600)
| ~ class_Divides_Osemiring__div(U_6599) ),
inference(clausify,[status(thm)],[f_1751_3]) ).
fof(f_1752_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq]) ).
fof(f_1752_2,plain,
! [U_6605,U_6604,U_6603,U_6602] :
( c_Divides_Odiv__class_Omod(U_6602,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6602),U_6603),U_6604),U_6605) = c_Divides_Odiv__class_Omod(U_6602,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6602),U_6603),c_Divides_Odiv__class_Omod(U_6602,U_6604,U_6605)),U_6605)
| ~ class_Divides_Osemiring__div(U_6602) ),
inference(variable_rename,[status(thm)],[f_1752_1]) ).
fof(f_1752_3,plain,
! [U_6602,U_6603,U_6604,U_6605] :
( c_Divides_Odiv__class_Omod(U_6602,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6602),U_6603),U_6604),U_6605) = c_Divides_Odiv__class_Omod(U_6602,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6602),U_6603),c_Divides_Odiv__class_Omod(U_6602,U_6604,U_6605)),U_6605)
| ~ class_Divides_Osemiring__div(U_6602) ),
inference(definitional_conversion,[status(esa)],[f_1752_2]) ).
cnf(f_1752_4,plain,
( c_Divides_Odiv__class_Omod(U_6602,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6602),U_6603),U_6604),U_6605) = c_Divides_Odiv__class_Omod(U_6602,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6602),U_6603),c_Divides_Odiv__class_Omod(U_6602,U_6604,U_6605)),U_6605)
| ~ class_Divides_Osemiring__div(U_6602) ),
inference(clausify,[status(thm)],[f_1752_3]) ).
fof(f_1753_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq]) ).
fof(f_1753_2,plain,
! [U_6609,U_6608,U_6607,U_6606] :
( c_Divides_Odiv__class_Omod(U_6606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6606),U_6607),U_6608),U_6609) = c_Divides_Odiv__class_Omod(U_6606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6606),c_Divides_Odiv__class_Omod(U_6606,U_6607,U_6609)),U_6608),U_6609)
| ~ class_Divides_Osemiring__div(U_6606) ),
inference(variable_rename,[status(thm)],[f_1753_1]) ).
fof(f_1753_3,plain,
! [U_6606,U_6607,U_6608,U_6609] :
( c_Divides_Odiv__class_Omod(U_6606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6606),U_6607),U_6608),U_6609) = c_Divides_Odiv__class_Omod(U_6606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6606),c_Divides_Odiv__class_Omod(U_6606,U_6607,U_6609)),U_6608),U_6609)
| ~ class_Divides_Osemiring__div(U_6606) ),
inference(definitional_conversion,[status(esa)],[f_1753_2]) ).
cnf(f_1753_4,plain,
( c_Divides_Odiv__class_Omod(U_6606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6606),U_6607),U_6608),U_6609) = c_Divides_Odiv__class_Omod(U_6606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6606),c_Divides_Odiv__class_Omod(U_6606,U_6607,U_6609)),U_6608),U_6609)
| ~ class_Divides_Osemiring__div(U_6606) ),
inference(clausify,[status(thm)],[f_1753_3]) ).
fof(f_1754_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__add__eq]) ).
fof(f_1754_2,plain,
! [U_6613,U_6612,U_6611,U_6610] :
( c_Divides_Odiv__class_Omod(U_6610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),U_6611),U_6612),U_6613) = c_Divides_Odiv__class_Omod(U_6610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),c_Divides_Odiv__class_Omod(U_6610,U_6611,U_6613)),c_Divides_Odiv__class_Omod(U_6610,U_6612,U_6613)),U_6613)
| ~ class_Divides_Osemiring__div(U_6610) ),
inference(variable_rename,[status(thm)],[f_1754_1]) ).
fof(f_1754_3,plain,
! [U_6610,U_6611,U_6612,U_6613] :
( c_Divides_Odiv__class_Omod(U_6610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),U_6611),U_6612),U_6613) = c_Divides_Odiv__class_Omod(U_6610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),c_Divides_Odiv__class_Omod(U_6610,U_6611,U_6613)),c_Divides_Odiv__class_Omod(U_6610,U_6612,U_6613)),U_6613)
| ~ class_Divides_Osemiring__div(U_6610) ),
inference(definitional_conversion,[status(esa)],[f_1754_2]) ).
cnf(f_1754_4,plain,
( c_Divides_Odiv__class_Omod(U_6610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),U_6611),U_6612),U_6613) = c_Divides_Odiv__class_Omod(U_6610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),c_Divides_Odiv__class_Omod(U_6610,U_6611,U_6613)),c_Divides_Odiv__class_Omod(U_6610,U_6612,U_6613)),U_6613)
| ~ class_Divides_Osemiring__div(U_6610) ),
inference(clausify,[status(thm)],[f_1754_3]) ).
fof(f_1755_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J]) ).
fof(f_1755_2,plain,
! [U_6617,U_6616,U_6615,U_6614] :
( c_Divides_Odiv__class_Omod(U_6614,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6614),U_6615),c_Divides_Odiv__class_Omod(U_6614,U_6616,U_6617)),U_6617) = c_Divides_Odiv__class_Omod(U_6614,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6614),U_6615),U_6616),U_6617)
| ~ class_Divides_Osemiring__div(U_6614) ),
inference(variable_rename,[status(thm)],[f_1755_1]) ).
fof(f_1755_3,plain,
! [U_6614,U_6615,U_6616,U_6617] :
( c_Divides_Odiv__class_Omod(U_6614,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6614),U_6615),c_Divides_Odiv__class_Omod(U_6614,U_6616,U_6617)),U_6617) = c_Divides_Odiv__class_Omod(U_6614,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6614),U_6615),U_6616),U_6617)
| ~ class_Divides_Osemiring__div(U_6614) ),
inference(definitional_conversion,[status(esa)],[f_1755_2]) ).
cnf(f_1755_4,plain,
( c_Divides_Odiv__class_Omod(U_6614,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6614),U_6615),c_Divides_Odiv__class_Omod(U_6614,U_6616,U_6617)),U_6617) = c_Divides_Odiv__class_Omod(U_6614,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6614),U_6615),U_6616),U_6617)
| ~ class_Divides_Osemiring__div(U_6614) ),
inference(clausify,[status(thm)],[f_1755_3]) ).
fof(f_1756_1,plain,
! [V_b,V_c,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J]) ).
fof(f_1756_2,plain,
! [U_6621,U_6620,U_6619,U_6618] :
( c_Divides_Odiv__class_Omod(U_6618,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6618),c_Divides_Odiv__class_Omod(U_6618,U_6619,U_6620)),U_6621),U_6620) = c_Divides_Odiv__class_Omod(U_6618,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6618),U_6619),U_6621),U_6620)
| ~ class_Divides_Osemiring__div(U_6618) ),
inference(variable_rename,[status(thm)],[f_1756_1]) ).
fof(f_1756_3,plain,
! [U_6618,U_6619,U_6620,U_6621] :
( c_Divides_Odiv__class_Omod(U_6618,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6618),c_Divides_Odiv__class_Omod(U_6618,U_6619,U_6620)),U_6621),U_6620) = c_Divides_Odiv__class_Omod(U_6618,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6618),U_6619),U_6621),U_6620)
| ~ class_Divides_Osemiring__div(U_6618) ),
inference(definitional_conversion,[status(esa)],[f_1756_2]) ).
cnf(f_1756_4,plain,
( c_Divides_Odiv__class_Omod(U_6618,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6618),c_Divides_Odiv__class_Omod(U_6618,U_6619,U_6620)),U_6621),U_6620) = c_Divides_Odiv__class_Omod(U_6618,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6618),U_6619),U_6621),U_6620)
| ~ class_Divides_Osemiring__div(U_6618) ),
inference(clausify,[status(thm)],[f_1756_3]) ).
fof(f_1757_1,plain,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( 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)
| c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
| c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__add__cong]) ).
fof(f_1757_2,plain,
! [U_6627,U_6626,U_6625,U_6624,U_6623,U_6622] :
( c_Divides_Odiv__class_Omod(U_6622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6622),U_6623),U_6626),U_6624) = c_Divides_Odiv__class_Omod(U_6622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6622),U_6625),U_6627),U_6624)
| c_Divides_Odiv__class_Omod(U_6622,U_6626,U_6624) != c_Divides_Odiv__class_Omod(U_6622,U_6627,U_6624)
| c_Divides_Odiv__class_Omod(U_6622,U_6623,U_6624) != c_Divides_Odiv__class_Omod(U_6622,U_6625,U_6624)
| ~ class_Divides_Osemiring__div(U_6622) ),
inference(variable_rename,[status(thm)],[f_1757_1]) ).
fof(f_1757_3,plain,
! [U_6622,U_6623,U_6624,U_6625,U_6626,U_6627] :
( c_Divides_Odiv__class_Omod(U_6622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6622),U_6623),U_6626),U_6624) = c_Divides_Odiv__class_Omod(U_6622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6622),U_6625),U_6627),U_6624)
| c_Divides_Odiv__class_Omod(U_6622,U_6626,U_6624) != c_Divides_Odiv__class_Omod(U_6622,U_6627,U_6624)
| c_Divides_Odiv__class_Omod(U_6622,U_6623,U_6624) != c_Divides_Odiv__class_Omod(U_6622,U_6625,U_6624)
| ~ class_Divides_Osemiring__div(U_6622) ),
inference(definitional_conversion,[status(esa)],[f_1757_2]) ).
cnf(f_1757_4,plain,
( c_Divides_Odiv__class_Omod(U_6622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6622),U_6623),U_6626),U_6624) = c_Divides_Odiv__class_Omod(U_6622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6622),U_6625),U_6627),U_6624)
| c_Divides_Odiv__class_Omod(U_6622,U_6626,U_6624) != c_Divides_Odiv__class_Omod(U_6622,U_6627,U_6624)
| c_Divides_Odiv__class_Omod(U_6622,U_6623,U_6624) != c_Divides_Odiv__class_Omod(U_6622,U_6625,U_6624)
| ~ class_Divides_Osemiring__div(U_6622) ),
inference(clausify,[status(thm)],[f_1757_3]) ).
fof(f_1758_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq]) ).
fof(f_1758_2,plain,
! [U_6631,U_6630,U_6629,U_6628] :
( c_Divides_Odiv__class_Omod(U_6628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),U_6629),U_6630),U_6631) = c_Divides_Odiv__class_Omod(U_6628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),U_6629),c_Divides_Odiv__class_Omod(U_6628,U_6630,U_6631)),U_6631)
| ~ class_Divides_Osemiring__div(U_6628) ),
inference(variable_rename,[status(thm)],[f_1758_1]) ).
fof(f_1758_3,plain,
! [U_6630,U_6628,U_6629,U_6631] :
( c_Divides_Odiv__class_Omod(U_6628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),U_6629),U_6630),U_6631) = c_Divides_Odiv__class_Omod(U_6628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),U_6629),c_Divides_Odiv__class_Omod(U_6628,U_6630,U_6631)),U_6631)
| ~ class_Divides_Osemiring__div(U_6628) ),
inference(definitional_conversion,[status(esa)],[f_1758_2]) ).
cnf(f_1758_4,plain,
( c_Divides_Odiv__class_Omod(U_6628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),U_6629),U_6630),U_6631) = c_Divides_Odiv__class_Omod(U_6628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),U_6629),c_Divides_Odiv__class_Omod(U_6628,U_6630,U_6631)),U_6631)
| ~ class_Divides_Osemiring__div(U_6628) ),
inference(clausify,[status(thm)],[f_1758_3]) ).
fof(f_1759_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq]) ).
fof(f_1759_2,plain,
! [U_6635,U_6634,U_6633,U_6632] :
( c_Divides_Odiv__class_Omod(U_6632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6633),U_6634),U_6635) = c_Divides_Odiv__class_Omod(U_6632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),c_Divides_Odiv__class_Omod(U_6632,U_6633,U_6635)),U_6634),U_6635)
| ~ class_Divides_Osemiring__div(U_6632) ),
inference(variable_rename,[status(thm)],[f_1759_1]) ).
fof(f_1759_3,plain,
! [U_6632,U_6633,U_6634,U_6635] :
( c_Divides_Odiv__class_Omod(U_6632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6633),U_6634),U_6635) = c_Divides_Odiv__class_Omod(U_6632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),c_Divides_Odiv__class_Omod(U_6632,U_6633,U_6635)),U_6634),U_6635)
| ~ class_Divides_Osemiring__div(U_6632) ),
inference(definitional_conversion,[status(esa)],[f_1759_2]) ).
cnf(f_1759_4,plain,
( c_Divides_Odiv__class_Omod(U_6632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6633),U_6634),U_6635) = c_Divides_Odiv__class_Omod(U_6632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),c_Divides_Odiv__class_Omod(U_6632,U_6633,U_6635)),U_6634),U_6635)
| ~ class_Divides_Osemiring__div(U_6632) ),
inference(clausify,[status(thm)],[f_1759_3]) ).
fof(f_1760_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__eq]) ).
fof(f_1760_2,plain,
! [U_6639,U_6638,U_6637,U_6636] :
( c_Divides_Odiv__class_Omod(U_6636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6637),U_6638),U_6639) = c_Divides_Odiv__class_Omod(U_6636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),c_Divides_Odiv__class_Omod(U_6636,U_6637,U_6639)),c_Divides_Odiv__class_Omod(U_6636,U_6638,U_6639)),U_6639)
| ~ class_Divides_Osemiring__div(U_6636) ),
inference(variable_rename,[status(thm)],[f_1760_1]) ).
fof(f_1760_3,plain,
! [U_6636,U_6637,U_6638,U_6639] :
( c_Divides_Odiv__class_Omod(U_6636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6637),U_6638),U_6639) = c_Divides_Odiv__class_Omod(U_6636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),c_Divides_Odiv__class_Omod(U_6636,U_6637,U_6639)),c_Divides_Odiv__class_Omod(U_6636,U_6638,U_6639)),U_6639)
| ~ class_Divides_Osemiring__div(U_6636) ),
inference(definitional_conversion,[status(esa)],[f_1760_2]) ).
cnf(f_1760_4,plain,
( c_Divides_Odiv__class_Omod(U_6636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6637),U_6638),U_6639) = c_Divides_Odiv__class_Omod(U_6636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),c_Divides_Odiv__class_Omod(U_6636,U_6637,U_6639)),c_Divides_Odiv__class_Omod(U_6636,U_6638,U_6639)),U_6639)
| ~ class_Divides_Osemiring__div(U_6636) ),
inference(clausify,[status(thm)],[f_1760_3]) ).
fof(f_1761_1,plain,
! [V_b,V_a,V_c,T_a] :
( 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))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1]) ).
fof(f_1761_2,plain,
! [U_6643,U_6642,U_6641,U_6640] :
( c_Divides_Odiv__class_Omod(U_6640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),U_6642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),U_6643)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),c_Divides_Odiv__class_Omod(U_6640,U_6642,U_6643))
| ~ class_Divides_Osemiring__div(U_6640) ),
inference(variable_rename,[status(thm)],[f_1761_1]) ).
fof(f_1761_3,plain,
! [U_6640,U_6641,U_6642,U_6643] :
( c_Divides_Odiv__class_Omod(U_6640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),U_6642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),U_6643)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),c_Divides_Odiv__class_Omod(U_6640,U_6642,U_6643))
| ~ class_Divides_Osemiring__div(U_6640) ),
inference(definitional_conversion,[status(esa)],[f_1761_2]) ).
cnf(f_1761_4,plain,
( c_Divides_Odiv__class_Omod(U_6640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),U_6642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),U_6643)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6640),U_6641),c_Divides_Odiv__class_Omod(U_6640,U_6642,U_6643))
| ~ class_Divides_Osemiring__div(U_6640) ),
inference(clausify,[status(thm)],[f_1761_3]) ).
fof(f_1762_1,plain,
! [V_b,V_c,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2]) ).
fof(f_1762_2,plain,
! [U_6647,U_6646,U_6645,U_6644] :
( c_Divides_Odiv__class_Omod(U_6644,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),U_6645),U_6646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),U_6647),U_6646)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),c_Divides_Odiv__class_Omod(U_6644,U_6645,U_6647)),U_6646)
| ~ class_Divides_Osemiring__div(U_6644) ),
inference(variable_rename,[status(thm)],[f_1762_1]) ).
fof(f_1762_3,plain,
! [U_6644,U_6645,U_6646,U_6647] :
( c_Divides_Odiv__class_Omod(U_6644,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),U_6645),U_6646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),U_6647),U_6646)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),c_Divides_Odiv__class_Omod(U_6644,U_6645,U_6647)),U_6646)
| ~ class_Divides_Osemiring__div(U_6644) ),
inference(definitional_conversion,[status(esa)],[f_1762_2]) ).
cnf(f_1762_4,plain,
( c_Divides_Odiv__class_Omod(U_6644,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),U_6645),U_6646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),U_6647),U_6646)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6644),c_Divides_Odiv__class_Omod(U_6644,U_6645,U_6647)),U_6646)
| ~ class_Divides_Osemiring__div(U_6644) ),
inference(clausify,[status(thm)],[f_1762_3]) ).
fof(f_1763_1,plain,
! [V_b,V_c,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J]) ).
fof(f_1763_2,plain,
! [U_6651,U_6650,U_6649,U_6648] :
( c_Divides_Odiv__class_Omod(U_6648,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6648),c_Divides_Odiv__class_Omod(U_6648,U_6649,U_6650)),U_6651),U_6650) = c_Divides_Odiv__class_Omod(U_6648,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6648),U_6649),U_6651),U_6650)
| ~ class_Divides_Osemiring__div(U_6648) ),
inference(variable_rename,[status(thm)],[f_1763_1]) ).
fof(f_1763_3,plain,
! [U_6648,U_6649,U_6650,U_6651] :
( c_Divides_Odiv__class_Omod(U_6648,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6648),c_Divides_Odiv__class_Omod(U_6648,U_6649,U_6650)),U_6651),U_6650) = c_Divides_Odiv__class_Omod(U_6648,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6648),U_6649),U_6651),U_6650)
| ~ class_Divides_Osemiring__div(U_6648) ),
inference(definitional_conversion,[status(esa)],[f_1763_2]) ).
cnf(f_1763_4,plain,
( c_Divides_Odiv__class_Omod(U_6648,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6648),c_Divides_Odiv__class_Omod(U_6648,U_6649,U_6650)),U_6651),U_6650) = c_Divides_Odiv__class_Omod(U_6648,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6648),U_6649),U_6651),U_6650)
| ~ class_Divides_Osemiring__div(U_6648) ),
inference(clausify,[status(thm)],[f_1763_3]) ).
fof(f_1764_1,plain,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( 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)
| c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
| c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__cong]) ).
fof(f_1764_2,plain,
! [U_6657,U_6656,U_6655,U_6654,U_6653,U_6652] :
( c_Divides_Odiv__class_Omod(U_6652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6652),U_6653),U_6656),U_6654) = c_Divides_Odiv__class_Omod(U_6652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6652),U_6655),U_6657),U_6654)
| c_Divides_Odiv__class_Omod(U_6652,U_6656,U_6654) != c_Divides_Odiv__class_Omod(U_6652,U_6657,U_6654)
| c_Divides_Odiv__class_Omod(U_6652,U_6653,U_6654) != c_Divides_Odiv__class_Omod(U_6652,U_6655,U_6654)
| ~ class_Divides_Osemiring__div(U_6652) ),
inference(variable_rename,[status(thm)],[f_1764_1]) ).
fof(f_1764_3,plain,
! [U_6652,U_6653,U_6654,U_6655,U_6656,U_6657] :
( c_Divides_Odiv__class_Omod(U_6652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6652),U_6653),U_6656),U_6654) = c_Divides_Odiv__class_Omod(U_6652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6652),U_6655),U_6657),U_6654)
| c_Divides_Odiv__class_Omod(U_6652,U_6656,U_6654) != c_Divides_Odiv__class_Omod(U_6652,U_6657,U_6654)
| c_Divides_Odiv__class_Omod(U_6652,U_6653,U_6654) != c_Divides_Odiv__class_Omod(U_6652,U_6655,U_6654)
| ~ class_Divides_Osemiring__div(U_6652) ),
inference(definitional_conversion,[status(esa)],[f_1764_2]) ).
cnf(f_1764_4,plain,
( c_Divides_Odiv__class_Omod(U_6652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6652),U_6653),U_6656),U_6654) = c_Divides_Odiv__class_Omod(U_6652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6652),U_6655),U_6657),U_6654)
| c_Divides_Odiv__class_Omod(U_6652,U_6656,U_6654) != c_Divides_Odiv__class_Omod(U_6652,U_6657,U_6654)
| c_Divides_Odiv__class_Omod(U_6652,U_6653,U_6654) != c_Divides_Odiv__class_Omod(U_6652,U_6655,U_6654)
| ~ class_Divides_Osemiring__div(U_6652) ),
inference(clausify,[status(thm)],[f_1764_3]) ).
fof(f_1765_1,plain,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( 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)
| c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
| c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__diff__cong]) ).
fof(f_1765_2,plain,
! [U_6663,U_6662,U_6661,U_6660,U_6659,U_6658] :
( c_Divides_Odiv__class_Omod(U_6658,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6658),U_6659),U_6662),U_6660) = c_Divides_Odiv__class_Omod(U_6658,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6658),U_6661),U_6663),U_6660)
| c_Divides_Odiv__class_Omod(U_6658,U_6662,U_6660) != c_Divides_Odiv__class_Omod(U_6658,U_6663,U_6660)
| c_Divides_Odiv__class_Omod(U_6658,U_6659,U_6660) != c_Divides_Odiv__class_Omod(U_6658,U_6661,U_6660)
| ~ class_Divides_Oring__div(U_6658) ),
inference(variable_rename,[status(thm)],[f_1765_1]) ).
fof(f_1765_3,plain,
! [U_6660,U_6658,U_6661,U_6659,U_6662,U_6663] :
( c_Divides_Odiv__class_Omod(U_6658,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6658),U_6659),U_6662),U_6660) = c_Divides_Odiv__class_Omod(U_6658,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6658),U_6661),U_6663),U_6660)
| c_Divides_Odiv__class_Omod(U_6658,U_6662,U_6660) != c_Divides_Odiv__class_Omod(U_6658,U_6663,U_6660)
| c_Divides_Odiv__class_Omod(U_6658,U_6659,U_6660) != c_Divides_Odiv__class_Omod(U_6658,U_6661,U_6660)
| ~ class_Divides_Oring__div(U_6658) ),
inference(definitional_conversion,[status(esa)],[f_1765_2]) ).
cnf(f_1765_4,plain,
( c_Divides_Odiv__class_Omod(U_6658,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6658),U_6659),U_6662),U_6660) = c_Divides_Odiv__class_Omod(U_6658,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6658),U_6661),U_6663),U_6660)
| c_Divides_Odiv__class_Omod(U_6658,U_6662,U_6660) != c_Divides_Odiv__class_Omod(U_6658,U_6663,U_6660)
| c_Divides_Odiv__class_Omod(U_6658,U_6659,U_6660) != c_Divides_Odiv__class_Omod(U_6658,U_6661,U_6660)
| ~ class_Divides_Oring__div(U_6658) ),
inference(clausify,[status(thm)],[f_1765_3]) ).
fof(f_1766_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__diff__eq]) ).
fof(f_1766_2,plain,
! [U_6667,U_6666,U_6665,U_6664] :
( c_Divides_Odiv__class_Omod(U_6664,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6664),U_6665),U_6666),U_6667) = c_Divides_Odiv__class_Omod(U_6664,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6664),c_Divides_Odiv__class_Omod(U_6664,U_6665,U_6667)),c_Divides_Odiv__class_Omod(U_6664,U_6666,U_6667)),U_6667)
| ~ class_Divides_Oring__div(U_6664) ),
inference(variable_rename,[status(thm)],[f_1766_1]) ).
fof(f_1766_3,plain,
! [U_6664,U_6665,U_6666,U_6667] :
( c_Divides_Odiv__class_Omod(U_6664,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6664),U_6665),U_6666),U_6667) = c_Divides_Odiv__class_Omod(U_6664,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6664),c_Divides_Odiv__class_Omod(U_6664,U_6665,U_6667)),c_Divides_Odiv__class_Omod(U_6664,U_6666,U_6667)),U_6667)
| ~ class_Divides_Oring__div(U_6664) ),
inference(definitional_conversion,[status(esa)],[f_1766_2]) ).
cnf(f_1766_4,plain,
( c_Divides_Odiv__class_Omod(U_6664,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6664),U_6665),U_6666),U_6667) = c_Divides_Odiv__class_Omod(U_6664,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6664),c_Divides_Odiv__class_Omod(U_6664,U_6665,U_6667)),c_Divides_Odiv__class_Omod(U_6664,U_6666,U_6667)),U_6667)
| ~ class_Divides_Oring__div(U_6664) ),
inference(clausify,[status(thm)],[f_1766_3]) ).
fof(f_1767_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq]) ).
fof(f_1767_2,plain,
! [U_6671,U_6670,U_6669,U_6668] :
( c_Divides_Odiv__class_Omod(U_6668,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6668),U_6669),U_6670),U_6671) = c_Divides_Odiv__class_Omod(U_6668,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6668),c_Divides_Odiv__class_Omod(U_6668,U_6669,U_6671)),U_6670),U_6671)
| ~ class_Divides_Oring__div(U_6668) ),
inference(variable_rename,[status(thm)],[f_1767_1]) ).
fof(f_1767_3,plain,
! [U_6668,U_6669,U_6670,U_6671] :
( c_Divides_Odiv__class_Omod(U_6668,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6668),U_6669),U_6670),U_6671) = c_Divides_Odiv__class_Omod(U_6668,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6668),c_Divides_Odiv__class_Omod(U_6668,U_6669,U_6671)),U_6670),U_6671)
| ~ class_Divides_Oring__div(U_6668) ),
inference(definitional_conversion,[status(esa)],[f_1767_2]) ).
cnf(f_1767_4,plain,
( c_Divides_Odiv__class_Omod(U_6668,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6668),U_6669),U_6670),U_6671) = c_Divides_Odiv__class_Omod(U_6668,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6668),c_Divides_Odiv__class_Omod(U_6668,U_6669,U_6671)),U_6670),U_6671)
| ~ class_Divides_Oring__div(U_6668) ),
inference(clausify,[status(thm)],[f_1767_3]) ).
fof(f_1768_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq]) ).
fof(f_1768_2,plain,
! [U_6675,U_6674,U_6673,U_6672] :
( c_Divides_Odiv__class_Omod(U_6672,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6672),U_6673),U_6674),U_6675) = c_Divides_Odiv__class_Omod(U_6672,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6672),U_6673),c_Divides_Odiv__class_Omod(U_6672,U_6674,U_6675)),U_6675)
| ~ class_Divides_Oring__div(U_6672) ),
inference(variable_rename,[status(thm)],[f_1768_1]) ).
fof(f_1768_3,plain,
! [U_6672,U_6673,U_6674,U_6675] :
( c_Divides_Odiv__class_Omod(U_6672,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6672),U_6673),U_6674),U_6675) = c_Divides_Odiv__class_Omod(U_6672,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6672),U_6673),c_Divides_Odiv__class_Omod(U_6672,U_6674,U_6675)),U_6675)
| ~ class_Divides_Oring__div(U_6672) ),
inference(definitional_conversion,[status(esa)],[f_1768_2]) ).
cnf(f_1768_4,plain,
( c_Divides_Odiv__class_Omod(U_6672,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6672),U_6673),U_6674),U_6675) = c_Divides_Odiv__class_Omod(U_6672,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6672),U_6673),c_Divides_Odiv__class_Omod(U_6672,U_6674,U_6675)),U_6675)
| ~ class_Divides_Oring__div(U_6672) ),
inference(clausify,[status(thm)],[f_1768_3]) ).
fof(f_1769_1,plain,
! [V_a_H,V_b,V_a,T_a] :
( 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)
| c_Divides_Odiv__class_Omod(T_a,V_a,V_b) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__minus__cong]) ).
fof(f_1769_2,plain,
! [U_6679,U_6678,U_6677,U_6676] :
( c_Divides_Odiv__class_Omod(U_6676,hAPP(c_Groups_Ouminus__class_Ouminus(U_6676),U_6677),U_6678) = c_Divides_Odiv__class_Omod(U_6676,hAPP(c_Groups_Ouminus__class_Ouminus(U_6676),U_6679),U_6678)
| c_Divides_Odiv__class_Omod(U_6676,U_6677,U_6678) != c_Divides_Odiv__class_Omod(U_6676,U_6679,U_6678)
| ~ class_Divides_Oring__div(U_6676) ),
inference(variable_rename,[status(thm)],[f_1769_1]) ).
fof(f_1769_3,plain,
! [U_6676,U_6677,U_6678,U_6679] :
( c_Divides_Odiv__class_Omod(U_6676,hAPP(c_Groups_Ouminus__class_Ouminus(U_6676),U_6677),U_6678) = c_Divides_Odiv__class_Omod(U_6676,hAPP(c_Groups_Ouminus__class_Ouminus(U_6676),U_6679),U_6678)
| c_Divides_Odiv__class_Omod(U_6676,U_6677,U_6678) != c_Divides_Odiv__class_Omod(U_6676,U_6679,U_6678)
| ~ class_Divides_Oring__div(U_6676) ),
inference(definitional_conversion,[status(esa)],[f_1769_2]) ).
cnf(f_1769_4,plain,
( c_Divides_Odiv__class_Omod(U_6676,hAPP(c_Groups_Ouminus__class_Ouminus(U_6676),U_6677),U_6678) = c_Divides_Odiv__class_Omod(U_6676,hAPP(c_Groups_Ouminus__class_Ouminus(U_6676),U_6679),U_6678)
| c_Divides_Odiv__class_Omod(U_6676,U_6677,U_6678) != c_Divides_Odiv__class_Omod(U_6676,U_6679,U_6678)
| ~ class_Divides_Oring__div(U_6676) ),
inference(clausify,[status(thm)],[f_1769_3]) ).
fof(f_1770_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__minus__eq]) ).
fof(f_1770_2,plain,
! [U_6682,U_6681,U_6680] :
( c_Divides_Odiv__class_Omod(U_6680,hAPP(c_Groups_Ouminus__class_Ouminus(U_6680),U_6681),U_6682) = c_Divides_Odiv__class_Omod(U_6680,hAPP(c_Groups_Ouminus__class_Ouminus(U_6680),c_Divides_Odiv__class_Omod(U_6680,U_6681,U_6682)),U_6682)
| ~ class_Divides_Oring__div(U_6680) ),
inference(variable_rename,[status(thm)],[f_1770_1]) ).
fof(f_1770_3,plain,
! [U_6681,U_6680,U_6682] :
( c_Divides_Odiv__class_Omod(U_6680,hAPP(c_Groups_Ouminus__class_Ouminus(U_6680),U_6681),U_6682) = c_Divides_Odiv__class_Omod(U_6680,hAPP(c_Groups_Ouminus__class_Ouminus(U_6680),c_Divides_Odiv__class_Omod(U_6680,U_6681,U_6682)),U_6682)
| ~ class_Divides_Oring__div(U_6680) ),
inference(definitional_conversion,[status(esa)],[f_1770_2]) ).
cnf(f_1770_4,plain,
( c_Divides_Odiv__class_Omod(U_6680,hAPP(c_Groups_Ouminus__class_Ouminus(U_6680),U_6681),U_6682) = c_Divides_Odiv__class_Omod(U_6680,hAPP(c_Groups_Ouminus__class_Ouminus(U_6680),c_Divides_Odiv__class_Omod(U_6680,U_6681,U_6682)),U_6682)
| ~ class_Divides_Oring__div(U_6680) ),
inference(clausify,[status(thm)],[f_1770_3]) ).
fof(f_1771_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_div__le__dividend]) ).
fof(f_1771_2,plain,
! [U_6684,U_6683] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6683),U_6684)),U_6683)),
inference(variable_rename,[status(thm)],[f_1771_1]) ).
fof(f_1771_3,plain,
! [U_6683,U_6684] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6683),U_6684)),U_6683)),
inference(definitional_conversion,[status(esa)],[f_1771_2]) ).
cnf(f_1771_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6683),U_6684)),U_6683)),
inference(clausify,[status(thm)],[f_1771_3]) ).
fof(f_1772_1,plain,
! [V_k,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_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__le__mono]) ).
fof(f_1772_2,plain,
! [U_6687,U_6686,U_6685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6685),U_6687)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6686),U_6687)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6685),U_6686)) ),
inference(variable_rename,[status(thm)],[f_1772_1]) ).
fof(f_1772_3,plain,
! [U_6685,U_6686,U_6687] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6685),U_6687)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6686),U_6687)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6685),U_6686)) ),
inference(definitional_conversion,[status(esa)],[f_1772_2]) ).
cnf(f_1772_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6685),U_6687)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6686),U_6687)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6685),U_6686)) ),
inference(clausify,[status(thm)],[f_1772_3]) ).
fof(f_1773_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_div__mult2__eq]) ).
fof(f_1773_2,plain,
! [U_6690,U_6689,U_6688] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6689),U_6690)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6688),U_6689)),U_6690),
inference(variable_rename,[status(thm)],[f_1773_1]) ).
fof(f_1773_3,plain,
! [U_6688,U_6689,U_6690] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6689),U_6690)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6688),U_6689)),U_6690),
inference(definitional_conversion,[status(esa)],[f_1773_2]) ).
cnf(f_1773_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6689),U_6690)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6688),U_6689)),U_6690),
inference(clausify,[status(thm)],[f_1773_3]) ).
fof(f_1774_1,plain,
! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zmod__self]) ).
fof(f_1774_2,plain,
! [U_6691] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6691,U_6691) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1774_1]) ).
fof(f_1774_3,plain,
! [U_6691] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6691,U_6691) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1774_2]) ).
cnf(f_1774_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6691,U_6691) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1774_3]) ).
fof(f_1775_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zmod__zero]) ).
fof(f_1775_2,plain,
! [U_6692] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_6692) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1775_1]) ).
fof(f_1775_3,plain,
! [U_6692] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_6692) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1775_2]) ).
cnf(f_1775_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_6692) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1775_3]) ).
fof(f_1776_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zdiv__int]) ).
fof(f_1776_2,plain,
! [U_6694,U_6693] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6693),U_6694)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6693)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6694)),
inference(variable_rename,[status(thm)],[f_1776_1]) ).
fof(f_1776_3,plain,
! [U_6693,U_6694] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6693),U_6694)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6693)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6694)),
inference(definitional_conversion,[status(esa)],[f_1776_2]) ).
cnf(f_1776_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6693),U_6694)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6693)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6694)),
inference(clausify,[status(thm)],[f_1776_3]) ).
fof(f_1777_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).
fof(f_1777_2,plain,
! [U_6696,U_6695] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6695)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6696)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6695),U_6696)),
inference(variable_rename,[status(thm)],[f_1777_1]) ).
fof(f_1777_3,plain,
! [U_6695,U_6696] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6695)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6696)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6695),U_6696)),
inference(definitional_conversion,[status(esa)],[f_1777_2]) ).
cnf(f_1777_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6695)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6696)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6695),U_6696)),
inference(clausify,[status(thm)],[f_1777_3]) ).
fof(f_1778_1,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I24_J]) ).
fof(f_1778_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(definitional_conversion,[status(esa)],[f_1778_1]) ).
cnf(f_1778_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(clausify,[status(thm)],[f_1778_2]) ).
fof(f_1779_1,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I7_J]) ).
fof(f_1779_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(definitional_conversion,[status(esa)],[f_1779_1]) ).
cnf(f_1779_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(clausify,[status(thm)],[f_1779_2]) ).
fof(f_1780_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zmod__zmult1__eq]) ).
fof(f_1780_2,plain,
! [U_6699,U_6698,U_6697] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6697),U_6698),U_6699) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6697),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6698,U_6699)),U_6699),
inference(variable_rename,[status(thm)],[f_1780_1]) ).
fof(f_1780_3,plain,
! [U_6697,U_6698,U_6699] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6697),U_6698),U_6699) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6697),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6698,U_6699)),U_6699),
inference(definitional_conversion,[status(esa)],[f_1780_2]) ).
cnf(f_1780_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6697),U_6698),U_6699) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6697),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6698,U_6699)),U_6699),
inference(clausify,[status(thm)],[f_1780_3]) ).
fof(f_1781_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zmod__simps_I3_J]) ).
fof(f_1781_2,plain,
! [U_6702,U_6701,U_6700] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6700),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6701,U_6702)),U_6702) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6700),U_6701),U_6702),
inference(variable_rename,[status(thm)],[f_1781_1]) ).
fof(f_1781_3,plain,
! [U_6700,U_6701,U_6702] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6700),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6701,U_6702)),U_6702) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6700),U_6701),U_6702),
inference(definitional_conversion,[status(esa)],[f_1781_2]) ).
cnf(f_1781_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6700),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6701,U_6702)),U_6702) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6700),U_6701),U_6702),
inference(clausify,[status(thm)],[f_1781_3]) ).
fof(f_1782_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zdiff__zmod__right]) ).
fof(f_1782_2,plain,
! [U_6705,U_6704,U_6703] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6703),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6704,U_6705)),U_6705) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6703),U_6704),U_6705),
inference(variable_rename,[status(thm)],[f_1782_1]) ).
fof(f_1782_3,plain,
! [U_6703,U_6704,U_6705] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6703),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6704,U_6705)),U_6705) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6703),U_6704),U_6705),
inference(definitional_conversion,[status(esa)],[f_1782_2]) ).
cnf(f_1782_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6703),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6704,U_6705)),U_6705) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6703),U_6704),U_6705),
inference(clausify,[status(thm)],[f_1782_3]) ).
fof(f_1783_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zdiff__zmod__left]) ).
fof(f_1783_2,plain,
! [U_6708,U_6707,U_6706] : 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,U_6706,U_6707)),U_6708),U_6707) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6706),U_6708),U_6707),
inference(variable_rename,[status(thm)],[f_1783_1]) ).
fof(f_1783_3,plain,
! [U_6706,U_6707,U_6708] : 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,U_6706,U_6707)),U_6708),U_6707) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6706),U_6708),U_6707),
inference(definitional_conversion,[status(esa)],[f_1783_2]) ).
cnf(f_1783_4,plain,
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,U_6706,U_6707)),U_6708),U_6707) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6706),U_6708),U_6707),
inference(clausify,[status(thm)],[f_1783_3]) ).
fof(f_1784_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmod__zminus2]) ).
fof(f_1784_2,plain,
! [U_6710,U_6709] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6709,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6710)) = 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),U_6709),U_6710)),
inference(variable_rename,[status(thm)],[f_1784_1]) ).
fof(f_1784_3,plain,
! [U_6709,U_6710] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6709,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6710)) = 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),U_6709),U_6710)),
inference(definitional_conversion,[status(esa)],[f_1784_2]) ).
cnf(f_1784_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6709,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6710)) = 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),U_6709),U_6710)),
inference(clausify,[status(thm)],[f_1784_3]) ).
fof(f_1785_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmod__zminus__zminus]) ).
fof(f_1785_2,plain,
! [U_6712,U_6711] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6711),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6712)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6711,U_6712)),
inference(variable_rename,[status(thm)],[f_1785_1]) ).
fof(f_1785_3,plain,
! [U_6711,U_6712] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6711),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6712)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6711,U_6712)),
inference(definitional_conversion,[status(esa)],[f_1785_2]) ).
cnf(f_1785_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6711),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6712)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6711,U_6712)),
inference(clausify,[status(thm)],[f_1785_3]) ).
fof(f_1786_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zminus__zmod]) ).
fof(f_1786_2,plain,
! [U_6714,U_6713] : 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,U_6713,U_6714)),U_6714) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6713),U_6714),
inference(variable_rename,[status(thm)],[f_1786_1]) ).
fof(f_1786_3,plain,
! [U_6713,U_6714] : 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,U_6713,U_6714)),U_6714) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6713),U_6714),
inference(definitional_conversion,[status(esa)],[f_1786_2]) ).
cnf(f_1786_4,plain,
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,U_6713,U_6714)),U_6714) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6713),U_6714),
inference(clausify,[status(thm)],[f_1786_3]) ).
fof(f_1787_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zpower__zmod]) ).
fof(f_1787_2,plain,
! [U_6717,U_6716,U_6715] : 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,U_6715,U_6716)),U_6717),U_6716) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6715),U_6717),U_6716),
inference(variable_rename,[status(thm)],[f_1787_1]) ).
fof(f_1787_3,plain,
! [U_6715,U_6716,U_6717] : 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,U_6715,U_6716)),U_6717),U_6716) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6715),U_6717),U_6716),
inference(definitional_conversion,[status(esa)],[f_1787_2]) ).
cnf(f_1787_4,plain,
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,U_6715,U_6716)),U_6717),U_6716) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6715),U_6717),U_6716),
inference(clausify,[status(thm)],[f_1787_3]) ).
fof(f_1788_1,plain,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I6_J]) ).
fof(f_1788_2,plain,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(definitional_conversion,[status(esa)],[f_1788_1]) ).
cnf(f_1788_3,plain,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(clausify,[status(thm)],[f_1788_2]) ).
fof(f_1789_1,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[fact_not__neg__0]) ).
fof(f_1789_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1789_1]) ).
cnf(f_1789_3,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1789_2]) ).
fof(f_1790_1,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[fact_not__neg__1]) ).
fof(f_1790_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1790_1]) ).
cnf(f_1790_3,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1790_2]) ).
fof(f_1791_1,plain,
! [V_a,V_b,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0]) ).
fof(f_1791_2,plain,
! [U_6720,U_6719,U_6718] :
( c_Divides_Odiv__class_Omod(U_6718,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6718),U_6719),U_6720),U_6719) = c_Groups_Ozero__class_Ozero(U_6718)
| ~ class_Divides_Osemiring__div(U_6718) ),
inference(variable_rename,[status(thm)],[f_1791_1]) ).
fof(f_1791_3,plain,
! [U_6718,U_6719,U_6720] :
( c_Divides_Odiv__class_Omod(U_6718,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6718),U_6719),U_6720),U_6719) = c_Groups_Ozero__class_Ozero(U_6718)
| ~ class_Divides_Osemiring__div(U_6718) ),
inference(definitional_conversion,[status(esa)],[f_1791_2]) ).
cnf(f_1791_4,plain,
( c_Divides_Odiv__class_Omod(U_6718,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6718),U_6719),U_6720),U_6719) = c_Groups_Ozero__class_Ozero(U_6718)
| ~ class_Divides_Osemiring__div(U_6718) ),
inference(clausify,[status(thm)],[f_1791_3]) ).
fof(f_1792_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0]) ).
fof(f_1792_2,plain,
! [U_6723,U_6722,U_6721] :
( c_Divides_Odiv__class_Omod(U_6721,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6721),U_6722),U_6723),U_6723) = c_Groups_Ozero__class_Ozero(U_6721)
| ~ class_Divides_Osemiring__div(U_6721) ),
inference(variable_rename,[status(thm)],[f_1792_1]) ).
fof(f_1792_3,plain,
! [U_6721,U_6722,U_6723] :
( c_Divides_Odiv__class_Omod(U_6721,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6721),U_6722),U_6723),U_6723) = c_Groups_Ozero__class_Ozero(U_6721)
| ~ class_Divides_Osemiring__div(U_6721) ),
inference(definitional_conversion,[status(esa)],[f_1792_2]) ).
cnf(f_1792_4,plain,
( c_Divides_Odiv__class_Omod(U_6721,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6721),U_6722),U_6723),U_6723) = c_Groups_Ozero__class_Ozero(U_6721)
| ~ class_Divides_Osemiring__div(U_6721) ),
inference(clausify,[status(thm)],[f_1792_3]) ).
fof(f_1793_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__self2]) ).
fof(f_1793_2,plain,
! [U_6727,U_6726,U_6725,U_6724] :
( c_Divides_Odiv__class_Omod(U_6724,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6724),U_6725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6724),U_6726),U_6727)),U_6726) = c_Divides_Odiv__class_Omod(U_6724,U_6725,U_6726)
| ~ class_Divides_Osemiring__div(U_6724) ),
inference(variable_rename,[status(thm)],[f_1793_1]) ).
fof(f_1793_3,plain,
! [U_6724,U_6725,U_6726,U_6727] :
( c_Divides_Odiv__class_Omod(U_6724,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6724),U_6725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6724),U_6726),U_6727)),U_6726) = c_Divides_Odiv__class_Omod(U_6724,U_6725,U_6726)
| ~ class_Divides_Osemiring__div(U_6724) ),
inference(definitional_conversion,[status(esa)],[f_1793_2]) ).
cnf(f_1793_4,plain,
( c_Divides_Odiv__class_Omod(U_6724,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6724),U_6725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6724),U_6726),U_6727)),U_6726) = c_Divides_Odiv__class_Omod(U_6724,U_6725,U_6726)
| ~ class_Divides_Osemiring__div(U_6724) ),
inference(clausify,[status(thm)],[f_1793_3]) ).
fof(f_1794_1,plain,
! [V_b,V_c,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mult__self1]) ).
fof(f_1794_2,plain,
! [U_6731,U_6730,U_6729,U_6728] :
( c_Divides_Odiv__class_Omod(U_6728,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6728),U_6729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6728),U_6730),U_6731)),U_6731) = c_Divides_Odiv__class_Omod(U_6728,U_6729,U_6731)
| ~ class_Divides_Osemiring__div(U_6728) ),
inference(variable_rename,[status(thm)],[f_1794_1]) ).
fof(f_1794_3,plain,
! [U_6728,U_6729,U_6730,U_6731] :
( c_Divides_Odiv__class_Omod(U_6728,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6728),U_6729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6728),U_6730),U_6731)),U_6731) = c_Divides_Odiv__class_Omod(U_6728,U_6729,U_6731)
| ~ class_Divides_Osemiring__div(U_6728) ),
inference(definitional_conversion,[status(esa)],[f_1794_2]) ).
cnf(f_1794_4,plain,
( c_Divides_Odiv__class_Omod(U_6728,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6728),U_6729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6728),U_6730),U_6731)),U_6731) = c_Divides_Odiv__class_Omod(U_6728,U_6729,U_6731)
| ~ class_Divides_Osemiring__div(U_6728) ),
inference(clausify,[status(thm)],[f_1794_3]) ).
fof(f_1795_1,plain,
! [V_a,T_a] :
( c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__by__1]) ).
fof(f_1795_2,plain,
! [U_6733,U_6732] :
( c_Divides_Odiv__class_Omod(U_6732,U_6733,c_Groups_Oone__class_Oone(U_6732)) = c_Groups_Ozero__class_Ozero(U_6732)
| ~ class_Divides_Osemiring__div(U_6732) ),
inference(variable_rename,[status(thm)],[f_1795_1]) ).
fof(f_1795_3,plain,
! [U_6732,U_6733] :
( c_Divides_Odiv__class_Omod(U_6732,U_6733,c_Groups_Oone__class_Oone(U_6732)) = c_Groups_Ozero__class_Ozero(U_6732)
| ~ class_Divides_Osemiring__div(U_6732) ),
inference(definitional_conversion,[status(esa)],[f_1795_2]) ).
cnf(f_1795_4,plain,
( c_Divides_Odiv__class_Omod(U_6732,U_6733,c_Groups_Oone__class_Oone(U_6732)) = c_Groups_Ozero__class_Ozero(U_6732)
| ~ class_Divides_Osemiring__div(U_6732) ),
inference(clausify,[status(thm)],[f_1795_3]) ).
fof(f_1796_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__div__trivial]) ).
fof(f_1796_2,plain,
! [U_6736,U_6735,U_6734] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6734),c_Divides_Odiv__class_Omod(U_6734,U_6735,U_6736)),U_6736) = c_Groups_Ozero__class_Ozero(U_6734)
| ~ class_Divides_Osemiring__div(U_6734) ),
inference(variable_rename,[status(thm)],[f_1796_1]) ).
fof(f_1796_3,plain,
! [U_6734,U_6735,U_6736] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6734),c_Divides_Odiv__class_Omod(U_6734,U_6735,U_6736)),U_6736) = c_Groups_Ozero__class_Ozero(U_6734)
| ~ class_Divides_Osemiring__div(U_6734) ),
inference(definitional_conversion,[status(esa)],[f_1796_2]) ).
cnf(f_1796_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6734),c_Divides_Odiv__class_Omod(U_6734,U_6735,U_6736)),U_6736) = c_Groups_Ozero__class_Ozero(U_6734)
| ~ class_Divides_Osemiring__div(U_6734) ),
inference(clausify,[status(thm)],[f_1796_3]) ).
fof(f_1797_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_div__1]) ).
fof(f_1797_2,plain,
! [U_6737] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6737),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_6737,
inference(variable_rename,[status(thm)],[f_1797_1]) ).
fof(f_1797_3,plain,
! [U_6737] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6737),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_6737,
inference(definitional_conversion,[status(esa)],[f_1797_2]) ).
cnf(f_1797_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6737),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_6737,
inference(clausify,[status(thm)],[f_1797_3]) ).
fof(f_1798_1,plain,
! [V_n,V_m] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__less]) ).
fof(f_1798_2,plain,
! [U_6739,U_6738] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6738),U_6739) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6738),U_6739)) ),
inference(variable_rename,[status(thm)],[f_1798_1]) ).
fof(f_1798_3,plain,
! [U_6738,U_6739] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6738),U_6739) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6738),U_6739)) ),
inference(definitional_conversion,[status(esa)],[f_1798_2]) ).
cnf(f_1798_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6738),U_6739) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6738),U_6739)) ),
inference(clausify,[status(thm)],[f_1798_3]) ).
fof(f_1799_1,plain,
! [V_n,V_m,V_k] :
( ( 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)
| V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( 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)
| V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj]) ).
fof(f_1799_2,plain,
! [U_6742,U_6741,U_6740] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6740),U_6741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6740),U_6742)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6741),U_6742)
| U_6740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6740),U_6741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6740),U_6742)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6740 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1799_1]) ).
fof(f_1799_3,plain,
( ! [U_6748,U_6746,U_6744] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6746)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6748)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6746),U_6748)
| U_6744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6747,U_6745,U_6743] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6743),U_6745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6743),U_6747)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6743 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1799_2]) ).
fof(f_1799_4,plain,
( ! [U_6744,U_6746,U_6748] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6746)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6748)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6746),U_6748)
| U_6744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6743,U_6745,U_6747] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6743),U_6745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6743),U_6747)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6743 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1799_3]) ).
cnf(f_1799_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6743),U_6745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6743),U_6747)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6743 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1799_4]) ).
cnf(f_1799_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6746)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6748)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6746),U_6748)
| U_6744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1799_4]) ).
fof(f_1800_1,plain,
! [V_y,V_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J]) ).
fof(f_1800_2,plain,
! [U_6750,U_6749] :
( 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,U_6749,U_6750)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6749)) ),
inference(variable_rename,[status(thm)],[f_1800_1]) ).
fof(f_1800_3,plain,
! [U_6749,U_6750] :
( 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,U_6749,U_6750)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6749)) ),
inference(definitional_conversion,[status(esa)],[f_1800_2]) ).
cnf(f_1800_4,plain,
( 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,U_6749,U_6750)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6749)) ),
inference(clausify,[status(thm)],[f_1800_3]) ).
fof(f_1801_1,plain,
! [V_k,V_m] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend]) ).
fof(f_1801_2,plain,
! [U_6752,U_6751] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6751,U_6752)),U_6751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6751)) ),
inference(variable_rename,[status(thm)],[f_1801_1]) ).
fof(f_1801_3,plain,
! [U_6751,U_6752] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6751,U_6752)),U_6751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6751)) ),
inference(definitional_conversion,[status(esa)],[f_1801_2]) ).
cnf(f_1801_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6751,U_6752)),U_6751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6751)) ),
inference(clausify,[status(thm)],[f_1801_3]) ).
fof(f_1802_1,plain,
! [V_a,V_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__mod__bound]) ).
fof(f_1802_2,plain,
! [U_6754,U_6753] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6753),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6754,U_6753)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6753),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1802_1]) ).
fof(f_1802_3,plain,
! [U_6753,U_6754] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6753),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6754,U_6753)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6753),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1802_2]) ).
cnf(f_1802_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6753),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6754,U_6753)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6753),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1802_3]) ).
fof(f_1803_1,plain,
! [V_a,V_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_pos__mod__bound]) ).
fof(f_1803_2,plain,
! [U_6756,U_6755] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6756,U_6755)),U_6755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6755)) ),
inference(variable_rename,[status(thm)],[f_1803_1]) ).
fof(f_1803_3,plain,
! [U_6755,U_6756] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6756,U_6755)),U_6755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6755)) ),
inference(definitional_conversion,[status(esa)],[f_1803_2]) ).
cnf(f_1803_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6756,U_6755)),U_6755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6755)) ),
inference(clausify,[status(thm)],[f_1803_3]) ).
fof(f_1804_1,plain,
! [V_d_2,V_m_2] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [B_q] : V_m_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) )
& ( ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff]) ).
fof(f_1804_2,plain,
! [U_6760,U_6759] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6759,U_6760) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_6758] : U_6759 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6760),U_6758) )
& ( ? [U_6757] : U_6759 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6760),U_6757)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6759,U_6760) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1804_1]) ).
fof(f_1804_3,plain,
( ! [U_6764,U_6762] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6762,U_6764) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_6758] : U_6762 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6764),U_6758) )
& ! [U_6763,U_6761] :
( ? [U_6757] : U_6761 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6763),U_6757)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6761,U_6763) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1804_2]) ).
fof(f_1804_4,plain,
( ! [U_6764,U_6762] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6762,U_6764) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_6758] : U_6762 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6764),U_6758) )
& ! [U_6763,U_6761] :
( U_6761 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6763),sK189(U_6763,U_6761))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6761,U_6763) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_6757,sK189(U_6763,U_6761))],[f_1804_3]) ).
fof(f_1804_5,plain,
( ! [U_6758,U_6762,U_6764] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6762,U_6764) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6762 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6764),U_6758) )
& ! [U_6761,U_6763] :
( U_6761 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6763),sK189(U_6763,U_6761))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6761,U_6763) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_1804_4]) ).
cnf(f_1804_6,plain,
( U_6761 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6763),sK189(U_6763,U_6761))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6761,U_6763) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1804_5]) ).
cnf(f_1804_7,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6762,U_6764) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6762 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6764),U_6758) ),
inference(clausify,[status(thm)],[f_1804_5]) ).
fof(f_1805_1,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I2_J]) ).
fof(f_1805_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1805_1]) ).
cnf(f_1805_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1805_2]) ).
fof(f_1806_1,plain,
! [V_l,V_k] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| 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) ),
inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__not__zero]) ).
fof(f_1806_2,plain,
! [U_6766,U_6765] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6765,U_6766) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6765,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6766)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1806_1]) ).
fof(f_1806_3,plain,
! [U_6766,U_6765] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6765,U_6766) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6765,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6766)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_1806_2]) ).
cnf(f_1806_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6765,U_6766) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6765,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6766)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1806_3]) ).
fof(f_1807_1,plain,
! [V_l,V_k] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| 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) ),
inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__not__zero]) ).
fof(f_1807_2,plain,
! [U_6768,U_6767] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6767,U_6768) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6767),U_6768) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1807_1]) ).
fof(f_1807_3,plain,
! [U_6767,U_6768] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6767,U_6768) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6767),U_6768) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_1807_2]) ).
cnf(f_1807_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6767,U_6768) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6767),U_6768) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1807_3]) ).
fof(f_1808_1,plain,
! [V_a] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
& 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) ),
inference(fof_nnf,[status(thm)],[fact_DIVISION__BY__ZERO]) ).
fof(f_1808_2,plain,
! [U_6769] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6769,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6769
& hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6769),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1808_1]) ).
fof(f_1808_3,plain,
( ! [U_6771] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6771,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6771
& ! [U_6770] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(miniscope,[status(thm)],[f_1808_2]) ).
fof(f_1808_4,plain,
( ! [U_6771] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6771,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6771
& ! [U_6770] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_1808_3]) ).
cnf(f_1808_5,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1808_4]) ).
cnf(f_1808_6,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6771,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6771,
inference(clausify,[status(thm)],[f_1808_4]) ).
fof(f_1809_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__trivial]) ).
fof(f_1809_2,plain,
! [U_6773,U_6772] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6772,U_6773)),U_6773) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1809_1]) ).
fof(f_1809_3,plain,
! [U_6772,U_6773] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6772,U_6773)),U_6773) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1809_2]) ).
cnf(f_1809_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6772,U_6773)),U_6773) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1809_3]) ).
fof(f_1810_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zdiv__zadd1__eq]) ).
fof(f_1810_2,plain,
! [U_6776,U_6775,U_6774] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6774),U_6775)),U_6776) = 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),U_6774),U_6776)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6775),U_6776))),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,U_6774,U_6776)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6775,U_6776))),U_6776)),
inference(variable_rename,[status(thm)],[f_1810_1]) ).
fof(f_1810_3,plain,
! [U_6774,U_6775,U_6776] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6774),U_6775)),U_6776) = 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),U_6774),U_6776)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6775),U_6776))),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,U_6774,U_6776)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6775,U_6776))),U_6776)),
inference(definitional_conversion,[status(esa)],[f_1810_2]) ).
cnf(f_1810_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6774),U_6775)),U_6776) = 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),U_6774),U_6776)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6775),U_6776))),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,U_6774,U_6776)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6775,U_6776))),U_6776)),
inference(clausify,[status(thm)],[f_1810_3]) ).
fof(f_1811_1,plain,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Int_OMin__def]) ).
fof(f_1811_2,plain,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_1811_1]) ).
cnf(f_1811_3,plain,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1811_2]) ).
fof(f_1812_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_mult__Min]) ).
fof(f_1812_2,plain,
! [U_6777] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_6777) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6777),
inference(variable_rename,[status(thm)],[f_1812_1]) ).
fof(f_1812_3,plain,
! [U_6777] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_6777) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6777),
inference(definitional_conversion,[status(esa)],[f_1812_2]) ).
cnf(f_1812_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_6777) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6777),
inference(clausify,[status(thm)],[f_1812_3]) ).
fof(f_1813_1,plain,
! [V_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_zmod__minus1]) ).
fof(f_1813_2,plain,
! [U_6778] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_6778) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6778),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6778)) ),
inference(variable_rename,[status(thm)],[f_1813_1]) ).
fof(f_1813_3,plain,
! [U_6778] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_6778) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6778),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6778)) ),
inference(definitional_conversion,[status(esa)],[f_1813_2]) ).
cnf(f_1813_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_6778) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6778),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6778)) ),
inference(clausify,[status(thm)],[f_1813_3]) ).
fof(f_1814_1,plain,
! [V_x_2] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__neg__eq__ge__0]) ).
fof(f_1814_2,plain,
! [U_6779] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6779)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6779))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6779)) ) ),
inference(variable_rename,[status(thm)],[f_1814_1]) ).
fof(f_1814_3,plain,
( ! [U_6781] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6781)) )
& ! [U_6780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6780)) ) ),
inference(miniscope,[status(thm)],[f_1814_2]) ).
fof(f_1814_4,plain,
( ! [U_6781] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6781)) )
& ! [U_6780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6780)) ) ),
inference(definitional_conversion,[status(esa)],[f_1814_3]) ).
cnf(f_1814_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6780)) ),
inference(clausify,[status(thm)],[f_1814_4]) ).
cnf(f_1814_6,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6781)) ),
inference(clausify,[status(thm)],[f_1814_4]) ).
fof(f_1815_1,plain,
! [V_Z_2] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_neg__def]) ).
fof(f_1815_2,plain,
! [U_6782] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6782),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6782),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6782)) ) ),
inference(variable_rename,[status(thm)],[f_1815_1]) ).
fof(f_1815_3,plain,
( ! [U_6784] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6784),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_6783] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6783),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6783)) ) ),
inference(miniscope,[status(thm)],[f_1815_2]) ).
fof(f_1815_4,plain,
( ! [U_6784] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6784),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_6783] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6783),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6783)) ) ),
inference(definitional_conversion,[status(esa)],[f_1815_3]) ).
cnf(f_1815_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6783),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6783)) ),
inference(clausify,[status(thm)],[f_1815_4]) ).
cnf(f_1815_6,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6784),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1815_4]) ).
fof(f_1816_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_neg__zminus__int]) ).
fof(f_1816_2,plain,
! [U_6785] : 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,U_6785))))),
inference(variable_rename,[status(thm)],[f_1816_1]) ).
fof(f_1816_3,plain,
! [U_6785] : 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,U_6785))))),
inference(definitional_conversion,[status(esa)],[f_1816_2]) ).
cnf(f_1816_4,plain,
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,U_6785))))),
inference(clausify,[status(thm)],[f_1816_3]) ).
fof(f_1817_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mod__equality]) ).
fof(f_1817_2,plain,
! [U_6789,U_6788,U_6787,U_6786] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6786),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6786),U_6787),U_6788)),U_6788)),c_Divides_Odiv__class_Omod(U_6786,U_6787,U_6788))),U_6789) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),U_6787),U_6789)
| ~ class_Divides_Osemiring__div(U_6786) ),
inference(variable_rename,[status(thm)],[f_1817_1]) ).
fof(f_1817_3,plain,
! [U_6786,U_6787,U_6788,U_6789] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6786),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6786),U_6787),U_6788)),U_6788)),c_Divides_Odiv__class_Omod(U_6786,U_6787,U_6788))),U_6789) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),U_6787),U_6789)
| ~ class_Divides_Osemiring__div(U_6786) ),
inference(definitional_conversion,[status(esa)],[f_1817_2]) ).
cnf(f_1817_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6786),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6786),U_6787),U_6788)),U_6788)),c_Divides_Odiv__class_Omod(U_6786,U_6787,U_6788))),U_6789) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6786),U_6787),U_6789)
| ~ class_Divides_Osemiring__div(U_6786) ),
inference(clausify,[status(thm)],[f_1817_3]) ).
fof(f_1818_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mod__equality2]) ).
fof(f_1818_2,plain,
! [U_6793,U_6792,U_6791,U_6790] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6790),U_6791),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6790),U_6792),U_6791))),c_Divides_Odiv__class_Omod(U_6790,U_6792,U_6791))),U_6793) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),U_6792),U_6793)
| ~ class_Divides_Osemiring__div(U_6790) ),
inference(variable_rename,[status(thm)],[f_1818_1]) ).
fof(f_1818_3,plain,
! [U_6790,U_6791,U_6792,U_6793] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6790),U_6791),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6790),U_6792),U_6791))),c_Divides_Odiv__class_Omod(U_6790,U_6792,U_6791))),U_6793) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),U_6792),U_6793)
| ~ class_Divides_Osemiring__div(U_6790) ),
inference(definitional_conversion,[status(esa)],[f_1818_2]) ).
cnf(f_1818_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6790),U_6791),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6790),U_6792),U_6791))),c_Divides_Odiv__class_Omod(U_6790,U_6792,U_6791))),U_6793) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6790),U_6792),U_6793)
| ~ class_Divides_Osemiring__div(U_6790) ),
inference(clausify,[status(thm)],[f_1818_3]) ).
fof(f_1819_1,plain,
! [V_b,V_a,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_a
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__div__equality]) ).
fof(f_1819_2,plain,
! [U_6796,U_6795,U_6794] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6794),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6794),U_6795),U_6796)),U_6796)),c_Divides_Odiv__class_Omod(U_6794,U_6795,U_6796)) = U_6795
| ~ class_Divides_Osemiring__div(U_6794) ),
inference(variable_rename,[status(thm)],[f_1819_1]) ).
fof(f_1819_3,plain,
! [U_6794,U_6795,U_6796] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6794),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6794),U_6795),U_6796)),U_6796)),c_Divides_Odiv__class_Omod(U_6794,U_6795,U_6796)) = U_6795
| ~ class_Divides_Osemiring__div(U_6794) ),
inference(definitional_conversion,[status(esa)],[f_1819_2]) ).
cnf(f_1819_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6794),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6794),U_6795),U_6796)),U_6796)),c_Divides_Odiv__class_Omod(U_6794,U_6795,U_6796)) = U_6795
| ~ class_Divides_Osemiring__div(U_6794) ),
inference(clausify,[status(thm)],[f_1819_3]) ).
fof(f_1820_1,plain,
! [V_a,V_b,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_a
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__div__equality2]) ).
fof(f_1820_2,plain,
! [U_6799,U_6798,U_6797] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6797),U_6798),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6797),U_6799),U_6798))),c_Divides_Odiv__class_Omod(U_6797,U_6799,U_6798)) = U_6799
| ~ class_Divides_Osemiring__div(U_6797) ),
inference(variable_rename,[status(thm)],[f_1820_1]) ).
fof(f_1820_3,plain,
! [U_6797,U_6798,U_6799] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6797),U_6798),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6797),U_6799),U_6798))),c_Divides_Odiv__class_Omod(U_6797,U_6799,U_6798)) = U_6799
| ~ class_Divides_Osemiring__div(U_6797) ),
inference(definitional_conversion,[status(esa)],[f_1820_2]) ).
cnf(f_1820_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6797),U_6798),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6797),U_6799),U_6798))),c_Divides_Odiv__class_Omod(U_6797,U_6799,U_6798)) = U_6799
| ~ class_Divides_Osemiring__div(U_6797) ),
inference(clausify,[status(thm)],[f_1820_3]) ).
fof(f_1821_1,plain,
! [V_b,V_a,T_a] :
( 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
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H]) ).
fof(f_1821_2,plain,
! [U_6802,U_6801,U_6800] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6800),c_Divides_Odiv__class_Omod(U_6800,U_6801,U_6802)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6800),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6800),U_6801),U_6802)),U_6802)) = U_6801
| ~ class_Divides_Osemiring__div(U_6800) ),
inference(variable_rename,[status(thm)],[f_1821_1]) ).
fof(f_1821_3,plain,
! [U_6800,U_6801,U_6802] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6800),c_Divides_Odiv__class_Omod(U_6800,U_6801,U_6802)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6800),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6800),U_6801),U_6802)),U_6802)) = U_6801
| ~ class_Divides_Osemiring__div(U_6800) ),
inference(definitional_conversion,[status(esa)],[f_1821_2]) ).
cnf(f_1821_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6800),c_Divides_Odiv__class_Omod(U_6800,U_6801,U_6802)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6800),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6800),U_6801),U_6802)),U_6802)) = U_6801
| ~ class_Divides_Osemiring__div(U_6800) ),
inference(clausify,[status(thm)],[f_1821_3]) ).
fof(f_1822_1,plain,
! [V_k,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_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_div__le__mono2]) ).
fof(f_1822_2,plain,
! [U_6805,U_6804,U_6803] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6805),U_6804)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6805),U_6803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6803),U_6804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6803)) ),
inference(variable_rename,[status(thm)],[f_1822_1]) ).
fof(f_1822_3,plain,
! [U_6803,U_6804,U_6805] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6805),U_6804)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6805),U_6803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6803),U_6804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6803)) ),
inference(definitional_conversion,[status(esa)],[f_1822_2]) ).
cnf(f_1822_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6805),U_6804)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6805),U_6803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6803),U_6804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6803)) ),
inference(clausify,[status(thm)],[f_1822_3]) ).
fof(f_1823_1,plain,
! [V_n,V_m,V_k] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1]) ).
fof(f_1823_2,plain,
! [U_6808,U_6807,U_6806] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6806),U_6807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6806),U_6808)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6807),U_6808)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6806)) ),
inference(variable_rename,[status(thm)],[f_1823_1]) ).
fof(f_1823_3,plain,
! [U_6806,U_6807,U_6808] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6806),U_6807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6806),U_6808)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6807),U_6808)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6806)) ),
inference(definitional_conversion,[status(esa)],[f_1823_2]) ).
cnf(f_1823_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6806),U_6807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6806),U_6808)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6807),U_6808)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6806)) ),
inference(clausify,[status(thm)],[f_1823_3]) ).
fof(f_1824_1,plain,
! [V_m,V_n] :
( 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
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m]) ).
fof(f_1824_2,plain,
! [U_6810,U_6809] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6809),U_6810)),U_6809) = U_6810
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6809)) ),
inference(variable_rename,[status(thm)],[f_1824_1]) ).
fof(f_1824_3,plain,
! [U_6809,U_6810] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6809),U_6810)),U_6809) = U_6810
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6809)) ),
inference(definitional_conversion,[status(esa)],[f_1824_2]) ).
cnf(f_1824_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6809),U_6810)),U_6809) = U_6810
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6809)) ),
inference(clausify,[status(thm)],[f_1824_3]) ).
fof(f_1825_1,plain,
! [V_m,V_n] :
( 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
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m]) ).
fof(f_1825_2,plain,
! [U_6812,U_6811] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6812),U_6811)),U_6811) = U_6812
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6811)) ),
inference(variable_rename,[status(thm)],[f_1825_1]) ).
fof(f_1825_3,plain,
! [U_6811,U_6812] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6812),U_6811)),U_6811) = U_6812
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6811)) ),
inference(definitional_conversion,[status(esa)],[f_1825_2]) ).
cnf(f_1825_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6812),U_6811)),U_6811) = U_6812
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6811)) ),
inference(clausify,[status(thm)],[f_1825_3]) ).
fof(f_1826_1,plain,
! [V_m,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__less__dividend]) ).
fof(f_1826_2,plain,
! [U_6814,U_6813] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6814),U_6813)),U_6814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6813)) ),
inference(variable_rename,[status(thm)],[f_1826_1]) ).
fof(f_1826_3,plain,
! [U_6813,U_6814] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6814),U_6813)),U_6814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6813)) ),
inference(definitional_conversion,[status(esa)],[f_1826_2]) ).
cnf(f_1826_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6814),U_6813)),U_6814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6813)) ),
inference(clausify,[status(thm)],[f_1826_3]) ).
fof(f_1827_1,plain,
! [V_z,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__minus1__right]) ).
fof(f_1827_2,plain,
! [U_6816,U_6815] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6815),U_6816),hAPP(c_Int_Onumber__class_Onumber__of(U_6815),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6815),U_6816)
| ~ class_Int_Onumber__ring(U_6815) ),
inference(variable_rename,[status(thm)],[f_1827_1]) ).
fof(f_1827_3,plain,
! [U_6815,U_6816] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6815),U_6816),hAPP(c_Int_Onumber__class_Onumber__of(U_6815),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6815),U_6816)
| ~ class_Int_Onumber__ring(U_6815) ),
inference(definitional_conversion,[status(esa)],[f_1827_2]) ).
cnf(f_1827_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6815),U_6816),hAPP(c_Int_Onumber__class_Onumber__of(U_6815),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6815),U_6816)
| ~ class_Int_Onumber__ring(U_6815) ),
inference(clausify,[status(thm)],[f_1827_3]) ).
fof(f_1828_1,plain,
! [V_z,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__minus1]) ).
fof(f_1828_2,plain,
! [U_6818,U_6817] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6817),hAPP(c_Int_Onumber__class_Onumber__of(U_6817),c_Int_OMin)),U_6818) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6817),U_6818)
| ~ class_Int_Onumber__ring(U_6817) ),
inference(variable_rename,[status(thm)],[f_1828_1]) ).
fof(f_1828_3,plain,
! [U_6817,U_6818] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6817),hAPP(c_Int_Onumber__class_Onumber__of(U_6817),c_Int_OMin)),U_6818) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6817),U_6818)
| ~ class_Int_Onumber__ring(U_6817) ),
inference(definitional_conversion,[status(esa)],[f_1828_2]) ).
cnf(f_1828_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6817),hAPP(c_Int_Onumber__class_Onumber__of(U_6817),c_Int_OMin)),U_6818) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6817),U_6818)
| ~ class_Int_Onumber__ring(U_6817) ),
inference(clausify,[status(thm)],[f_1828_3]) ).
fof(f_1829_1,plain,
! [V_b,V_a] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial]) ).
fof(f_1829_2,plain,
! [U_6820,U_6819] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6819,U_6820) = U_6819
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6820),U_6819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6819),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1829_1]) ).
fof(f_1829_3,plain,
! [U_6819,U_6820] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6819,U_6820) = U_6819
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6820),U_6819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6819),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1829_2]) ).
cnf(f_1829_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6819,U_6820) = U_6819
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6820),U_6819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6819),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1829_3]) ).
fof(f_1830_1,plain,
! [V_a,V_b] :
( ( 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)))
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__mod__conj]) ).
fof(f_1830_2,plain,
! [U_6822,U_6821] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6822,U_6821)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6822,U_6821)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1830_1]) ).
fof(f_1830_3,plain,
( ! [U_6822,U_6821] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6822,U_6821)))
| ~ sP605(U_6822,U_6821) )
& ! [U_6822,U_6821] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6822,U_6821)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP605(U_6822,U_6821) )
& ! [U_6822,U_6821] :
( sP605(U_6822,U_6821)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP605])],[f_1830_2]) ).
cnf(f_1830_4,plain,
( sP605(U_6822,U_6821)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1830_3]) ).
cnf(f_1830_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6822,U_6821)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP605(U_6822,U_6821) ),
inference(clausify,[status(thm)],[f_1830_3]) ).
cnf(f_1830_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6822,U_6821)))
| ~ sP605(U_6822,U_6821) ),
inference(clausify,[status(thm)],[f_1830_3]) ).
fof(f_1831_1,plain,
! [V_a,V_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__mod__sign]) ).
fof(f_1831_2,plain,
! [U_6824,U_6823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6824,U_6823)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6823),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1831_1]) ).
fof(f_1831_3,plain,
! [U_6823,U_6824] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6824,U_6823)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6823),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1831_2]) ).
cnf(f_1831_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6824,U_6823)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6823),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1831_3]) ).
fof(f_1832_1,plain,
! [V_b,V_a] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial]) ).
fof(f_1832_2,plain,
! [U_6826,U_6825] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6825,U_6826) = U_6825
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6825),U_6826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6825)) ),
inference(variable_rename,[status(thm)],[f_1832_1]) ).
fof(f_1832_3,plain,
! [U_6825,U_6826] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6825,U_6826) = U_6825
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6825),U_6826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6825)) ),
inference(definitional_conversion,[status(esa)],[f_1832_2]) ).
cnf(f_1832_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6825,U_6826) = U_6825
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6825),U_6826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6825)) ),
inference(clausify,[status(thm)],[f_1832_3]) ).
fof(f_1833_1,plain,
! [V_a,V_b] :
( ( 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))
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_pos__mod__conj]) ).
fof(f_1833_2,plain,
! [U_6828,U_6827] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6828,U_6827)),U_6827))
& 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,U_6828,U_6827))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6827)) ),
inference(variable_rename,[status(thm)],[f_1833_1]) ).
fof(f_1833_3,plain,
( ! [U_6827,U_6828] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6828,U_6827)),U_6827))
| ~ sP606(U_6827,U_6828) )
& ! [U_6827,U_6828] :
( 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,U_6828,U_6827)))
| ~ sP606(U_6827,U_6828) )
& ! [U_6827,U_6828] :
( sP606(U_6827,U_6828)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6827)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP606])],[f_1833_2]) ).
cnf(f_1833_4,plain,
( sP606(U_6827,U_6828)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6827)) ),
inference(clausify,[status(thm)],[f_1833_3]) ).
cnf(f_1833_5,plain,
( 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,U_6828,U_6827)))
| ~ sP606(U_6827,U_6828) ),
inference(clausify,[status(thm)],[f_1833_3]) ).
cnf(f_1833_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6828,U_6827)),U_6827))
| ~ sP606(U_6827,U_6828) ),
inference(clausify,[status(thm)],[f_1833_3]) ).
fof(f_1834_1,plain,
! [V_a,V_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_pos__mod__sign]) ).
fof(f_1834_2,plain,
! [U_6830,U_6829] :
( 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,U_6830,U_6829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6829)) ),
inference(variable_rename,[status(thm)],[f_1834_1]) ).
fof(f_1834_3,plain,
! [U_6830,U_6829] :
( 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,U_6830,U_6829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6829)) ),
inference(definitional_conversion,[status(esa)],[f_1834_2]) ).
cnf(f_1834_4,plain,
( 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,U_6830,U_6829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6829)) ),
inference(clausify,[status(thm)],[f_1834_3]) ).
fof(f_1835_1,plain,
! [T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Min]) ).
fof(f_1835_2,plain,
! [U_6831] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_6831),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6831),c_Groups_Oone__class_Oone(U_6831))
| ~ class_Int_Onumber__ring(U_6831) ),
inference(variable_rename,[status(thm)],[f_1835_1]) ).
fof(f_1835_3,plain,
! [U_6831] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_6831),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6831),c_Groups_Oone__class_Oone(U_6831))
| ~ class_Int_Onumber__ring(U_6831) ),
inference(definitional_conversion,[status(esa)],[f_1835_2]) ).
cnf(f_1835_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_6831),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6831),c_Groups_Oone__class_Oone(U_6831))
| ~ class_Int_Onumber__ring(U_6831) ),
inference(clausify,[status(thm)],[f_1835_3]) ).
fof(f_1836_1,plain,
! [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),c_Int_OMin)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J]) ).
fof(f_1836_2,plain,
! [U_6832] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6832),c_Groups_Oone__class_Oone(U_6832)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6832),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_6832) ),
inference(variable_rename,[status(thm)],[f_1836_1]) ).
fof(f_1836_3,plain,
! [U_6832] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6832),c_Groups_Oone__class_Oone(U_6832)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6832),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_6832) ),
inference(definitional_conversion,[status(esa)],[f_1836_2]) ).
cnf(f_1836_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6832),c_Groups_Oone__class_Oone(U_6832)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6832),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_6832) ),
inference(clausify,[status(thm)],[f_1836_3]) ).
fof(f_1837_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__minus1]) ).
fof(f_1837_2,plain,
! [U_6834,U_6833] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6833),U_6834),hAPP(c_Int_Onumber__class_Onumber__of(U_6833),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6833),U_6834)
| ~ class_Int_Onumber__ring(U_6833)
| ~ class_Fields_Ofield__inverse__zero(U_6833) ),
inference(variable_rename,[status(thm)],[f_1837_1]) ).
fof(f_1837_3,plain,
! [U_6833,U_6834] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6833),U_6834),hAPP(c_Int_Onumber__class_Onumber__of(U_6833),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6833),U_6834)
| ~ class_Int_Onumber__ring(U_6833)
| ~ class_Fields_Ofield__inverse__zero(U_6833) ),
inference(definitional_conversion,[status(esa)],[f_1837_2]) ).
cnf(f_1837_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6833),U_6834),hAPP(c_Int_Onumber__class_Onumber__of(U_6833),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6833),U_6834)
| ~ class_Int_Onumber__ring(U_6833)
| ~ class_Fields_Ofield__inverse__zero(U_6833) ),
inference(clausify,[status(thm)],[f_1837_3]) ).
fof(f_1838_1,plain,
! [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(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if]) ).
fof(f_1838_2,plain,
! [U_6836,U_6835] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6835,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6836)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6835,U_6836)),U_6836)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6835,U_6836) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6835,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6836)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6835,U_6836) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1838_1]) ).
fof(f_1838_3,plain,
( ! [U_6840,U_6838] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6840)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,U_6840)),U_6840)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,U_6840) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_6839,U_6837] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6837,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6839)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6837,U_6839) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1838_2]) ).
fof(f_1838_4,plain,
( ! [U_6838,U_6840] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6840)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,U_6840)),U_6840)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,U_6840) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_6839,U_6837] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6837,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6839)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6837,U_6839) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_1838_3]) ).
cnf(f_1838_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6837,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6839)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6837,U_6839) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1838_4]) ).
cnf(f_1838_6,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6840)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,U_6840)),U_6840)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6838,U_6840) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1838_4]) ).
fof(f_1839_1,plain,
! [V_b,V_a] :
( ( 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))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if]) ).
fof(f_1839_2,plain,
! [U_6842,U_6841] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6841),U_6842) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6842),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6841,U_6842))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6841,U_6842) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6841),U_6842) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6841,U_6842) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1839_1]) ).
fof(f_1839_3,plain,
( ! [U_6846,U_6844] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6844),U_6846) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6846),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6844,U_6846))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6844,U_6846) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_6845,U_6843] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6843),U_6845) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6843,U_6845) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1839_2]) ).
fof(f_1839_4,plain,
( ! [U_6846,U_6844] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6844),U_6846) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6846),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6844,U_6846))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6844,U_6846) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_6843,U_6845] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6843),U_6845) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6843,U_6845) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_1839_3]) ).
cnf(f_1839_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6843),U_6845) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6843,U_6845) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1839_4]) ).
cnf(f_1839_6,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6844),U_6846) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6846),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6844,U_6846))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6844,U_6846) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1839_4]) ).
fof(f_1840_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__equality]) ).
fof(f_1840_2,plain,
! [U_6848,U_6847] : U_6847 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6848),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6847),U_6848))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6847,U_6848)),
inference(variable_rename,[status(thm)],[f_1840_1]) ).
fof(f_1840_3,plain,
! [U_6848,U_6847] : U_6847 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6848),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6847),U_6848))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6847,U_6848)),
inference(definitional_conversion,[status(esa)],[f_1840_2]) ).
cnf(f_1840_4,plain,
U_6847 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6848),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6847),U_6848))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6847,U_6848)),
inference(clausify,[status(thm)],[f_1840_3]) ).
fof(f_1841_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zdiv__zmult1__eq]) ).
fof(f_1841_2,plain,
! [U_6851,U_6850,U_6849] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),U_6850)),U_6851) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6850),U_6851))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6850,U_6851))),U_6851)),
inference(variable_rename,[status(thm)],[f_1841_1]) ).
fof(f_1841_3,plain,
! [U_6849,U_6850,U_6851] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),U_6850)),U_6851) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6850),U_6851))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6850,U_6851))),U_6851)),
inference(definitional_conversion,[status(esa)],[f_1841_2]) ).
cnf(f_1841_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),U_6850)),U_6851) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6850),U_6851))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6849),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6850,U_6851))),U_6851)),
inference(clausify,[status(thm)],[f_1841_3]) ).
fof(f_1842_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zdiv__zmod__equality]) ).
fof(f_1842_2,plain,
! [U_6854,U_6853,U_6852] : 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),U_6852),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6853),U_6852))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6853,U_6852))),U_6854) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6853),U_6854),
inference(variable_rename,[status(thm)],[f_1842_1]) ).
fof(f_1842_3,plain,
! [U_6852,U_6853,U_6854] : 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),U_6852),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6853),U_6852))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6853,U_6852))),U_6854) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6853),U_6854),
inference(definitional_conversion,[status(esa)],[f_1842_2]) ).
cnf(f_1842_4,plain,
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),U_6852),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6853),U_6852))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6853,U_6852))),U_6854) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6853),U_6854),
inference(clausify,[status(thm)],[f_1842_3]) ).
fof(f_1843_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zdiv__zmod__equality2]) ).
fof(f_1843_2,plain,
! [U_6857,U_6856,U_6855] : 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),U_6855),U_6856)),U_6856)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6855,U_6856))),U_6857) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6855),U_6857),
inference(variable_rename,[status(thm)],[f_1843_1]) ).
fof(f_1843_3,plain,
! [U_6855,U_6856,U_6857] : 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),U_6855),U_6856)),U_6856)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6855,U_6856))),U_6857) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6855),U_6857),
inference(definitional_conversion,[status(esa)],[f_1843_2]) ).
cnf(f_1843_4,plain,
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),U_6855),U_6856)),U_6856)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6855,U_6856))),U_6857) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6855),U_6857),
inference(clausify,[status(thm)],[f_1843_3]) ).
fof(f_1844_1,plain,
! [V_n,V_m] :
( V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| V_m = c_Groups_Oone__class_Oone(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) ),
inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff__lemma]) ).
fof(f_1844_2,plain,
! [U_6859,U_6858] :
( U_6858 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_6858 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6858),U_6859) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1844_1]) ).
fof(f_1844_3,plain,
! [U_6858,U_6859] :
( U_6858 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_6858 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6858),U_6859) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_1844_2]) ).
cnf(f_1844_4,plain,
( U_6858 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_6858 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6858),U_6859) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1844_3]) ).
fof(f_1845_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( V_n_2 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| V_m_2 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( ( V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff]) ).
fof(f_1845_2,plain,
! [U_6861,U_6860] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6860),U_6861) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_6861 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_6860 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( U_6861 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6860 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( ( U_6861 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& U_6860 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( U_6861 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_6860 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6860),U_6861) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1845_1]) ).
fof(f_1845_3,plain,
( ! [U_6865,U_6863] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6863),U_6865) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_6865 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_6863 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( U_6865 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6863 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ! [U_6864,U_6862] :
( ( U_6864 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& U_6862 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( U_6864 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_6862 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6862),U_6864) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1845_2]) ).
fof(f_1845_4,plain,
( ! [U_6863,U_6865] :
( U_6865 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_6863 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP609(U_6863,U_6865) )
& ! [U_6863,U_6865] :
( U_6865 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6863 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP609(U_6863,U_6865) )
& ! [U_6862,U_6864] :
( U_6864 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP608(U_6862,U_6864) )
& ! [U_6862,U_6864] :
( U_6862 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP608(U_6862,U_6864) )
& ! [U_6862,U_6864] :
( U_6864 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP607(U_6862,U_6864) )
& ! [U_6862,U_6864] :
( U_6862 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP607(U_6862,U_6864) )
& ! [U_6863,U_6865] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6863),U_6865) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| sP609(U_6863,U_6865) )
& ! [U_6862,U_6864] :
( sP608(U_6862,U_6864)
| sP607(U_6862,U_6864)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6862),U_6864) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP607,sP608,sP609])],[f_1845_3]) ).
cnf(f_1845_5,plain,
( sP608(U_6862,U_6864)
| sP607(U_6862,U_6864)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6862),U_6864) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1845_4]) ).
cnf(f_1845_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6863),U_6865) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| sP609(U_6863,U_6865) ),
inference(clausify,[status(thm)],[f_1845_4]) ).
cnf(f_1845_7,plain,
( U_6862 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP607(U_6862,U_6864) ),
inference(clausify,[status(thm)],[f_1845_4]) ).
cnf(f_1845_8,plain,
( U_6864 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP607(U_6862,U_6864) ),
inference(clausify,[status(thm)],[f_1845_4]) ).
cnf(f_1845_9,plain,
( U_6862 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP608(U_6862,U_6864) ),
inference(clausify,[status(thm)],[f_1845_4]) ).
cnf(f_1845_10,plain,
( U_6864 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP608(U_6862,U_6864) ),
inference(clausify,[status(thm)],[f_1845_4]) ).
cnf(f_1845_11,plain,
( U_6865 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6863 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP609(U_6863,U_6865) ),
inference(clausify,[status(thm)],[f_1845_4]) ).
cnf(f_1845_12,plain,
( U_6865 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_6863 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP609(U_6863,U_6865) ),
inference(clausify,[status(thm)],[f_1845_4]) ).
fof(f_1846_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmult__div__cancel]) ).
fof(f_1846_2,plain,
! [U_6867,U_6866] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6866),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6867),U_6866)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6867),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6867,U_6866)),
inference(variable_rename,[status(thm)],[f_1846_1]) ).
fof(f_1846_3,plain,
! [U_6867,U_6866] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6866),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6867),U_6866)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6867),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6867,U_6866)),
inference(definitional_conversion,[status(esa)],[f_1846_2]) ).
cnf(f_1846_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6866),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6867),U_6866)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6867),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6867,U_6866)),
inference(clausify,[status(thm)],[f_1846_3]) ).
fof(f_1847_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__equality_H]) ).
fof(f_1847_2,plain,
! [U_6869,U_6868] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6868,U_6869) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6868),U_6869)),U_6869)),
inference(variable_rename,[status(thm)],[f_1847_1]) ).
fof(f_1847_3,plain,
! [U_6869,U_6868] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6868,U_6869) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6868),U_6869)),U_6869)),
inference(definitional_conversion,[status(esa)],[f_1847_2]) ).
cnf(f_1847_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6868,U_6869) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6868),U_6869)),U_6869)),
inference(clausify,[status(thm)],[f_1847_3]) ).
fof(f_1848_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_zdiv__minus1__right]) ).
fof(f_1848_2,plain,
! [U_6870] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6870),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6870),
inference(variable_rename,[status(thm)],[f_1848_1]) ).
fof(f_1848_3,plain,
! [U_6870] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6870),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6870),
inference(definitional_conversion,[status(esa)],[f_1848_2]) ).
cnf(f_1848_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6870),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6870),
inference(clausify,[status(thm)],[f_1848_3]) ).
fof(f_1849_1,plain,
! [V_v] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ),
inference(fof_nnf,[status(thm)],[fact_neg__imp__number__of__eq__0]) ).
fof(f_1849_2,plain,
! [U_6871] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6871) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6871))) ),
inference(variable_rename,[status(thm)],[f_1849_1]) ).
fof(f_1849_3,plain,
! [U_6871] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6871) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6871))) ),
inference(definitional_conversion,[status(esa)],[f_1849_2]) ).
cnf(f_1849_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6871) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6871))) ),
inference(clausify,[status(thm)],[f_1849_3]) ).
fof(f_1850_1,plain,
! [V_v] :
( ( 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)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
inference(fof_nnf,[status(thm)],[fact_int__nat__number__of]) ).
fof(f_1850_2,plain,
! [U_6872] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6872)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6872)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6872))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6872)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6872))) ) ),
inference(variable_rename,[status(thm)],[f_1850_1]) ).
fof(f_1850_3,plain,
( ! [U_6874] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6874)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6874)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6874))) )
& ! [U_6873] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6873)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6873))) ) ),
inference(miniscope,[status(thm)],[f_1850_2]) ).
fof(f_1850_4,plain,
( ! [U_6874] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6874)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6874)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6874))) )
& ! [U_6873] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6873)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6873))) ) ),
inference(definitional_conversion,[status(esa)],[f_1850_3]) ).
cnf(f_1850_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6873)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6873))) ),
inference(clausify,[status(thm)],[f_1850_4]) ).
cnf(f_1850_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6874)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6874)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6874))) ),
inference(clausify,[status(thm)],[f_1850_4]) ).
fof(f_1851_1,plain,
! [V_m,V_n] :
( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__geq]) ).
fof(f_1851_2,plain,
! [U_6876,U_6875] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6876),U_6875) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6876),U_6875)),U_6875))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6876),U_6875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6875)) ),
inference(variable_rename,[status(thm)],[f_1851_1]) ).
fof(f_1851_3,plain,
! [U_6876,U_6875] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6876),U_6875) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6876),U_6875)),U_6875))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6876),U_6875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6875)) ),
inference(definitional_conversion,[status(esa)],[f_1851_2]) ).
cnf(f_1851_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6876),U_6875) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6876),U_6875)),U_6875))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6876),U_6875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6875)) ),
inference(clausify,[status(thm)],[f_1851_3]) ).
fof(f_1852_1,plain,
! [V_m,V_n] :
( ( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__if]) ).
fof(f_1852_2,plain,
! [U_6878,U_6877] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6878),U_6877) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6878),U_6877)),U_6877))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6878),U_6877)) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6878),U_6877) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6878),U_6877)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6877)) ),
inference(variable_rename,[status(thm)],[f_1852_1]) ).
fof(f_1852_3,plain,
( ! [U_6877,U_6878] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6878),U_6877) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6878),U_6877)),U_6877))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6878),U_6877))
| ~ sP610(U_6877,U_6878) )
& ! [U_6877,U_6878] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6878),U_6877) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6878),U_6877))
| ~ sP610(U_6877,U_6878) )
& ! [U_6877,U_6878] :
( sP610(U_6877,U_6878)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6877)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP610])],[f_1852_2]) ).
cnf(f_1852_4,plain,
( sP610(U_6877,U_6878)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6877)) ),
inference(clausify,[status(thm)],[f_1852_3]) ).
cnf(f_1852_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6878),U_6877) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6878),U_6877))
| ~ sP610(U_6877,U_6878) ),
inference(clausify,[status(thm)],[f_1852_3]) ).
cnf(f_1852_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6878),U_6877) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6878),U_6877)),U_6877))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6878),U_6877))
| ~ sP610(U_6877,U_6878) ),
inference(clausify,[status(thm)],[f_1852_3]) ).
fof(f_1853_1,plain,
! [V_k_2,V_n_2,V_Pa_2] :
( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_Pa_2,B_i))
& 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_Pa_2,B_i))
| 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div]) ).
fof(f_1853_2,plain,
! [U_6885,U_6884,U_6883] :
( ( hBOOL(hAPP(U_6883,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6884),U_6885)))
| ( ? [U_6882,U_6881] :
( ~ hBOOL(hAPP(U_6883,U_6882))
& U_6884 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6885),U_6882)),U_6881)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6881),U_6885)) )
& U_6885 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_6883,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_6885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_6880,U_6879] :
( hBOOL(hAPP(U_6883,U_6880))
| U_6884 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6885),U_6880)),U_6879)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6879),U_6885)) )
| U_6885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_6883,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6885 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_6883,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6884),U_6885))) ) ),
inference(variable_rename,[status(thm)],[f_1853_1]) ).
fof(f_1853_3,plain,
( ! [U_6891,U_6889,U_6887] :
( hBOOL(hAPP(U_6887,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6889),U_6891)))
| ( ? [U_6882,U_6881] :
( ~ hBOOL(hAPP(U_6887,U_6882))
& U_6889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6891),U_6882)),U_6881)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6881),U_6891)) )
& U_6891 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_6887,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_6891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6890,U_6888,U_6886] :
( ( ( ! [U_6880,U_6879] :
( hBOOL(hAPP(U_6886,U_6880))
| U_6888 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6890),U_6880)),U_6879)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6879),U_6890)) )
| U_6890 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_6886,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6890 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_6886,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6888),U_6890))) ) ),
inference(miniscope,[status(thm)],[f_1853_2]) ).
fof(f_1853_4,plain,
( ! [U_6891,U_6889,U_6887] :
( hBOOL(hAPP(U_6887,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6889),U_6891)))
| ( ? [U_6881] :
( ~ hBOOL(hAPP(U_6887,sK190(U_6891,U_6889,U_6887)))
& U_6889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6891),sK190(U_6891,U_6889,U_6887))),U_6881)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6881),U_6891)) )
& U_6891 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_6887,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_6891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6890,U_6888,U_6886] :
( ( ( ! [U_6880,U_6879] :
( hBOOL(hAPP(U_6886,U_6880))
| U_6888 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6890),U_6880)),U_6879)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6879),U_6890)) )
| U_6890 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_6886,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6890 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_6886,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6888),U_6890))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_6882,sK190(U_6891,U_6889,U_6887))],[f_1853_3]) ).
fof(f_1853_5,plain,
( ! [U_6891,U_6889,U_6887] :
( hBOOL(hAPP(U_6887,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6889),U_6891)))
| ( ~ hBOOL(hAPP(U_6887,sK190(U_6891,U_6889,U_6887)))
& U_6889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6891),sK190(U_6891,U_6889,U_6887))),sK191(U_6891,U_6889,U_6887))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK191(U_6891,U_6889,U_6887)),U_6891))
& U_6891 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_6887,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_6891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6890,U_6888,U_6886] :
( ( ( ! [U_6880,U_6879] :
( hBOOL(hAPP(U_6886,U_6880))
| U_6888 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6890),U_6880)),U_6879)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6879),U_6890)) )
| U_6890 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_6886,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6890 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_6886,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6888),U_6890))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_6881,sK191(U_6891,U_6889,U_6887))],[f_1853_4]) ).
fof(f_1853_6,plain,
( ! [U_6887,U_6889,U_6891] :
( ~ hBOOL(hAPP(U_6887,sK190(U_6891,U_6889,U_6887)))
| ~ sP613(U_6887,U_6889,U_6891) )
& ! [U_6887,U_6889,U_6891] :
( U_6889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6891),sK190(U_6891,U_6889,U_6887))),sK191(U_6891,U_6889,U_6887))
| ~ sP613(U_6887,U_6889,U_6891) )
& ! [U_6887,U_6889,U_6891] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK191(U_6891,U_6889,U_6887)),U_6891))
| ~ sP613(U_6887,U_6889,U_6891) )
& ! [U_6887,U_6889,U_6891] :
( U_6891 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP613(U_6887,U_6889,U_6891) )
& ! [U_6887,U_6891] :
( ~ hBOOL(hAPP(U_6887,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP612(U_6887,U_6891) )
& ! [U_6887,U_6891] :
( U_6891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP612(U_6887,U_6891) )
& ! [U_6879,U_6880,U_6886,U_6888,U_6890] :
( hBOOL(hAPP(U_6886,U_6880))
| U_6888 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6890),U_6880)),U_6879)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6879),U_6890))
| U_6890 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP611(U_6879,U_6880,U_6886,U_6888,U_6890) )
& ! [U_6879,U_6880,U_6886,U_6888,U_6890] :
( hBOOL(hAPP(U_6886,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6890 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP611(U_6879,U_6880,U_6886,U_6888,U_6890) )
& ! [U_6887,U_6889,U_6891] :
( hBOOL(hAPP(U_6887,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6889),U_6891)))
| sP613(U_6887,U_6889,U_6891)
| sP612(U_6887,U_6891) )
& ! [U_6879,U_6880,U_6886,U_6888,U_6890] :
( sP611(U_6879,U_6880,U_6886,U_6888,U_6890)
| ~ hBOOL(hAPP(U_6886,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6888),U_6890))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP611,sP612,sP613])],[f_1853_5]) ).
cnf(f_1853_7,plain,
( sP611(U_6879,U_6880,U_6886,U_6888,U_6890)
| ~ hBOOL(hAPP(U_6886,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6888),U_6890))) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_8,plain,
( hBOOL(hAPP(U_6887,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6889),U_6891)))
| sP613(U_6887,U_6889,U_6891)
| sP612(U_6887,U_6891) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_9,plain,
( hBOOL(hAPP(U_6886,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6890 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP611(U_6879,U_6880,U_6886,U_6888,U_6890) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_10,plain,
( hBOOL(hAPP(U_6886,U_6880))
| U_6888 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6890),U_6880)),U_6879)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6879),U_6890))
| U_6890 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP611(U_6879,U_6880,U_6886,U_6888,U_6890) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_11,plain,
( U_6891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP612(U_6887,U_6891) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_12,plain,
( ~ hBOOL(hAPP(U_6887,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP612(U_6887,U_6891) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_13,plain,
( U_6891 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP613(U_6887,U_6889,U_6891) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_14,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK191(U_6891,U_6889,U_6887)),U_6891))
| ~ sP613(U_6887,U_6889,U_6891) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_15,plain,
( U_6889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6891),sK190(U_6891,U_6889,U_6887))),sK191(U_6891,U_6889,U_6887))
| ~ sP613(U_6887,U_6889,U_6891) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
cnf(f_1853_16,plain,
( ~ hBOOL(hAPP(U_6887,sK190(U_6891,U_6889,U_6887)))
| ~ sP613(U_6887,U_6889,U_6891) ),
inference(clausify,[status(thm)],[f_1853_6]) ).
fof(f_1854_1,plain,
! [V_b,V_a] :
( 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)
| ~ 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial]) ).
fof(f_1854_2,plain,
! [U_6893,U_6892] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6892,U_6893) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6892),U_6893)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6892),U_6893)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
inference(variable_rename,[status(thm)],[f_1854_1]) ).
fof(f_1854_3,plain,
! [U_6893,U_6892] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6892,U_6893) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6892),U_6893)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6892),U_6893)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
inference(definitional_conversion,[status(esa)],[f_1854_2]) ).
cnf(f_1854_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6892,U_6893) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6892),U_6893)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6892),U_6893)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
inference(clausify,[status(thm)],[f_1854_3]) ).
fof(f_1855_1,plain,
! [V_x,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus1__divide]) ).
fof(f_1855_2,plain,
! [U_6895,U_6894] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6894),hAPP(c_Int_Onumber__class_Onumber__of(U_6894),c_Int_OMin)),U_6895) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6894),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6894),c_Groups_Oone__class_Oone(U_6894)),U_6895))
| ~ class_Int_Onumber__ring(U_6894)
| ~ class_Fields_Ofield__inverse__zero(U_6894) ),
inference(variable_rename,[status(thm)],[f_1855_1]) ).
fof(f_1855_3,plain,
! [U_6895,U_6894] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6894),hAPP(c_Int_Onumber__class_Onumber__of(U_6894),c_Int_OMin)),U_6895) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6894),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6894),c_Groups_Oone__class_Oone(U_6894)),U_6895))
| ~ class_Int_Onumber__ring(U_6894)
| ~ class_Fields_Ofield__inverse__zero(U_6894) ),
inference(definitional_conversion,[status(esa)],[f_1855_2]) ).
cnf(f_1855_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6894),hAPP(c_Int_Onumber__class_Onumber__of(U_6894),c_Int_OMin)),U_6895) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6894),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6894),c_Groups_Oone__class_Oone(U_6894)),U_6895))
| ~ class_Int_Onumber__ring(U_6894)
| ~ class_Fields_Ofield__inverse__zero(U_6894) ),
inference(clausify,[status(thm)],[f_1855_3]) ).
fof(f_1856_1,plain,
! [V_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_div__eq__minus1]) ).
fof(f_1856_2,plain,
! [U_6896] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_6896) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6896)) ),
inference(variable_rename,[status(thm)],[f_1856_1]) ).
fof(f_1856_3,plain,
! [U_6896] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_6896) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6896)) ),
inference(definitional_conversion,[status(esa)],[f_1856_2]) ).
cnf(f_1856_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_6896) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6896)) ),
inference(clausify,[status(thm)],[f_1856_3]) ).
fof(f_1857_1,plain,
! [V_m,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__div__geq]) ).
fof(f_1857_2,plain,
! [U_6898,U_6897] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6898),U_6897) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6898),U_6897)),U_6897))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6897),U_6898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6897)) ),
inference(variable_rename,[status(thm)],[f_1857_1]) ).
fof(f_1857_3,plain,
! [U_6897,U_6898] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6898),U_6897) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6898),U_6897)),U_6897))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6897),U_6898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6897)) ),
inference(definitional_conversion,[status(esa)],[f_1857_2]) ).
cnf(f_1857_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6898),U_6897) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6898),U_6897)),U_6897))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6897),U_6898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6897)) ),
inference(clausify,[status(thm)],[f_1857_3]) ).
fof(f_1858_1,plain,
! [V_m_2,V_q_2,V_n_2] :
( ( ( ( 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))))
& 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)) )
| V_q_2 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) )
& ( V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)
| ~ 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))))
| ~ 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)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
inference(fof_nnf,[status(thm)],[fact_split__div__lemma]) ).
fof(f_1858_2,plain,
! [U_6901,U_6900,U_6899] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),hAPP(c_Nat_OSuc,U_6900))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),U_6900)),U_6901)) )
| U_6900 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6901),U_6899) )
& ( U_6900 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6901),U_6899)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),hAPP(c_Nat_OSuc,U_6900))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),U_6900)),U_6901)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6899)) ),
inference(variable_rename,[status(thm)],[f_1858_1]) ).
fof(f_1858_3,plain,
( ! [U_6899,U_6900,U_6901] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),hAPP(c_Nat_OSuc,U_6900))))
| ~ sP614(U_6899,U_6900,U_6901) )
& ! [U_6899,U_6900,U_6901] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),U_6900)),U_6901))
| ~ sP614(U_6899,U_6900,U_6901) )
& ! [U_6899,U_6900,U_6901] :
( sP614(U_6899,U_6900,U_6901)
| U_6900 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6901),U_6899)
| ~ sP615(U_6899,U_6900,U_6901) )
& ! [U_6899,U_6900,U_6901] :
( U_6900 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6901),U_6899)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),hAPP(c_Nat_OSuc,U_6900))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),U_6900)),U_6901))
| ~ sP615(U_6899,U_6900,U_6901) )
& ! [U_6899,U_6900,U_6901] :
( sP615(U_6899,U_6900,U_6901)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6899)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP614,sP615])],[f_1858_2]) ).
cnf(f_1858_4,plain,
( sP615(U_6899,U_6900,U_6901)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6899)) ),
inference(clausify,[status(thm)],[f_1858_3]) ).
cnf(f_1858_5,plain,
( U_6900 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6901),U_6899)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),hAPP(c_Nat_OSuc,U_6900))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),U_6900)),U_6901))
| ~ sP615(U_6899,U_6900,U_6901) ),
inference(clausify,[status(thm)],[f_1858_3]) ).
cnf(f_1858_6,plain,
( sP614(U_6899,U_6900,U_6901)
| U_6900 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6901),U_6899)
| ~ sP615(U_6899,U_6900,U_6901) ),
inference(clausify,[status(thm)],[f_1858_3]) ).
cnf(f_1858_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),U_6900)),U_6901))
| ~ sP614(U_6899,U_6900,U_6901) ),
inference(clausify,[status(thm)],[f_1858_3]) ).
cnf(f_1858_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6899),hAPP(c_Nat_OSuc,U_6900))))
| ~ sP614(U_6899,U_6900,U_6901) ),
inference(clausify,[status(thm)],[f_1858_3]) ).
fof(f_1859_1,plain,
! [V_n_2,V_m_2,V_Pa_2] :
( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
| ( ! [B_q] :
( ~ hBOOL(hAPP(V_Pa_2,B_q))
| ~ 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))))
| ~ 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)) )
& ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [B_q] :
( hBOOL(hAPP(V_Pa_2,B_q))
& 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))))
& 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)) )
| ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).
fof(f_1859_2,plain,
! [U_6906,U_6905,U_6904] :
( ( hBOOL(hAPP(U_6904,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6905),U_6906)))
| ( ! [U_6903] :
( ~ hBOOL(hAPP(U_6904,U_6903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6906),hAPP(c_Nat_OSuc,U_6903))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6906),U_6903)),U_6905)) )
& ( ~ hBOOL(hAPP(U_6904,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6906 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [U_6902] :
( hBOOL(hAPP(U_6904,U_6902))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6906),hAPP(c_Nat_OSuc,U_6902))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6906),U_6902)),U_6905)) )
| ( hBOOL(hAPP(U_6904,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_6906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_6904,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6905),U_6906))) ) ),
inference(variable_rename,[status(thm)],[f_1859_1]) ).
fof(f_1859_3,plain,
( ! [U_6912,U_6910,U_6908] :
( hBOOL(hAPP(U_6908,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6910),U_6912)))
| ( ! [U_6903] :
( ~ hBOOL(hAPP(U_6908,U_6903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6912),hAPP(c_Nat_OSuc,U_6903))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6912),U_6903)),U_6910)) )
& ( ~ hBOOL(hAPP(U_6908,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6912 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_6911,U_6909,U_6907] :
( ? [U_6902] :
( hBOOL(hAPP(U_6907,U_6902))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6911),hAPP(c_Nat_OSuc,U_6902))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6911),U_6902)),U_6909)) )
| ( hBOOL(hAPP(U_6907,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_6911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_6907,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6909),U_6911))) ) ),
inference(miniscope,[status(thm)],[f_1859_2]) ).
fof(f_1859_4,plain,
( ! [U_6912,U_6910,U_6908] :
( hBOOL(hAPP(U_6908,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6910),U_6912)))
| ( ! [U_6903] :
( ~ hBOOL(hAPP(U_6908,U_6903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6912),hAPP(c_Nat_OSuc,U_6903))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6912),U_6903)),U_6910)) )
& ( ~ hBOOL(hAPP(U_6908,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6912 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_6911,U_6909,U_6907] :
( ( hBOOL(hAPP(U_6907,sK192(U_6911,U_6909,U_6907)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6911),hAPP(c_Nat_OSuc,sK192(U_6911,U_6909,U_6907)))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6911),sK192(U_6911,U_6909,U_6907))),U_6909)) )
| ( hBOOL(hAPP(U_6907,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_6911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_6907,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6909),U_6911))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_6902,sK192(U_6911,U_6909,U_6907))],[f_1859_3]) ).
fof(f_1859_5,plain,
( ! [U_6903,U_6910,U_6908,U_6912] :
( ~ hBOOL(hAPP(U_6908,U_6903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6912),hAPP(c_Nat_OSuc,U_6903))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6912),U_6903)),U_6910))
| ~ sP618(U_6903,U_6910,U_6908,U_6912) )
& ! [U_6903,U_6910,U_6908,U_6912] :
( ~ hBOOL(hAPP(U_6908,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6912 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP618(U_6903,U_6910,U_6908,U_6912) )
& ! [U_6911,U_6907,U_6909] :
( hBOOL(hAPP(U_6907,sK192(U_6911,U_6909,U_6907)))
| ~ sP617(U_6911,U_6907,U_6909) )
& ! [U_6911,U_6907,U_6909] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6911),hAPP(c_Nat_OSuc,sK192(U_6911,U_6909,U_6907)))))
| ~ sP617(U_6911,U_6907,U_6909) )
& ! [U_6911,U_6907,U_6909] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6911),sK192(U_6911,U_6909,U_6907))),U_6909))
| ~ sP617(U_6911,U_6907,U_6909) )
& ! [U_6911,U_6907] :
( hBOOL(hAPP(U_6907,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP616(U_6911,U_6907) )
& ! [U_6911,U_6907] :
( U_6911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP616(U_6911,U_6907) )
& ! [U_6903,U_6910,U_6908,U_6912] :
( hBOOL(hAPP(U_6908,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6910),U_6912)))
| sP618(U_6903,U_6910,U_6908,U_6912) )
& ! [U_6911,U_6907,U_6909] :
( sP617(U_6911,U_6907,U_6909)
| sP616(U_6911,U_6907)
| ~ hBOOL(hAPP(U_6907,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6909),U_6911))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP616,sP617,sP618])],[f_1859_4]) ).
cnf(f_1859_6,plain,
( sP617(U_6911,U_6907,U_6909)
| sP616(U_6911,U_6907)
| ~ hBOOL(hAPP(U_6907,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6909),U_6911))) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
cnf(f_1859_7,plain,
( hBOOL(hAPP(U_6908,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6910),U_6912)))
| sP618(U_6903,U_6910,U_6908,U_6912) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
cnf(f_1859_8,plain,
( U_6911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP616(U_6911,U_6907) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
cnf(f_1859_9,plain,
( hBOOL(hAPP(U_6907,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP616(U_6911,U_6907) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
cnf(f_1859_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6911),sK192(U_6911,U_6909,U_6907))),U_6909))
| ~ sP617(U_6911,U_6907,U_6909) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
cnf(f_1859_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6911),hAPP(c_Nat_OSuc,sK192(U_6911,U_6909,U_6907)))))
| ~ sP617(U_6911,U_6907,U_6909) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
cnf(f_1859_12,plain,
( hBOOL(hAPP(U_6907,sK192(U_6911,U_6909,U_6907)))
| ~ sP617(U_6911,U_6907,U_6909) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
cnf(f_1859_13,plain,
( ~ hBOOL(hAPP(U_6908,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6912 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP618(U_6903,U_6910,U_6908,U_6912) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
cnf(f_1859_14,plain,
( ~ hBOOL(hAPP(U_6908,U_6903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6912),hAPP(c_Nat_OSuc,U_6903))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6912),U_6903)),U_6910))
| ~ sP618(U_6903,U_6910,U_6908,U_6912) ),
inference(clausify,[status(thm)],[f_1859_5]) ).
fof(f_1860_1,plain,
! [V_v_H_2,V_v_2] :
( ( 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)
| ( ( ( V_v_2 != V_v_H_2
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) )
| ( ~ 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)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) )
& ( ( ( ( ( V_v_2 = V_v_H_2
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) )
& ( 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)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) )
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__nat__number__of]) ).
fof(f_1860_2,plain,
! [U_6914,U_6913] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6913) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6914)
| ( ( ( U_6913 != U_6914
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6914))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6913) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6914))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6913))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6914)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6913))) ) )
& ( ( ( ( ( U_6913 = U_6914
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6914))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6913) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6914))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6913))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6914)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6913))) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6913) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6914) ) ),
inference(variable_rename,[status(thm)],[f_1860_1]) ).
fof(f_1860_3,plain,
( ! [U_6918,U_6916] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6916) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6918)
| ( ( ( U_6916 != U_6918
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916))) ) )
& ! [U_6917,U_6915] :
( ( ( ( ( U_6915 = U_6917
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915))) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6915) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6917) ) ),
inference(miniscope,[status(thm)],[f_1860_2]) ).
fof(f_1860_4,plain,
( ! [U_6918,U_6916] :
( U_6916 != U_6918
| ~ sP623(U_6918,U_6916) )
& ! [U_6918,U_6916] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918)))
| ~ sP623(U_6918,U_6916) )
& ! [U_6918,U_6916] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP622(U_6918,U_6916) )
& ! [U_6918,U_6916] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918)))
| ~ sP622(U_6918,U_6916) )
& ! [U_6918,U_6916] :
( sP623(U_6918,U_6916)
| sP622(U_6918,U_6916)
| ~ sP624(U_6918,U_6916) )
& ! [U_6918,U_6916] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916)))
| ~ sP624(U_6918,U_6916) )
& ! [U_6918,U_6916] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP621(U_6918,U_6916) )
& ! [U_6918,U_6916] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916)))
| ~ sP621(U_6918,U_6916) )
& ! [U_6917,U_6915] :
( U_6915 = U_6917
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917)))
| ~ sP619(U_6917,U_6915) )
& ! [U_6917,U_6915] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917)))
| ~ sP619(U_6917,U_6915) )
& ! [U_6917,U_6915] :
( sP619(U_6917,U_6915)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915)))
| ~ sP620(U_6917,U_6915) )
& ! [U_6917,U_6915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915)))
| ~ sP620(U_6917,U_6915) )
& ! [U_6918,U_6916] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6916) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6918)
| sP624(U_6918,U_6916)
| sP621(U_6918,U_6916) )
& ! [U_6917,U_6915] :
( sP620(U_6917,U_6915)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6915) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6917) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP619,sP620,sP621,sP622,sP623,sP624])],[f_1860_3]) ).
cnf(f_1860_5,plain,
( sP620(U_6917,U_6915)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6915) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6917) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6916) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6918)
| sP624(U_6918,U_6916)
| sP621(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915)))
| ~ sP620(U_6917,U_6915) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_8,plain,
( sP619(U_6917,U_6915)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915)))
| ~ sP620(U_6917,U_6915) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_9,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6915) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917)))
| ~ sP619(U_6917,U_6915) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_10,plain,
( U_6915 = U_6917
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6917)))
| ~ sP619(U_6917,U_6915) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_11,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916)))
| ~ sP621(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP621(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_13,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916)))
| ~ sP624(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_14,plain,
( sP623(U_6918,U_6916)
| sP622(U_6918,U_6916)
| ~ sP624(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_15,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918)))
| ~ sP622(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_16,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6916) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP622(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_17,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6918)))
| ~ sP623(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
cnf(f_1860_18,plain,
( U_6916 != U_6918
| ~ sP623(U_6918,U_6916) ),
inference(clausify,[status(thm)],[f_1860_4]) ).
fof(f_1861_1,plain,
! [V_k,V_v_H,V_v] :
( ( ( ( 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)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__left]) ).
fof(f_1861_2,plain,
! [U_6921,U_6920,U_6919] :
( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6920)),U_6921)) = 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),U_6919),U_6920))),U_6921)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6920))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6920)),U_6921)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6919)),U_6921)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6920))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6919))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6920)),U_6921)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6920)),U_6921)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6919))) ) ),
inference(variable_rename,[status(thm)],[f_1861_1]) ).
fof(f_1861_3,plain,
( ! [U_6927,U_6925,U_6923] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6925)),U_6927)) = 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),U_6923),U_6925))),U_6927)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6925))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6925)),U_6927)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),U_6927)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6925))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6923))) )
& ! [U_6926,U_6924,U_6922] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6924)),U_6926)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6924)),U_6926)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6922))) ) ),
inference(miniscope,[status(thm)],[f_1861_2]) ).
fof(f_1861_4,plain,
( ! [U_6925,U_6927,U_6923] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6925)),U_6927)) = 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),U_6923),U_6925))),U_6927)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6925)))
| ~ sP625(U_6925,U_6927,U_6923) )
& ! [U_6925,U_6927,U_6923] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6925)),U_6927)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),U_6927)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6925)))
| ~ sP625(U_6925,U_6927,U_6923) )
& ! [U_6925,U_6927,U_6923] :
( sP625(U_6925,U_6927,U_6923)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6923))) )
& ! [U_6924,U_6926,U_6922] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6924)),U_6926)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6924)),U_6926)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6922))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP625])],[f_1861_3]) ).
cnf(f_1861_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6924)),U_6926)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6924)),U_6926)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6922))) ),
inference(clausify,[status(thm)],[f_1861_4]) ).
cnf(f_1861_6,plain,
( sP625(U_6925,U_6927,U_6923)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6923))) ),
inference(clausify,[status(thm)],[f_1861_4]) ).
cnf(f_1861_7,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6925)),U_6927)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),U_6927)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6925)))
| ~ sP625(U_6925,U_6927,U_6923) ),
inference(clausify,[status(thm)],[f_1861_4]) ).
cnf(f_1861_8,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6923)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6925)),U_6927)) = 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),U_6923),U_6925))),U_6927)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6925)))
| ~ sP625(U_6925,U_6927,U_6923) ),
inference(clausify,[status(thm)],[f_1861_4]) ).
fof(f_1862_1,plain,
! [V_k_2,V_n_2,V_Pa_2] :
( ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_Pa_2,B_j))
& 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_Pa_2,B_j))
& 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
| ( ~ hBOOL(hAPP(V_Pa_2,V_n_2))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_Pa_2,B_j))
| 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [B_i,B_j] :
( hBOOL(hAPP(V_Pa_2,B_j))
| 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
& ( hBOOL(hAPP(V_Pa_2,V_n_2))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zmod]) ).
fof(f_1862_2,plain,
! [U_6938,U_6937,U_6936] :
( ( hBOOL(hAPP(U_6936,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6937,U_6938)))
| ( ? [U_6935,U_6934] :
( ~ hBOOL(hAPP(U_6936,U_6934))
& U_6937 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6938),U_6935)),U_6934)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6934),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6938),U_6934)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6938),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6933,U_6932] :
( ~ hBOOL(hAPP(U_6936,U_6932))
& U_6937 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6938),U_6933)),U_6932)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6932),U_6938))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) )
| ( ~ hBOOL(hAPP(U_6936,U_6937))
& U_6938 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_6931,U_6930] :
( hBOOL(hAPP(U_6936,U_6930))
| U_6937 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6938),U_6931)),U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6938),U_6930)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6938),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6929,U_6928] :
( hBOOL(hAPP(U_6936,U_6928))
| U_6937 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6938),U_6929)),U_6928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6928),U_6938))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6928)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) )
& ( hBOOL(hAPP(U_6936,U_6937))
| U_6938 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6936,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6937,U_6938))) ) ),
inference(variable_rename,[status(thm)],[f_1862_1]) ).
fof(f_1862_3,plain,
( ! [U_6944,U_6942,U_6940] :
( hBOOL(hAPP(U_6940,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6942,U_6944)))
| ( ? [U_6935,U_6934] :
( ~ hBOOL(hAPP(U_6940,U_6934))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),U_6935)),U_6934)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6934),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),U_6934)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6933,U_6932] :
( ~ hBOOL(hAPP(U_6940,U_6932))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),U_6933)),U_6932)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6932),U_6944))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) )
| ( ~ hBOOL(hAPP(U_6940,U_6942))
& U_6944 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6943,U_6941,U_6939] :
( ( ( ! [U_6931,U_6930] :
( hBOOL(hAPP(U_6939,U_6930))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6931)),U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),U_6930)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6929,U_6928] :
( hBOOL(hAPP(U_6939,U_6928))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6929)),U_6928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6928),U_6943))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6928)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6943)) )
& ( hBOOL(hAPP(U_6939,U_6941))
| U_6943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6939,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6941,U_6943))) ) ),
inference(miniscope,[status(thm)],[f_1862_2]) ).
fof(f_1862_4,plain,
( ! [U_6944,U_6942,U_6940] :
( hBOOL(hAPP(U_6940,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6942,U_6944)))
| ( ? [U_6935,U_6934] :
( ~ hBOOL(hAPP(U_6940,U_6934))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),U_6935)),U_6934)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6934),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),U_6934)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6932] :
( ~ hBOOL(hAPP(U_6940,U_6932))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK193(U_6944,U_6942,U_6940))),U_6932)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6932),U_6944))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) )
| ( ~ hBOOL(hAPP(U_6940,U_6942))
& U_6944 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6943,U_6941,U_6939] :
( ( ( ! [U_6931,U_6930] :
( hBOOL(hAPP(U_6939,U_6930))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6931)),U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),U_6930)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6929,U_6928] :
( hBOOL(hAPP(U_6939,U_6928))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6929)),U_6928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6928),U_6943))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6928)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6943)) )
& ( hBOOL(hAPP(U_6939,U_6941))
| U_6943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6939,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6941,U_6943))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_6933,sK193(U_6944,U_6942,U_6940))],[f_1862_3]) ).
fof(f_1862_5,plain,
( ! [U_6944,U_6942,U_6940] :
( hBOOL(hAPP(U_6940,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6942,U_6944)))
| ( ? [U_6935,U_6934] :
( ~ hBOOL(hAPP(U_6940,U_6934))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),U_6935)),U_6934)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6934),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),U_6934)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6940,sK194(U_6944,U_6942,U_6940)))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK193(U_6944,U_6942,U_6940))),sK194(U_6944,U_6942,U_6940))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK194(U_6944,U_6942,U_6940)),U_6944))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK194(U_6944,U_6942,U_6940)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) )
| ( ~ hBOOL(hAPP(U_6940,U_6942))
& U_6944 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6943,U_6941,U_6939] :
( ( ( ! [U_6931,U_6930] :
( hBOOL(hAPP(U_6939,U_6930))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6931)),U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),U_6930)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6929,U_6928] :
( hBOOL(hAPP(U_6939,U_6928))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6929)),U_6928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6928),U_6943))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6928)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6943)) )
& ( hBOOL(hAPP(U_6939,U_6941))
| U_6943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6939,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6941,U_6943))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_6932,sK194(U_6944,U_6942,U_6940))],[f_1862_4]) ).
fof(f_1862_6,plain,
( ! [U_6944,U_6942,U_6940] :
( hBOOL(hAPP(U_6940,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6942,U_6944)))
| ( ? [U_6934] :
( ~ hBOOL(hAPP(U_6940,U_6934))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK195(U_6944,U_6942,U_6940))),U_6934)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6934),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),U_6934)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6940,sK194(U_6944,U_6942,U_6940)))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK193(U_6944,U_6942,U_6940))),sK194(U_6944,U_6942,U_6940))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK194(U_6944,U_6942,U_6940)),U_6944))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK194(U_6944,U_6942,U_6940)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) )
| ( ~ hBOOL(hAPP(U_6940,U_6942))
& U_6944 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6943,U_6941,U_6939] :
( ( ( ! [U_6931,U_6930] :
( hBOOL(hAPP(U_6939,U_6930))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6931)),U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),U_6930)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6929,U_6928] :
( hBOOL(hAPP(U_6939,U_6928))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6929)),U_6928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6928),U_6943))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6928)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6943)) )
& ( hBOOL(hAPP(U_6939,U_6941))
| U_6943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6939,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6941,U_6943))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_6935,sK195(U_6944,U_6942,U_6940))],[f_1862_5]) ).
fof(f_1862_7,plain,
( ! [U_6944,U_6942,U_6940] :
( hBOOL(hAPP(U_6940,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6942,U_6944)))
| ( ~ hBOOL(hAPP(U_6940,sK196(U_6944,U_6942,U_6940)))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK195(U_6944,U_6942,U_6940))),sK196(U_6944,U_6942,U_6940))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK196(U_6944,U_6942,U_6940)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),sK196(U_6944,U_6942,U_6940)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6940,sK194(U_6944,U_6942,U_6940)))
& U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK193(U_6944,U_6942,U_6940))),sK194(U_6944,U_6942,U_6940))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK194(U_6944,U_6942,U_6940)),U_6944))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK194(U_6944,U_6942,U_6940)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) )
| ( ~ hBOOL(hAPP(U_6940,U_6942))
& U_6944 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6943,U_6941,U_6939] :
( ( ( ! [U_6931,U_6930] :
( hBOOL(hAPP(U_6939,U_6930))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6931)),U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),U_6930)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6929,U_6928] :
( hBOOL(hAPP(U_6939,U_6928))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6929)),U_6928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6928),U_6943))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6928)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6943)) )
& ( hBOOL(hAPP(U_6939,U_6941))
| U_6943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6939,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6941,U_6943))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_6934,sK196(U_6944,U_6942,U_6940))],[f_1862_6]) ).
fof(f_1862_8,plain,
( ! [U_6940,U_6944,U_6942] :
( ~ hBOOL(hAPP(U_6940,sK196(U_6944,U_6942,U_6940)))
| ~ sP629(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK195(U_6944,U_6942,U_6940))),sK196(U_6944,U_6942,U_6940))
| ~ sP629(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK196(U_6944,U_6942,U_6940)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP629(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),sK196(U_6944,U_6942,U_6940)))
| ~ sP629(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP629(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( ~ hBOOL(hAPP(U_6940,sK194(U_6944,U_6942,U_6940)))
| ~ sP628(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK193(U_6944,U_6942,U_6940))),sK194(U_6944,U_6942,U_6940))
| ~ sP628(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK194(U_6944,U_6942,U_6940)),U_6944))
| ~ sP628(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK194(U_6944,U_6942,U_6940)))
| ~ sP628(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944))
| ~ sP628(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( ~ hBOOL(hAPP(U_6940,U_6942))
| ~ sP627(U_6940,U_6944,U_6942) )
& ! [U_6940,U_6944,U_6942] :
( U_6944 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP627(U_6940,U_6944,U_6942) )
& ! [U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943] :
( hBOOL(hAPP(U_6939,U_6930))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6931)),U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),U_6930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP626(U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943) )
& ! [U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943] :
( hBOOL(hAPP(U_6939,U_6928))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6929)),U_6928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6928),U_6943))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6943))
| ~ sP626(U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943) )
& ! [U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943] :
( hBOOL(hAPP(U_6939,U_6941))
| U_6943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP626(U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943) )
& ! [U_6940,U_6944,U_6942] :
( hBOOL(hAPP(U_6940,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6942,U_6944)))
| sP629(U_6940,U_6944,U_6942)
| sP628(U_6940,U_6944,U_6942)
| sP627(U_6940,U_6944,U_6942) )
& ! [U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943] :
( sP626(U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943)
| ~ hBOOL(hAPP(U_6939,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6941,U_6943))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP626,sP627,sP628,sP629])],[f_1862_7]) ).
cnf(f_1862_9,plain,
( sP626(U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943)
| ~ hBOOL(hAPP(U_6939,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6941,U_6943))) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_10,plain,
( hBOOL(hAPP(U_6940,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6942,U_6944)))
| sP629(U_6940,U_6944,U_6942)
| sP628(U_6940,U_6944,U_6942)
| sP627(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_11,plain,
( hBOOL(hAPP(U_6939,U_6941))
| U_6943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP626(U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_12,plain,
( hBOOL(hAPP(U_6939,U_6928))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6929)),U_6928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6928),U_6943))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6943))
| ~ sP626(U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_13,plain,
( hBOOL(hAPP(U_6939,U_6930))
| U_6941 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6943),U_6931)),U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),U_6930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6943),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP626(U_6929,U_6930,U_6941,U_6928,U_6931,U_6939,U_6943) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_14,plain,
( U_6944 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP627(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_15,plain,
( ~ hBOOL(hAPP(U_6940,U_6942))
| ~ sP627(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_16,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944))
| ~ sP628(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_17,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK194(U_6944,U_6942,U_6940)))
| ~ sP628(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_18,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK194(U_6944,U_6942,U_6940)),U_6944))
| ~ sP628(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_19,plain,
( U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK193(U_6944,U_6942,U_6940))),sK194(U_6944,U_6942,U_6940))
| ~ sP628(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_20,plain,
( ~ hBOOL(hAPP(U_6940,sK194(U_6944,U_6942,U_6940)))
| ~ sP628(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_21,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP629(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_22,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6944),sK196(U_6944,U_6942,U_6940)))
| ~ sP629(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_23,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK196(U_6944,U_6942,U_6940)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP629(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_24,plain,
( U_6942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),sK195(U_6944,U_6942,U_6940))),sK196(U_6944,U_6942,U_6940))
| ~ sP629(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
cnf(f_1862_25,plain,
( ~ hBOOL(hAPP(U_6940,sK196(U_6944,U_6942,U_6940)))
| ~ sP629(U_6940,U_6944,U_6942) ),
inference(clausify,[status(thm)],[f_1862_8]) ).
fof(f_1863_1,plain,
! [V_q,V_b,V_r,V_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3]) ).
fof(f_1863_2,plain,
! [U_6948,U_6947,U_6946,U_6945] :
( 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),U_6947),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6948,U_6945))),U_6946)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6946))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6945)) ),
inference(variable_rename,[status(thm)],[f_1863_1]) ).
fof(f_1863_3,plain,
! [U_6945,U_6946,U_6948,U_6947] :
( 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),U_6947),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6948,U_6945))),U_6946)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6946))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6945)) ),
inference(definitional_conversion,[status(esa)],[f_1863_2]) ).
cnf(f_1863_4,plain,
( 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),U_6947),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6948,U_6945))),U_6946)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6946))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6945)) ),
inference(clausify,[status(thm)],[f_1863_3]) ).
fof(f_1864_1,plain,
! [V_q,V_b,V_r,V_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4]) ).
fof(f_1864_2,plain,
! [U_6952,U_6951,U_6950,U_6949] :
( 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),U_6951),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6952,U_6949))),U_6950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6951),U_6949)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6950),U_6951))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6949)) ),
inference(variable_rename,[status(thm)],[f_1864_1]) ).
fof(f_1864_3,plain,
! [U_6949,U_6951,U_6950,U_6952] :
( 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),U_6951),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6952,U_6949))),U_6950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6951),U_6949)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6950),U_6951))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6949)) ),
inference(definitional_conversion,[status(esa)],[f_1864_2]) ).
cnf(f_1864_4,plain,
( 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),U_6951),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6952,U_6949))),U_6950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6951),U_6949)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6950),U_6951))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6949)) ),
inference(clausify,[status(thm)],[f_1864_3]) ).
fof(f_1865_1,plain,
! [V_q,V_r,V_b,V_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1]) ).
fof(f_1865_2,plain,
! [U_6956,U_6955,U_6954,U_6953] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6954),U_6953)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6954),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6956,U_6953))),U_6955)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6955),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6954),U_6955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6953)) ),
inference(variable_rename,[status(thm)],[f_1865_1]) ).
fof(f_1865_3,plain,
! [U_6956,U_6953,U_6955,U_6954] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6954),U_6953)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6954),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6956,U_6953))),U_6955)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6955),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6954),U_6955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6953)) ),
inference(definitional_conversion,[status(esa)],[f_1865_2]) ).
cnf(f_1865_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6954),U_6953)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6954),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6956,U_6953))),U_6955)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6955),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6954),U_6955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6953)) ),
inference(clausify,[status(thm)],[f_1865_3]) ).
fof(f_1866_1,plain,
! [V_q,V_r,V_b,V_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux2]) ).
fof(f_1866_2,plain,
! [U_6960,U_6959,U_6958,U_6957] :
( 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),U_6958),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6960,U_6957))),U_6959)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6959),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6958),U_6959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6957)) ),
inference(variable_rename,[status(thm)],[f_1866_1]) ).
fof(f_1866_3,plain,
! [U_6960,U_6959,U_6958,U_6957] :
( 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),U_6958),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6960,U_6957))),U_6959)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6959),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6958),U_6959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6957)) ),
inference(definitional_conversion,[status(esa)],[f_1866_2]) ).
cnf(f_1866_4,plain,
( 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),U_6958),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6960,U_6957))),U_6959)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6959),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6958),U_6959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6957)) ),
inference(clausify,[status(thm)],[f_1866_3]) ).
fof(f_1867_1,plain,
! [V_y,V_q_1,V_b_1,V_a_1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y
| V_b_1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
| 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) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).
fof(f_1867_2,plain,
! [U_6964,U_6963,U_6962,U_6961] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6961,U_6962) = U_6964
| U_6962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6964),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6962),U_6964)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6962)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6964),U_6962))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6964)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6962)) )
| U_6961 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6962),U_6963)),U_6964) ),
inference(variable_rename,[status(thm)],[f_1867_1]) ).
fof(f_1867_3,plain,
( ! [U_6962,U_6964] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6964),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6962),U_6964))
| ~ sP631(U_6962,U_6964) )
& ! [U_6962,U_6964] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6962))
| ~ sP631(U_6962,U_6964) )
& ! [U_6962,U_6964] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6964),U_6962))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6964))
| ~ sP630(U_6962,U_6964) )
& ! [U_6962,U_6964] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6962))
| ~ sP630(U_6962,U_6964) )
& ! [U_6961,U_6962,U_6963,U_6964] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6961,U_6962) = U_6964
| U_6962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP631(U_6962,U_6964)
| sP630(U_6962,U_6964)
| U_6961 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6962),U_6963)),U_6964) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP630,sP631])],[f_1867_2]) ).
cnf(f_1867_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6961,U_6962) = U_6964
| U_6962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP631(U_6962,U_6964)
| sP630(U_6962,U_6964)
| U_6961 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6962),U_6963)),U_6964) ),
inference(clausify,[status(thm)],[f_1867_3]) ).
cnf(f_1867_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6962))
| ~ sP630(U_6962,U_6964) ),
inference(clausify,[status(thm)],[f_1867_3]) ).
cnf(f_1867_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6964),U_6962))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6964))
| ~ sP630(U_6962,U_6964) ),
inference(clausify,[status(thm)],[f_1867_3]) ).
cnf(f_1867_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6962))
| ~ sP631(U_6962,U_6964) ),
inference(clausify,[status(thm)],[f_1867_3]) ).
cnf(f_1867_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6964),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6962),U_6964))
| ~ sP631(U_6962,U_6964) ),
inference(clausify,[status(thm)],[f_1867_3]) ).
fof(f_1868_1,plain,
! [V_b,V_a,V_c] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq]) ).
fof(f_1868_2,plain,
! [U_6967,U_6966,U_6965] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6967),U_6965)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6967),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6966),U_6967),U_6965))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6966,U_6967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6965)) ),
inference(variable_rename,[status(thm)],[f_1868_1]) ).
fof(f_1868_3,plain,
! [U_6967,U_6965,U_6966] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6967),U_6965)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6967),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6966),U_6967),U_6965))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6966,U_6967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6965)) ),
inference(definitional_conversion,[status(esa)],[f_1868_2]) ).
cnf(f_1868_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6967),U_6965)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6967),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6966),U_6967),U_6965))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6966,U_6967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6965)) ),
inference(clausify,[status(thm)],[f_1868_3]) ).
fof(f_1869_1,plain,
! [V_a,V_b] :
( ( ( 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))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2__eq__if]) ).
fof(f_1869_2,plain,
! [U_6969,U_6968] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6968)) = 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),U_6969),U_6968))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6969,U_6968) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6968)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),U_6968))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6969,U_6968) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_6968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1869_1]) ).
fof(f_1869_3,plain,
( ! [U_6968,U_6969] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6968)) = 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),U_6969),U_6968))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6969,U_6968) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP632(U_6968,U_6969) )
& ! [U_6968,U_6969] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6968)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),U_6968))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6969,U_6968) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP632(U_6968,U_6969) )
& ! [U_6968,U_6969] :
( sP632(U_6968,U_6969)
| U_6968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP632])],[f_1869_2]) ).
cnf(f_1869_4,plain,
( sP632(U_6968,U_6969)
| U_6968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1869_3]) ).
cnf(f_1869_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6968)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),U_6968))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6969,U_6968) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP632(U_6968,U_6969) ),
inference(clausify,[status(thm)],[f_1869_3]) ).
cnf(f_1869_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6968)) = 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),U_6969),U_6968))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6969,U_6968) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP632(U_6968,U_6969) ),
inference(clausify,[status(thm)],[f_1869_3]) ).
fof(f_1870_1,plain,
! [V_a,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) = 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))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__zminus1__eq__if]) ).
fof(f_1870_2,plain,
! [U_6971,U_6970] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6971)),U_6970) = 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),U_6971),U_6970))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6971,U_6970) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6971)),U_6970) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6971),U_6970))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6971,U_6970) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_6970 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1870_1]) ).
fof(f_1870_3,plain,
( ! [U_6971,U_6970] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6971)),U_6970) = 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),U_6971),U_6970))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6971,U_6970) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP633(U_6971,U_6970) )
& ! [U_6971,U_6970] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6971)),U_6970) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6971),U_6970))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6971,U_6970) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP633(U_6971,U_6970) )
& ! [U_6971,U_6970] :
( sP633(U_6971,U_6970)
| U_6970 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP633])],[f_1870_2]) ).
cnf(f_1870_4,plain,
( sP633(U_6971,U_6970)
| U_6970 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1870_3]) ).
cnf(f_1870_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6971)),U_6970) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6971),U_6970))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6971,U_6970) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP633(U_6971,U_6970) ),
inference(clausify,[status(thm)],[f_1870_3]) ).
cnf(f_1870_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6971)),U_6970) = 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),U_6971),U_6970))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6971,U_6970) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP633(U_6971,U_6970) ),
inference(clausify,[status(thm)],[f_1870_3]) ).
fof(f_1871_1,plain,
! [V_k,V_l] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) )
& ( c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) ) ),
inference(fof_nnf,[status(thm)],[fact_z3mod__def]) ).
fof(f_1871_2,plain,
! [U_6973,U_6972] :
( ( c_SMT_Oz3mod(U_6973,U_6972) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6973,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6972))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6972)) )
& ( c_SMT_Oz3mod(U_6973,U_6972) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6973,U_6972)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6972)) ) ),
inference(variable_rename,[status(thm)],[f_1871_1]) ).
fof(f_1871_3,plain,
( ! [U_6977,U_6975] :
( c_SMT_Oz3mod(U_6977,U_6975) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6977,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6975))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6975)) )
& ! [U_6976,U_6974] :
( c_SMT_Oz3mod(U_6976,U_6974) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6976,U_6974)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6974)) ) ),
inference(miniscope,[status(thm)],[f_1871_2]) ).
fof(f_1871_4,plain,
( ! [U_6977,U_6975] :
( c_SMT_Oz3mod(U_6977,U_6975) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6977,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6975))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6975)) )
& ! [U_6974,U_6976] :
( c_SMT_Oz3mod(U_6976,U_6974) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6976,U_6974)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6974)) ) ),
inference(definitional_conversion,[status(esa)],[f_1871_3]) ).
cnf(f_1871_5,plain,
( c_SMT_Oz3mod(U_6976,U_6974) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6976,U_6974)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6974)) ),
inference(clausify,[status(thm)],[f_1871_4]) ).
cnf(f_1871_6,plain,
( c_SMT_Oz3mod(U_6977,U_6975) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6977,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6975))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6975)) ),
inference(clausify,[status(thm)],[f_1871_4]) ).
fof(f_1872_1,plain,
! [V_n,V_v] :
( ( 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)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__nat__number__of__add]) ).
fof(f_1872_2,plain,
! [U_6979,U_6978] :
( ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6978)),U_6979)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6978))),U_6979)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6978))) )
& ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6978)),U_6979)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6979)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6978))) ) ),
inference(variable_rename,[status(thm)],[f_1872_1]) ).
fof(f_1872_3,plain,
( ! [U_6983,U_6981] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6981)),U_6983)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6981))),U_6983)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6981))) )
& ! [U_6982,U_6980] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6980)),U_6982)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6982)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6980))) ) ),
inference(miniscope,[status(thm)],[f_1872_2]) ).
fof(f_1872_4,plain,
( ! [U_6981,U_6983] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6981)),U_6983)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6981))),U_6983)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6981))) )
& ! [U_6982,U_6980] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6980)),U_6982)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6982)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6980))) ) ),
inference(definitional_conversion,[status(esa)],[f_1872_3]) ).
cnf(f_1872_5,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6980)),U_6982)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6982)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6980))) ),
inference(clausify,[status(thm)],[f_1872_4]) ).
cnf(f_1872_6,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6981)),U_6983)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6981))),U_6983)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6981))) ),
inference(clausify,[status(thm)],[f_1872_4]) ).
fof(f_1873_1,plain,
! [V_v] :
( ( 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))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__nat__number__of]) ).
fof(f_1873_2,plain,
! [U_6984] :
( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6984)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6984))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6984))) )
& ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6984)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6984))) ) ),
inference(variable_rename,[status(thm)],[f_1873_1]) ).
fof(f_1873_3,plain,
( ! [U_6986] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6986)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6986))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6986))) )
& ! [U_6985] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6985)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6985))) ) ),
inference(miniscope,[status(thm)],[f_1873_2]) ).
fof(f_1873_4,plain,
( ! [U_6986] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6986)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6986))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6986))) )
& ! [U_6985] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6985)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6985))) ) ),
inference(definitional_conversion,[status(esa)],[f_1873_3]) ).
cnf(f_1873_5,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6985)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6985))) ),
inference(clausify,[status(thm)],[f_1873_4]) ).
cnf(f_1873_6,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6986)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6986))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6986))) ),
inference(clausify,[status(thm)],[f_1873_4]) ).
fof(f_1874_1,plain,
! [V_u_2] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int]) ).
fof(f_1874_2,plain,
! [U_6987] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6987) = 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,U_6987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6987)) ),
inference(variable_rename,[status(thm)],[f_1874_1]) ).
fof(f_1874_3,plain,
! [U_6987] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6987) = 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,U_6987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6987)) ),
inference(definitional_conversion,[status(esa)],[f_1874_2]) ).
cnf(f_1874_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6987) = 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,U_6987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6987)) ),
inference(clausify,[status(thm)],[f_1874_3]) ).
fof(f_1875_1,plain,
! [V_x] :
( ? [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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_negD]) ).
fof(f_1875_2,plain,
! [U_6989] :
( ? [U_6988] : U_6989 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6988)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6989),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1875_1]) ).
fof(f_1875_3,plain,
! [U_6989] :
( U_6989 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK197(U_6989))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6989),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_6988,sK197(U_6989))],[f_1875_2]) ).
fof(f_1875_4,plain,
! [U_6989] :
( U_6989 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK197(U_6989))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6989),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1875_3]) ).
cnf(f_1875_5,plain,
( U_6989 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK197(U_6989))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6989),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1875_4]) ).
fof(f_1876_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).
fof(f_1876_2,plain,
! [U_6991,U_6990] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6990),U_6991) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6990,U_6991)),U_6991),
inference(variable_rename,[status(thm)],[f_1876_1]) ).
fof(f_1876_3,plain,
! [U_6990,U_6991] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6990),U_6991) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6990,U_6991)),U_6991),
inference(definitional_conversion,[status(esa)],[f_1876_2]) ).
cnf(f_1876_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6990),U_6991) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6990,U_6991)),U_6991),
inference(clausify,[status(thm)],[f_1876_3]) ).
fof(f_1877_1,plain,
! [V_n,V_m] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_mod__less]) ).
fof(f_1877_2,plain,
! [U_6993,U_6992] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6992,U_6993) = U_6992
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6992),U_6993)) ),
inference(variable_rename,[status(thm)],[f_1877_1]) ).
fof(f_1877_3,plain,
! [U_6992,U_6993] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6992,U_6993) = U_6992
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6992),U_6993)) ),
inference(definitional_conversion,[status(esa)],[f_1877_2]) ).
cnf(f_1877_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6992,U_6993) = U_6992
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6992),U_6993)) ),
inference(clausify,[status(thm)],[f_1877_3]) ).
fof(f_1878_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_div__add1__eq]) ).
fof(f_1878_2,plain,
! [U_6996,U_6995,U_6994] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6994),U_6995)),U_6996) = 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),U_6994),U_6996)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6995),U_6996))),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,U_6994,U_6996)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6995,U_6996))),U_6996)),
inference(variable_rename,[status(thm)],[f_1878_1]) ).
fof(f_1878_3,plain,
! [U_6994,U_6995,U_6996] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6994),U_6995)),U_6996) = 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),U_6994),U_6996)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6995),U_6996))),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,U_6994,U_6996)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6995,U_6996))),U_6996)),
inference(definitional_conversion,[status(esa)],[f_1878_2]) ).
cnf(f_1878_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6994),U_6995)),U_6996) = 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),U_6994),U_6996)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6995),U_6996))),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,U_6994,U_6996)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6995,U_6996))),U_6996)),
inference(clausify,[status(thm)],[f_1878_3]) ).
fof(f_1879_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mod__less__eq__dividend]) ).
fof(f_1879_2,plain,
! [U_6998,U_6997] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6997,U_6998)),U_6997)),
inference(variable_rename,[status(thm)],[f_1879_1]) ).
fof(f_1879_3,plain,
! [U_6997,U_6998] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6997,U_6998)),U_6997)),
inference(definitional_conversion,[status(esa)],[f_1879_2]) ).
cnf(f_1879_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6997,U_6998)),U_6997)),
inference(clausify,[status(thm)],[f_1879_3]) ).
fof(f_1880_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mod__mult__distrib]) ).
fof(f_1880_2,plain,
! [U_7001,U_7000,U_6999] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6999,U_7000)),U_7001) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6999),U_7001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7000),U_7001)),
inference(variable_rename,[status(thm)],[f_1880_1]) ).
fof(f_1880_3,plain,
! [U_6999,U_7000,U_7001] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6999,U_7000)),U_7001) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6999),U_7001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7000),U_7001)),
inference(definitional_conversion,[status(esa)],[f_1880_2]) ).
cnf(f_1880_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6999,U_7000)),U_7001) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6999),U_7001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7000),U_7001)),
inference(clausify,[status(thm)],[f_1880_3]) ).
fof(f_1881_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mod__mult__distrib2]) ).
fof(f_1881_2,plain,
! [U_7004,U_7003,U_7002] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7003,U_7004)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),U_7003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),U_7004)),
inference(variable_rename,[status(thm)],[f_1881_1]) ).
fof(f_1881_3,plain,
! [U_7002,U_7003,U_7004] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7003,U_7004)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),U_7003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),U_7004)),
inference(definitional_conversion,[status(esa)],[f_1881_2]) ).
cnf(f_1881_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7003,U_7004)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),U_7003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7002),U_7004)),
inference(clausify,[status(thm)],[f_1881_3]) ).
fof(f_1882_1,plain,
! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n,
inference(fof_nnf,[status(thm)],[fact_nat__int]) ).
fof(f_1882_2,plain,
! [U_7005] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7005)) = U_7005,
inference(variable_rename,[status(thm)],[f_1882_1]) ).
fof(f_1882_3,plain,
! [U_7005] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7005)) = U_7005,
inference(definitional_conversion,[status(esa)],[f_1882_2]) ).
cnf(f_1882_4,plain,
hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7005)) = U_7005,
inference(clausify,[status(thm)],[f_1882_3]) ).
fof(f_1883_1,plain,
! [V_y,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J]) ).
fof(f_1883_2,plain,
! [U_7007,U_7006] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_7006),hAPP(c_Int_Onat,U_7007)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7006,U_7007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7006)) ),
inference(variable_rename,[status(thm)],[f_1883_1]) ).
fof(f_1883_3,plain,
! [U_7006,U_7007] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_7006),hAPP(c_Int_Onat,U_7007)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7006,U_7007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7006)) ),
inference(definitional_conversion,[status(esa)],[f_1883_2]) ).
cnf(f_1883_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_7006),hAPP(c_Int_Onat,U_7007)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7006,U_7007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7006)) ),
inference(clausify,[status(thm)],[f_1883_3]) ).
fof(f_1884_1,plain,
! [V_y,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib]) ).
fof(f_1884_2,plain,
! [U_7009,U_7008] :
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7008,U_7009)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_7008),hAPP(c_Int_Onat,U_7009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7008)) ),
inference(variable_rename,[status(thm)],[f_1884_1]) ).
fof(f_1884_3,plain,
! [U_7009,U_7008] :
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7008,U_7009)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_7008),hAPP(c_Int_Onat,U_7009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7008)) ),
inference(definitional_conversion,[status(esa)],[f_1884_2]) ).
cnf(f_1884_4,plain,
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7008,U_7009)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_7008),hAPP(c_Int_Onat,U_7009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7008)) ),
inference(clausify,[status(thm)],[f_1884_3]) ).
fof(f_1885_1,plain,
hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat__0]) ).
fof(f_1885_2,plain,
hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1885_1]) ).
cnf(f_1885_3,plain,
hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1885_2]) ).
fof(f_1886_1,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
fof(f_1886_2,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_1886_1]) ).
cnf(f_1886_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1886_2]) ).
fof(f_1887_1,plain,
! [V_n,V_m] :
( ( 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))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n ) ),
inference(fof_nnf,[status(thm)],[fact_mod__Suc]) ).
fof(f_1887_2,plain,
! [U_7011,U_7010] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7010),U_7011) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7010,U_7011))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7010,U_7011)) = U_7011 )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7010),U_7011) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7010,U_7011)) != U_7011 ) ),
inference(variable_rename,[status(thm)],[f_1887_1]) ).
fof(f_1887_3,plain,
( ! [U_7015,U_7013] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7013),U_7015) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7013,U_7015))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7013,U_7015)) = U_7015 )
& ! [U_7014,U_7012] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7012),U_7014) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7012,U_7014)) != U_7014 ) ),
inference(miniscope,[status(thm)],[f_1887_2]) ).
fof(f_1887_4,plain,
( ! [U_7013,U_7015] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7013),U_7015) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7013,U_7015))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7013,U_7015)) = U_7015 )
& ! [U_7012,U_7014] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7012),U_7014) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7012,U_7014)) != U_7014 ) ),
inference(definitional_conversion,[status(esa)],[f_1887_3]) ).
cnf(f_1887_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7012),U_7014) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7012,U_7014)) != U_7014 ),
inference(clausify,[status(thm)],[f_1887_4]) ).
cnf(f_1887_6,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7013),U_7015) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7013,U_7015))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7013,U_7015)) = U_7015 ),
inference(clausify,[status(thm)],[f_1887_4]) ).
fof(f_1888_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_mod__1]) ).
fof(f_1888_2,plain,
! [U_7016] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7016,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1888_1]) ).
fof(f_1888_3,plain,
! [U_7016] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7016,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1888_2]) ).
cnf(f_1888_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7016,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1888_3]) ).
fof(f_1889_1,plain,
! [V_m,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_mod__less__divisor]) ).
fof(f_1889_2,plain,
! [U_7018,U_7017] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7018,U_7017)),U_7017))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7017)) ),
inference(variable_rename,[status(thm)],[f_1889_1]) ).
fof(f_1889_3,plain,
! [U_7017,U_7018] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7018,U_7017)),U_7017))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7017)) ),
inference(definitional_conversion,[status(esa)],[f_1889_2]) ).
cnf(f_1889_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7018,U_7017)),U_7017))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7017)) ),
inference(clausify,[status(thm)],[f_1889_3]) ).
fof(f_1890_1,plain,
! [V_z_H_2,V_z_2] :
( ( ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
| V_z_2 != V_z_H_2 )
& ( V_z_2 = V_z_H_2
| hAPP(c_Int_Onat,V_z_2) != hAPP(c_Int_Onat,V_z_H_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff]) ).
fof(f_1890_2,plain,
! [U_7020,U_7019] :
( ( ( hAPP(c_Int_Onat,U_7019) = hAPP(c_Int_Onat,U_7020)
| U_7019 != U_7020 )
& ( U_7019 = U_7020
| hAPP(c_Int_Onat,U_7019) != hAPP(c_Int_Onat,U_7020) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7020))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7019)) ),
inference(variable_rename,[status(thm)],[f_1890_1]) ).
fof(f_1890_3,plain,
( ! [U_7019,U_7020] :
( hAPP(c_Int_Onat,U_7019) = hAPP(c_Int_Onat,U_7020)
| U_7019 != U_7020
| ~ sP634(U_7019,U_7020) )
& ! [U_7019,U_7020] :
( U_7019 = U_7020
| hAPP(c_Int_Onat,U_7019) != hAPP(c_Int_Onat,U_7020)
| ~ sP634(U_7019,U_7020) )
& ! [U_7019,U_7020] :
( sP634(U_7019,U_7020)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7020))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7019)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP634])],[f_1890_2]) ).
cnf(f_1890_4,plain,
( sP634(U_7019,U_7020)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7020))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7019)) ),
inference(clausify,[status(thm)],[f_1890_3]) ).
cnf(f_1890_5,plain,
( U_7019 = U_7020
| hAPP(c_Int_Onat,U_7019) != hAPP(c_Int_Onat,U_7020)
| ~ sP634(U_7019,U_7020) ),
inference(clausify,[status(thm)],[f_1890_3]) ).
cnf(f_1890_6,plain,
( hAPP(c_Int_Onat,U_7019) = hAPP(c_Int_Onat,U_7020)
| U_7019 != U_7020
| ~ sP634(U_7019,U_7020) ),
inference(clausify,[status(thm)],[f_1890_3]) ).
fof(f_1891_1,plain,
! [V_Pa_2] :
( ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
| ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat]) ).
fof(f_1891_2,plain,
! [U_7025] :
( ( ? [U_7024] : hBOOL(hAPP(U_7025,U_7024))
| ! [U_7023] :
( ~ hBOOL(hAPP(U_7025,hAPP(c_Int_Onat,U_7023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7023)) ) )
& ( ? [U_7022] :
( hBOOL(hAPP(U_7025,hAPP(c_Int_Onat,U_7022)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7022)) )
| ! [U_7021] : ~ hBOOL(hAPP(U_7025,U_7021)) ) ),
inference(variable_rename,[status(thm)],[f_1891_1]) ).
fof(f_1891_3,plain,
( ! [U_7027] :
( ? [U_7024] : hBOOL(hAPP(U_7027,U_7024))
| ! [U_7023] :
( ~ hBOOL(hAPP(U_7027,hAPP(c_Int_Onat,U_7023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7023)) ) )
& ! [U_7026] :
( ? [U_7022] :
( hBOOL(hAPP(U_7026,hAPP(c_Int_Onat,U_7022)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7022)) )
| ! [U_7021] : ~ hBOOL(hAPP(U_7026,U_7021)) ) ),
inference(miniscope,[status(thm)],[f_1891_2]) ).
fof(f_1891_4,plain,
( ! [U_7027] :
( ? [U_7024] : hBOOL(hAPP(U_7027,U_7024))
| ! [U_7023] :
( ~ hBOOL(hAPP(U_7027,hAPP(c_Int_Onat,U_7023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7023)) ) )
& ! [U_7026] :
( ( hBOOL(hAPP(U_7026,hAPP(c_Int_Onat,sK198(U_7026))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK198(U_7026))) )
| ! [U_7021] : ~ hBOOL(hAPP(U_7026,U_7021)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_7022,sK198(U_7026))],[f_1891_3]) ).
fof(f_1891_5,plain,
( ! [U_7027] :
( hBOOL(hAPP(U_7027,sK199(U_7027)))
| ! [U_7023] :
( ~ hBOOL(hAPP(U_7027,hAPP(c_Int_Onat,U_7023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7023)) ) )
& ! [U_7026] :
( ( hBOOL(hAPP(U_7026,hAPP(c_Int_Onat,sK198(U_7026))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK198(U_7026))) )
| ! [U_7021] : ~ hBOOL(hAPP(U_7026,U_7021)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_7024,sK199(U_7027))],[f_1891_4]) ).
fof(f_1891_6,plain,
( ! [U_7026] :
( hBOOL(hAPP(U_7026,hAPP(c_Int_Onat,sK198(U_7026))))
| ~ sP635(U_7026) )
& ! [U_7026] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK198(U_7026)))
| ~ sP635(U_7026) )
& ! [U_7023,U_7027] :
( hBOOL(hAPP(U_7027,sK199(U_7027)))
| ~ hBOOL(hAPP(U_7027,hAPP(c_Int_Onat,U_7023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7023)) )
& ! [U_7021,U_7026] :
( sP635(U_7026)
| ~ hBOOL(hAPP(U_7026,U_7021)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP635])],[f_1891_5]) ).
cnf(f_1891_7,plain,
( sP635(U_7026)
| ~ hBOOL(hAPP(U_7026,U_7021)) ),
inference(clausify,[status(thm)],[f_1891_6]) ).
cnf(f_1891_8,plain,
( hBOOL(hAPP(U_7027,sK199(U_7027)))
| ~ hBOOL(hAPP(U_7027,hAPP(c_Int_Onat,U_7023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7023)) ),
inference(clausify,[status(thm)],[f_1891_6]) ).
cnf(f_1891_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK198(U_7026)))
| ~ sP635(U_7026) ),
inference(clausify,[status(thm)],[f_1891_6]) ).
cnf(f_1891_10,plain,
( hBOOL(hAPP(U_7026,hAPP(c_Int_Onat,sK198(U_7026))))
| ~ sP635(U_7026) ),
inference(clausify,[status(thm)],[f_1891_6]) ).
fof(f_1892_1,plain,
! [V_Pa_2] :
( ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ? [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat]) ).
fof(f_1892_2,plain,
! [U_7032] :
( ( ! [U_7031] : hBOOL(hAPP(U_7032,U_7031))
| ? [U_7030] :
( ~ hBOOL(hAPP(U_7032,hAPP(c_Int_Onat,U_7030)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7030)) ) )
& ( ! [U_7029] :
( hBOOL(hAPP(U_7032,hAPP(c_Int_Onat,U_7029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029)) )
| ? [U_7028] : ~ hBOOL(hAPP(U_7032,U_7028)) ) ),
inference(variable_rename,[status(thm)],[f_1892_1]) ).
fof(f_1892_3,plain,
( ! [U_7034] :
( ! [U_7031] : hBOOL(hAPP(U_7034,U_7031))
| ? [U_7030] :
( ~ hBOOL(hAPP(U_7034,hAPP(c_Int_Onat,U_7030)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7030)) ) )
& ! [U_7033] :
( ! [U_7029] :
( hBOOL(hAPP(U_7033,hAPP(c_Int_Onat,U_7029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029)) )
| ? [U_7028] : ~ hBOOL(hAPP(U_7033,U_7028)) ) ),
inference(miniscope,[status(thm)],[f_1892_2]) ).
fof(f_1892_4,plain,
( ! [U_7034] :
( ! [U_7031] : hBOOL(hAPP(U_7034,U_7031))
| ? [U_7030] :
( ~ hBOOL(hAPP(U_7034,hAPP(c_Int_Onat,U_7030)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7030)) ) )
& ! [U_7033] :
( ! [U_7029] :
( hBOOL(hAPP(U_7033,hAPP(c_Int_Onat,U_7029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029)) )
| ~ hBOOL(hAPP(U_7033,sK200(U_7033))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_7028,sK200(U_7033))],[f_1892_3]) ).
fof(f_1892_5,plain,
( ! [U_7034] :
( ! [U_7031] : hBOOL(hAPP(U_7034,U_7031))
| ( ~ hBOOL(hAPP(U_7034,hAPP(c_Int_Onat,sK201(U_7034))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK201(U_7034))) ) )
& ! [U_7033] :
( ! [U_7029] :
( hBOOL(hAPP(U_7033,hAPP(c_Int_Onat,U_7029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029)) )
| ~ hBOOL(hAPP(U_7033,sK200(U_7033))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_7030,sK201(U_7034))],[f_1892_4]) ).
fof(f_1892_6,plain,
( ! [U_7034] :
( ~ hBOOL(hAPP(U_7034,hAPP(c_Int_Onat,sK201(U_7034))))
| ~ sP636(U_7034) )
& ! [U_7034] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK201(U_7034)))
| ~ sP636(U_7034) )
& ! [U_7031,U_7034] :
( hBOOL(hAPP(U_7034,U_7031))
| sP636(U_7034) )
& ! [U_7029,U_7033] :
( hBOOL(hAPP(U_7033,hAPP(c_Int_Onat,U_7029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029))
| ~ hBOOL(hAPP(U_7033,sK200(U_7033))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP636])],[f_1892_5]) ).
cnf(f_1892_7,plain,
( hBOOL(hAPP(U_7033,hAPP(c_Int_Onat,U_7029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029))
| ~ hBOOL(hAPP(U_7033,sK200(U_7033))) ),
inference(clausify,[status(thm)],[f_1892_6]) ).
cnf(f_1892_8,plain,
( hBOOL(hAPP(U_7034,U_7031))
| sP636(U_7034) ),
inference(clausify,[status(thm)],[f_1892_6]) ).
cnf(f_1892_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK201(U_7034)))
| ~ sP636(U_7034) ),
inference(clausify,[status(thm)],[f_1892_6]) ).
cnf(f_1892_10,plain,
( ~ hBOOL(hAPP(U_7034,hAPP(c_Int_Onat,sK201(U_7034))))
| ~ sP636(U_7034) ),
inference(clausify,[status(thm)],[f_1892_6]) ).
fof(f_1893_1,plain,
! [V_y_2,V_x_2] :
( ( ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Int_Onat,V_x_2) != hAPP(c_Int_Onat,V_y_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J]) ).
fof(f_1893_2,plain,
! [U_7036,U_7035] :
( ( ( hAPP(c_Int_Onat,U_7035) = hAPP(c_Int_Onat,U_7036)
| U_7035 != U_7036 )
& ( U_7035 = U_7036
| hAPP(c_Int_Onat,U_7035) != hAPP(c_Int_Onat,U_7036) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7035)) ),
inference(variable_rename,[status(thm)],[f_1893_1]) ).
fof(f_1893_3,plain,
( ! [U_7035,U_7036] :
( hAPP(c_Int_Onat,U_7035) = hAPP(c_Int_Onat,U_7036)
| U_7035 != U_7036
| ~ sP637(U_7035,U_7036) )
& ! [U_7035,U_7036] :
( U_7035 = U_7036
| hAPP(c_Int_Onat,U_7035) != hAPP(c_Int_Onat,U_7036)
| ~ sP637(U_7035,U_7036) )
& ! [U_7035,U_7036] :
( sP637(U_7035,U_7036)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7035)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP637])],[f_1893_2]) ).
cnf(f_1893_4,plain,
( sP637(U_7035,U_7036)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7035)) ),
inference(clausify,[status(thm)],[f_1893_3]) ).
cnf(f_1893_5,plain,
( U_7035 = U_7036
| hAPP(c_Int_Onat,U_7035) != hAPP(c_Int_Onat,U_7036)
| ~ sP637(U_7035,U_7036) ),
inference(clausify,[status(thm)],[f_1893_3]) ).
cnf(f_1893_6,plain,
( hAPP(c_Int_Onat,U_7035) = hAPP(c_Int_Onat,U_7036)
| U_7035 != U_7036
| ~ sP637(U_7035,U_7036) ),
inference(clausify,[status(thm)],[f_1893_3]) ).
fof(f_1894_1,plain,
! [V_d_2,V_m_2] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [B_q] : V_m_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) )
& ( ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff]) ).
fof(f_1894_2,plain,
! [U_7040,U_7039] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7039,U_7040) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_7038] : U_7039 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7040),U_7038) )
& ( ? [U_7037] : U_7039 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7040),U_7037)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7039,U_7040) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1894_1]) ).
fof(f_1894_3,plain,
( ! [U_7044,U_7042] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7042,U_7044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_7038] : U_7042 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7044),U_7038) )
& ! [U_7043,U_7041] :
( ? [U_7037] : U_7041 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7043),U_7037)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7041,U_7043) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1894_2]) ).
fof(f_1894_4,plain,
( ! [U_7044,U_7042] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7042,U_7044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_7038] : U_7042 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7044),U_7038) )
& ! [U_7043,U_7041] :
( U_7041 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7043),sK202(U_7043,U_7041))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7041,U_7043) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_7037,sK202(U_7043,U_7041))],[f_1894_3]) ).
fof(f_1894_5,plain,
( ! [U_7038,U_7042,U_7044] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7042,U_7044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7042 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7044),U_7038) )
& ! [U_7041,U_7043] :
( U_7041 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7043),sK202(U_7043,U_7041))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7041,U_7043) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1894_4]) ).
cnf(f_1894_6,plain,
( U_7041 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7043),sK202(U_7043,U_7041))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7041,U_7043) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1894_5]) ).
cnf(f_1894_7,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7042,U_7044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7042 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7044),U_7038) ),
inference(clausify,[status(thm)],[f_1894_5]) ).
fof(f_1895_1,plain,
! [V_n,V_m] :
( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_mod__geq]) ).
fof(f_1895_2,plain,
! [U_7046,U_7045] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7045,U_7046) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7045),U_7046),U_7046)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7045),U_7046)) ),
inference(variable_rename,[status(thm)],[f_1895_1]) ).
fof(f_1895_3,plain,
! [U_7045,U_7046] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7045,U_7046) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7045),U_7046),U_7046)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7045),U_7046)) ),
inference(definitional_conversion,[status(esa)],[f_1895_2]) ).
cnf(f_1895_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7045,U_7046) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7045),U_7046),U_7046)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7045),U_7046)) ),
inference(clausify,[status(thm)],[f_1895_3]) ).
fof(f_1896_1,plain,
! [V_n,V_m] :
( ( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
inference(fof_nnf,[status(thm)],[fact_mod__if]) ).
fof(f_1896_2,plain,
! [U_7048,U_7047] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7047,U_7048) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7047),U_7048),U_7048)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7047),U_7048)) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7047,U_7048) = U_7047
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7047),U_7048)) ) ),
inference(variable_rename,[status(thm)],[f_1896_1]) ).
fof(f_1896_3,plain,
( ! [U_7052,U_7050] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7050,U_7052) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7050),U_7052),U_7052)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7050),U_7052)) )
& ! [U_7051,U_7049] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7049,U_7051) = U_7049
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7049),U_7051)) ) ),
inference(miniscope,[status(thm)],[f_1896_2]) ).
fof(f_1896_4,plain,
( ! [U_7052,U_7050] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7050,U_7052) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7050),U_7052),U_7052)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7050),U_7052)) )
& ! [U_7049,U_7051] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7049,U_7051) = U_7049
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7049),U_7051)) ) ),
inference(definitional_conversion,[status(esa)],[f_1896_3]) ).
cnf(f_1896_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7049,U_7051) = U_7049
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7049),U_7051)) ),
inference(clausify,[status(thm)],[f_1896_4]) ).
cnf(f_1896_6,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7050,U_7052) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7050),U_7052),U_7052)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7050),U_7052)) ),
inference(clausify,[status(thm)],[f_1896_4]) ).
fof(f_1897_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_mod__mult__self3]) ).
fof(f_1897_2,plain,
! [U_7055,U_7054,U_7053] : 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),U_7053),U_7054)),U_7055),U_7054) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7055,U_7054),
inference(variable_rename,[status(thm)],[f_1897_1]) ).
fof(f_1897_3,plain,
! [U_7053,U_7055,U_7054] : 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),U_7053),U_7054)),U_7055),U_7054) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7055,U_7054),
inference(definitional_conversion,[status(esa)],[f_1897_2]) ).
cnf(f_1897_4,plain,
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),U_7053),U_7054)),U_7055),U_7054) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7055,U_7054),
inference(clausify,[status(thm)],[f_1897_3]) ).
fof(f_1898_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mod__mult2__eq]) ).
fof(f_1898_2,plain,
! [U_7058,U_7057,U_7056] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7056,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),U_7058)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7056),U_7057),U_7058))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7056,U_7057)),
inference(variable_rename,[status(thm)],[f_1898_1]) ).
fof(f_1898_3,plain,
! [U_7056,U_7057,U_7058] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7056,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),U_7058)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7056),U_7057),U_7058))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7056,U_7057)),
inference(definitional_conversion,[status(esa)],[f_1898_2]) ).
cnf(f_1898_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7056,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),U_7058)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7056),U_7057),U_7058))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7056,U_7057)),
inference(clausify,[status(thm)],[f_1898_3]) ).
fof(f_1899_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_div__mult1__eq]) ).
fof(f_1899_2,plain,
! [U_7061,U_7060,U_7059] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),U_7060)),U_7061) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7060),U_7061))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7060,U_7061))),U_7061)),
inference(variable_rename,[status(thm)],[f_1899_1]) ).
fof(f_1899_3,plain,
! [U_7059,U_7060,U_7061] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),U_7060)),U_7061) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7060),U_7061))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7060,U_7061))),U_7061)),
inference(definitional_conversion,[status(esa)],[f_1899_2]) ).
cnf(f_1899_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),U_7060)),U_7061) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7060),U_7061))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7059),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7060,U_7061))),U_7061)),
inference(clausify,[status(thm)],[f_1899_3]) ).
fof(f_1900_1,plain,
! [V_m,V_n] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_le__mod__geq]) ).
fof(f_1900_2,plain,
! [U_7063,U_7062] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7063,U_7062) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7063),U_7062),U_7062)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7062),U_7063)) ),
inference(variable_rename,[status(thm)],[f_1900_1]) ).
fof(f_1900_3,plain,
! [U_7062,U_7063] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7063,U_7062) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7063),U_7062),U_7062)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7062),U_7063)) ),
inference(definitional_conversion,[status(esa)],[f_1900_2]) ).
cnf(f_1900_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7063,U_7062) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7063),U_7062),U_7062)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7062),U_7063)) ),
inference(clausify,[status(thm)],[f_1900_3]) ).
fof(f_1901_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__def]) ).
fof(f_1901_2,plain,
! [U_7064] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7064) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7064)),
inference(variable_rename,[status(thm)],[f_1901_1]) ).
fof(f_1901_3,plain,
! [U_7064] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7064) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7064)),
inference(definitional_conversion,[status(esa)],[f_1901_2]) ).
cnf(f_1901_4,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7064) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7064)),
inference(clausify,[status(thm)],[f_1901_3]) ).
fof(f_1902_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__number__of]) ).
fof(f_1902_2,plain,
! [U_7065] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7065)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7065),
inference(variable_rename,[status(thm)],[f_1902_1]) ).
fof(f_1902_3,plain,
! [U_7065] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7065)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7065),
inference(definitional_conversion,[status(esa)],[f_1902_2]) ).
cnf(f_1902_4,plain,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7065)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7065),
inference(clausify,[status(thm)],[f_1902_3]) ).
fof(f_1903_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_div__mod__equality_H]) ).
fof(f_1903_2,plain,
! [U_7067,U_7066] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7066),U_7067)),U_7067) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7066),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7066,U_7067)),
inference(variable_rename,[status(thm)],[f_1903_1]) ).
fof(f_1903_3,plain,
! [U_7066,U_7067] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7066),U_7067)),U_7067) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7066),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7066,U_7067)),
inference(definitional_conversion,[status(esa)],[f_1903_2]) ).
cnf(f_1903_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7066),U_7067)),U_7067) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7066),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7066,U_7067)),
inference(clausify,[status(thm)],[f_1903_3]) ).
fof(f_1904_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mult__div__cancel]) ).
fof(f_1904_2,plain,
! [U_7069,U_7068] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7068),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7069),U_7068)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7069),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7069,U_7068)),
inference(variable_rename,[status(thm)],[f_1904_1]) ).
fof(f_1904_3,plain,
! [U_7068,U_7069] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7068),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7069),U_7068)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7069),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7069,U_7068)),
inference(definitional_conversion,[status(esa)],[f_1904_2]) ).
cnf(f_1904_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7068),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7069),U_7068)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7069),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7069,U_7068)),
inference(clausify,[status(thm)],[f_1904_3]) ).
fof(f_1905_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).
fof(f_1905_2,plain,
! [U_7071,U_7070] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7070,U_7071) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7070),U_7071)),U_7071)),
inference(variable_rename,[status(thm)],[f_1905_1]) ).
fof(f_1905_3,plain,
! [U_7070,U_7071] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7070,U_7071) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7070),U_7071)),U_7071)),
inference(definitional_conversion,[status(esa)],[f_1905_2]) ).
cnf(f_1905_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7070,U_7071) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7070),U_7071)),U_7071)),
inference(clausify,[status(thm)],[f_1905_3]) ).
fof(f_1906_1,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I2_J]) ).
fof(f_1906_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_1906_1]) ).
cnf(f_1906_3,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1906_2]) ).
fof(f_1907_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zmod__int]) ).
fof(f_1907_2,plain,
! [U_7073,U_7072] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7072,U_7073)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7072),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7073)),
inference(variable_rename,[status(thm)],[f_1907_1]) ).
fof(f_1907_3,plain,
! [U_7072,U_7073] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7072,U_7073)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7072),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7073)),
inference(definitional_conversion,[status(esa)],[f_1907_2]) ).
cnf(f_1907_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7072,U_7073)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7072),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7073)),
inference(clausify,[status(thm)],[f_1907_3]) ).
fof(f_1908_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).
fof(f_1908_2,plain,
! [U_7075,U_7074] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7074),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7075)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7074,U_7075)),
inference(variable_rename,[status(thm)],[f_1908_1]) ).
fof(f_1908_3,plain,
! [U_7074,U_7075] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7074),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7075)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7074,U_7075)),
inference(definitional_conversion,[status(esa)],[f_1908_2]) ).
cnf(f_1908_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7074),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7075)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7074,U_7075)),
inference(clausify,[status(thm)],[f_1908_3]) ).
fof(f_1909_1,plain,
! [V_z] :
( hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) ),
inference(fof_nnf,[status(thm)],[fact_neg__nat]) ).
fof(f_1909_2,plain,
! [U_7076] :
( hAPP(c_Int_Onat,U_7076) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7076)) ),
inference(variable_rename,[status(thm)],[f_1909_1]) ).
fof(f_1909_3,plain,
! [U_7076] :
( hAPP(c_Int_Onat,U_7076) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7076)) ),
inference(definitional_conversion,[status(esa)],[f_1909_2]) ).
cnf(f_1909_4,plain,
( hAPP(c_Int_Onat,U_7076) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7076)) ),
inference(clausify,[status(thm)],[f_1909_3]) ).
fof(f_1910_1,plain,
! [V_z] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
| hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) ),
inference(fof_nnf,[status(thm)],[fact_not__neg__nat]) ).
fof(f_1910_2,plain,
! [U_7077] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7077)) = U_7077
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7077)) ),
inference(variable_rename,[status(thm)],[f_1910_1]) ).
fof(f_1910_3,plain,
! [U_7077] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7077)) = U_7077
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7077)) ),
inference(definitional_conversion,[status(esa)],[f_1910_2]) ).
cnf(f_1910_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7077)) = U_7077
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7077)) ),
inference(clausify,[status(thm)],[f_1910_3]) ).
fof(f_1911_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).
fof(f_1911_2,plain,
! [U_7078] : 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)),U_7078)) = U_7078,
inference(variable_rename,[status(thm)],[f_1911_1]) ).
fof(f_1911_3,plain,
! [U_7078] : 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)),U_7078)) = U_7078,
inference(definitional_conversion,[status(esa)],[f_1911_2]) ).
cnf(f_1911_4,plain,
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)),U_7078)) = U_7078,
inference(clausify,[status(thm)],[f_1911_3]) ).
fof(f_1912_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).
fof(f_1912_2,plain,
! [U_7080,U_7079] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7079),U_7080) = 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)),U_7079)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7080))),
inference(variable_rename,[status(thm)],[f_1912_1]) ).
fof(f_1912_3,plain,
! [U_7079,U_7080] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7079),U_7080) = 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)),U_7079)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7080))),
inference(definitional_conversion,[status(esa)],[f_1912_2]) ).
cnf(f_1912_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7079),U_7080) = 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)),U_7079)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7080))),
inference(clausify,[status(thm)],[f_1912_3]) ).
fof(f_1913_1,plain,
! [V_v_H,V_v] :
( ( ( ( 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)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
inference(fof_nnf,[status(thm)],[fact_mod__nat__number__of]) ).
fof(f_1913_2,plain,
! [U_7082,U_7081] :
( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7081),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7082)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7081),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7082)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7082))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7081),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7082)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7081)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7082))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7081))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7081),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7082)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7081))) ) ),
inference(variable_rename,[status(thm)],[f_1913_1]) ).
fof(f_1913_3,plain,
( ! [U_7086,U_7084] :
( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7086)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7086)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7084))) )
& ! [U_7085,U_7083] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7083),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7085)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7083))) ) ),
inference(miniscope,[status(thm)],[f_1913_2]) ).
fof(f_1913_4,plain,
( ! [U_7086,U_7084] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7086)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086)))
| ~ sP638(U_7086,U_7084) )
& ! [U_7086,U_7084] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7086)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086)))
| ~ sP638(U_7086,U_7084) )
& ! [U_7086,U_7084] :
( sP638(U_7086,U_7084)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7084))) )
& ! [U_7083,U_7085] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7083),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7085)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7083))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP638])],[f_1913_3]) ).
cnf(f_1913_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7083),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7085)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7083))) ),
inference(clausify,[status(thm)],[f_1913_4]) ).
cnf(f_1913_6,plain,
( sP638(U_7086,U_7084)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7084))) ),
inference(clausify,[status(thm)],[f_1913_4]) ).
cnf(f_1913_7,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7086)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086)))
| ~ sP638(U_7086,U_7084) ),
inference(clausify,[status(thm)],[f_1913_4]) ).
cnf(f_1913_8,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7086)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7086)))
| ~ sP638(U_7086,U_7084) ),
inference(clausify,[status(thm)],[f_1913_4]) ).
fof(f_1914_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J]) ).
fof(f_1914_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1914_1]) ).
cnf(f_1914_3,plain,
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))),
inference(clausify,[status(thm)],[f_1914_2]) ).
fof(f_1915_1,plain,
! [V_z] :
( hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__0]) ).
fof(f_1915_2,plain,
! [U_7087] :
( hAPP(c_Int_Onat,U_7087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7087),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1915_1]) ).
fof(f_1915_3,plain,
! [U_7087] :
( hAPP(c_Int_Onat,U_7087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7087),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1915_2]) ).
cnf(f_1915_4,plain,
( hAPP(c_Int_Onat,U_7087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7087),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1915_3]) ).
fof(f_1916_1,plain,
! [V_i_2] :
( ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,V_i_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__iff]) ).
fof(f_1916_2,plain,
! [U_7088] :
( ( hAPP(c_Int_Onat,U_7088) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7088),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7088),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7088) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1916_1]) ).
fof(f_1916_3,plain,
( ! [U_7090] :
( hAPP(c_Int_Onat,U_7090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7090),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7089] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7089) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1916_2]) ).
fof(f_1916_4,plain,
( ! [U_7090] :
( hAPP(c_Int_Onat,U_7090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7090),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7089] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7089) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1916_3]) ).
cnf(f_1916_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7089) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1916_4]) ).
cnf(f_1916_6,plain,
( hAPP(c_Int_Onat,U_7090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7090),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1916_4]) ).
fof(f_1917_1,plain,
! [V_w_2,V_z_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__mono__iff]) ).
fof(f_1917_2,plain,
! [U_7092,U_7091] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7092)),hAPP(c_Int_Onat,U_7091)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7091)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7092)),hAPP(c_Int_Onat,U_7091))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7091)) ),
inference(variable_rename,[status(thm)],[f_1917_1]) ).
fof(f_1917_3,plain,
( ! [U_7092,U_7091] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7092)),hAPP(c_Int_Onat,U_7091)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7091))
| ~ sP639(U_7092,U_7091) )
& ! [U_7092,U_7091] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7092)),hAPP(c_Int_Onat,U_7091)))
| ~ sP639(U_7092,U_7091) )
& ! [U_7092,U_7091] :
( sP639(U_7092,U_7091)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7091)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP639])],[f_1917_2]) ).
cnf(f_1917_4,plain,
( sP639(U_7092,U_7091)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7091)) ),
inference(clausify,[status(thm)],[f_1917_3]) ).
cnf(f_1917_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7092)),hAPP(c_Int_Onat,U_7091)))
| ~ sP639(U_7092,U_7091) ),
inference(clausify,[status(thm)],[f_1917_3]) ).
cnf(f_1917_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7092)),hAPP(c_Int_Onat,U_7091)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7091))
| ~ sP639(U_7092,U_7091) ),
inference(clausify,[status(thm)],[f_1917_3]) ).
fof(f_1918_1,plain,
! [V_z_2,V_w_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__nat__conj]) ).
fof(f_1918_2,plain,
! [U_7094,U_7093] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7093)),hAPP(c_Int_Onat,U_7094)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7093),U_7094))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7094)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7093),U_7094))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7094)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7093)),hAPP(c_Int_Onat,U_7094))) ) ),
inference(variable_rename,[status(thm)],[f_1918_1]) ).
fof(f_1918_3,plain,
( ! [U_7098,U_7096] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7096)),hAPP(c_Int_Onat,U_7098)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7096),U_7098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7098)) )
& ! [U_7097,U_7095] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7095),U_7097))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7097)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7095)),hAPP(c_Int_Onat,U_7097))) ) ),
inference(miniscope,[status(thm)],[f_1918_2]) ).
fof(f_1918_4,plain,
( ! [U_7095,U_7097] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7095),U_7097))
| ~ sP640(U_7095,U_7097) )
& ! [U_7095,U_7097] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7097))
| ~ sP640(U_7095,U_7097) )
& ! [U_7098,U_7096] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7096)),hAPP(c_Int_Onat,U_7098)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7096),U_7098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7098)) )
& ! [U_7095,U_7097] :
( sP640(U_7095,U_7097)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7095)),hAPP(c_Int_Onat,U_7097))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP640])],[f_1918_3]) ).
cnf(f_1918_5,plain,
( sP640(U_7095,U_7097)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7095)),hAPP(c_Int_Onat,U_7097))) ),
inference(clausify,[status(thm)],[f_1918_4]) ).
cnf(f_1918_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7096)),hAPP(c_Int_Onat,U_7098)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7096),U_7098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7098)) ),
inference(clausify,[status(thm)],[f_1918_4]) ).
cnf(f_1918_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7097))
| ~ sP640(U_7095,U_7097) ),
inference(clausify,[status(thm)],[f_1918_4]) ).
cnf(f_1918_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7095),U_7097))
| ~ sP640(U_7095,U_7097) ),
inference(clausify,[status(thm)],[f_1918_4]) ).
fof(f_1919_1,plain,
! [V_m,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_mod__le__divisor]) ).
fof(f_1919_2,plain,
! [U_7100,U_7099] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7100,U_7099)),U_7099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7099)) ),
inference(variable_rename,[status(thm)],[f_1919_1]) ).
fof(f_1919_3,plain,
! [U_7099,U_7100] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7100,U_7099)),U_7099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7099)) ),
inference(definitional_conversion,[status(esa)],[f_1919_2]) ).
cnf(f_1919_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7100,U_7099)),U_7099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7099)) ),
inference(clausify,[status(thm)],[f_1919_3]) ).
fof(f_1920_1,plain,
! [V_y_2,V_x_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J]) ).
fof(f_1920_2,plain,
! [U_7102,U_7101] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7101)),hAPP(c_Int_Onat,U_7102)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7101),U_7102)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7101),U_7102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7101)),hAPP(c_Int_Onat,U_7102))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7101)) ),
inference(variable_rename,[status(thm)],[f_1920_1]) ).
fof(f_1920_3,plain,
( ! [U_7101,U_7102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7101)),hAPP(c_Int_Onat,U_7102)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7101),U_7102))
| ~ sP641(U_7101,U_7102) )
& ! [U_7101,U_7102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7101),U_7102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7101)),hAPP(c_Int_Onat,U_7102)))
| ~ sP641(U_7101,U_7102) )
& ! [U_7101,U_7102] :
( sP641(U_7101,U_7102)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7101)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP641])],[f_1920_2]) ).
cnf(f_1920_4,plain,
( sP641(U_7101,U_7102)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7101)) ),
inference(clausify,[status(thm)],[f_1920_3]) ).
cnf(f_1920_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7101),U_7102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7101)),hAPP(c_Int_Onat,U_7102)))
| ~ sP641(U_7101,U_7102) ),
inference(clausify,[status(thm)],[f_1920_3]) ).
cnf(f_1920_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7101)),hAPP(c_Int_Onat,U_7102)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7101),U_7102))
| ~ sP641(U_7101,U_7102) ),
inference(clausify,[status(thm)],[f_1920_3]) ).
fof(f_1921_1,plain,
hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_nat__1]) ).
fof(f_1921_2,plain,
hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_1921_1]) ).
cnf(f_1921_3,plain,
hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1921_2]) ).
fof(f_1922_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_mod__mult__self4]) ).
fof(f_1922_2,plain,
! [U_7105,U_7104,U_7103] : 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),U_7103),U_7104)),U_7105)),U_7104) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7105),U_7104),
inference(variable_rename,[status(thm)],[f_1922_1]) ).
fof(f_1922_3,plain,
! [U_7105,U_7104,U_7103] : 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),U_7103),U_7104)),U_7105)),U_7104) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7105),U_7104),
inference(definitional_conversion,[status(esa)],[f_1922_2]) ).
cnf(f_1922_4,plain,
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),U_7103),U_7104)),U_7105)),U_7104) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7105),U_7104),
inference(clausify,[status(thm)],[f_1922_3]) ).
fof(f_1923_1,plain,
! [V_z] :
( ( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ) ),
inference(fof_nnf,[status(thm)],[fact_int__nat__eq]) ).
fof(f_1923_2,plain,
! [U_7106] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7106)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7106)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7106)) = U_7106
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7106)) ) ),
inference(variable_rename,[status(thm)],[f_1923_1]) ).
fof(f_1923_3,plain,
( ! [U_7108] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7108)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7108)) )
& ! [U_7107] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7107)) = U_7107
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7107)) ) ),
inference(miniscope,[status(thm)],[f_1923_2]) ).
fof(f_1923_4,plain,
( ! [U_7108] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7108)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7108)) )
& ! [U_7107] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7107)) = U_7107
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7107)) ) ),
inference(definitional_conversion,[status(esa)],[f_1923_3]) ).
cnf(f_1923_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7107)) = U_7107
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7107)) ),
inference(clausify,[status(thm)],[f_1923_4]) ).
cnf(f_1923_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7108)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7108)) ),
inference(clausify,[status(thm)],[f_1923_4]) ).
fof(f_1924_1,plain,
! [V_z_2,V_m_2] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| V_m_2 != hAPP(c_Int_Onat,V_z_2) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
& V_m_2 = hAPP(c_Int_Onat,V_z_2) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) != V_z_2 ) ),
inference(fof_nnf,[status(thm)],[fact_int__eq__iff]) ).
fof(f_1924_2,plain,
! [U_7110,U_7109] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7109) = U_7110
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7110))
| U_7109 != hAPP(c_Int_Onat,U_7110) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7110))
& U_7109 = hAPP(c_Int_Onat,U_7110) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7109) != U_7110 ) ),
inference(variable_rename,[status(thm)],[f_1924_1]) ).
fof(f_1924_3,plain,
( ! [U_7114,U_7112] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7112) = U_7114
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7114))
| U_7112 != hAPP(c_Int_Onat,U_7114) )
& ! [U_7113,U_7111] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7113))
& U_7111 = hAPP(c_Int_Onat,U_7113) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7111) != U_7113 ) ),
inference(miniscope,[status(thm)],[f_1924_2]) ).
fof(f_1924_4,plain,
( ! [U_7113,U_7111] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7113))
| ~ sP642(U_7113,U_7111) )
& ! [U_7113,U_7111] :
( U_7111 = hAPP(c_Int_Onat,U_7113)
| ~ sP642(U_7113,U_7111) )
& ! [U_7114,U_7112] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7112) = U_7114
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7114))
| U_7112 != hAPP(c_Int_Onat,U_7114) )
& ! [U_7113,U_7111] :
( sP642(U_7113,U_7111)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7111) != U_7113 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP642])],[f_1924_3]) ).
cnf(f_1924_5,plain,
( sP642(U_7113,U_7111)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7111) != U_7113 ),
inference(clausify,[status(thm)],[f_1924_4]) ).
cnf(f_1924_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7112) = U_7114
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7114))
| U_7112 != hAPP(c_Int_Onat,U_7114) ),
inference(clausify,[status(thm)],[f_1924_4]) ).
cnf(f_1924_7,plain,
( U_7111 = hAPP(c_Int_Onat,U_7113)
| ~ sP642(U_7113,U_7111) ),
inference(clausify,[status(thm)],[f_1924_4]) ).
cnf(f_1924_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7113))
| ~ sP642(U_7113,U_7111) ),
inference(clausify,[status(thm)],[f_1924_4]) ).
fof(f_1925_1,plain,
! [V_z] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__le]) ).
fof(f_1925_2,plain,
! [U_7115] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7115)) = U_7115
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7115)) ),
inference(variable_rename,[status(thm)],[f_1925_1]) ).
fof(f_1925_3,plain,
! [U_7115] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7115)) = U_7115
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7115)) ),
inference(definitional_conversion,[status(esa)],[f_1925_2]) ).
cnf(f_1925_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7115)) = U_7115
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7115)) ),
inference(clausify,[status(thm)],[f_1925_3]) ).
fof(f_1926_1,plain,
! [V_z_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
| ~ 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)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless]) ).
fof(f_1926_2,plain,
! [U_7117,U_7116] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7116),hAPP(c_Int_Onat,U_7117)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7116)),U_7117)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7116)),U_7117))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7116),hAPP(c_Int_Onat,U_7117))) ) ),
inference(variable_rename,[status(thm)],[f_1926_1]) ).
fof(f_1926_3,plain,
( ! [U_7121,U_7119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7119),hAPP(c_Int_Onat,U_7121)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7119)),U_7121)) )
& ! [U_7120,U_7118] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7118)),U_7120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7118),hAPP(c_Int_Onat,U_7120))) ) ),
inference(miniscope,[status(thm)],[f_1926_2]) ).
fof(f_1926_4,plain,
( ! [U_7119,U_7121] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7119),hAPP(c_Int_Onat,U_7121)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7119)),U_7121)) )
& ! [U_7120,U_7118] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7118)),U_7120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7118),hAPP(c_Int_Onat,U_7120))) ) ),
inference(definitional_conversion,[status(esa)],[f_1926_3]) ).
cnf(f_1926_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7118)),U_7120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7118),hAPP(c_Int_Onat,U_7120))) ),
inference(clausify,[status(thm)],[f_1926_4]) ).
cnf(f_1926_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7119),hAPP(c_Int_Onat,U_7121)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7119)),U_7121)) ),
inference(clausify,[status(thm)],[f_1926_4]) ).
fof(f_1927_1,plain,
! [V_y,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J]) ).
fof(f_1927_2,plain,
! [U_7123,U_7122] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7122)),hAPP(c_Int_Onat,U_7123)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7122),U_7123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7122)) ),
inference(variable_rename,[status(thm)],[f_1927_1]) ).
fof(f_1927_3,plain,
! [U_7122,U_7123] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7122)),hAPP(c_Int_Onat,U_7123)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7122),U_7123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7122)) ),
inference(definitional_conversion,[status(esa)],[f_1927_2]) ).
cnf(f_1927_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7122)),hAPP(c_Int_Onat,U_7123)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7122),U_7123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7122)) ),
inference(clausify,[status(thm)],[f_1927_3]) ).
fof(f_1928_1,plain,
! [V_y,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_nat__div__distrib]) ).
fof(f_1928_2,plain,
! [U_7125,U_7124] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7124),U_7125)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7124)),hAPP(c_Int_Onat,U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7124)) ),
inference(variable_rename,[status(thm)],[f_1928_1]) ).
fof(f_1928_3,plain,
! [U_7124,U_7125] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7124),U_7125)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7124)),hAPP(c_Int_Onat,U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7124)) ),
inference(definitional_conversion,[status(esa)],[f_1928_2]) ).
cnf(f_1928_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7124),U_7125)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7124)),hAPP(c_Int_Onat,U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7124)) ),
inference(clausify,[status(thm)],[f_1928_3]) ).
fof(f_1929_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__zminus__int]) ).
fof(f_1929_2,plain,
! [U_7126] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7126))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1929_1]) ).
fof(f_1929_3,plain,
! [U_7126] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7126))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1929_2]) ).
cnf(f_1929_4,plain,
hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7126))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1929_3]) ).
fof(f_1930_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).
fof(f_1930_2,plain,
! [U_7128,U_7127] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7127,U_7128) = 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),U_7127),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7128))),
inference(variable_rename,[status(thm)],[f_1930_1]) ).
fof(f_1930_3,plain,
! [U_7127,U_7128] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7127,U_7128) = 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),U_7127),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7128))),
inference(definitional_conversion,[status(esa)],[f_1930_2]) ).
cnf(f_1930_4,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7127,U_7128) = 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),U_7127),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7128))),
inference(clausify,[status(thm)],[f_1930_3]) ).
fof(f_1931_1,plain,
! [V_v_H] :
( ( 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)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
& ( 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))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ),
inference(fof_nnf,[status(thm)],[fact_one__mod__nat__number__of]) ).
fof(f_1931_2,plain,
! [U_7129] :
( ( 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),U_7129)) = 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),U_7129)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7129))) )
& ( 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),U_7129)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7129))) ) ),
inference(variable_rename,[status(thm)],[f_1931_1]) ).
fof(f_1931_3,plain,
( ! [U_7131] :
( 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),U_7131)) = 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),U_7131)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7131))) )
& ! [U_7130] :
( 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),U_7130)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7130))) ) ),
inference(miniscope,[status(thm)],[f_1931_2]) ).
fof(f_1931_4,plain,
( ! [U_7131] :
( 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),U_7131)) = 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),U_7131)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7131))) )
& ! [U_7130] :
( 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),U_7130)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7130))) ) ),
inference(definitional_conversion,[status(esa)],[f_1931_3]) ).
cnf(f_1931_5,plain,
( 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),U_7130)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7130))) ),
inference(clausify,[status(thm)],[f_1931_4]) ).
cnf(f_1931_6,plain,
( 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),U_7131)) = 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),U_7131)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7131))) ),
inference(clausify,[status(thm)],[f_1931_4]) ).
fof(f_1932_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_succ__def]) ).
fof(f_1932_2,plain,
! [U_7132] : c_Int_Osucc(U_7132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7132),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_1932_1]) ).
fof(f_1932_3,plain,
! [U_7132] : c_Int_Osucc(U_7132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7132),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_1932_2]) ).
cnf(f_1932_4,plain,
c_Int_Osucc(U_7132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7132),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1932_3]) ).
fof(f_1933_1,plain,
! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I2_J]) ).
fof(f_1933_2,plain,
! [U_7133] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7133),c_Int_OMin) = c_Int_Osucc(U_7133),
inference(variable_rename,[status(thm)],[f_1933_1]) ).
fof(f_1933_3,plain,
! [U_7133] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7133),c_Int_OMin) = c_Int_Osucc(U_7133),
inference(definitional_conversion,[status(esa)],[f_1933_2]) ).
cnf(f_1933_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7133),c_Int_OMin) = c_Int_Osucc(U_7133),
inference(clausify,[status(thm)],[f_1933_3]) ).
fof(f_1934_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).
fof(f_1934_2,plain,
! [U_7134] : 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)),U_7134)) = hAPP(c_Int_Onat,U_7134),
inference(variable_rename,[status(thm)],[f_1934_1]) ).
fof(f_1934_3,plain,
! [U_7134] : 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)),U_7134)) = hAPP(c_Int_Onat,U_7134),
inference(definitional_conversion,[status(esa)],[f_1934_2]) ).
cnf(f_1934_4,plain,
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)),U_7134)) = hAPP(c_Int_Onat,U_7134),
inference(clausify,[status(thm)],[f_1934_3]) ).
fof(f_1935_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_card__atLeastLessThan__int]) ).
fof(f_1935_2,plain,
! [U_7136,U_7135] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7135),U_7136)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7136),U_7135)),
inference(variable_rename,[status(thm)],[f_1935_1]) ).
fof(f_1935_3,plain,
! [U_7135,U_7136] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7135),U_7136)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7136),U_7135)),
inference(definitional_conversion,[status(esa)],[f_1935_2]) ).
cnf(f_1935_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7135),U_7136)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7136),U_7135)),
inference(clausify,[status(thm)],[f_1935_3]) ).
fof(f_1936_1,plain,
! [V_z_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq]) ).
fof(f_1936_2,plain,
! [U_7137] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7137)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7137)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7137))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7137))) ) ),
inference(variable_rename,[status(thm)],[f_1936_1]) ).
fof(f_1936_3,plain,
( ! [U_7139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7139)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7139)) )
& ! [U_7138] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7138))) ) ),
inference(miniscope,[status(thm)],[f_1936_2]) ).
fof(f_1936_4,plain,
( ! [U_7139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7139)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7139)) )
& ! [U_7138] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7138))) ) ),
inference(definitional_conversion,[status(esa)],[f_1936_3]) ).
cnf(f_1936_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7138))) ),
inference(clausify,[status(thm)],[f_1936_4]) ).
cnf(f_1936_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7139)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7139)) ),
inference(clausify,[status(thm)],[f_1936_4]) ).
fof(f_1937_1,plain,
! [V_z_2,V_w_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless]) ).
fof(f_1937_2,plain,
! [U_7141,U_7140] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7140),U_7141)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7140),U_7141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7140)) ),
inference(variable_rename,[status(thm)],[f_1937_1]) ).
fof(f_1937_3,plain,
( ! [U_7140,U_7141] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7140),U_7141))
| ~ sP643(U_7140,U_7141) )
& ! [U_7140,U_7141] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7140),U_7141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ sP643(U_7140,U_7141) )
& ! [U_7140,U_7141] :
( sP643(U_7140,U_7141)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7140)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP643])],[f_1937_2]) ).
cnf(f_1937_4,plain,
( sP643(U_7140,U_7141)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7140)) ),
inference(clausify,[status(thm)],[f_1937_3]) ).
cnf(f_1937_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7140),U_7141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ sP643(U_7140,U_7141) ),
inference(clausify,[status(thm)],[f_1937_3]) ).
cnf(f_1937_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7140),U_7141))
| ~ sP643(U_7140,U_7141) ),
inference(clausify,[status(thm)],[f_1937_3]) ).
fof(f_1938_1,plain,
! [V_y_2,V_x_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J]) ).
fof(f_1938_2,plain,
! [U_7143,U_7142] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7142)),hAPP(c_Int_Onat,U_7143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7142),U_7143)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7142),U_7143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7142)),hAPP(c_Int_Onat,U_7143))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7142)) ),
inference(variable_rename,[status(thm)],[f_1938_1]) ).
fof(f_1938_3,plain,
( ! [U_7143,U_7142] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7142)),hAPP(c_Int_Onat,U_7143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7142),U_7143))
| ~ sP644(U_7143,U_7142) )
& ! [U_7143,U_7142] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7142),U_7143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7142)),hAPP(c_Int_Onat,U_7143)))
| ~ sP644(U_7143,U_7142) )
& ! [U_7143,U_7142] :
( sP644(U_7143,U_7142)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7142)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP644])],[f_1938_2]) ).
cnf(f_1938_4,plain,
( sP644(U_7143,U_7142)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7142)) ),
inference(clausify,[status(thm)],[f_1938_3]) ).
cnf(f_1938_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7142),U_7143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7142)),hAPP(c_Int_Onat,U_7143)))
| ~ sP644(U_7143,U_7142) ),
inference(clausify,[status(thm)],[f_1938_3]) ).
cnf(f_1938_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7142)),hAPP(c_Int_Onat,U_7143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7142),U_7143))
| ~ sP644(U_7143,U_7142) ),
inference(clausify,[status(thm)],[f_1938_3]) ).
fof(f_1939_1,plain,
! [V_m_2,V_w_2] :
( ( hAPP(c_Int_Onat,V_w_2) = V_m_2
| ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
| ( V_w_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
& ( ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
& ( V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
| hAPP(c_Int_Onat,V_w_2) != V_m_2 ) ),
inference(fof_nnf,[status(thm)],[fact_nat__eq__iff]) ).
fof(f_1939_2,plain,
! [U_7145,U_7144] :
( ( hAPP(c_Int_Onat,U_7144) = U_7145
| ( U_7145 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7144)) )
| ( U_7144 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7145)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7144)) ) )
& ( ( ( U_7145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7144)) )
& ( U_7144 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7145)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7144)) ) )
| hAPP(c_Int_Onat,U_7144) != U_7145 ) ),
inference(variable_rename,[status(thm)],[f_1939_1]) ).
fof(f_1939_3,plain,
( ! [U_7149,U_7147] :
( hAPP(c_Int_Onat,U_7147) = U_7149
| ( U_7149 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7147)) )
| ( U_7147 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7149)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7147)) ) )
& ! [U_7148,U_7146] :
( ( ( U_7148 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7146)) )
& ( U_7146 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7148)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7146)) ) )
| hAPP(c_Int_Onat,U_7146) != U_7148 ) ),
inference(miniscope,[status(thm)],[f_1939_2]) ).
fof(f_1939_4,plain,
( ! [U_7147,U_7149] :
( U_7149 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP647(U_7147,U_7149) )
& ! [U_7147,U_7149] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7147))
| ~ sP647(U_7147,U_7149) )
& ! [U_7147,U_7149] :
( U_7147 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7149)
| ~ sP646(U_7147,U_7149) )
& ! [U_7147,U_7149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7147))
| ~ sP646(U_7147,U_7149) )
& ! [U_7146,U_7148] :
( U_7148 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7146))
| ~ sP645(U_7146,U_7148) )
& ! [U_7146,U_7148] :
( U_7146 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7148)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7146))
| ~ sP645(U_7146,U_7148) )
& ! [U_7147,U_7149] :
( hAPP(c_Int_Onat,U_7147) = U_7149
| sP647(U_7147,U_7149)
| sP646(U_7147,U_7149) )
& ! [U_7146,U_7148] :
( sP645(U_7146,U_7148)
| hAPP(c_Int_Onat,U_7146) != U_7148 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP645,sP646,sP647])],[f_1939_3]) ).
cnf(f_1939_5,plain,
( sP645(U_7146,U_7148)
| hAPP(c_Int_Onat,U_7146) != U_7148 ),
inference(clausify,[status(thm)],[f_1939_4]) ).
cnf(f_1939_6,plain,
( hAPP(c_Int_Onat,U_7147) = U_7149
| sP647(U_7147,U_7149)
| sP646(U_7147,U_7149) ),
inference(clausify,[status(thm)],[f_1939_4]) ).
cnf(f_1939_7,plain,
( U_7146 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7148)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7146))
| ~ sP645(U_7146,U_7148) ),
inference(clausify,[status(thm)],[f_1939_4]) ).
cnf(f_1939_8,plain,
( U_7148 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7146))
| ~ sP645(U_7146,U_7148) ),
inference(clausify,[status(thm)],[f_1939_4]) ).
cnf(f_1939_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7147))
| ~ sP646(U_7147,U_7149) ),
inference(clausify,[status(thm)],[f_1939_4]) ).
cnf(f_1939_10,plain,
( U_7147 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7149)
| ~ sP646(U_7147,U_7149) ),
inference(clausify,[status(thm)],[f_1939_4]) ).
cnf(f_1939_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7147))
| ~ sP647(U_7147,U_7149) ),
inference(clausify,[status(thm)],[f_1939_4]) ).
cnf(f_1939_12,plain,
( U_7149 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP647(U_7147,U_7149) ),
inference(clausify,[status(thm)],[f_1939_4]) ).
fof(f_1940_1,plain,
! [V_w_2,V_m_2] :
( ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
| ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
| ( V_w_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
& ( ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
& ( V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
| V_m_2 != hAPP(c_Int_Onat,V_w_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__eq__iff2]) ).
fof(f_1940_2,plain,
! [U_7151,U_7150] :
( ( U_7150 = hAPP(c_Int_Onat,U_7151)
| ( U_7150 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7151)) )
| ( U_7151 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7150)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7151)) ) )
& ( ( ( U_7150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7151)) )
& ( U_7151 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7150)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7151)) ) )
| U_7150 != hAPP(c_Int_Onat,U_7151) ) ),
inference(variable_rename,[status(thm)],[f_1940_1]) ).
fof(f_1940_3,plain,
( ! [U_7155,U_7153] :
( U_7153 = hAPP(c_Int_Onat,U_7155)
| ( U_7153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7155)) )
| ( U_7155 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7153)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7155)) ) )
& ! [U_7154,U_7152] :
( ( ( U_7152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7154)) )
& ( U_7154 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7152)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7154)) ) )
| U_7152 != hAPP(c_Int_Onat,U_7154) ) ),
inference(miniscope,[status(thm)],[f_1940_2]) ).
fof(f_1940_4,plain,
( ! [U_7155,U_7153] :
( U_7153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP650(U_7155,U_7153) )
& ! [U_7155,U_7153] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7155))
| ~ sP650(U_7155,U_7153) )
& ! [U_7155,U_7153] :
( U_7155 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7153)
| ~ sP649(U_7155,U_7153) )
& ! [U_7155,U_7153] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7155))
| ~ sP649(U_7155,U_7153) )
& ! [U_7154,U_7152] :
( U_7152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7154))
| ~ sP648(U_7154,U_7152) )
& ! [U_7154,U_7152] :
( U_7154 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7152)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7154))
| ~ sP648(U_7154,U_7152) )
& ! [U_7155,U_7153] :
( U_7153 = hAPP(c_Int_Onat,U_7155)
| sP650(U_7155,U_7153)
| sP649(U_7155,U_7153) )
& ! [U_7154,U_7152] :
( sP648(U_7154,U_7152)
| U_7152 != hAPP(c_Int_Onat,U_7154) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP648,sP649,sP650])],[f_1940_3]) ).
cnf(f_1940_5,plain,
( sP648(U_7154,U_7152)
| U_7152 != hAPP(c_Int_Onat,U_7154) ),
inference(clausify,[status(thm)],[f_1940_4]) ).
cnf(f_1940_6,plain,
( U_7153 = hAPP(c_Int_Onat,U_7155)
| sP650(U_7155,U_7153)
| sP649(U_7155,U_7153) ),
inference(clausify,[status(thm)],[f_1940_4]) ).
cnf(f_1940_7,plain,
( U_7154 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7152)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7154))
| ~ sP648(U_7154,U_7152) ),
inference(clausify,[status(thm)],[f_1940_4]) ).
cnf(f_1940_8,plain,
( U_7152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7154))
| ~ sP648(U_7154,U_7152) ),
inference(clausify,[status(thm)],[f_1940_4]) ).
cnf(f_1940_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7155))
| ~ sP649(U_7155,U_7153) ),
inference(clausify,[status(thm)],[f_1940_4]) ).
cnf(f_1940_10,plain,
( U_7155 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7153)
| ~ sP649(U_7155,U_7153) ),
inference(clausify,[status(thm)],[f_1940_4]) ).
cnf(f_1940_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7155))
| ~ sP650(U_7155,U_7153) ),
inference(clausify,[status(thm)],[f_1940_4]) ).
cnf(f_1940_12,plain,
( U_7153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP650(U_7155,U_7153) ),
inference(clausify,[status(thm)],[f_1940_4]) ).
fof(f_1941_1,plain,
! [V_z_2,V_w_2] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle]) ).
fof(f_1941_2,plain,
! [U_7157,U_7156] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7156)),hAPP(c_Int_Onat,U_7157)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7156),U_7157)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7156),U_7157))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7156)),hAPP(c_Int_Onat,U_7157))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7157))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7156)) ) ),
inference(variable_rename,[status(thm)],[f_1941_1]) ).
fof(f_1941_3,plain,
( ! [U_7156,U_7157] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7156)),hAPP(c_Int_Onat,U_7157)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7156),U_7157))
| ~ sP652(U_7156,U_7157) )
& ! [U_7156,U_7157] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7156),U_7157))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7156)),hAPP(c_Int_Onat,U_7157)))
| ~ sP652(U_7156,U_7157) )
& ! [U_7156,U_7157] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7157))
| ~ sP651(U_7156,U_7157) )
& ! [U_7156,U_7157] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7156))
| ~ sP651(U_7156,U_7157) )
& ! [U_7156,U_7157] :
( sP652(U_7156,U_7157)
| sP651(U_7156,U_7157) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP651,sP652])],[f_1941_2]) ).
cnf(f_1941_4,plain,
( sP652(U_7156,U_7157)
| sP651(U_7156,U_7157) ),
inference(clausify,[status(thm)],[f_1941_3]) ).
cnf(f_1941_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7156))
| ~ sP651(U_7156,U_7157) ),
inference(clausify,[status(thm)],[f_1941_3]) ).
cnf(f_1941_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7157))
| ~ sP651(U_7156,U_7157) ),
inference(clausify,[status(thm)],[f_1941_3]) ).
cnf(f_1941_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7156),U_7157))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7156)),hAPP(c_Int_Onat,U_7157)))
| ~ sP652(U_7156,U_7157) ),
inference(clausify,[status(thm)],[f_1941_3]) ).
cnf(f_1941_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7156)),hAPP(c_Int_Onat,U_7157)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7156),U_7157))
| ~ sP652(U_7156,U_7157) ),
inference(clausify,[status(thm)],[f_1941_3]) ).
fof(f_1942_1,plain,
! [V_i_2,V_Pa_2] :
( ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
| ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [B_n] :
( ~ hBOOL(hAPP(V_Pa_2,B_n))
& V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
& ( ( ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [B_n] :
( hBOOL(hAPP(V_Pa_2,B_n))
| V_i_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
| ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__nat]) ).
fof(f_1942_2,plain,
! [U_7161,U_7160] :
( ( hBOOL(hAPP(U_7160,hAPP(c_Int_Onat,U_7161)))
| ( ~ hBOOL(hAPP(U_7160,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7161),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [U_7159] :
( ~ hBOOL(hAPP(U_7160,U_7159))
& U_7161 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7159) ) )
& ( ( ( hBOOL(hAPP(U_7160,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7161),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7158] :
( hBOOL(hAPP(U_7160,U_7158))
| U_7161 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7158) ) )
| ~ hBOOL(hAPP(U_7160,hAPP(c_Int_Onat,U_7161))) ) ),
inference(variable_rename,[status(thm)],[f_1942_1]) ).
fof(f_1942_3,plain,
( ! [U_7165,U_7163] :
( hBOOL(hAPP(U_7163,hAPP(c_Int_Onat,U_7165)))
| ( ~ hBOOL(hAPP(U_7163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7165),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [U_7159] :
( ~ hBOOL(hAPP(U_7163,U_7159))
& U_7165 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7159) ) )
& ! [U_7164,U_7162] :
( ( ( hBOOL(hAPP(U_7162,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7164),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7158] :
( hBOOL(hAPP(U_7162,U_7158))
| U_7164 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7158) ) )
| ~ hBOOL(hAPP(U_7162,hAPP(c_Int_Onat,U_7164))) ) ),
inference(miniscope,[status(thm)],[f_1942_2]) ).
fof(f_1942_4,plain,
( ! [U_7165,U_7163] :
( hBOOL(hAPP(U_7163,hAPP(c_Int_Onat,U_7165)))
| ( ~ hBOOL(hAPP(U_7163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7165),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_7163,sK203(U_7165,U_7163)))
& U_7165 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK203(U_7165,U_7163)) ) )
& ! [U_7164,U_7162] :
( ( ( hBOOL(hAPP(U_7162,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7164),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7158] :
( hBOOL(hAPP(U_7162,U_7158))
| U_7164 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7158) ) )
| ~ hBOOL(hAPP(U_7162,hAPP(c_Int_Onat,U_7164))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_7159,sK203(U_7165,U_7163))],[f_1942_3]) ).
fof(f_1942_5,plain,
( ! [U_7165,U_7163] :
( ~ hBOOL(hAPP(U_7163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP655(U_7165,U_7163) )
& ! [U_7165,U_7163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7165),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP655(U_7165,U_7163) )
& ! [U_7165,U_7163] :
( ~ hBOOL(hAPP(U_7163,sK203(U_7165,U_7163)))
| ~ sP654(U_7165,U_7163) )
& ! [U_7165,U_7163] :
( U_7165 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK203(U_7165,U_7163))
| ~ sP654(U_7165,U_7163) )
& ! [U_7164,U_7162,U_7158] :
( hBOOL(hAPP(U_7162,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7164),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP653(U_7164,U_7162,U_7158) )
& ! [U_7164,U_7162,U_7158] :
( hBOOL(hAPP(U_7162,U_7158))
| U_7164 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7158)
| ~ sP653(U_7164,U_7162,U_7158) )
& ! [U_7165,U_7163] :
( hBOOL(hAPP(U_7163,hAPP(c_Int_Onat,U_7165)))
| sP655(U_7165,U_7163)
| sP654(U_7165,U_7163) )
& ! [U_7164,U_7162,U_7158] :
( sP653(U_7164,U_7162,U_7158)
| ~ hBOOL(hAPP(U_7162,hAPP(c_Int_Onat,U_7164))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP653,sP654,sP655])],[f_1942_4]) ).
cnf(f_1942_6,plain,
( sP653(U_7164,U_7162,U_7158)
| ~ hBOOL(hAPP(U_7162,hAPP(c_Int_Onat,U_7164))) ),
inference(clausify,[status(thm)],[f_1942_5]) ).
cnf(f_1942_7,plain,
( hBOOL(hAPP(U_7163,hAPP(c_Int_Onat,U_7165)))
| sP655(U_7165,U_7163)
| sP654(U_7165,U_7163) ),
inference(clausify,[status(thm)],[f_1942_5]) ).
cnf(f_1942_8,plain,
( hBOOL(hAPP(U_7162,U_7158))
| U_7164 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7158)
| ~ sP653(U_7164,U_7162,U_7158) ),
inference(clausify,[status(thm)],[f_1942_5]) ).
cnf(f_1942_9,plain,
( hBOOL(hAPP(U_7162,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7164),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP653(U_7164,U_7162,U_7158) ),
inference(clausify,[status(thm)],[f_1942_5]) ).
cnf(f_1942_10,plain,
( U_7165 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK203(U_7165,U_7163))
| ~ sP654(U_7165,U_7163) ),
inference(clausify,[status(thm)],[f_1942_5]) ).
cnf(f_1942_11,plain,
( ~ hBOOL(hAPP(U_7163,sK203(U_7165,U_7163)))
| ~ sP654(U_7165,U_7163) ),
inference(clausify,[status(thm)],[f_1942_5]) ).
cnf(f_1942_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7165),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP655(U_7165,U_7163) ),
inference(clausify,[status(thm)],[f_1942_5]) ).
cnf(f_1942_13,plain,
( ~ hBOOL(hAPP(U_7163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP655(U_7165,U_7163) ),
inference(clausify,[status(thm)],[f_1942_5]) ).
fof(f_1943_1,plain,
! [V_k_2,V_n_2,V_Pa_2] :
( ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_Pa_2,B_j))
& 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)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(V_Pa_2,V_n_2))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_Pa_2,B_j))
| 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(V_Pa_2,V_n_2))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__mod]) ).
fof(f_1943_2,plain,
! [U_7172,U_7171,U_7170] :
( ( hBOOL(hAPP(U_7170,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7171,U_7172)))
| ( ? [U_7169,U_7168] :
( ~ hBOOL(hAPP(U_7170,U_7168))
& U_7171 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7172),U_7169)),U_7168)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7168),U_7172)) )
& U_7172 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7170,U_7171))
& U_7172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_7167,U_7166] :
( hBOOL(hAPP(U_7170,U_7166))
| U_7171 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7172),U_7167)),U_7166)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7166),U_7172)) )
| U_7172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7170,U_7171))
| U_7172 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7170,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7171,U_7172))) ) ),
inference(variable_rename,[status(thm)],[f_1943_1]) ).
fof(f_1943_3,plain,
( ! [U_7178,U_7176,U_7174] :
( hBOOL(hAPP(U_7174,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7176,U_7178)))
| ( ? [U_7169,U_7168] :
( ~ hBOOL(hAPP(U_7174,U_7168))
& U_7176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7178),U_7169)),U_7168)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7168),U_7178)) )
& U_7178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7174,U_7176))
& U_7178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7177,U_7175,U_7173] :
( ( ( ! [U_7167,U_7166] :
( hBOOL(hAPP(U_7173,U_7166))
| U_7175 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7177),U_7167)),U_7166)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7166),U_7177)) )
| U_7177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7173,U_7175))
| U_7177 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7173,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7175,U_7177))) ) ),
inference(miniscope,[status(thm)],[f_1943_2]) ).
fof(f_1943_4,plain,
( ! [U_7178,U_7176,U_7174] :
( hBOOL(hAPP(U_7174,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7176,U_7178)))
| ( ? [U_7168] :
( ~ hBOOL(hAPP(U_7174,U_7168))
& U_7176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7178),sK204(U_7178,U_7176,U_7174))),U_7168)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7168),U_7178)) )
& U_7178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7174,U_7176))
& U_7178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7177,U_7175,U_7173] :
( ( ( ! [U_7167,U_7166] :
( hBOOL(hAPP(U_7173,U_7166))
| U_7175 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7177),U_7167)),U_7166)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7166),U_7177)) )
| U_7177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7173,U_7175))
| U_7177 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7173,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7175,U_7177))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_7169,sK204(U_7178,U_7176,U_7174))],[f_1943_3]) ).
fof(f_1943_5,plain,
( ! [U_7178,U_7176,U_7174] :
( hBOOL(hAPP(U_7174,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7176,U_7178)))
| ( ~ hBOOL(hAPP(U_7174,sK205(U_7178,U_7176,U_7174)))
& U_7176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7178),sK204(U_7178,U_7176,U_7174))),sK205(U_7178,U_7176,U_7174))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK205(U_7178,U_7176,U_7174)),U_7178))
& U_7178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7174,U_7176))
& U_7178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7177,U_7175,U_7173] :
( ( ( ! [U_7167,U_7166] :
( hBOOL(hAPP(U_7173,U_7166))
| U_7175 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7177),U_7167)),U_7166)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7166),U_7177)) )
| U_7177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7173,U_7175))
| U_7177 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7173,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7175,U_7177))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_7168,sK205(U_7178,U_7176,U_7174))],[f_1943_4]) ).
fof(f_1943_6,plain,
( ! [U_7174,U_7176,U_7178] :
( ~ hBOOL(hAPP(U_7174,sK205(U_7178,U_7176,U_7174)))
| ~ sP658(U_7174,U_7176,U_7178) )
& ! [U_7174,U_7176,U_7178] :
( U_7176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7178),sK204(U_7178,U_7176,U_7174))),sK205(U_7178,U_7176,U_7174))
| ~ sP658(U_7174,U_7176,U_7178) )
& ! [U_7174,U_7176,U_7178] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK205(U_7178,U_7176,U_7174)),U_7178))
| ~ sP658(U_7174,U_7176,U_7178) )
& ! [U_7174,U_7176,U_7178] :
( U_7178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP658(U_7174,U_7176,U_7178) )
& ! [U_7174,U_7176,U_7178] :
( ~ hBOOL(hAPP(U_7174,U_7176))
| ~ sP657(U_7174,U_7176,U_7178) )
& ! [U_7174,U_7176,U_7178] :
( U_7178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP657(U_7174,U_7176,U_7178) )
& ! [U_7177,U_7167,U_7166,U_7173,U_7175] :
( hBOOL(hAPP(U_7173,U_7166))
| U_7175 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7177),U_7167)),U_7166)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7166),U_7177))
| U_7177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP656(U_7177,U_7167,U_7166,U_7173,U_7175) )
& ! [U_7177,U_7167,U_7166,U_7173,U_7175] :
( hBOOL(hAPP(U_7173,U_7175))
| U_7177 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP656(U_7177,U_7167,U_7166,U_7173,U_7175) )
& ! [U_7174,U_7176,U_7178] :
( hBOOL(hAPP(U_7174,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7176,U_7178)))
| sP658(U_7174,U_7176,U_7178)
| sP657(U_7174,U_7176,U_7178) )
& ! [U_7177,U_7167,U_7166,U_7173,U_7175] :
( sP656(U_7177,U_7167,U_7166,U_7173,U_7175)
| ~ hBOOL(hAPP(U_7173,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7175,U_7177))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP656,sP657,sP658])],[f_1943_5]) ).
cnf(f_1943_7,plain,
( sP656(U_7177,U_7167,U_7166,U_7173,U_7175)
| ~ hBOOL(hAPP(U_7173,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7175,U_7177))) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_8,plain,
( hBOOL(hAPP(U_7174,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7176,U_7178)))
| sP658(U_7174,U_7176,U_7178)
| sP657(U_7174,U_7176,U_7178) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_9,plain,
( hBOOL(hAPP(U_7173,U_7175))
| U_7177 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP656(U_7177,U_7167,U_7166,U_7173,U_7175) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_10,plain,
( hBOOL(hAPP(U_7173,U_7166))
| U_7175 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7177),U_7167)),U_7166)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7166),U_7177))
| U_7177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP656(U_7177,U_7167,U_7166,U_7173,U_7175) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_11,plain,
( U_7178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP657(U_7174,U_7176,U_7178) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_12,plain,
( ~ hBOOL(hAPP(U_7174,U_7176))
| ~ sP657(U_7174,U_7176,U_7178) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_13,plain,
( U_7178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP658(U_7174,U_7176,U_7178) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_14,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK205(U_7178,U_7176,U_7174)),U_7178))
| ~ sP658(U_7174,U_7176,U_7178) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_15,plain,
( U_7176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7178),sK204(U_7178,U_7176,U_7174))),sK205(U_7178,U_7176,U_7174))
| ~ sP658(U_7174,U_7176,U_7178) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
cnf(f_1943_16,plain,
( ~ hBOOL(hAPP(U_7174,sK205(U_7178,U_7176,U_7174)))
| ~ sP658(U_7174,U_7176,U_7178) ),
inference(clausify,[status(thm)],[f_1943_6]) ).
fof(f_1944_1,plain,
! [V_q,V_b,V_r,V_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) ),
inference(fof_nnf,[status(thm)],[fact_mod__lemma]) ).
fof(f_1944_2,plain,
! [U_7182,U_7181,U_7180,U_7179] :
( 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),U_7181),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7182,U_7179))),U_7180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7181),U_7179)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7180),U_7181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7179)) ),
inference(variable_rename,[status(thm)],[f_1944_1]) ).
fof(f_1944_3,plain,
! [U_7180,U_7181,U_7182,U_7179] :
( 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),U_7181),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7182,U_7179))),U_7180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7181),U_7179)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7180),U_7181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7179)) ),
inference(definitional_conversion,[status(esa)],[f_1944_2]) ).
cnf(f_1944_4,plain,
( 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),U_7181),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7182,U_7179))),U_7180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7181),U_7179)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7180),U_7181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7179)) ),
inference(clausify,[status(thm)],[f_1944_3]) ).
fof(f_1945_1,plain,
! [V_z_H,V_z] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__distrib]) ).
fof(f_1945_2,plain,
! [U_7184,U_7183] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7183),U_7184)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7183)),hAPP(c_Int_Onat,U_7184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7183)) ),
inference(variable_rename,[status(thm)],[f_1945_1]) ).
fof(f_1945_3,plain,
! [U_7184,U_7183] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7183),U_7184)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7183)),hAPP(c_Int_Onat,U_7184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7183)) ),
inference(definitional_conversion,[status(esa)],[f_1945_2]) ).
cnf(f_1945_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7183),U_7184)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7183)),hAPP(c_Int_Onat,U_7184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7183)) ),
inference(clausify,[status(thm)],[f_1945_3]) ).
fof(f_1946_1,plain,
! [V_y,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J]) ).
fof(f_1946_2,plain,
! [U_7186,U_7185] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7185)),hAPP(c_Int_Onat,U_7186)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7185),U_7186))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7186))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7185)) ),
inference(variable_rename,[status(thm)],[f_1946_1]) ).
fof(f_1946_3,plain,
! [U_7185,U_7186] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7185)),hAPP(c_Int_Onat,U_7186)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7185),U_7186))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7186))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7185)) ),
inference(definitional_conversion,[status(esa)],[f_1946_2]) ).
cnf(f_1946_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7185)),hAPP(c_Int_Onat,U_7186)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7185),U_7186))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7186))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7185)) ),
inference(clausify,[status(thm)],[f_1946_3]) ).
fof(f_1947_1,plain,
! [V_v_2,V_m_2] :
( ( 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)
| ~ 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)))
| V_m_2 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) )
& ( ( 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)))
& V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) )
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of]) ).
fof(f_1947_2,plain,
! [U_7188,U_7187] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7187) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7188)
| ~ 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),U_7188)))
| U_7187 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7188)) )
& ( ( 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),U_7188)))
& U_7187 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7188)) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7187) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7188) ) ),
inference(variable_rename,[status(thm)],[f_1947_1]) ).
fof(f_1947_3,plain,
( ! [U_7192,U_7190] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7190) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7192)
| ~ 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),U_7192)))
| U_7190 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7192)) )
& ! [U_7191,U_7189] :
( ( 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),U_7191)))
& U_7189 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7191)) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7189) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7191) ) ),
inference(miniscope,[status(thm)],[f_1947_2]) ).
fof(f_1947_4,plain,
( ! [U_7189,U_7191] :
( 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),U_7191)))
| ~ sP659(U_7189,U_7191) )
& ! [U_7189,U_7191] :
( U_7189 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7191))
| ~ sP659(U_7189,U_7191) )
& ! [U_7192,U_7190] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7190) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7192)
| ~ 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),U_7192)))
| U_7190 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7192)) )
& ! [U_7189,U_7191] :
( sP659(U_7189,U_7191)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7189) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7191) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP659])],[f_1947_3]) ).
cnf(f_1947_5,plain,
( sP659(U_7189,U_7191)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7189) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7191) ),
inference(clausify,[status(thm)],[f_1947_4]) ).
cnf(f_1947_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7190) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7192)
| ~ 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),U_7192)))
| U_7190 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7192)) ),
inference(clausify,[status(thm)],[f_1947_4]) ).
cnf(f_1947_7,plain,
( U_7189 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7191))
| ~ sP659(U_7189,U_7191) ),
inference(clausify,[status(thm)],[f_1947_4]) ).
cnf(f_1947_8,plain,
( 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),U_7191)))
| ~ sP659(U_7189,U_7191) ),
inference(clausify,[status(thm)],[f_1947_4]) ).
fof(f_1948_1,plain,
! [V_z_H,V_z] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib]) ).
fof(f_1948_2,plain,
! [U_7194,U_7193] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),U_7194)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7193)),hAPP(c_Int_Onat,U_7194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193)) ),
inference(variable_rename,[status(thm)],[f_1948_1]) ).
fof(f_1948_3,plain,
! [U_7193,U_7194] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),U_7194)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7193)),hAPP(c_Int_Onat,U_7194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193)) ),
inference(definitional_conversion,[status(esa)],[f_1948_2]) ).
cnf(f_1948_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),U_7194)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7193)),hAPP(c_Int_Onat,U_7194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193)) ),
inference(clausify,[status(thm)],[f_1948_3]) ).
fof(f_1949_1,plain,
! [V_y,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J]) ).
fof(f_1949_2,plain,
! [U_7196,U_7195] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7195)),hAPP(c_Int_Onat,U_7196)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7195),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195)) ),
inference(variable_rename,[status(thm)],[f_1949_1]) ).
fof(f_1949_3,plain,
! [U_7196,U_7195] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7195)),hAPP(c_Int_Onat,U_7196)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7195),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195)) ),
inference(definitional_conversion,[status(esa)],[f_1949_2]) ).
cnf(f_1949_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7195)),hAPP(c_Int_Onat,U_7196)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7195),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195)) ),
inference(clausify,[status(thm)],[f_1949_3]) ).
fof(f_1950_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).
fof(f_1950_2,plain,
! [U_7198,U_7197] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7197),U_7198) = 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)),U_7197)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7198))),
inference(variable_rename,[status(thm)],[f_1950_1]) ).
fof(f_1950_3,plain,
! [U_7197,U_7198] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7197),U_7198) = 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)),U_7197)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7198))),
inference(definitional_conversion,[status(esa)],[f_1950_2]) ).
cnf(f_1950_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7197),U_7198) = 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)),U_7197)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7198))),
inference(clausify,[status(thm)],[f_1950_3]) ).
fof(f_1951_1,plain,
! [V_z,V_z_H] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib]) ).
fof(f_1951_2,plain,
! [U_7200,U_7199] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7200),U_7199)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7200)),hAPP(c_Int_Onat,U_7199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7199),U_7200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7199)) ),
inference(variable_rename,[status(thm)],[f_1951_1]) ).
fof(f_1951_3,plain,
! [U_7199,U_7200] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7200),U_7199)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7200)),hAPP(c_Int_Onat,U_7199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7199),U_7200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7199)) ),
inference(definitional_conversion,[status(esa)],[f_1951_2]) ).
cnf(f_1951_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7200),U_7199)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7200)),hAPP(c_Int_Onat,U_7199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7199),U_7200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7199)) ),
inference(clausify,[status(thm)],[f_1951_3]) ).
fof(f_1952_1,plain,
! [V_m,V_k] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__times__mod__eq]) ).
fof(f_1952_2,plain,
! [U_7202,U_7201] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7201),U_7202)),U_7201) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7201)) ),
inference(variable_rename,[status(thm)],[f_1952_1]) ).
fof(f_1952_3,plain,
! [U_7201,U_7202] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7201),U_7202)),U_7201) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7201)) ),
inference(definitional_conversion,[status(esa)],[f_1952_2]) ).
cnf(f_1952_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7201),U_7202)),U_7201) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7201)) ),
inference(clausify,[status(thm)],[f_1952_3]) ).
fof(f_1953_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_card__greaterThanAtMost__int]) ).
fof(f_1953_2,plain,
! [U_7204,U_7203] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7203,U_7204)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7204),U_7203)),
inference(variable_rename,[status(thm)],[f_1953_1]) ).
fof(f_1953_3,plain,
! [U_7203,U_7204] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7203,U_7204)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7204),U_7203)),
inference(definitional_conversion,[status(esa)],[f_1953_2]) ).
cnf(f_1953_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7203,U_7204)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7204),U_7203)),
inference(clausify,[status(thm)],[f_1953_3]) ).
fof(f_1954_1,plain,
! [V_n,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J]) ).
fof(f_1954_2,plain,
! [U_7206,U_7205] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7205)),U_7206) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7205),U_7206))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7205)) ),
inference(variable_rename,[status(thm)],[f_1954_1]) ).
fof(f_1954_3,plain,
! [U_7205,U_7206] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7205)),U_7206) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7205),U_7206))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7205)) ),
inference(definitional_conversion,[status(esa)],[f_1954_2]) ).
cnf(f_1954_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7205)),U_7206) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7205),U_7206))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7205)) ),
inference(clausify,[status(thm)],[f_1954_3]) ).
fof(f_1955_1,plain,
! [V_n,V_z] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_nat__power__eq]) ).
fof(f_1955_2,plain,
! [U_7208,U_7207] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7207),U_7208)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7207)),U_7208)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7207)) ),
inference(variable_rename,[status(thm)],[f_1955_1]) ).
fof(f_1955_3,plain,
! [U_7207,U_7208] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7207),U_7208)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7207)),U_7208)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7207)) ),
inference(definitional_conversion,[status(esa)],[f_1955_2]) ).
cnf(f_1955_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7207),U_7208)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7207)),U_7208)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7207)) ),
inference(clausify,[status(thm)],[f_1955_3]) ).
fof(f_1956_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).
fof(f_1956_2,plain,
! [U_7209] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7209) = 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),U_7209))),
inference(variable_rename,[status(thm)],[f_1956_1]) ).
fof(f_1956_3,plain,
! [U_7209] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7209) = 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),U_7209))),
inference(definitional_conversion,[status(esa)],[f_1956_2]) ).
cnf(f_1956_4,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7209) = 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),U_7209))),
inference(clausify,[status(thm)],[f_1956_3]) ).
fof(f_1957_1,plain,
! [V_y,V_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J]) ).
fof(f_1957_2,plain,
! [U_7211,U_7210] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7210)),hAPP(c_Int_Onat,U_7211)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7210,U_7211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7210)) ),
inference(variable_rename,[status(thm)],[f_1957_1]) ).
fof(f_1957_3,plain,
! [U_7210,U_7211] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7210)),hAPP(c_Int_Onat,U_7211)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7210,U_7211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7210)) ),
inference(definitional_conversion,[status(esa)],[f_1957_2]) ).
cnf(f_1957_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7210)),hAPP(c_Int_Onat,U_7211)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7210,U_7211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7210)) ),
inference(clausify,[status(thm)],[f_1957_3]) ).
fof(f_1958_1,plain,
! [V_z_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq]) ).
fof(f_1958_2,plain,
! [U_7212] :
( ( 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,U_7212)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7212)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7212))
| ~ 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,U_7212))) ) ),
inference(variable_rename,[status(thm)],[f_1958_1]) ).
fof(f_1958_3,plain,
( ! [U_7214] :
( 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,U_7214)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7214)) )
& ! [U_7213] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7213))
| ~ 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,U_7213))) ) ),
inference(miniscope,[status(thm)],[f_1958_2]) ).
fof(f_1958_4,plain,
( ! [U_7214] :
( 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,U_7214)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7214)) )
& ! [U_7213] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7213))
| ~ 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,U_7213))) ) ),
inference(definitional_conversion,[status(esa)],[f_1958_3]) ).
cnf(f_1958_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7213))
| ~ 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,U_7213))) ),
inference(clausify,[status(thm)],[f_1958_4]) ).
cnf(f_1958_6,plain,
( 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,U_7214)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7214)) ),
inference(clausify,[status(thm)],[f_1958_4]) ).
fof(f_1959_1,plain,
! [V_m_2,V_w_2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__iff]) ).
fof(f_1959_2,plain,
! [U_7216,U_7215] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7215)),U_7216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7215),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7216))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7215),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7216)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7215)),U_7216)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7215)) ),
inference(variable_rename,[status(thm)],[f_1959_1]) ).
fof(f_1959_3,plain,
( ! [U_7216,U_7215] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7215)),U_7216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7215),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7216)))
| ~ sP660(U_7216,U_7215) )
& ! [U_7216,U_7215] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7215),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7216)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7215)),U_7216))
| ~ sP660(U_7216,U_7215) )
& ! [U_7216,U_7215] :
( sP660(U_7216,U_7215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7215)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP660])],[f_1959_2]) ).
cnf(f_1959_4,plain,
( sP660(U_7216,U_7215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7215)) ),
inference(clausify,[status(thm)],[f_1959_3]) ).
cnf(f_1959_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7215),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7216)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7215)),U_7216))
| ~ sP660(U_7216,U_7215) ),
inference(clausify,[status(thm)],[f_1959_3]) ).
cnf(f_1959_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7215)),U_7216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7215),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7216)))
| ~ sP660(U_7216,U_7215) ),
inference(clausify,[status(thm)],[f_1959_3]) ).
fof(f_1960_1,plain,
! [V_z] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1]) ).
fof(f_1960_2,plain,
! [U_7217] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7217)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7217)) ),
inference(variable_rename,[status(thm)],[f_1960_1]) ).
fof(f_1960_3,plain,
! [U_7217] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7217)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7217)) ),
inference(definitional_conversion,[status(esa)],[f_1960_2]) ).
cnf(f_1960_4,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7217)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7217)) ),
inference(clausify,[status(thm)],[f_1960_3]) ).
fof(f_1961_1,plain,
! [V_k,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__succ]) ).
fof(f_1961_2,plain,
! [U_7219,U_7218] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7218),c_Int_Osucc(U_7219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7218),c_Groups_Oone__class_Oone(U_7218)),hAPP(c_Int_Onumber__class_Onumber__of(U_7218),U_7219))
| ~ class_Int_Onumber__ring(U_7218) ),
inference(variable_rename,[status(thm)],[f_1961_1]) ).
fof(f_1961_3,plain,
! [U_7218,U_7219] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7218),c_Int_Osucc(U_7219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7218),c_Groups_Oone__class_Oone(U_7218)),hAPP(c_Int_Onumber__class_Onumber__of(U_7218),U_7219))
| ~ class_Int_Onumber__ring(U_7218) ),
inference(definitional_conversion,[status(esa)],[f_1961_2]) ).
cnf(f_1961_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7218),c_Int_Osucc(U_7219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7218),c_Groups_Oone__class_Oone(U_7218)),hAPP(c_Int_Onumber__class_Onumber__of(U_7218),U_7219))
| ~ class_Int_Onumber__ring(U_7218) ),
inference(clausify,[status(thm)],[f_1961_3]) ).
fof(f_1962_1,plain,
! [V_z_H,V_z] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg]) ).
fof(f_1962_2,plain,
! [U_7221,U_7220] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7220),U_7221)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7220))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7220),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1962_1]) ).
fof(f_1962_3,plain,
! [U_7220,U_7221] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7220),U_7221)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7220))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7220),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1962_2]) ).
cnf(f_1962_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7220),U_7221)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7220))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7220),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1962_3]) ).
fof(f_1963_1,plain,
! [V_v_H,V_v] :
( ( 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)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
inference(fof_nnf,[status(thm)],[fact_div__nat__number__of]) ).
fof(f_1963_2,plain,
! [U_7223,U_7222] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7222)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7223)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7222)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7223)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7222))) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7222)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7223)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7222))) ) ),
inference(variable_rename,[status(thm)],[f_1963_1]) ).
fof(f_1963_3,plain,
( ! [U_7227,U_7225] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7225)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7227)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7225)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7227)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7225))) )
& ! [U_7226,U_7224] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7226)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7224))) ) ),
inference(miniscope,[status(thm)],[f_1963_2]) ).
fof(f_1963_4,plain,
( ! [U_7225,U_7227] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7225)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7227)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7225)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7227)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7225))) )
& ! [U_7226,U_7224] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7226)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7224))) ) ),
inference(definitional_conversion,[status(esa)],[f_1963_3]) ).
cnf(f_1963_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7226)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7224))) ),
inference(clausify,[status(thm)],[f_1963_4]) ).
cnf(f_1963_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7225)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7227)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7225)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7227)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7225))) ),
inference(clausify,[status(thm)],[f_1963_4]) ).
fof(f_1964_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_card__atLeastAtMost__int]) ).
fof(f_1964_2,plain,
! [U_7229,U_7228] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7228,U_7229)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7229),U_7228)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1964_1]) ).
fof(f_1964_3,plain,
! [U_7228,U_7229] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7228,U_7229)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7229),U_7228)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1964_2]) ).
cnf(f_1964_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7228,U_7229)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7229),U_7228)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1964_3]) ).
fof(f_1965_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_one__div__nat__number__of]) ).
fof(f_1965_2,plain,
! [U_7230] : 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),U_7230)) = 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),U_7230))),
inference(variable_rename,[status(thm)],[f_1965_1]) ).
fof(f_1965_3,plain,
! [U_7230] : 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),U_7230)) = 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),U_7230))),
inference(definitional_conversion,[status(esa)],[f_1965_2]) ).
cnf(f_1965_4,plain,
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),U_7230)) = 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),U_7230))),
inference(clausify,[status(thm)],[f_1965_3]) ).
fof(f_1966_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_card__greaterThanLessThan__int]) ).
fof(f_1966_2,plain,
! [U_7232,U_7231] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7231,U_7232)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7232),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7231),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_1966_1]) ).
fof(f_1966_3,plain,
! [U_7231,U_7232] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7231,U_7232)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7232),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7231),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(definitional_conversion,[status(esa)],[f_1966_2]) ).
cnf(f_1966_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7231,U_7232)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7232),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7231),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_1966_3]) ).
fof(f_1967_1,plain,
! [V_w,V_v] :
( ( 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)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( 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))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
inference(fof_nnf,[status(thm)],[fact_power__nat__number__of__number__of]) ).
fof(f_1967_2,plain,
! [U_7234,U_7233] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7233)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7234)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7233)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7234)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7233))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7233)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7234)) = 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),U_7234))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7233))) ) ),
inference(variable_rename,[status(thm)],[f_1967_1]) ).
fof(f_1967_3,plain,
( ! [U_7238,U_7236] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236))) )
& ! [U_7237,U_7235] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7235)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7237)) = 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),U_7237))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7235))) ) ),
inference(miniscope,[status(thm)],[f_1967_2]) ).
fof(f_1967_4,plain,
( ! [U_7236,U_7238] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236))) )
& ! [U_7237,U_7235] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7235)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7237)) = 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),U_7237))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7235))) ) ),
inference(definitional_conversion,[status(esa)],[f_1967_3]) ).
cnf(f_1967_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7235)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7237)) = 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),U_7237))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7235))) ),
inference(clausify,[status(thm)],[f_1967_4]) ).
cnf(f_1967_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236))) ),
inference(clausify,[status(thm)],[f_1967_4]) ).
fof(f_1968_1,plain,
! [V_n,V_v] :
( ( 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))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
inference(fof_nnf,[status(thm)],[fact_power__nat__number__of]) ).
fof(f_1968_2,plain,
! [U_7240,U_7239] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7239)),U_7240) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7239)),U_7240))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7239))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7239)),U_7240) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7240)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7239))) ) ),
inference(variable_rename,[status(thm)],[f_1968_1]) ).
fof(f_1968_3,plain,
( ! [U_7244,U_7242] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7242)),U_7244) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7242)),U_7244))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7242))) )
& ! [U_7243,U_7241] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7241)),U_7243) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7243)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7241))) ) ),
inference(miniscope,[status(thm)],[f_1968_2]) ).
fof(f_1968_4,plain,
( ! [U_7242,U_7244] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7242)),U_7244) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7242)),U_7244))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7242))) )
& ! [U_7243,U_7241] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7241)),U_7243) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7243)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7241))) ) ),
inference(definitional_conversion,[status(esa)],[f_1968_3]) ).
cnf(f_1968_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7241)),U_7243) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7243)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7241))) ),
inference(clausify,[status(thm)],[f_1968_4]) ).
cnf(f_1968_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7242)),U_7244) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7242)),U_7244))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7242))) ),
inference(clausify,[status(thm)],[f_1968_4]) ).
fof(f_1969_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__aux__def]) ).
fof(f_1969_2,plain,
! [U_7246,U_7245] : c_Int_Onat__aux(U_7245,U_7246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7245)),U_7246),
inference(variable_rename,[status(thm)],[f_1969_1]) ).
fof(f_1969_3,plain,
! [U_7246,U_7245] : c_Int_Onat__aux(U_7245,U_7246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7245)),U_7246),
inference(definitional_conversion,[status(esa)],[f_1969_2]) ).
cnf(f_1969_4,plain,
c_Int_Onat__aux(U_7245,U_7246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7245)),U_7246),
inference(clausify,[status(thm)],[f_1969_3]) ).
fof(f_1970_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_transfer__morphism__nat__int]) ).
fof(f_1970_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1970_1]) ).
cnf(f_1970_3,plain,
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))),
inference(clausify,[status(thm)],[f_1970_2]) ).
fof(f_1971_1,plain,
! [V_n_2,V_m_2] :
( 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)))
| ~ c_Nat__Transfer_Ois__nat(V_n_2)
| ~ c_Nat__Transfer_Ois__nat(V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions]) ).
fof(f_1971_2,plain,
! [U_7248,U_7247] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7247,U_7248) = 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,U_7247),hAPP(c_Int_Onat,U_7248)))
| ~ c_Nat__Transfer_Ois__nat(U_7248)
| ~ c_Nat__Transfer_Ois__nat(U_7247) ),
inference(variable_rename,[status(thm)],[f_1971_1]) ).
fof(f_1971_3,plain,
! [U_7247,U_7248] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7247,U_7248) = 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,U_7247),hAPP(c_Int_Onat,U_7248)))
| ~ c_Nat__Transfer_Ois__nat(U_7248)
| ~ c_Nat__Transfer_Ois__nat(U_7247) ),
inference(definitional_conversion,[status(esa)],[f_1971_2]) ).
cnf(f_1971_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7247,U_7248) = 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,U_7247),hAPP(c_Int_Onat,U_7248)))
| ~ c_Nat__Transfer_Ois__nat(U_7248)
| ~ c_Nat__Transfer_Ois__nat(U_7247) ),
inference(clausify,[status(thm)],[f_1971_3]) ).
fof(f_1972_1,plain,
! [V_k,T_a] :
( ( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__of__nat]) ).
fof(f_1972_2,plain,
! [U_7250,U_7249] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7249),U_7250) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7249),hAPP(c_Int_Onat,U_7250))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7250),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_7249),U_7250) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7249),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7249),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7250))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7250),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ class_Rings_Oring__1(U_7249) ),
inference(variable_rename,[status(thm)],[f_1972_1]) ).
fof(f_1972_3,plain,
( ! [U_7250,U_7249] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7249),U_7250) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7249),hAPP(c_Int_Onat,U_7250))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP661(U_7250,U_7249) )
& ! [U_7250,U_7249] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7249),U_7250) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7249),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7249),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7250))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP661(U_7250,U_7249) )
& ! [U_7250,U_7249] :
( sP661(U_7250,U_7249)
| ~ class_Rings_Oring__1(U_7249) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP661])],[f_1972_2]) ).
cnf(f_1972_4,plain,
( sP661(U_7250,U_7249)
| ~ class_Rings_Oring__1(U_7249) ),
inference(clausify,[status(thm)],[f_1972_3]) ).
cnf(f_1972_5,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7249),U_7250) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7249),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7249),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7250))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP661(U_7250,U_7249) ),
inference(clausify,[status(thm)],[f_1972_3]) ).
cnf(f_1972_6,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7249),U_7250) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7249),hAPP(c_Int_Onat,U_7250))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP661(U_7250,U_7249) ),
inference(clausify,[status(thm)],[f_1972_3]) ).
fof(f_1973_1,plain,
! [V_B_2,V_A_2] :
( 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)))
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J]) ).
fof(f_1973_2,plain,
! [U_7252,U_7251] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7251),U_7252) = 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),U_7251)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7252)))
| ~ c_Nat__Transfer_Onat__set(U_7252)
| ~ c_Nat__Transfer_Onat__set(U_7251) ),
inference(variable_rename,[status(thm)],[f_1973_1]) ).
fof(f_1973_3,plain,
! [U_7252,U_7251] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7251),U_7252) = 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),U_7251)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7252)))
| ~ c_Nat__Transfer_Onat__set(U_7252)
| ~ c_Nat__Transfer_Onat__set(U_7251) ),
inference(definitional_conversion,[status(esa)],[f_1973_2]) ).
cnf(f_1973_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7251),U_7252) = 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),U_7251)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7252)))
| ~ c_Nat__Transfer_Onat__set(U_7252)
| ~ c_Nat__Transfer_Onat__set(U_7251) ),
inference(clausify,[status(thm)],[f_1973_3]) ).
fof(f_1974_1,plain,
! [V_y_2,V_x_2] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2))
| ~ c_Nat__Transfer_Ois__nat(V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures]) ).
fof(f_1974_2,plain,
! [U_7254,U_7253] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7253,U_7254))
| ~ c_Nat__Transfer_Ois__nat(U_7253) ),
inference(variable_rename,[status(thm)],[f_1974_1]) ).
fof(f_1974_3,plain,
! [U_7254,U_7253] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7253,U_7254))
| ~ c_Nat__Transfer_Ois__nat(U_7253) ),
inference(definitional_conversion,[status(esa)],[f_1974_2]) ).
cnf(f_1974_4,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7253,U_7254))
| ~ c_Nat__Transfer_Ois__nat(U_7253) ),
inference(clausify,[status(thm)],[f_1974_3]) ).
fof(f_1975_1,plain,
! [V_z_2,V_w_2,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)
| V_w_2 != V_z_2 )
& ( V_w_2 = V_z_2
| 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) ) )
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff]) ).
fof(f_1975_2,plain,
! [U_7257,U_7256,U_7255] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7256) = hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7257)
| U_7256 != U_7257 )
& ( U_7256 = U_7257
| hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7256) != hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7257) ) )
| ~ class_Int_Oring__char__0(U_7255) ),
inference(variable_rename,[status(thm)],[f_1975_1]) ).
fof(f_1975_3,plain,
( ! [U_7255,U_7256,U_7257] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7256) = hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7257)
| U_7256 != U_7257
| ~ sP662(U_7255,U_7256,U_7257) )
& ! [U_7255,U_7256,U_7257] :
( U_7256 = U_7257
| hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7256) != hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7257)
| ~ sP662(U_7255,U_7256,U_7257) )
& ! [U_7255,U_7256,U_7257] :
( sP662(U_7255,U_7256,U_7257)
| ~ class_Int_Oring__char__0(U_7255) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP662])],[f_1975_2]) ).
cnf(f_1975_4,plain,
( sP662(U_7255,U_7256,U_7257)
| ~ class_Int_Oring__char__0(U_7255) ),
inference(clausify,[status(thm)],[f_1975_3]) ).
cnf(f_1975_5,plain,
( U_7256 = U_7257
| hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7256) != hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7257)
| ~ sP662(U_7255,U_7256,U_7257) ),
inference(clausify,[status(thm)],[f_1975_3]) ).
cnf(f_1975_6,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7256) = hAPP(c_Int_Oring__1__class_Oof__int(U_7255),U_7257)
| U_7256 != U_7257
| ~ sP662(U_7255,U_7256,U_7257) ),
inference(clausify,[status(thm)],[f_1975_3]) ).
fof(f_1976_1,plain,
! [V_B_2,V_A_2] :
( 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))
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J]) ).
fof(f_1976_2,plain,
! [U_7259,U_7258] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7258),U_7259))
| ~ c_Nat__Transfer_Onat__set(U_7259)
| ~ c_Nat__Transfer_Onat__set(U_7258) ),
inference(variable_rename,[status(thm)],[f_1976_1]) ).
fof(f_1976_3,plain,
! [U_7259,U_7258] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7258),U_7259))
| ~ c_Nat__Transfer_Onat__set(U_7259)
| ~ c_Nat__Transfer_Onat__set(U_7258) ),
inference(definitional_conversion,[status(esa)],[f_1976_2]) ).
cnf(f_1976_4,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7258),U_7259))
| ~ c_Nat__Transfer_Onat__set(U_7259)
| ~ c_Nat__Transfer_Onat__set(U_7258) ),
inference(clausify,[status(thm)],[f_1976_3]) ).
fof(f_1977_1,plain,
! [V_B_2,V_A_2] :
( 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))
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J]) ).
fof(f_1977_2,plain,
! [U_7261,U_7260] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7260),U_7261))
| ~ c_Nat__Transfer_Onat__set(U_7261)
| ~ c_Nat__Transfer_Onat__set(U_7260) ),
inference(variable_rename,[status(thm)],[f_1977_1]) ).
fof(f_1977_3,plain,
! [U_7260,U_7261] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7260),U_7261))
| ~ c_Nat__Transfer_Onat__set(U_7261)
| ~ c_Nat__Transfer_Onat__set(U_7260) ),
inference(definitional_conversion,[status(esa)],[f_1977_2]) ).
cnf(f_1977_4,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7260),U_7261))
| ~ c_Nat__Transfer_Onat__set(U_7261)
| ~ c_Nat__Transfer_Onat__set(U_7260) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
fof(f_1978_1,plain,
! [V_x_2,V_A_2] :
( c_Nat__Transfer_Ois__nat(V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J]) ).
fof(f_1978_2,plain,
! [U_7263,U_7262] :
( c_Nat__Transfer_Ois__nat(U_7263)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7263),U_7262))
| ~ c_Nat__Transfer_Onat__set(U_7262) ),
inference(variable_rename,[status(thm)],[f_1978_1]) ).
fof(f_1978_3,plain,
! [U_7263,U_7262] :
( c_Nat__Transfer_Ois__nat(U_7263)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7263),U_7262))
| ~ c_Nat__Transfer_Onat__set(U_7262) ),
inference(definitional_conversion,[status(esa)],[f_1978_2]) ).
cnf(f_1978_4,plain,
( c_Nat__Transfer_Ois__nat(U_7263)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7263),U_7262))
| ~ c_Nat__Transfer_Onat__set(U_7262) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
fof(f_1979_1,plain,
! [V_k,T_a] :
( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__eq]) ).
fof(f_1979_2,plain,
! [U_7265,U_7264] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7264),U_7265) = hAPP(c_Int_Oring__1__class_Oof__int(U_7264),U_7265)
| ~ class_Int_Onumber__ring(U_7264) ),
inference(variable_rename,[status(thm)],[f_1979_1]) ).
fof(f_1979_3,plain,
! [U_7264,U_7265] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7264),U_7265) = hAPP(c_Int_Oring__1__class_Oof__int(U_7264),U_7265)
| ~ class_Int_Onumber__ring(U_7264) ),
inference(definitional_conversion,[status(esa)],[f_1979_2]) ).
cnf(f_1979_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7264),U_7265) = hAPP(c_Int_Oring__1__class_Oof__int(U_7264),U_7265)
| ~ class_Int_Onumber__ring(U_7264) ),
inference(clausify,[status(thm)],[f_1979_3]) ).
fof(f_1980_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_int__number__of__def]) ).
fof(f_1980_2,plain,
! [U_7266] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7266) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_7266),
inference(variable_rename,[status(thm)],[f_1980_1]) ).
fof(f_1980_3,plain,
! [U_7266] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7266) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_7266),
inference(definitional_conversion,[status(esa)],[f_1980_2]) ).
cnf(f_1980_4,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7266) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_7266),
inference(clausify,[status(thm)],[f_1980_3]) ).
fof(f_1981_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_of__int__int__eq]) ).
fof(f_1981_2,plain,
! [U_7267] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7267)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7267),
inference(variable_rename,[status(thm)],[f_1981_1]) ).
fof(f_1981_3,plain,
! [U_7267] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7267)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7267),
inference(definitional_conversion,[status(esa)],[f_1981_2]) ).
cnf(f_1981_4,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7267)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7267),
inference(clausify,[status(thm)],[f_1981_3]) ).
fof(f_1982_1,plain,
! [V_B_2,V_A_2] :
( ( ( V_A_2 = V_B_2
| 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) )
& ( 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)
| V_A_2 != V_B_2 ) )
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I3_J]) ).
fof(f_1982_2,plain,
! [U_7269,U_7268] :
( ( ( U_7268 = U_7269
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7268) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7269) )
& ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7268) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7269)
| U_7268 != U_7269 ) )
| ~ c_Nat__Transfer_Onat__set(U_7269)
| ~ c_Nat__Transfer_Onat__set(U_7268) ),
inference(variable_rename,[status(thm)],[f_1982_1]) ).
fof(f_1982_3,plain,
( ! [U_7268,U_7269] :
( U_7268 = U_7269
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7268) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7269)
| ~ sP663(U_7268,U_7269) )
& ! [U_7268,U_7269] :
( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7268) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7269)
| U_7268 != U_7269
| ~ sP663(U_7268,U_7269) )
& ! [U_7268,U_7269] :
( sP663(U_7268,U_7269)
| ~ c_Nat__Transfer_Onat__set(U_7269)
| ~ c_Nat__Transfer_Onat__set(U_7268) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP663])],[f_1982_2]) ).
cnf(f_1982_4,plain,
( sP663(U_7268,U_7269)
| ~ c_Nat__Transfer_Onat__set(U_7269)
| ~ c_Nat__Transfer_Onat__set(U_7268) ),
inference(clausify,[status(thm)],[f_1982_3]) ).
cnf(f_1982_5,plain,
( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7268) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7269)
| U_7268 != U_7269
| ~ sP663(U_7268,U_7269) ),
inference(clausify,[status(thm)],[f_1982_3]) ).
cnf(f_1982_6,plain,
( U_7268 = U_7269
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7268) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7269)
| ~ sP663(U_7268,U_7269) ),
inference(clausify,[status(thm)],[f_1982_3]) ).
fof(f_1983_1,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J]) ).
fof(f_1983_2,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_1983_1]) ).
cnf(f_1983_3,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1983_2]) ).
fof(f_1984_1,plain,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))
| ~ c_Nat__Transfer_Ois__nat(V_y)
| ~ c_Nat__Transfer_Ois__nat(V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J]) ).
fof(f_1984_2,plain,
! [U_7271,U_7270] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7270),U_7271))
| ~ c_Nat__Transfer_Ois__nat(U_7271)
| ~ c_Nat__Transfer_Ois__nat(U_7270) ),
inference(variable_rename,[status(thm)],[f_1984_1]) ).
fof(f_1984_3,plain,
! [U_7271,U_7270] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7270),U_7271))
| ~ c_Nat__Transfer_Ois__nat(U_7271)
| ~ c_Nat__Transfer_Ois__nat(U_7270) ),
inference(definitional_conversion,[status(esa)],[f_1984_2]) ).
cnf(f_1984_4,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7270),U_7271))
| ~ c_Nat__Transfer_Ois__nat(U_7271)
| ~ c_Nat__Transfer_Ois__nat(U_7270) ),
inference(clausify,[status(thm)],[f_1984_3]) ).
fof(f_1985_1,plain,
! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).
fof(f_1985_2,plain,
! [U_7272] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7272)),
inference(variable_rename,[status(thm)],[f_1985_1]) ).
fof(f_1985_3,plain,
! [U_7272] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7272)),
inference(definitional_conversion,[status(esa)],[f_1985_2]) ).
cnf(f_1985_4,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7272)),
inference(clausify,[status(thm)],[f_1985_3]) ).
fof(f_1986_1,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J]) ).
fof(f_1986_2,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_1986_1]) ).
cnf(f_1986_3,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1986_2]) ).
fof(f_1987_1,plain,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))
| ~ c_Nat__Transfer_Ois__nat(V_y)
| ~ c_Nat__Transfer_Ois__nat(V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J]) ).
fof(f_1987_2,plain,
! [U_7274,U_7273] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7273),U_7274))
| ~ c_Nat__Transfer_Ois__nat(U_7274)
| ~ c_Nat__Transfer_Ois__nat(U_7273) ),
inference(variable_rename,[status(thm)],[f_1987_1]) ).
fof(f_1987_3,plain,
! [U_7273,U_7274] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7273),U_7274))
| ~ c_Nat__Transfer_Ois__nat(U_7274)
| ~ c_Nat__Transfer_Ois__nat(U_7273) ),
inference(definitional_conversion,[status(esa)],[f_1987_2]) ).
cnf(f_1987_4,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7273),U_7274))
| ~ c_Nat__Transfer_Ois__nat(U_7274)
| ~ c_Nat__Transfer_Ois__nat(U_7273) ),
inference(clausify,[status(thm)],[f_1987_3]) ).
fof(f_1988_1,plain,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))
| ~ c_Nat__Transfer_Ois__nat(V_y)
| ~ c_Nat__Transfer_Ois__nat(V_x) ),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J]) ).
fof(f_1988_2,plain,
! [U_7276,U_7275] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7275,U_7276))
| ~ c_Nat__Transfer_Ois__nat(U_7276)
| ~ c_Nat__Transfer_Ois__nat(U_7275) ),
inference(variable_rename,[status(thm)],[f_1988_1]) ).
fof(f_1988_3,plain,
! [U_7276,U_7275] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7275,U_7276))
| ~ c_Nat__Transfer_Ois__nat(U_7276)
| ~ c_Nat__Transfer_Ois__nat(U_7275) ),
inference(definitional_conversion,[status(esa)],[f_1988_2]) ).
cnf(f_1988_4,plain,
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7275,U_7276))
| ~ c_Nat__Transfer_Ois__nat(U_7276)
| ~ c_Nat__Transfer_Ois__nat(U_7275) ),
inference(clausify,[status(thm)],[f_1988_3]) ).
fof(f_1989_1,plain,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))
| ~ c_Nat__Transfer_Ois__nat(V_y)
| ~ c_Nat__Transfer_Ois__nat(V_x) ),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J]) ).
fof(f_1989_2,plain,
! [U_7278,U_7277] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7277),U_7278))
| ~ c_Nat__Transfer_Ois__nat(U_7278)
| ~ c_Nat__Transfer_Ois__nat(U_7277) ),
inference(variable_rename,[status(thm)],[f_1989_1]) ).
fof(f_1989_3,plain,
! [U_7278,U_7277] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7277),U_7278))
| ~ c_Nat__Transfer_Ois__nat(U_7278)
| ~ c_Nat__Transfer_Ois__nat(U_7277) ),
inference(definitional_conversion,[status(esa)],[f_1989_2]) ).
cnf(f_1989_4,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7277),U_7278))
| ~ c_Nat__Transfer_Ois__nat(U_7278)
| ~ c_Nat__Transfer_Ois__nat(U_7277) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
fof(f_1990_1,plain,
! [V_n,V_x] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))
| ~ c_Nat__Transfer_Ois__nat(V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J]) ).
fof(f_1990_2,plain,
! [U_7280,U_7279] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7279),U_7280))
| ~ c_Nat__Transfer_Ois__nat(U_7279) ),
inference(variable_rename,[status(thm)],[f_1990_1]) ).
fof(f_1990_3,plain,
! [U_7279,U_7280] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7279),U_7280))
| ~ c_Nat__Transfer_Ois__nat(U_7279) ),
inference(definitional_conversion,[status(esa)],[f_1990_2]) ).
cnf(f_1990_4,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7279),U_7280))
| ~ c_Nat__Transfer_Ois__nat(U_7279) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
fof(f_1991_1,plain,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y))
| ~ c_Nat__Transfer_Ois__nat(V_y)
| ~ c_Nat__Transfer_Ois__nat(V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J]) ).
fof(f_1991_2,plain,
! [U_7282,U_7281] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7281,U_7282))
| ~ c_Nat__Transfer_Ois__nat(U_7282)
| ~ c_Nat__Transfer_Ois__nat(U_7281) ),
inference(variable_rename,[status(thm)],[f_1991_1]) ).
fof(f_1991_3,plain,
! [U_7281,U_7282] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7281,U_7282))
| ~ c_Nat__Transfer_Ois__nat(U_7282)
| ~ c_Nat__Transfer_Ois__nat(U_7281) ),
inference(definitional_conversion,[status(esa)],[f_1991_2]) ).
cnf(f_1991_4,plain,
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7281,U_7282))
| ~ c_Nat__Transfer_Ois__nat(U_7282)
| ~ c_Nat__Transfer_Ois__nat(U_7281) ),
inference(clausify,[status(thm)],[f_1991_3]) ).
fof(f_1992_1,plain,
! [V_A_2,V_x_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) ) )
| ~ c_Nat__Transfer_Onat__set(V_A_2)
| ~ c_Nat__Transfer_Ois__nat(V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I2_J]) ).
fof(f_1992_2,plain,
! [U_7284,U_7283] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7283),U_7284))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7283)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7284))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7283)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7283),U_7284)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7284)
| ~ c_Nat__Transfer_Ois__nat(U_7283) ),
inference(variable_rename,[status(thm)],[f_1992_1]) ).
fof(f_1992_3,plain,
( ! [U_7283,U_7284] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7283),U_7284))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7283)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7284)))
| ~ sP664(U_7283,U_7284) )
& ! [U_7283,U_7284] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7283)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7283),U_7284))
| ~ sP664(U_7283,U_7284) )
& ! [U_7283,U_7284] :
( sP664(U_7283,U_7284)
| ~ c_Nat__Transfer_Onat__set(U_7284)
| ~ c_Nat__Transfer_Ois__nat(U_7283) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP664])],[f_1992_2]) ).
cnf(f_1992_4,plain,
( sP664(U_7283,U_7284)
| ~ c_Nat__Transfer_Onat__set(U_7284)
| ~ c_Nat__Transfer_Ois__nat(U_7283) ),
inference(clausify,[status(thm)],[f_1992_3]) ).
cnf(f_1992_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7283)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7283),U_7284))
| ~ sP664(U_7283,U_7284) ),
inference(clausify,[status(thm)],[f_1992_3]) ).
cnf(f_1992_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7283),U_7284))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7283)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7284)))
| ~ sP664(U_7283,U_7284) ),
inference(clausify,[status(thm)],[f_1992_3]) ).
fof(f_1993_1,plain,
! [V_z_2,T_b] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff]) ).
fof(f_1993_2,plain,
! [U_7286,U_7285] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7285),U_7286) = c_Groups_Ozero__class_Ozero(U_7285)
| U_7286 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_7286 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_7285),U_7286) != c_Groups_Ozero__class_Ozero(U_7285) ) )
| ~ class_Int_Oring__char__0(U_7285) ),
inference(variable_rename,[status(thm)],[f_1993_1]) ).
fof(f_1993_3,plain,
( ! [U_7286,U_7285] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7285),U_7286) = c_Groups_Ozero__class_Ozero(U_7285)
| U_7286 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP665(U_7286,U_7285) )
& ! [U_7286,U_7285] :
( U_7286 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_7285),U_7286) != c_Groups_Ozero__class_Ozero(U_7285)
| ~ sP665(U_7286,U_7285) )
& ! [U_7286,U_7285] :
( sP665(U_7286,U_7285)
| ~ class_Int_Oring__char__0(U_7285) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP665])],[f_1993_2]) ).
cnf(f_1993_4,plain,
( sP665(U_7286,U_7285)
| ~ class_Int_Oring__char__0(U_7285) ),
inference(clausify,[status(thm)],[f_1993_3]) ).
cnf(f_1993_5,plain,
( U_7286 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_7285),U_7286) != c_Groups_Ozero__class_Ozero(U_7285)
| ~ sP665(U_7286,U_7285) ),
inference(clausify,[status(thm)],[f_1993_3]) ).
cnf(f_1993_6,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7285),U_7286) = c_Groups_Ozero__class_Ozero(U_7285)
| U_7286 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP665(U_7286,U_7285) ),
inference(clausify,[status(thm)],[f_1993_3]) ).
fof(f_1994_1,plain,
! [V_z_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
| V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) ) )
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff]) ).
fof(f_1994_2,plain,
! [U_7288,U_7287] :
( ( ( c_Groups_Ozero__class_Ozero(U_7287) = hAPP(c_Int_Oring__1__class_Oof__int(U_7287),U_7288)
| U_7288 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_7288 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_7287) != hAPP(c_Int_Oring__1__class_Oof__int(U_7287),U_7288) ) )
| ~ class_Int_Oring__char__0(U_7287) ),
inference(variable_rename,[status(thm)],[f_1994_1]) ).
fof(f_1994_3,plain,
( ! [U_7288,U_7287] :
( c_Groups_Ozero__class_Ozero(U_7287) = hAPP(c_Int_Oring__1__class_Oof__int(U_7287),U_7288)
| U_7288 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP666(U_7288,U_7287) )
& ! [U_7288,U_7287] :
( U_7288 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_7287) != hAPP(c_Int_Oring__1__class_Oof__int(U_7287),U_7288)
| ~ sP666(U_7288,U_7287) )
& ! [U_7288,U_7287] :
( sP666(U_7288,U_7287)
| ~ class_Int_Oring__char__0(U_7287) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP666])],[f_1994_2]) ).
cnf(f_1994_4,plain,
( sP666(U_7288,U_7287)
| ~ class_Int_Oring__char__0(U_7287) ),
inference(clausify,[status(thm)],[f_1994_3]) ).
cnf(f_1994_5,plain,
( U_7288 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_7287) != hAPP(c_Int_Oring__1__class_Oof__int(U_7287),U_7288)
| ~ sP666(U_7288,U_7287) ),
inference(clausify,[status(thm)],[f_1994_3]) ).
cnf(f_1994_6,plain,
( c_Groups_Ozero__class_Ozero(U_7287) = hAPP(c_Int_Oring__1__class_Oof__int(U_7287),U_7288)
| U_7288 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP666(U_7288,U_7287) ),
inference(clausify,[status(thm)],[f_1994_3]) ).
fof(f_1995_1,plain,
! [T_a] :
( 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)
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0]) ).
fof(f_1995_2,plain,
! [U_7289] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7289),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_7289)
| ~ class_Rings_Oring__1(U_7289) ),
inference(variable_rename,[status(thm)],[f_1995_1]) ).
fof(f_1995_3,plain,
! [U_7289] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7289),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_7289)
| ~ class_Rings_Oring__1(U_7289) ),
inference(definitional_conversion,[status(esa)],[f_1995_2]) ).
cnf(f_1995_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7289),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_7289)
| ~ class_Rings_Oring__1(U_7289) ),
inference(clausify,[status(thm)],[f_1995_3]) ).
fof(f_1996_1,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J]) ).
fof(f_1996_2,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_1996_1]) ).
cnf(f_1996_3,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_1996_2]) ).
fof(f_1997_1,plain,
! [V_z_2,V_w_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__le__iff]) ).
fof(f_1997_2,plain,
! [U_7292,U_7291,U_7290] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7290),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7291)),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7292)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7291),U_7292)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7291),U_7292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7290),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7291)),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7292))) ) )
| ~ class_Rings_Olinordered__idom(U_7290) ),
inference(variable_rename,[status(thm)],[f_1997_1]) ).
fof(f_1997_3,plain,
( ! [U_7290,U_7291,U_7292] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7290),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7291)),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7292)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7291),U_7292))
| ~ sP667(U_7290,U_7291,U_7292) )
& ! [U_7290,U_7291,U_7292] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7291),U_7292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7290),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7291)),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7292)))
| ~ sP667(U_7290,U_7291,U_7292) )
& ! [U_7290,U_7291,U_7292] :
( sP667(U_7290,U_7291,U_7292)
| ~ class_Rings_Olinordered__idom(U_7290) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP667])],[f_1997_2]) ).
cnf(f_1997_4,plain,
( sP667(U_7290,U_7291,U_7292)
| ~ class_Rings_Olinordered__idom(U_7290) ),
inference(clausify,[status(thm)],[f_1997_3]) ).
cnf(f_1997_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7291),U_7292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7290),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7291)),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7292)))
| ~ sP667(U_7290,U_7291,U_7292) ),
inference(clausify,[status(thm)],[f_1997_3]) ).
cnf(f_1997_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7290),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7291)),hAPP(c_Int_Oring__1__class_Oof__int(U_7290),U_7292)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7291),U_7292))
| ~ sP667(U_7290,U_7291,U_7292) ),
inference(clausify,[status(thm)],[f_1997_3]) ).
fof(f_1998_1,plain,
! [V_z_2,V_w_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__less__iff]) ).
fof(f_1998_2,plain,
! [U_7295,U_7294,U_7293] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7293),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7294)),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7295)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7294),U_7295)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7294),U_7295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7293),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7294)),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7295))) ) )
| ~ class_Rings_Olinordered__idom(U_7293) ),
inference(variable_rename,[status(thm)],[f_1998_1]) ).
fof(f_1998_3,plain,
( ! [U_7294,U_7295,U_7293] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7293),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7294)),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7295)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7294),U_7295))
| ~ sP668(U_7294,U_7295,U_7293) )
& ! [U_7294,U_7295,U_7293] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7294),U_7295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7293),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7294)),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7295)))
| ~ sP668(U_7294,U_7295,U_7293) )
& ! [U_7294,U_7295,U_7293] :
( sP668(U_7294,U_7295,U_7293)
| ~ class_Rings_Olinordered__idom(U_7293) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP668])],[f_1998_2]) ).
cnf(f_1998_4,plain,
( sP668(U_7294,U_7295,U_7293)
| ~ class_Rings_Olinordered__idom(U_7293) ),
inference(clausify,[status(thm)],[f_1998_3]) ).
cnf(f_1998_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7294),U_7295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7293),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7294)),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7295)))
| ~ sP668(U_7294,U_7295,U_7293) ),
inference(clausify,[status(thm)],[f_1998_3]) ).
cnf(f_1998_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7293),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7294)),hAPP(c_Int_Oring__1__class_Oof__int(U_7293),U_7295)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7294),U_7295))
| ~ sP668(U_7294,U_7295,U_7293) ),
inference(clausify,[status(thm)],[f_1998_3]) ).
fof(f_1999_1,plain,
! [V_z,V_w,T_a] :
( 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))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__add]) ).
fof(f_1999_2,plain,
! [U_7298,U_7297,U_7296] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7297),U_7298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7296),hAPP(c_Int_Oring__1__class_Oof__int(U_7296),U_7297)),hAPP(c_Int_Oring__1__class_Oof__int(U_7296),U_7298))
| ~ class_Rings_Oring__1(U_7296) ),
inference(variable_rename,[status(thm)],[f_1999_1]) ).
fof(f_1999_3,plain,
! [U_7297,U_7296,U_7298] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7297),U_7298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7296),hAPP(c_Int_Oring__1__class_Oof__int(U_7296),U_7297)),hAPP(c_Int_Oring__1__class_Oof__int(U_7296),U_7298))
| ~ class_Rings_Oring__1(U_7296) ),
inference(definitional_conversion,[status(esa)],[f_1999_2]) ).
cnf(f_1999_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7297),U_7298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7296),hAPP(c_Int_Oring__1__class_Oof__int(U_7296),U_7297)),hAPP(c_Int_Oring__1__class_Oof__int(U_7296),U_7298))
| ~ class_Rings_Oring__1(U_7296) ),
inference(clausify,[status(thm)],[f_1999_3]) ).
fof(f_2000_1,plain,
! [V_v,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq]) ).
fof(f_2000_2,plain,
! [U_7300,U_7299] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7299),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7300)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7299),U_7300)
| ~ class_Int_Onumber__ring(U_7299) ),
inference(variable_rename,[status(thm)],[f_2000_1]) ).
fof(f_2000_3,plain,
! [U_7299,U_7300] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7299),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7300)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7299),U_7300)
| ~ class_Int_Onumber__ring(U_7299) ),
inference(definitional_conversion,[status(esa)],[f_2000_2]) ).
cnf(f_2000_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7299),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7300)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7299),U_7300)
| ~ class_Int_Onumber__ring(U_7299) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
fof(f_2001_1,plain,
! [V_z,V_w,T_a] :
( 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))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__mult]) ).
fof(f_2001_2,plain,
! [U_7303,U_7302,U_7301] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7302),U_7303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7301),hAPP(c_Int_Oring__1__class_Oof__int(U_7301),U_7302)),hAPP(c_Int_Oring__1__class_Oof__int(U_7301),U_7303))
| ~ class_Rings_Oring__1(U_7301) ),
inference(variable_rename,[status(thm)],[f_2001_1]) ).
fof(f_2001_3,plain,
! [U_7301,U_7302,U_7303] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7302),U_7303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7301),hAPP(c_Int_Oring__1__class_Oof__int(U_7301),U_7302)),hAPP(c_Int_Oring__1__class_Oof__int(U_7301),U_7303))
| ~ class_Rings_Oring__1(U_7301) ),
inference(definitional_conversion,[status(esa)],[f_2001_2]) ).
cnf(f_2001_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7302),U_7303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7301),hAPP(c_Int_Oring__1__class_Oof__int(U_7301),U_7302)),hAPP(c_Int_Oring__1__class_Oof__int(U_7301),U_7303))
| ~ class_Rings_Oring__1(U_7301) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
fof(f_2002_1,plain,
! [T_a] :
( 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)
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__1]) ).
fof(f_2002_2,plain,
! [U_7304] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7304),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_7304)
| ~ class_Rings_Oring__1(U_7304) ),
inference(variable_rename,[status(thm)],[f_2002_1]) ).
fof(f_2002_3,plain,
! [U_7304] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7304),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_7304)
| ~ class_Rings_Oring__1(U_7304) ),
inference(definitional_conversion,[status(esa)],[f_2002_2]) ).
cnf(f_2002_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7304),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_7304)
| ~ class_Rings_Oring__1(U_7304) ),
inference(clausify,[status(thm)],[f_2002_3]) ).
fof(f_2003_1,plain,
! [V_z,V_w,T_a] :
( 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))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__diff]) ).
fof(f_2003_2,plain,
! [U_7307,U_7306,U_7305] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7306),U_7307)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7305),hAPP(c_Int_Oring__1__class_Oof__int(U_7305),U_7306)),hAPP(c_Int_Oring__1__class_Oof__int(U_7305),U_7307))
| ~ class_Rings_Oring__1(U_7305) ),
inference(variable_rename,[status(thm)],[f_2003_1]) ).
fof(f_2003_3,plain,
! [U_7305,U_7306,U_7307] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7306),U_7307)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7305),hAPP(c_Int_Oring__1__class_Oof__int(U_7305),U_7306)),hAPP(c_Int_Oring__1__class_Oof__int(U_7305),U_7307))
| ~ class_Rings_Oring__1(U_7305) ),
inference(definitional_conversion,[status(esa)],[f_2003_2]) ).
cnf(f_2003_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7306),U_7307)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7305),hAPP(c_Int_Oring__1__class_Oof__int(U_7305),U_7306)),hAPP(c_Int_Oring__1__class_Oof__int(U_7305),U_7307))
| ~ class_Rings_Oring__1(U_7305) ),
inference(clausify,[status(thm)],[f_2003_3]) ).
fof(f_2004_1,plain,
! [V_n,T_a] :
( 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)
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq]) ).
fof(f_2004_2,plain,
! [U_7309,U_7308] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7308),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7309)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7308),U_7309)
| ~ class_Rings_Oring__1(U_7308) ),
inference(variable_rename,[status(thm)],[f_2004_1]) ).
fof(f_2004_3,plain,
! [U_7308,U_7309] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7308),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7309)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7308),U_7309)
| ~ class_Rings_Oring__1(U_7308) ),
inference(definitional_conversion,[status(esa)],[f_2004_2]) ).
cnf(f_2004_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7308),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7309)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7308),U_7309)
| ~ class_Rings_Oring__1(U_7308) ),
inference(clausify,[status(thm)],[f_2004_3]) ).
fof(f_2005_1,plain,
! [V_z,T_a] :
( 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))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__minus]) ).
fof(f_2005_2,plain,
! [U_7311,U_7310] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7310),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7311)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7310),hAPP(c_Int_Oring__1__class_Oof__int(U_7310),U_7311))
| ~ class_Rings_Oring__1(U_7310) ),
inference(variable_rename,[status(thm)],[f_2005_1]) ).
fof(f_2005_3,plain,
! [U_7310,U_7311] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7310),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7311)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7310),hAPP(c_Int_Oring__1__class_Oof__int(U_7310),U_7311))
| ~ class_Rings_Oring__1(U_7310) ),
inference(definitional_conversion,[status(esa)],[f_2005_2]) ).
cnf(f_2005_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7310),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7311)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7310),hAPP(c_Int_Oring__1__class_Oof__int(U_7310),U_7311))
| ~ class_Rings_Oring__1(U_7310) ),
inference(clausify,[status(thm)],[f_2005_3]) ).
fof(f_2006_1,plain,
! [V_z_2,T_b] :
( 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)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__of__int]) ).
fof(f_2006_2,plain,
! [U_7313,U_7312] :
( hBOOL(hAPP(hAPP(c_member(U_7312),hAPP(c_Int_Oring__1__class_Oof__int(U_7312),U_7313)),c_Int_Oring__1__class_OInts(U_7312)))
| ~ class_Rings_Oring__1(U_7312) ),
inference(variable_rename,[status(thm)],[f_2006_1]) ).
fof(f_2006_3,plain,
! [U_7312,U_7313] :
( hBOOL(hAPP(hAPP(c_member(U_7312),hAPP(c_Int_Oring__1__class_Oof__int(U_7312),U_7313)),c_Int_Oring__1__class_OInts(U_7312)))
| ~ class_Rings_Oring__1(U_7312) ),
inference(definitional_conversion,[status(esa)],[f_2006_2]) ).
cnf(f_2006_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7312),hAPP(c_Int_Oring__1__class_Oof__int(U_7312),U_7313)),c_Int_Oring__1__class_OInts(U_7312)))
| ~ class_Rings_Oring__1(U_7312) ),
inference(clausify,[status(thm)],[f_2006_3]) ).
fof(f_2007_1,plain,
! [V_n,V_z,T_a] :
( 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)
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__power]) ).
fof(f_2007_2,plain,
! [U_7316,U_7315,U_7314] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7314),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7315),U_7316)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7314),hAPP(c_Int_Oring__1__class_Oof__int(U_7314),U_7315)),U_7316)
| ~ class_Rings_Oring__1(U_7314) ),
inference(variable_rename,[status(thm)],[f_2007_1]) ).
fof(f_2007_3,plain,
! [U_7314,U_7315,U_7316] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7314),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7315),U_7316)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7314),hAPP(c_Int_Oring__1__class_Oof__int(U_7314),U_7315)),U_7316)
| ~ class_Rings_Oring__1(U_7314) ),
inference(definitional_conversion,[status(esa)],[f_2007_2]) ).
cnf(f_2007_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7314),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7315),U_7316)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7314),hAPP(c_Int_Oring__1__class_Oof__int(U_7314),U_7315)),U_7316)
| ~ class_Rings_Oring__1(U_7314) ),
inference(clausify,[status(thm)],[f_2007_3]) ).
fof(f_2008_1,plain,
! [V_S_2] :
( ( c_Nat__Transfer_Onat__set(V_S_2)
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) )
| ~ c_Nat__Transfer_Onat__set(V_S_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__set__def]) ).
fof(f_2008_2,plain,
! [U_7319] :
( ( c_Nat__Transfer_Onat__set(U_7319)
| ? [U_7318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7318))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7318),U_7319)) ) )
& ( ! [U_7317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7317))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7317),U_7319)) )
| ~ c_Nat__Transfer_Onat__set(U_7319) ) ),
inference(variable_rename,[status(thm)],[f_2008_1]) ).
fof(f_2008_3,plain,
( ! [U_7321] :
( c_Nat__Transfer_Onat__set(U_7321)
| ? [U_7318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7318))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7318),U_7321)) ) )
& ! [U_7320] :
( ! [U_7317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7317))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7317),U_7320)) )
| ~ c_Nat__Transfer_Onat__set(U_7320) ) ),
inference(miniscope,[status(thm)],[f_2008_2]) ).
fof(f_2008_4,plain,
( ! [U_7321] :
( c_Nat__Transfer_Onat__set(U_7321)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK206(U_7321)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_7321)),U_7321)) ) )
& ! [U_7320] :
( ! [U_7317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7317))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7317),U_7320)) )
| ~ c_Nat__Transfer_Onat__set(U_7320) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_7318,sK206(U_7321))],[f_2008_3]) ).
fof(f_2008_5,plain,
( ! [U_7321] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK206(U_7321)))
| ~ sP669(U_7321) )
& ! [U_7321] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_7321)),U_7321))
| ~ sP669(U_7321) )
& ! [U_7321] :
( c_Nat__Transfer_Onat__set(U_7321)
| sP669(U_7321) )
& ! [U_7317,U_7320] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7317))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7317),U_7320))
| ~ c_Nat__Transfer_Onat__set(U_7320) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP669])],[f_2008_4]) ).
cnf(f_2008_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7317))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7317),U_7320))
| ~ c_Nat__Transfer_Onat__set(U_7320) ),
inference(clausify,[status(thm)],[f_2008_5]) ).
cnf(f_2008_7,plain,
( c_Nat__Transfer_Onat__set(U_7321)
| sP669(U_7321) ),
inference(clausify,[status(thm)],[f_2008_5]) ).
cnf(f_2008_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_7321)),U_7321))
| ~ sP669(U_7321) ),
inference(clausify,[status(thm)],[f_2008_5]) ).
cnf(f_2008_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK206(U_7321)))
| ~ sP669(U_7321) ),
inference(clausify,[status(thm)],[f_2008_5]) ).
fof(f_2009_1,plain,
! [V_x_2] :
( ( c_Nat__Transfer_Ois__nat(V_x_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
| ~ c_Nat__Transfer_Ois__nat(V_x_2) ) ),
inference(fof_nnf,[status(thm)],[fact_is__nat__def]) ).
fof(f_2009_2,plain,
! [U_7322] :
( ( c_Nat__Transfer_Ois__nat(U_7322)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7322)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7322))
| ~ c_Nat__Transfer_Ois__nat(U_7322) ) ),
inference(variable_rename,[status(thm)],[f_2009_1]) ).
fof(f_2009_3,plain,
( ! [U_7324] :
( c_Nat__Transfer_Ois__nat(U_7324)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324)) )
& ! [U_7323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7323))
| ~ c_Nat__Transfer_Ois__nat(U_7323) ) ),
inference(miniscope,[status(thm)],[f_2009_2]) ).
fof(f_2009_4,plain,
( ! [U_7324] :
( c_Nat__Transfer_Ois__nat(U_7324)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324)) )
& ! [U_7323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7323))
| ~ c_Nat__Transfer_Ois__nat(U_7323) ) ),
inference(definitional_conversion,[status(esa)],[f_2009_3]) ).
cnf(f_2009_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7323))
| ~ c_Nat__Transfer_Ois__nat(U_7323) ),
inference(clausify,[status(thm)],[f_2009_4]) ).
cnf(f_2009_6,plain,
( c_Nat__Transfer_Ois__nat(U_7324)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324)) ),
inference(clausify,[status(thm)],[f_2009_4]) ).
fof(f_2010_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).
fof(f_2010_2,plain,
! [U_7325] : 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)),U_7325)),
inference(variable_rename,[status(thm)],[f_2010_1]) ).
fof(f_2010_3,plain,
! [U_7325] : 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)),U_7325)),
inference(definitional_conversion,[status(esa)],[f_2010_2]) ).
cnf(f_2010_4,plain,
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)),U_7325)),
inference(clausify,[status(thm)],[f_2010_3]) ).
fof(f_2011_1,plain,
! [T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__int__m1]) ).
fof(f_2011_2,plain,
! [U_7326] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7326),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7326),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_7326) ),
inference(variable_rename,[status(thm)],[f_2011_1]) ).
fof(f_2011_3,plain,
! [U_7326] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7326),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7326),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_7326) ),
inference(definitional_conversion,[status(esa)],[f_2011_2]) ).
cnf(f_2011_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7326),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7326),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_7326) ),
inference(clausify,[status(thm)],[f_2011_3]) ).
fof(f_2012_1,plain,
! [V_y_2,V_x_2] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures]) ).
fof(f_2012_2,plain,
! [U_7328,U_7327] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7327,U_7328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7327)) ),
inference(variable_rename,[status(thm)],[f_2012_1]) ).
fof(f_2012_3,plain,
! [U_7327,U_7328] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7327,U_7328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7327)) ),
inference(definitional_conversion,[status(esa)],[f_2012_2]) ).
cnf(f_2012_4,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7327,U_7328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7327)) ),
inference(clausify,[status(thm)],[f_2012_3]) ).
fof(f_2013_1,plain,
! [V_B_2,V_A_2] :
( 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)))
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J]) ).
fof(f_2013_2,plain,
! [U_7330,U_7329] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7329),U_7330) = 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),U_7329)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7330)))
| ~ c_Nat__Transfer_Onat__set(U_7330)
| ~ c_Nat__Transfer_Onat__set(U_7329) ),
inference(variable_rename,[status(thm)],[f_2013_1]) ).
fof(f_2013_3,plain,
! [U_7329,U_7330] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7329),U_7330) = 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),U_7329)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7330)))
| ~ c_Nat__Transfer_Onat__set(U_7330)
| ~ c_Nat__Transfer_Onat__set(U_7329) ),
inference(definitional_conversion,[status(esa)],[f_2013_2]) ).
cnf(f_2013_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7329),U_7330) = 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),U_7329)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7330)))
| ~ c_Nat__Transfer_Onat__set(U_7330)
| ~ c_Nat__Transfer_Onat__set(U_7329) ),
inference(clausify,[status(thm)],[f_2013_3]) ).
fof(f_2014_1,plain,
! [V_A_2] :
( 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
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed]) ).
fof(f_2014_2,plain,
! [U_7331] :
( 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),U_7331)) = U_7331
| ~ c_Nat__Transfer_Onat__set(U_7331) ),
inference(variable_rename,[status(thm)],[f_2014_1]) ).
fof(f_2014_3,plain,
! [U_7331] :
( 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),U_7331)) = U_7331
| ~ c_Nat__Transfer_Onat__set(U_7331) ),
inference(definitional_conversion,[status(esa)],[f_2014_2]) ).
cnf(f_2014_4,plain,
( 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),U_7331)) = U_7331
| ~ c_Nat__Transfer_Onat__set(U_7331) ),
inference(clausify,[status(thm)],[f_2014_3]) ).
fof(f_2015_1,plain,
! [V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J]) ).
fof(f_2015_2,plain,
! [U_7333,U_7332] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7333))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7333),U_7332))
| ~ c_Nat__Transfer_Onat__set(U_7332) ),
inference(variable_rename,[status(thm)],[f_2015_1]) ).
fof(f_2015_3,plain,
! [U_7332,U_7333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7333))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7333),U_7332))
| ~ c_Nat__Transfer_Onat__set(U_7332) ),
inference(definitional_conversion,[status(esa)],[f_2015_2]) ).
cnf(f_2015_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7333))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7333),U_7332))
| ~ c_Nat__Transfer_Onat__set(U_7332) ),
inference(clausify,[status(thm)],[f_2015_3]) ).
fof(f_2016_1,plain,
! [V_z_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff]) ).
fof(f_2016_2,plain,
! [U_7335,U_7334] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7334),c_Groups_Ozero__class_Ozero(U_7334)),hAPP(c_Int_Oring__1__class_Oof__int(U_7334),U_7335)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7335)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7334),c_Groups_Ozero__class_Ozero(U_7334)),hAPP(c_Int_Oring__1__class_Oof__int(U_7334),U_7335))) ) )
| ~ class_Rings_Olinordered__idom(U_7334) ),
inference(variable_rename,[status(thm)],[f_2016_1]) ).
fof(f_2016_3,plain,
( ! [U_7334,U_7335] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7334),c_Groups_Ozero__class_Ozero(U_7334)),hAPP(c_Int_Oring__1__class_Oof__int(U_7334),U_7335)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7335))
| ~ sP670(U_7334,U_7335) )
& ! [U_7334,U_7335] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7334),c_Groups_Ozero__class_Ozero(U_7334)),hAPP(c_Int_Oring__1__class_Oof__int(U_7334),U_7335)))
| ~ sP670(U_7334,U_7335) )
& ! [U_7334,U_7335] :
( sP670(U_7334,U_7335)
| ~ class_Rings_Olinordered__idom(U_7334) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP670])],[f_2016_2]) ).
cnf(f_2016_4,plain,
( sP670(U_7334,U_7335)
| ~ class_Rings_Olinordered__idom(U_7334) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
cnf(f_2016_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7334),c_Groups_Ozero__class_Ozero(U_7334)),hAPP(c_Int_Oring__1__class_Oof__int(U_7334),U_7335)))
| ~ sP670(U_7334,U_7335) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
cnf(f_2016_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7334),c_Groups_Ozero__class_Ozero(U_7334)),hAPP(c_Int_Oring__1__class_Oof__int(U_7334),U_7335)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7335))
| ~ sP670(U_7334,U_7335) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
fof(f_2017_1,plain,
! [V_z_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff]) ).
fof(f_2017_2,plain,
! [U_7337,U_7336] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7336),hAPP(c_Int_Oring__1__class_Oof__int(U_7336),U_7337)),c_Groups_Ozero__class_Ozero(U_7336)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7337),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7337),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7336),hAPP(c_Int_Oring__1__class_Oof__int(U_7336),U_7337)),c_Groups_Ozero__class_Ozero(U_7336))) ) )
| ~ class_Rings_Olinordered__idom(U_7336) ),
inference(variable_rename,[status(thm)],[f_2017_1]) ).
fof(f_2017_3,plain,
( ! [U_7336,U_7337] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7336),hAPP(c_Int_Oring__1__class_Oof__int(U_7336),U_7337)),c_Groups_Ozero__class_Ozero(U_7336)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7337),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP671(U_7336,U_7337) )
& ! [U_7336,U_7337] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7337),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7336),hAPP(c_Int_Oring__1__class_Oof__int(U_7336),U_7337)),c_Groups_Ozero__class_Ozero(U_7336)))
| ~ sP671(U_7336,U_7337) )
& ! [U_7336,U_7337] :
( sP671(U_7336,U_7337)
| ~ class_Rings_Olinordered__idom(U_7336) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP671])],[f_2017_2]) ).
cnf(f_2017_4,plain,
( sP671(U_7336,U_7337)
| ~ class_Rings_Olinordered__idom(U_7336) ),
inference(clausify,[status(thm)],[f_2017_3]) ).
cnf(f_2017_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7337),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7336),hAPP(c_Int_Oring__1__class_Oof__int(U_7336),U_7337)),c_Groups_Ozero__class_Ozero(U_7336)))
| ~ sP671(U_7336,U_7337) ),
inference(clausify,[status(thm)],[f_2017_3]) ).
cnf(f_2017_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7336),hAPP(c_Int_Oring__1__class_Oof__int(U_7336),U_7337)),c_Groups_Ozero__class_Ozero(U_7336)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7337),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP671(U_7336,U_7337) ),
inference(clausify,[status(thm)],[f_2017_3]) ).
fof(f_2018_1,plain,
! [V_z_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff]) ).
fof(f_2018_2,plain,
! [U_7339,U_7338] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7338),c_Groups_Ozero__class_Ozero(U_7338)),hAPP(c_Int_Oring__1__class_Oof__int(U_7338),U_7339)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7338),c_Groups_Ozero__class_Ozero(U_7338)),hAPP(c_Int_Oring__1__class_Oof__int(U_7338),U_7339))) ) )
| ~ class_Rings_Olinordered__idom(U_7338) ),
inference(variable_rename,[status(thm)],[f_2018_1]) ).
fof(f_2018_3,plain,
( ! [U_7338,U_7339] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7338),c_Groups_Ozero__class_Ozero(U_7338)),hAPP(c_Int_Oring__1__class_Oof__int(U_7338),U_7339)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339))
| ~ sP672(U_7338,U_7339) )
& ! [U_7338,U_7339] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7338),c_Groups_Ozero__class_Ozero(U_7338)),hAPP(c_Int_Oring__1__class_Oof__int(U_7338),U_7339)))
| ~ sP672(U_7338,U_7339) )
& ! [U_7338,U_7339] :
( sP672(U_7338,U_7339)
| ~ class_Rings_Olinordered__idom(U_7338) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP672])],[f_2018_2]) ).
cnf(f_2018_4,plain,
( sP672(U_7338,U_7339)
| ~ class_Rings_Olinordered__idom(U_7338) ),
inference(clausify,[status(thm)],[f_2018_3]) ).
cnf(f_2018_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7338),c_Groups_Ozero__class_Ozero(U_7338)),hAPP(c_Int_Oring__1__class_Oof__int(U_7338),U_7339)))
| ~ sP672(U_7338,U_7339) ),
inference(clausify,[status(thm)],[f_2018_3]) ).
cnf(f_2018_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7338),c_Groups_Ozero__class_Ozero(U_7338)),hAPP(c_Int_Oring__1__class_Oof__int(U_7338),U_7339)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339))
| ~ sP672(U_7338,U_7339) ),
inference(clausify,[status(thm)],[f_2018_3]) ).
fof(f_2019_1,plain,
! [V_z_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff]) ).
fof(f_2019_2,plain,
! [U_7341,U_7340] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7340),hAPP(c_Int_Oring__1__class_Oof__int(U_7340),U_7341)),c_Groups_Ozero__class_Ozero(U_7340)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7341),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7341),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7340),hAPP(c_Int_Oring__1__class_Oof__int(U_7340),U_7341)),c_Groups_Ozero__class_Ozero(U_7340))) ) )
| ~ class_Rings_Olinordered__idom(U_7340) ),
inference(variable_rename,[status(thm)],[f_2019_1]) ).
fof(f_2019_3,plain,
( ! [U_7341,U_7340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7340),hAPP(c_Int_Oring__1__class_Oof__int(U_7340),U_7341)),c_Groups_Ozero__class_Ozero(U_7340)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7341),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP673(U_7341,U_7340) )
& ! [U_7341,U_7340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7341),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7340),hAPP(c_Int_Oring__1__class_Oof__int(U_7340),U_7341)),c_Groups_Ozero__class_Ozero(U_7340)))
| ~ sP673(U_7341,U_7340) )
& ! [U_7341,U_7340] :
( sP673(U_7341,U_7340)
| ~ class_Rings_Olinordered__idom(U_7340) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP673])],[f_2019_2]) ).
cnf(f_2019_4,plain,
( sP673(U_7341,U_7340)
| ~ class_Rings_Olinordered__idom(U_7340) ),
inference(clausify,[status(thm)],[f_2019_3]) ).
cnf(f_2019_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7341),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7340),hAPP(c_Int_Oring__1__class_Oof__int(U_7340),U_7341)),c_Groups_Ozero__class_Ozero(U_7340)))
| ~ sP673(U_7341,U_7340) ),
inference(clausify,[status(thm)],[f_2019_3]) ).
cnf(f_2019_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7340),hAPP(c_Int_Oring__1__class_Oof__int(U_7340),U_7341)),c_Groups_Ozero__class_Ozero(U_7340)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7341),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP673(U_7341,U_7340) ),
inference(clausify,[status(thm)],[f_2019_3]) ).
fof(f_2020_1,plain,
! [V_z,T_a] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__nat]) ).
fof(f_2020_2,plain,
! [U_7343,U_7342] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7342),hAPP(c_Int_Onat,U_7343)) = hAPP(c_Int_Oring__1__class_Oof__int(U_7342),U_7343)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7343))
| ~ class_Rings_Oring__1(U_7342) ),
inference(variable_rename,[status(thm)],[f_2020_1]) ).
fof(f_2020_3,plain,
! [U_7342,U_7343] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7342),hAPP(c_Int_Onat,U_7343)) = hAPP(c_Int_Oring__1__class_Oof__int(U_7342),U_7343)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7343))
| ~ class_Rings_Oring__1(U_7342) ),
inference(definitional_conversion,[status(esa)],[f_2020_2]) ).
cnf(f_2020_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7342),hAPP(c_Int_Onat,U_7343)) = hAPP(c_Int_Oring__1__class_Oof__int(U_7342),U_7343)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7343))
| ~ class_Rings_Oring__1(U_7342) ),
inference(clausify,[status(thm)],[f_2020_3]) ).
fof(f_2021_1,plain,
! [V_A_2] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) ) )
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I1_J]) ).
fof(f_2021_2,plain,
! [U_7344] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7344))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7344))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7344)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7344)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7344) ),
inference(variable_rename,[status(thm)],[f_2021_1]) ).
fof(f_2021_3,plain,
( ! [U_7344] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7344))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7344)))
| ~ sP674(U_7344) )
& ! [U_7344] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7344)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7344))
| ~ sP674(U_7344) )
& ! [U_7344] :
( sP674(U_7344)
| ~ c_Nat__Transfer_Onat__set(U_7344) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP674])],[f_2021_2]) ).
cnf(f_2021_4,plain,
( sP674(U_7344)
| ~ c_Nat__Transfer_Onat__set(U_7344) ),
inference(clausify,[status(thm)],[f_2021_3]) ).
cnf(f_2021_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7344)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7344))
| ~ sP674(U_7344) ),
inference(clausify,[status(thm)],[f_2021_3]) ).
cnf(f_2021_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7344))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7344)))
| ~ sP674(U_7344) ),
inference(clausify,[status(thm)],[f_2021_3]) ).
fof(f_2022_1,plain,
! [V_A_2] :
( 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))
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J]) ).
fof(f_2022_2,plain,
! [U_7345] :
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_7345) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7345))
| ~ c_Nat__Transfer_Onat__set(U_7345) ),
inference(variable_rename,[status(thm)],[f_2022_1]) ).
fof(f_2022_3,plain,
! [U_7345] :
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_7345) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7345))
| ~ c_Nat__Transfer_Onat__set(U_7345) ),
inference(definitional_conversion,[status(esa)],[f_2022_2]) ).
cnf(f_2022_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_7345) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7345))
| ~ c_Nat__Transfer_Onat__set(U_7345) ),
inference(clausify,[status(thm)],[f_2022_3]) ).
fof(f_2023_1,plain,
! [V_B_2,V_A_2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I5_J]) ).
fof(f_2023_2,plain,
! [U_7347,U_7346] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7346),U_7347))
| ~ 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),U_7346)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7347))) )
& ( 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),U_7346)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7346),U_7347)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7347)
| ~ c_Nat__Transfer_Onat__set(U_7346) ),
inference(variable_rename,[status(thm)],[f_2023_1]) ).
fof(f_2023_3,plain,
( ! [U_7347,U_7346] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7346),U_7347))
| ~ 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),U_7346)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7347)))
| ~ sP675(U_7347,U_7346) )
& ! [U_7347,U_7346] :
( 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),U_7346)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7346),U_7347))
| ~ sP675(U_7347,U_7346) )
& ! [U_7347,U_7346] :
( sP675(U_7347,U_7346)
| ~ c_Nat__Transfer_Onat__set(U_7347)
| ~ c_Nat__Transfer_Onat__set(U_7346) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP675])],[f_2023_2]) ).
cnf(f_2023_4,plain,
( sP675(U_7347,U_7346)
| ~ c_Nat__Transfer_Onat__set(U_7347)
| ~ c_Nat__Transfer_Onat__set(U_7346) ),
inference(clausify,[status(thm)],[f_2023_3]) ).
cnf(f_2023_5,plain,
( 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),U_7346)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7346),U_7347))
| ~ sP675(U_7347,U_7346) ),
inference(clausify,[status(thm)],[f_2023_3]) ).
cnf(f_2023_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7346),U_7347))
| ~ 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),U_7346)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7347)))
| ~ sP675(U_7347,U_7346) ),
inference(clausify,[status(thm)],[f_2023_3]) ).
fof(f_2024_1,plain,
! [V_B_2,V_A_2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ 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))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| ~ c_Nat__Transfer_Onat__set(V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I4_J]) ).
fof(f_2024_2,plain,
! [U_7349,U_7348] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7348),U_7349))
| ~ 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),U_7348)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7349))) )
& ( 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),U_7348)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7349)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7348),U_7349)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7349)
| ~ c_Nat__Transfer_Onat__set(U_7348) ),
inference(variable_rename,[status(thm)],[f_2024_1]) ).
fof(f_2024_3,plain,
( ! [U_7349,U_7348] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7348),U_7349))
| ~ 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),U_7348)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7349)))
| ~ sP676(U_7349,U_7348) )
& ! [U_7349,U_7348] :
( 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),U_7348)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7349)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7348),U_7349))
| ~ sP676(U_7349,U_7348) )
& ! [U_7349,U_7348] :
( sP676(U_7349,U_7348)
| ~ c_Nat__Transfer_Onat__set(U_7349)
| ~ c_Nat__Transfer_Onat__set(U_7348) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP676])],[f_2024_2]) ).
cnf(f_2024_4,plain,
( sP676(U_7349,U_7348)
| ~ c_Nat__Transfer_Onat__set(U_7349)
| ~ c_Nat__Transfer_Onat__set(U_7348) ),
inference(clausify,[status(thm)],[f_2024_3]) ).
cnf(f_2024_5,plain,
( 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),U_7348)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7349)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7348),U_7349))
| ~ sP676(U_7349,U_7348) ),
inference(clausify,[status(thm)],[f_2024_3]) ).
cnf(f_2024_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7348),U_7349))
| ~ 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),U_7348)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7349)))
| ~ sP676(U_7349,U_7348) ),
inference(clausify,[status(thm)],[f_2024_3]) ).
fof(f_2025_1,plain,
! [V_k] :
( ? [B_n] :
( V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__imp__eq__int]) ).
fof(f_2025_2,plain,
! [U_7351] :
( ? [U_7350] :
( U_7351 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7350)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7350)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7351)) ),
inference(variable_rename,[status(thm)],[f_2025_1]) ).
fof(f_2025_3,plain,
! [U_7351] :
( ( U_7351 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK207(U_7351))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK207(U_7351))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7351)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_7350,sK207(U_7351))],[f_2025_2]) ).
fof(f_2025_4,plain,
( ! [U_7351] :
( U_7351 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK207(U_7351))
| ~ sP677(U_7351) )
& ! [U_7351] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK207(U_7351)))
| ~ sP677(U_7351) )
& ! [U_7351] :
( sP677(U_7351)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7351)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP677])],[f_2025_3]) ).
cnf(f_2025_5,plain,
( sP677(U_7351)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7351)) ),
inference(clausify,[status(thm)],[f_2025_4]) ).
cnf(f_2025_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK207(U_7351)))
| ~ sP677(U_7351) ),
inference(clausify,[status(thm)],[f_2025_4]) ).
cnf(f_2025_7,plain,
( U_7351 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK207(U_7351))
| ~ sP677(U_7351) ),
inference(clausify,[status(thm)],[f_2025_4]) ).
fof(f_2026_1,plain,
! [V_z,V_x,V_d] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) ),
inference(fof_nnf,[status(thm)],[fact_decr__lemma]) ).
fof(f_2026_2,plain,
! [U_7354,U_7353,U_7352] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7353),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),U_7353),U_7354))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7352))),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7352)) ),
inference(variable_rename,[status(thm)],[f_2026_1]) ).
fof(f_2026_3,plain,
! [U_7352,U_7353,U_7354] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7353),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),U_7353),U_7354))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7352))),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7352)) ),
inference(definitional_conversion,[status(esa)],[f_2026_2]) ).
cnf(f_2026_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7353),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),U_7353),U_7354))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7352))),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7352)) ),
inference(clausify,[status(thm)],[f_2026_3]) ).
fof(f_2027_1,plain,
! [V_x,V_z,V_d] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) ),
inference(fof_nnf,[status(thm)],[fact_incr__lemma]) ).
fof(f_2027_2,plain,
! [U_7357,U_7356,U_7355] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7357),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),U_7357),U_7356))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7355))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7355)) ),
inference(variable_rename,[status(thm)],[f_2027_1]) ).
fof(f_2027_3,plain,
! [U_7355,U_7356,U_7357] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7357),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),U_7357),U_7356))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7355))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7355)) ),
inference(definitional_conversion,[status(esa)],[f_2027_2]) ).
cnf(f_2027_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7357),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),U_7357),U_7356))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7355))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7355)) ),
inference(clausify,[status(thm)],[f_2027_3]) ).
fof(f_2028_1,plain,
! [V_v] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__add__number__of]) ).
fof(f_2028_2,plain,
! [U_7358] :
( ( 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),U_7358)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7358))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7358),c_Int_OPls)) )
& ( 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),U_7358)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7358),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2028_1]) ).
fof(f_2028_3,plain,
( ! [U_7360] :
( 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),U_7360)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7360))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7360),c_Int_OPls)) )
& ! [U_7359] :
( 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),U_7359)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7359),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2028_2]) ).
fof(f_2028_4,plain,
( ! [U_7360] :
( 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),U_7360)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7360))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7360),c_Int_OPls)) )
& ! [U_7359] :
( 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),U_7359)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7359),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2028_3]) ).
cnf(f_2028_5,plain,
( 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),U_7359)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7359),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2028_4]) ).
cnf(f_2028_6,plain,
( 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),U_7360)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7360))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7360),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2028_4]) ).
fof(f_2029_1,plain,
! [V_v] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__1]) ).
fof(f_2029_2,plain,
! [U_7361] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7361)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7361))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7361),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7361)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7361),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2029_1]) ).
fof(f_2029_3,plain,
( ! [U_7363] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7363)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7363),c_Int_OPls)) )
& ! [U_7362] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7362)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7362),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2029_2]) ).
fof(f_2029_4,plain,
( ! [U_7363] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7363)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7363),c_Int_OPls)) )
& ! [U_7362] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7362)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7362),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2029_3]) ).
cnf(f_2029_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7362)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7362),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2029_4]) ).
cnf(f_2029_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7363)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7363),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2029_4]) ).
fof(f_2030_1,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).
fof(f_2030_2,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_2030_1]) ).
cnf(f_2030_3,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_2030_2]) ).
fof(f_2031_1,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I19_J]) ).
fof(f_2031_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2031_1]) ).
cnf(f_2031_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2031_2]) ).
fof(f_2032_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__ge__self]) ).
fof(f_2032_2,plain,
! [U_7365,U_7364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7364),U_7365),hAPP(c_Groups_Oabs__class_Oabs(U_7364),U_7365)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7364) ),
inference(variable_rename,[status(thm)],[f_2032_1]) ).
fof(f_2032_3,plain,
! [U_7364,U_7365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7364),U_7365),hAPP(c_Groups_Oabs__class_Oabs(U_7364),U_7365)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7364) ),
inference(definitional_conversion,[status(esa)],[f_2032_2]) ).
cnf(f_2032_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7364),U_7365),hAPP(c_Groups_Oabs__class_Oabs(U_7364),U_7365)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7364) ),
inference(clausify,[status(thm)],[f_2032_3]) ).
fof(f_2033_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__D1]) ).
fof(f_2033_2,plain,
! [U_7368,U_7367,U_7366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7366),U_7367),U_7368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7366),hAPP(c_Groups_Oabs__class_Oabs(U_7366),U_7367)),U_7368))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7366) ),
inference(variable_rename,[status(thm)],[f_2033_1]) ).
fof(f_2033_3,plain,
! [U_7366,U_7367,U_7368] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7366),U_7367),U_7368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7366),hAPP(c_Groups_Oabs__class_Oabs(U_7366),U_7367)),U_7368))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7366) ),
inference(definitional_conversion,[status(esa)],[f_2033_2]) ).
cnf(f_2033_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7366),U_7367),U_7368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7366),hAPP(c_Groups_Oabs__class_Oabs(U_7366),U_7367)),U_7368))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7366) ),
inference(clausify,[status(thm)],[f_2033_3]) ).
fof(f_2034_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__add__abs]) ).
fof(f_2034_2,plain,
! [U_7371,U_7370,U_7369] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7369),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7369),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7370)),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7371))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7369),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7370)),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7371))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7369) ),
inference(variable_rename,[status(thm)],[f_2034_1]) ).
fof(f_2034_3,plain,
! [U_7369,U_7370,U_7371] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7369),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7369),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7370)),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7371))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7369),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7370)),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7371))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7369) ),
inference(definitional_conversion,[status(esa)],[f_2034_2]) ).
cnf(f_2034_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7369),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7369),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7370)),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7371))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7369),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7370)),hAPP(c_Groups_Oabs__class_Oabs(U_7369),U_7371))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7369) ),
inference(clausify,[status(thm)],[f_2034_3]) ).
fof(f_2035_1,plain,
! [V_a,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_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult__self]) ).
fof(f_2035_2,plain,
! [U_7373,U_7372] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7372),hAPP(c_Groups_Oabs__class_Oabs(U_7372),U_7373)),hAPP(c_Groups_Oabs__class_Oabs(U_7372),U_7373)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7372),U_7373),U_7373)
| ~ class_Rings_Olinordered__idom(U_7372) ),
inference(variable_rename,[status(thm)],[f_2035_1]) ).
fof(f_2035_3,plain,
! [U_7372,U_7373] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7372),hAPP(c_Groups_Oabs__class_Oabs(U_7372),U_7373)),hAPP(c_Groups_Oabs__class_Oabs(U_7372),U_7373)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7372),U_7373),U_7373)
| ~ class_Rings_Olinordered__idom(U_7372) ),
inference(definitional_conversion,[status(esa)],[f_2035_2]) ).
cnf(f_2035_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7372),hAPP(c_Groups_Oabs__class_Oabs(U_7372),U_7373)),hAPP(c_Groups_Oabs__class_Oabs(U_7372),U_7373)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7372),U_7373),U_7373)
| ~ class_Rings_Olinordered__idom(U_7372) ),
inference(clausify,[status(thm)],[f_2035_3]) ).
fof(f_2036_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult]) ).
fof(f_2036_2,plain,
! [U_7376,U_7375,U_7374] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7374),U_7375),U_7376)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7374),hAPP(c_Groups_Oabs__class_Oabs(U_7374),U_7375)),hAPP(c_Groups_Oabs__class_Oabs(U_7374),U_7376))
| ~ class_Rings_Olinordered__idom(U_7374) ),
inference(variable_rename,[status(thm)],[f_2036_1]) ).
fof(f_2036_3,plain,
! [U_7374,U_7375,U_7376] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7374),U_7375),U_7376)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7374),hAPP(c_Groups_Oabs__class_Oabs(U_7374),U_7375)),hAPP(c_Groups_Oabs__class_Oabs(U_7374),U_7376))
| ~ class_Rings_Olinordered__idom(U_7374) ),
inference(definitional_conversion,[status(esa)],[f_2036_2]) ).
cnf(f_2036_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7374),U_7375),U_7376)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7374),hAPP(c_Groups_Oabs__class_Oabs(U_7374),U_7375)),hAPP(c_Groups_Oabs__class_Oabs(U_7374),U_7376))
| ~ class_Rings_Olinordered__idom(U_7374) ),
inference(clausify,[status(thm)],[f_2036_3]) ).
fof(f_2037_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__commute]) ).
fof(f_2037_2,plain,
! [U_7379,U_7378,U_7377] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7377),U_7378),U_7379)) = hAPP(c_Groups_Oabs__class_Oabs(U_7377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7377),U_7379),U_7378))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7377) ),
inference(variable_rename,[status(thm)],[f_2037_1]) ).
fof(f_2037_3,plain,
! [U_7377,U_7378,U_7379] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7377),U_7378),U_7379)) = hAPP(c_Groups_Oabs__class_Oabs(U_7377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7377),U_7379),U_7378))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7377) ),
inference(definitional_conversion,[status(esa)],[f_2037_2]) ).
cnf(f_2037_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7377),U_7378),U_7379)) = hAPP(c_Groups_Oabs__class_Oabs(U_7377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7377),U_7379),U_7378))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7377) ),
inference(clausify,[status(thm)],[f_2037_3]) ).
fof(f_2038_1,plain,
! [T_a] :
( hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__one]) ).
fof(f_2038_2,plain,
! [U_7380] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7380),c_Groups_Oone__class_Oone(U_7380)) = c_Groups_Oone__class_Oone(U_7380)
| ~ class_Rings_Olinordered__idom(U_7380) ),
inference(variable_rename,[status(thm)],[f_2038_1]) ).
fof(f_2038_3,plain,
! [U_7380] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7380),c_Groups_Oone__class_Oone(U_7380)) = c_Groups_Oone__class_Oone(U_7380)
| ~ class_Rings_Olinordered__idom(U_7380) ),
inference(definitional_conversion,[status(esa)],[f_2038_2]) ).
cnf(f_2038_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7380),c_Groups_Oone__class_Oone(U_7380)) = c_Groups_Oone__class_Oone(U_7380)
| ~ class_Rings_Olinordered__idom(U_7380) ),
inference(clausify,[status(thm)],[f_2038_3]) ).
fof(f_2039_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel]) ).
fof(f_2039_2,plain,
! [U_7382,U_7381] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7381),hAPP(c_Groups_Ouminus__class_Ouminus(U_7381),U_7382)) = hAPP(c_Groups_Oabs__class_Oabs(U_7381),U_7382)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7381) ),
inference(variable_rename,[status(thm)],[f_2039_1]) ).
fof(f_2039_3,plain,
! [U_7381,U_7382] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7381),hAPP(c_Groups_Ouminus__class_Ouminus(U_7381),U_7382)) = hAPP(c_Groups_Oabs__class_Oabs(U_7381),U_7382)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7381) ),
inference(definitional_conversion,[status(esa)],[f_2039_2]) ).
cnf(f_2039_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7381),hAPP(c_Groups_Ouminus__class_Ouminus(U_7381),U_7382)) = hAPP(c_Groups_Oabs__class_Oabs(U_7381),U_7382)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7381) ),
inference(clausify,[status(thm)],[f_2039_3]) ).
fof(f_2040_1,plain,
! [V_a,T_a] :
( 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)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__idempotent]) ).
fof(f_2040_2,plain,
! [U_7384,U_7383] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7383),hAPP(c_Groups_Oabs__class_Oabs(U_7383),U_7384)) = hAPP(c_Groups_Oabs__class_Oabs(U_7383),U_7384)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7383) ),
inference(variable_rename,[status(thm)],[f_2040_1]) ).
fof(f_2040_3,plain,
! [U_7383,U_7384] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7383),hAPP(c_Groups_Oabs__class_Oabs(U_7383),U_7384)) = hAPP(c_Groups_Oabs__class_Oabs(U_7383),U_7384)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7383) ),
inference(definitional_conversion,[status(esa)],[f_2040_2]) ).
cnf(f_2040_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7383),hAPP(c_Groups_Oabs__class_Oabs(U_7383),U_7384)) = hAPP(c_Groups_Oabs__class_Oabs(U_7383),U_7384)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7383) ),
inference(clausify,[status(thm)],[f_2040_3]) ).
fof(f_2041_1,plain,
! [T_a] :
( hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__zero]) ).
fof(f_2041_2,plain,
! [U_7385] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7385),c_Groups_Ozero__class_Ozero(U_7385)) = c_Groups_Ozero__class_Ozero(U_7385)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7385) ),
inference(variable_rename,[status(thm)],[f_2041_1]) ).
fof(f_2041_3,plain,
! [U_7385] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7385),c_Groups_Ozero__class_Ozero(U_7385)) = c_Groups_Ozero__class_Ozero(U_7385)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7385) ),
inference(definitional_conversion,[status(esa)],[f_2041_2]) ).
cnf(f_2041_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7385),c_Groups_Ozero__class_Ozero(U_7385)) = c_Groups_Ozero__class_Ozero(U_7385)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7385) ),
inference(clausify,[status(thm)],[f_2041_3]) ).
fof(f_2042_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).
fof(f_2042_2,plain,
! [U_7387,U_7386] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_7386),U_7387) = c_Groups_Ozero__class_Ozero(U_7386)
| U_7387 != c_Groups_Ozero__class_Ozero(U_7386) )
& ( U_7387 = c_Groups_Ozero__class_Ozero(U_7386)
| hAPP(c_Groups_Oabs__class_Oabs(U_7386),U_7387) != c_Groups_Ozero__class_Ozero(U_7386) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_7386) ),
inference(variable_rename,[status(thm)],[f_2042_1]) ).
fof(f_2042_3,plain,
( ! [U_7386,U_7387] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7386),U_7387) = c_Groups_Ozero__class_Ozero(U_7386)
| U_7387 != c_Groups_Ozero__class_Ozero(U_7386)
| ~ sP678(U_7386,U_7387) )
& ! [U_7386,U_7387] :
( U_7387 = c_Groups_Ozero__class_Ozero(U_7386)
| hAPP(c_Groups_Oabs__class_Oabs(U_7386),U_7387) != c_Groups_Ozero__class_Ozero(U_7386)
| ~ sP678(U_7386,U_7387) )
& ! [U_7386,U_7387] :
( sP678(U_7386,U_7387)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7386) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP678])],[f_2042_2]) ).
cnf(f_2042_4,plain,
( sP678(U_7386,U_7387)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7386) ),
inference(clausify,[status(thm)],[f_2042_3]) ).
cnf(f_2042_5,plain,
( U_7387 = c_Groups_Ozero__class_Ozero(U_7386)
| hAPP(c_Groups_Oabs__class_Oabs(U_7386),U_7387) != c_Groups_Ozero__class_Ozero(U_7386)
| ~ sP678(U_7386,U_7387) ),
inference(clausify,[status(thm)],[f_2042_3]) ).
cnf(f_2042_6,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7386),U_7387) = c_Groups_Ozero__class_Ozero(U_7386)
| U_7387 != c_Groups_Ozero__class_Ozero(U_7386)
| ~ sP678(U_7386,U_7387) ),
inference(clausify,[status(thm)],[f_2042_3]) ).
fof(f_2043_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_abs__int__eq]) ).
fof(f_2043_2,plain,
! [U_7388] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7388)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7388),
inference(variable_rename,[status(thm)],[f_2043_1]) ).
fof(f_2043_3,plain,
! [U_7388] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7388)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7388),
inference(definitional_conversion,[status(esa)],[f_2043_2]) ).
cnf(f_2043_4,plain,
hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7388)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7388),
inference(clausify,[status(thm)],[f_2043_3]) ).
fof(f_2044_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__divide]) ).
fof(f_2044_2,plain,
! [U_7391,U_7390,U_7389] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7389),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7389),U_7390),U_7391)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7389),hAPP(c_Groups_Oabs__class_Oabs(U_7389),U_7390)),hAPP(c_Groups_Oabs__class_Oabs(U_7389),U_7391))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7389) ),
inference(variable_rename,[status(thm)],[f_2044_1]) ).
fof(f_2044_3,plain,
! [U_7389,U_7390,U_7391] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7389),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7389),U_7390),U_7391)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7389),hAPP(c_Groups_Oabs__class_Oabs(U_7389),U_7390)),hAPP(c_Groups_Oabs__class_Oabs(U_7389),U_7391))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7389) ),
inference(definitional_conversion,[status(esa)],[f_2044_2]) ).
cnf(f_2044_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7389),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7389),U_7390),U_7391)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7389),hAPP(c_Groups_Oabs__class_Oabs(U_7389),U_7390)),hAPP(c_Groups_Oabs__class_Oabs(U_7389),U_7391))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7389) ),
inference(clausify,[status(thm)],[f_2044_3]) ).
fof(f_2045_1,plain,
! [V_n,V_a,T_a] :
( 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)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__abs]) ).
fof(f_2045_2,plain,
! [U_7394,U_7393,U_7392] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7392),hAPP(hAPP(c_Power_Opower__class_Opower(U_7392),U_7393),U_7394)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7392),hAPP(c_Groups_Oabs__class_Oabs(U_7392),U_7393)),U_7394)
| ~ class_Rings_Olinordered__idom(U_7392) ),
inference(variable_rename,[status(thm)],[f_2045_1]) ).
fof(f_2045_3,plain,
! [U_7392,U_7393,U_7394] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7392),hAPP(hAPP(c_Power_Opower__class_Opower(U_7392),U_7393),U_7394)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7392),hAPP(c_Groups_Oabs__class_Oabs(U_7392),U_7393)),U_7394)
| ~ class_Rings_Olinordered__idom(U_7392) ),
inference(definitional_conversion,[status(esa)],[f_2045_2]) ).
cnf(f_2045_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7392),hAPP(hAPP(c_Power_Opower__class_Opower(U_7392),U_7393),U_7394)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7392),hAPP(c_Groups_Oabs__class_Oabs(U_7392),U_7393)),U_7394)
| ~ class_Rings_Olinordered__idom(U_7392) ),
inference(clausify,[status(thm)],[f_2045_3]) ).
fof(f_2046_1,plain,
! [V_n,T_a] :
( 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)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__nat]) ).
fof(f_2046_2,plain,
! [U_7396,U_7395] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7395),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7395),U_7396)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7395),U_7396)
| ~ class_Rings_Olinordered__idom(U_7395) ),
inference(variable_rename,[status(thm)],[f_2046_1]) ).
fof(f_2046_3,plain,
! [U_7395,U_7396] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7395),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7395),U_7396)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7395),U_7396)
| ~ class_Rings_Olinordered__idom(U_7395) ),
inference(definitional_conversion,[status(esa)],[f_2046_2]) ).
cnf(f_2046_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7395),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7395),U_7396)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7395),U_7396)
| ~ class_Rings_Olinordered__idom(U_7395) ),
inference(clausify,[status(thm)],[f_2046_3]) ).
fof(f_2047_1,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I2_J]) ).
fof(f_2047_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2047_1]) ).
cnf(f_2047_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2047_2]) ).
fof(f_2048_1,plain,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
inference(fof_nnf,[status(thm)],[fact_add__Pls__right]) ).
fof(f_2048_2,plain,
! [U_7397] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7397),c_Int_OPls) = U_7397,
inference(variable_rename,[status(thm)],[f_2048_1]) ).
fof(f_2048_3,plain,
! [U_7397] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7397),c_Int_OPls) = U_7397,
inference(definitional_conversion,[status(esa)],[f_2048_2]) ).
cnf(f_2048_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7397),c_Int_OPls) = U_7397,
inference(clausify,[status(thm)],[f_2048_3]) ).
fof(f_2049_1,plain,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
inference(fof_nnf,[status(thm)],[fact_add__Pls]) ).
fof(f_2049_2,plain,
! [U_7398] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_7398) = U_7398,
inference(variable_rename,[status(thm)],[f_2049_1]) ).
fof(f_2049_3,plain,
! [U_7398] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_7398) = U_7398,
inference(definitional_conversion,[status(esa)],[f_2049_2]) ).
cnf(f_2049_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_7398) = U_7398,
inference(clausify,[status(thm)],[f_2049_3]) ).
fof(f_2050_1,plain,
! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_mult__Pls]) ).
fof(f_2050_2,plain,
! [U_7399] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_7399) = c_Int_OPls,
inference(variable_rename,[status(thm)],[f_2050_1]) ).
fof(f_2050_3,plain,
! [U_7399] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_7399) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2050_2]) ).
cnf(f_2050_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_7399) = c_Int_OPls,
inference(clausify,[status(thm)],[f_2050_3]) ).
fof(f_2051_1,plain,
! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I1_J]) ).
fof(f_2051_2,plain,
! [U_7400] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7400),c_Int_OPls) = U_7400,
inference(variable_rename,[status(thm)],[f_2051_1]) ).
fof(f_2051_3,plain,
! [U_7400] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7400),c_Int_OPls) = U_7400,
inference(definitional_conversion,[status(esa)],[f_2051_2]) ).
cnf(f_2051_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7400),c_Int_OPls) = U_7400,
inference(clausify,[status(thm)],[f_2051_3]) ).
fof(f_2052_1,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_minus__Pls]) ).
fof(f_2052_2,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2052_1]) ).
cnf(f_2052_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_2052_2]) ).
fof(f_2053_1,plain,
c_Int_OPls != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).
fof(f_2053_2,plain,
c_Int_OPls != c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_2053_1]) ).
cnf(f_2053_3,plain,
c_Int_OPls != c_Int_OMin,
inference(clausify,[status(thm)],[f_2053_2]) ).
fof(f_2054_1,plain,
c_Int_OMin != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).
fof(f_2054_2,plain,
c_Int_OMin != c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2054_1]) ).
cnf(f_2054_3,plain,
c_Int_OMin != c_Int_OPls,
inference(clausify,[status(thm)],[f_2054_2]) ).
fof(f_2055_1,plain,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I1_J]) ).
fof(f_2055_2,plain,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2055_1]) ).
cnf(f_2055_3,plain,
hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2055_2]) ).
fof(f_2056_1,plain,
! [V_a,T_a] :
( 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)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__ge__zero]) ).
fof(f_2056_2,plain,
! [U_7402,U_7401] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7401),c_Groups_Ozero__class_Ozero(U_7401)),hAPP(c_Groups_Oabs__class_Oabs(U_7401),U_7402)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7401) ),
inference(variable_rename,[status(thm)],[f_2056_1]) ).
fof(f_2056_3,plain,
! [U_7401,U_7402] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7401),c_Groups_Ozero__class_Ozero(U_7401)),hAPP(c_Groups_Oabs__class_Oabs(U_7401),U_7402)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7401) ),
inference(definitional_conversion,[status(esa)],[f_2056_2]) ).
cnf(f_2056_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7401),c_Groups_Ozero__class_Ozero(U_7401)),hAPP(c_Groups_Oabs__class_Oabs(U_7401),U_7402)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7401) ),
inference(clausify,[status(thm)],[f_2056_3]) ).
fof(f_2057_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).
fof(f_2057_2,plain,
! [U_7404,U_7403] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7403),hAPP(c_Groups_Oabs__class_Oabs(U_7403),U_7404)),c_Groups_Ozero__class_Ozero(U_7403)))
| U_7404 != c_Groups_Ozero__class_Ozero(U_7403) )
& ( U_7404 = c_Groups_Ozero__class_Ozero(U_7403)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7403),hAPP(c_Groups_Oabs__class_Oabs(U_7403),U_7404)),c_Groups_Ozero__class_Ozero(U_7403))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_7403) ),
inference(variable_rename,[status(thm)],[f_2057_1]) ).
fof(f_2057_3,plain,
( ! [U_7403,U_7404] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7403),hAPP(c_Groups_Oabs__class_Oabs(U_7403),U_7404)),c_Groups_Ozero__class_Ozero(U_7403)))
| U_7404 != c_Groups_Ozero__class_Ozero(U_7403)
| ~ sP679(U_7403,U_7404) )
& ! [U_7403,U_7404] :
( U_7404 = c_Groups_Ozero__class_Ozero(U_7403)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7403),hAPP(c_Groups_Oabs__class_Oabs(U_7403),U_7404)),c_Groups_Ozero__class_Ozero(U_7403)))
| ~ sP679(U_7403,U_7404) )
& ! [U_7403,U_7404] :
( sP679(U_7403,U_7404)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7403) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP679])],[f_2057_2]) ).
cnf(f_2057_4,plain,
( sP679(U_7403,U_7404)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7403) ),
inference(clausify,[status(thm)],[f_2057_3]) ).
cnf(f_2057_5,plain,
( U_7404 = c_Groups_Ozero__class_Ozero(U_7403)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7403),hAPP(c_Groups_Oabs__class_Oabs(U_7403),U_7404)),c_Groups_Ozero__class_Ozero(U_7403)))
| ~ sP679(U_7403,U_7404) ),
inference(clausify,[status(thm)],[f_2057_3]) ).
cnf(f_2057_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7403),hAPP(c_Groups_Oabs__class_Oabs(U_7403),U_7404)),c_Groups_Ozero__class_Ozero(U_7403)))
| U_7404 != c_Groups_Ozero__class_Ozero(U_7403)
| ~ sP679(U_7403,U_7404) ),
inference(clausify,[status(thm)],[f_2057_3]) ).
fof(f_2058_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg]) ).
fof(f_2058_2,plain,
! [U_7406,U_7405] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7405),U_7406) = U_7406
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7405),c_Groups_Ozero__class_Ozero(U_7405)),U_7406))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7405) ),
inference(variable_rename,[status(thm)],[f_2058_1]) ).
fof(f_2058_3,plain,
! [U_7405,U_7406] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7405),U_7406) = U_7406
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7405),c_Groups_Ozero__class_Ozero(U_7405)),U_7406))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7405) ),
inference(definitional_conversion,[status(esa)],[f_2058_2]) ).
cnf(f_2058_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7405),U_7406) = U_7406
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7405),c_Groups_Ozero__class_Ozero(U_7405)),U_7406))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7405) ),
inference(clausify,[status(thm)],[f_2058_3]) ).
fof(f_2059_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__pos]) ).
fof(f_2059_2,plain,
! [U_7408,U_7407] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7407),U_7408) = U_7408
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7407),c_Groups_Ozero__class_Ozero(U_7407)),U_7408))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7407) ),
inference(variable_rename,[status(thm)],[f_2059_1]) ).
fof(f_2059_3,plain,
! [U_7408,U_7407] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7407),U_7408) = U_7408
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7407),c_Groups_Ozero__class_Ozero(U_7407)),U_7408))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7407) ),
inference(definitional_conversion,[status(esa)],[f_2059_2]) ).
cnf(f_2059_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7407),U_7408) = U_7408
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7407),c_Groups_Ozero__class_Ozero(U_7407)),U_7408))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7407) ),
inference(clausify,[status(thm)],[f_2059_3]) ).
fof(f_2060_1,plain,
! [V_a_2,T_b] :
( ( ( 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)))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
| ~ 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))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).
fof(f_2060_2,plain,
! [U_7410,U_7409] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7409),c_Groups_Ozero__class_Ozero(U_7409)),hAPP(c_Groups_Oabs__class_Oabs(U_7409),U_7410)))
| U_7410 = c_Groups_Ozero__class_Ozero(U_7409) )
& ( U_7410 != c_Groups_Ozero__class_Ozero(U_7409)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7409),c_Groups_Ozero__class_Ozero(U_7409)),hAPP(c_Groups_Oabs__class_Oabs(U_7409),U_7410))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_7409) ),
inference(variable_rename,[status(thm)],[f_2060_1]) ).
fof(f_2060_3,plain,
( ! [U_7409,U_7410] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7409),c_Groups_Ozero__class_Ozero(U_7409)),hAPP(c_Groups_Oabs__class_Oabs(U_7409),U_7410)))
| U_7410 = c_Groups_Ozero__class_Ozero(U_7409)
| ~ sP680(U_7409,U_7410) )
& ! [U_7409,U_7410] :
( U_7410 != c_Groups_Ozero__class_Ozero(U_7409)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7409),c_Groups_Ozero__class_Ozero(U_7409)),hAPP(c_Groups_Oabs__class_Oabs(U_7409),U_7410)))
| ~ sP680(U_7409,U_7410) )
& ! [U_7409,U_7410] :
( sP680(U_7409,U_7410)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7409) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP680])],[f_2060_2]) ).
cnf(f_2060_4,plain,
( sP680(U_7409,U_7410)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7409) ),
inference(clausify,[status(thm)],[f_2060_3]) ).
cnf(f_2060_5,plain,
( U_7410 != c_Groups_Ozero__class_Ozero(U_7409)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7409),c_Groups_Ozero__class_Ozero(U_7409)),hAPP(c_Groups_Oabs__class_Oabs(U_7409),U_7410)))
| ~ sP680(U_7409,U_7410) ),
inference(clausify,[status(thm)],[f_2060_3]) ).
cnf(f_2060_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7409),c_Groups_Ozero__class_Ozero(U_7409)),hAPP(c_Groups_Oabs__class_Oabs(U_7409),U_7410)))
| U_7410 = c_Groups_Ozero__class_Ozero(U_7409)
| ~ sP680(U_7409,U_7410) ),
inference(clausify,[status(thm)],[f_2060_3]) ).
fof(f_2061_1,plain,
! [V_a,T_a] :
( ~ 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)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__not__less__zero]) ).
fof(f_2061_2,plain,
! [U_7412,U_7411] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7411),hAPP(c_Groups_Oabs__class_Oabs(U_7411),U_7412)),c_Groups_Ozero__class_Ozero(U_7411)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7411) ),
inference(variable_rename,[status(thm)],[f_2061_1]) ).
fof(f_2061_3,plain,
! [U_7411,U_7412] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7411),hAPP(c_Groups_Oabs__class_Oabs(U_7411),U_7412)),c_Groups_Ozero__class_Ozero(U_7411)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7411) ),
inference(definitional_conversion,[status(esa)],[f_2061_2]) ).
cnf(f_2061_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7411),hAPP(c_Groups_Oabs__class_Oabs(U_7411),U_7412)),c_Groups_Ozero__class_Ozero(U_7411)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7411) ),
inference(clausify,[status(thm)],[f_2061_3]) ).
fof(f_2062_1,plain,
! [V_b,V_a,T_a] :
( 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))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq]) ).
fof(f_2062_2,plain,
! [U_7415,U_7414,U_7413] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7413),hAPP(c_Groups_Oabs__class_Oabs(U_7413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7413),U_7414),U_7415))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7413),hAPP(c_Groups_Oabs__class_Oabs(U_7413),U_7414)),hAPP(c_Groups_Oabs__class_Oabs(U_7413),U_7415))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7413) ),
inference(variable_rename,[status(thm)],[f_2062_1]) ).
fof(f_2062_3,plain,
! [U_7413,U_7414,U_7415] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7413),hAPP(c_Groups_Oabs__class_Oabs(U_7413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7413),U_7414),U_7415))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7413),hAPP(c_Groups_Oabs__class_Oabs(U_7413),U_7414)),hAPP(c_Groups_Oabs__class_Oabs(U_7413),U_7415))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7413) ),
inference(definitional_conversion,[status(esa)],[f_2062_2]) ).
cnf(f_2062_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7413),hAPP(c_Groups_Oabs__class_Oabs(U_7413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7413),U_7414),U_7415))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7413),hAPP(c_Groups_Oabs__class_Oabs(U_7413),U_7414)),hAPP(c_Groups_Oabs__class_Oabs(U_7413),U_7415))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7413) ),
inference(clausify,[status(thm)],[f_2062_3]) ).
fof(f_2063_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult__less]) ).
fof(f_2063_2,plain,
! [U_7420,U_7419,U_7418,U_7417,U_7416] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7417)),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7419))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7416),U_7418),U_7420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7419)),U_7420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7417)),U_7418))
| ~ class_Rings_Olinordered__idom(U_7416) ),
inference(variable_rename,[status(thm)],[f_2063_1]) ).
fof(f_2063_3,plain,
! [U_7418,U_7416,U_7417,U_7419,U_7420] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7417)),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7419))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7416),U_7418),U_7420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7419)),U_7420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7417)),U_7418))
| ~ class_Rings_Olinordered__idom(U_7416) ),
inference(definitional_conversion,[status(esa)],[f_2063_2]) ).
cnf(f_2063_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7417)),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7419))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7416),U_7418),U_7420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7419)),U_7420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),hAPP(c_Groups_Oabs__class_Oabs(U_7416),U_7417)),U_7418))
| ~ class_Rings_Olinordered__idom(U_7416) ),
inference(clausify,[status(thm)],[f_2063_3]) ).
fof(f_2064_1,plain,
! [V_b,V_a,T_a] :
( 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))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3]) ).
fof(f_2064_2,plain,
! [U_7423,U_7422,U_7421] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7421),hAPP(c_Groups_Oabs__class_Oabs(U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7421),hAPP(c_Groups_Oabs__class_Oabs(U_7421),U_7422)),hAPP(c_Groups_Oabs__class_Oabs(U_7421),U_7423)))),hAPP(c_Groups_Oabs__class_Oabs(U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7421),U_7422),U_7423))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7421) ),
inference(variable_rename,[status(thm)],[f_2064_1]) ).
fof(f_2064_3,plain,
! [U_7422,U_7421,U_7423] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7421),hAPP(c_Groups_Oabs__class_Oabs(U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7421),hAPP(c_Groups_Oabs__class_Oabs(U_7421),U_7422)),hAPP(c_Groups_Oabs__class_Oabs(U_7421),U_7423)))),hAPP(c_Groups_Oabs__class_Oabs(U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7421),U_7422),U_7423))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7421) ),
inference(definitional_conversion,[status(esa)],[f_2064_2]) ).
cnf(f_2064_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7421),hAPP(c_Groups_Oabs__class_Oabs(U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7421),hAPP(c_Groups_Oabs__class_Oabs(U_7421),U_7422)),hAPP(c_Groups_Oabs__class_Oabs(U_7421),U_7423)))),hAPP(c_Groups_Oabs__class_Oabs(U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7421),U_7422),U_7423))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7421) ),
inference(clausify,[status(thm)],[f_2064_3]) ).
fof(f_2065_1,plain,
! [V_b,V_a,T_a] :
( 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))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2]) ).
fof(f_2065_2,plain,
! [U_7426,U_7425,U_7424] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7424),hAPP(c_Groups_Oabs__class_Oabs(U_7424),U_7425)),hAPP(c_Groups_Oabs__class_Oabs(U_7424),U_7426))),hAPP(c_Groups_Oabs__class_Oabs(U_7424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7424),U_7425),U_7426))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7424) ),
inference(variable_rename,[status(thm)],[f_2065_1]) ).
fof(f_2065_3,plain,
! [U_7424,U_7425,U_7426] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7424),hAPP(c_Groups_Oabs__class_Oabs(U_7424),U_7425)),hAPP(c_Groups_Oabs__class_Oabs(U_7424),U_7426))),hAPP(c_Groups_Oabs__class_Oabs(U_7424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7424),U_7425),U_7426))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7424) ),
inference(definitional_conversion,[status(esa)],[f_2065_2]) ).
cnf(f_2065_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7424),hAPP(c_Groups_Oabs__class_Oabs(U_7424),U_7425)),hAPP(c_Groups_Oabs__class_Oabs(U_7424),U_7426))),hAPP(c_Groups_Oabs__class_Oabs(U_7424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7424),U_7425),U_7426))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7424) ),
inference(clausify,[status(thm)],[f_2065_3]) ).
fof(f_2066_1,plain,
! [V_b,V_a,T_a] :
( 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))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym]) ).
fof(f_2066_2,plain,
! [U_7429,U_7428,U_7427] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7427),hAPP(c_Groups_Oabs__class_Oabs(U_7427),U_7428)),hAPP(c_Groups_Oabs__class_Oabs(U_7427),U_7429))),hAPP(c_Groups_Oabs__class_Oabs(U_7427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7427),U_7429),U_7428))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7427) ),
inference(variable_rename,[status(thm)],[f_2066_1]) ).
fof(f_2066_3,plain,
! [U_7427,U_7428,U_7429] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7427),hAPP(c_Groups_Oabs__class_Oabs(U_7427),U_7428)),hAPP(c_Groups_Oabs__class_Oabs(U_7427),U_7429))),hAPP(c_Groups_Oabs__class_Oabs(U_7427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7427),U_7429),U_7428))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7427) ),
inference(definitional_conversion,[status(esa)],[f_2066_2]) ).
cnf(f_2066_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7427),hAPP(c_Groups_Oabs__class_Oabs(U_7427),U_7428)),hAPP(c_Groups_Oabs__class_Oabs(U_7427),U_7429))),hAPP(c_Groups_Oabs__class_Oabs(U_7427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7427),U_7429),U_7428))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7427) ),
inference(clausify,[status(thm)],[f_2066_3]) ).
fof(f_2067_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__D2]) ).
fof(f_2067_2,plain,
! [U_7432,U_7431,U_7430] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7430),hAPP(c_Groups_Ouminus__class_Ouminus(U_7430),U_7431)),U_7432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7430),hAPP(c_Groups_Oabs__class_Oabs(U_7430),U_7431)),U_7432))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7430) ),
inference(variable_rename,[status(thm)],[f_2067_1]) ).
fof(f_2067_3,plain,
! [U_7430,U_7431,U_7432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7430),hAPP(c_Groups_Ouminus__class_Ouminus(U_7430),U_7431)),U_7432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7430),hAPP(c_Groups_Oabs__class_Oabs(U_7430),U_7431)),U_7432))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7430) ),
inference(definitional_conversion,[status(esa)],[f_2067_2]) ).
cnf(f_2067_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7430),hAPP(c_Groups_Ouminus__class_Ouminus(U_7430),U_7431)),U_7432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7430),hAPP(c_Groups_Oabs__class_Oabs(U_7430),U_7431)),U_7432))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7430) ),
inference(clausify,[status(thm)],[f_2067_3]) ).
fof(f_2068_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__leI]) ).
fof(f_2068_2,plain,
! [U_7435,U_7434,U_7433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),hAPP(c_Groups_Oabs__class_Oabs(U_7433),U_7434)),U_7435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),hAPP(c_Groups_Ouminus__class_Ouminus(U_7433),U_7434)),U_7435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),U_7434),U_7435))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7433) ),
inference(variable_rename,[status(thm)],[f_2068_1]) ).
fof(f_2068_3,plain,
! [U_7433,U_7434,U_7435] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),hAPP(c_Groups_Oabs__class_Oabs(U_7433),U_7434)),U_7435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),hAPP(c_Groups_Ouminus__class_Ouminus(U_7433),U_7434)),U_7435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),U_7434),U_7435))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7433) ),
inference(definitional_conversion,[status(esa)],[f_2068_2]) ).
cnf(f_2068_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),hAPP(c_Groups_Oabs__class_Oabs(U_7433),U_7434)),U_7435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),hAPP(c_Groups_Ouminus__class_Ouminus(U_7433),U_7434)),U_7435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7433),U_7434),U_7435))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7433) ),
inference(clausify,[status(thm)],[f_2068_3]) ).
fof(f_2069_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( 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))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( ( 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))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
| ~ 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)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).
fof(f_2069_2,plain,
! [U_7438,U_7437,U_7436] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Oabs__class_Oabs(U_7436),U_7437)),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(U_7436),U_7437)),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),U_7437),U_7438)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(U_7436),U_7437)),U_7438))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),U_7437),U_7438)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Oabs__class_Oabs(U_7436),U_7437)),U_7438)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_7436) ),
inference(variable_rename,[status(thm)],[f_2069_1]) ).
fof(f_2069_3,plain,
( ! [U_7437,U_7436,U_7438] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(U_7436),U_7437)),U_7438))
| ~ sP681(U_7437,U_7436,U_7438) )
& ! [U_7437,U_7436,U_7438] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),U_7437),U_7438))
| ~ sP681(U_7437,U_7436,U_7438) )
& ! [U_7437,U_7436,U_7438] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Oabs__class_Oabs(U_7436),U_7437)),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(U_7436),U_7437)),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),U_7437),U_7438))
| ~ sP682(U_7437,U_7436,U_7438) )
& ! [U_7437,U_7436,U_7438] :
( sP681(U_7437,U_7436,U_7438)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Oabs__class_Oabs(U_7436),U_7437)),U_7438))
| ~ sP682(U_7437,U_7436,U_7438) )
& ! [U_7437,U_7436,U_7438] :
( sP682(U_7437,U_7436,U_7438)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7436) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP681,sP682])],[f_2069_2]) ).
cnf(f_2069_4,plain,
( sP682(U_7437,U_7436,U_7438)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7436) ),
inference(clausify,[status(thm)],[f_2069_3]) ).
cnf(f_2069_5,plain,
( sP681(U_7437,U_7436,U_7438)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Oabs__class_Oabs(U_7436),U_7437)),U_7438))
| ~ sP682(U_7437,U_7436,U_7438) ),
inference(clausify,[status(thm)],[f_2069_3]) ).
cnf(f_2069_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Oabs__class_Oabs(U_7436),U_7437)),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(U_7436),U_7437)),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),U_7437),U_7438))
| ~ sP682(U_7437,U_7436,U_7438) ),
inference(clausify,[status(thm)],[f_2069_3]) ).
cnf(f_2069_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),U_7437),U_7438))
| ~ sP681(U_7437,U_7436,U_7438) ),
inference(clausify,[status(thm)],[f_2069_3]) ).
cnf(f_2069_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(U_7436),U_7437)),U_7438))
| ~ sP681(U_7437,U_7436,U_7438) ),
inference(clausify,[status(thm)],[f_2069_3]) ).
fof(f_2070_1,plain,
! [V_a,T_a] :
( 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)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self]) ).
fof(f_2070_2,plain,
! [U_7440,U_7439] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7439),hAPP(c_Groups_Ouminus__class_Ouminus(U_7439),U_7440)),hAPP(c_Groups_Oabs__class_Oabs(U_7439),U_7440)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7439) ),
inference(variable_rename,[status(thm)],[f_2070_1]) ).
fof(f_2070_3,plain,
! [U_7440,U_7439] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7439),hAPP(c_Groups_Ouminus__class_Ouminus(U_7439),U_7440)),hAPP(c_Groups_Oabs__class_Oabs(U_7439),U_7440)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7439) ),
inference(definitional_conversion,[status(esa)],[f_2070_2]) ).
cnf(f_2070_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7439),hAPP(c_Groups_Ouminus__class_Ouminus(U_7439),U_7440)),hAPP(c_Groups_Oabs__class_Oabs(U_7439),U_7440)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7439) ),
inference(clausify,[status(thm)],[f_2070_3]) ).
fof(f_2071_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).
fof(f_2071_2,plain,
! [U_7443,U_7442,U_7441] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Oabs__class_Oabs(U_7441),U_7442)),U_7443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Ouminus__class_Ouminus(U_7441),U_7442)),U_7443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),U_7442),U_7443)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Ouminus__class_Ouminus(U_7441),U_7442)),U_7443))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),U_7442),U_7443)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Oabs__class_Oabs(U_7441),U_7442)),U_7443)) ) )
| ~ class_Rings_Olinordered__idom(U_7441) ),
inference(variable_rename,[status(thm)],[f_2071_1]) ).
fof(f_2071_3,plain,
( ! [U_7441,U_7442,U_7443] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Ouminus__class_Ouminus(U_7441),U_7442)),U_7443))
| ~ sP683(U_7441,U_7442,U_7443) )
& ! [U_7441,U_7442,U_7443] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),U_7442),U_7443))
| ~ sP683(U_7441,U_7442,U_7443) )
& ! [U_7441,U_7442,U_7443] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Oabs__class_Oabs(U_7441),U_7442)),U_7443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Ouminus__class_Ouminus(U_7441),U_7442)),U_7443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),U_7442),U_7443))
| ~ sP684(U_7441,U_7442,U_7443) )
& ! [U_7441,U_7442,U_7443] :
( sP683(U_7441,U_7442,U_7443)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Oabs__class_Oabs(U_7441),U_7442)),U_7443))
| ~ sP684(U_7441,U_7442,U_7443) )
& ! [U_7441,U_7442,U_7443] :
( sP684(U_7441,U_7442,U_7443)
| ~ class_Rings_Olinordered__idom(U_7441) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP683,sP684])],[f_2071_2]) ).
cnf(f_2071_4,plain,
( sP684(U_7441,U_7442,U_7443)
| ~ class_Rings_Olinordered__idom(U_7441) ),
inference(clausify,[status(thm)],[f_2071_3]) ).
cnf(f_2071_5,plain,
( sP683(U_7441,U_7442,U_7443)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Oabs__class_Oabs(U_7441),U_7442)),U_7443))
| ~ sP684(U_7441,U_7442,U_7443) ),
inference(clausify,[status(thm)],[f_2071_3]) ).
cnf(f_2071_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Oabs__class_Oabs(U_7441),U_7442)),U_7443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Ouminus__class_Ouminus(U_7441),U_7442)),U_7443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),U_7442),U_7443))
| ~ sP684(U_7441,U_7442,U_7443) ),
inference(clausify,[status(thm)],[f_2071_3]) ).
cnf(f_2071_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),U_7442),U_7443))
| ~ sP683(U_7441,U_7442,U_7443) ),
inference(clausify,[status(thm)],[f_2071_3]) ).
cnf(f_2071_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7441),hAPP(c_Groups_Ouminus__class_Ouminus(U_7441),U_7442)),U_7443))
| ~ sP683(U_7441,U_7442,U_7443) ),
inference(clausify,[status(thm)],[f_2071_3]) ).
fof(f_2072_1,plain,
! [V_a,V_b,T_a] :
( 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))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide]) ).
fof(f_2072_2,plain,
! [U_7446,U_7445,U_7444] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7444),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7444),U_7446),U_7445)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7444),hAPP(c_Groups_Oabs__class_Oabs(U_7444),U_7446)),hAPP(c_Groups_Oabs__class_Oabs(U_7444),U_7445))
| U_7445 = c_Groups_Ozero__class_Ozero(U_7444)
| ~ class_Fields_Olinordered__field(U_7444) ),
inference(variable_rename,[status(thm)],[f_2072_1]) ).
fof(f_2072_3,plain,
! [U_7446,U_7445,U_7444] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7444),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7444),U_7446),U_7445)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7444),hAPP(c_Groups_Oabs__class_Oabs(U_7444),U_7446)),hAPP(c_Groups_Oabs__class_Oabs(U_7444),U_7445))
| U_7445 = c_Groups_Ozero__class_Ozero(U_7444)
| ~ class_Fields_Olinordered__field(U_7444) ),
inference(definitional_conversion,[status(esa)],[f_2072_2]) ).
cnf(f_2072_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7444),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7444),U_7446),U_7445)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7444),hAPP(c_Groups_Oabs__class_Oabs(U_7444),U_7446)),hAPP(c_Groups_Oabs__class_Oabs(U_7444),U_7445))
| U_7445 = c_Groups_Ozero__class_Ozero(U_7444)
| ~ class_Fields_Olinordered__field(U_7444) ),
inference(clausify,[status(thm)],[f_2072_3]) ).
fof(f_2073_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__power__minus]) ).
fof(f_2073_2,plain,
! [U_7449,U_7448,U_7447] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7447),hAPP(hAPP(c_Power_Opower__class_Opower(U_7447),hAPP(c_Groups_Ouminus__class_Ouminus(U_7447),U_7448)),U_7449)) = hAPP(c_Groups_Oabs__class_Oabs(U_7447),hAPP(hAPP(c_Power_Opower__class_Opower(U_7447),U_7448),U_7449))
| ~ class_Rings_Olinordered__idom(U_7447) ),
inference(variable_rename,[status(thm)],[f_2073_1]) ).
fof(f_2073_3,plain,
! [U_7447,U_7448,U_7449] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7447),hAPP(hAPP(c_Power_Opower__class_Opower(U_7447),hAPP(c_Groups_Ouminus__class_Ouminus(U_7447),U_7448)),U_7449)) = hAPP(c_Groups_Oabs__class_Oabs(U_7447),hAPP(hAPP(c_Power_Opower__class_Opower(U_7447),U_7448),U_7449))
| ~ class_Rings_Olinordered__idom(U_7447) ),
inference(definitional_conversion,[status(esa)],[f_2073_2]) ).
cnf(f_2073_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7447),hAPP(hAPP(c_Power_Opower__class_Opower(U_7447),hAPP(c_Groups_Ouminus__class_Ouminus(U_7447),U_7448)),U_7449)) = hAPP(c_Groups_Oabs__class_Oabs(U_7447),hAPP(hAPP(c_Power_Opower__class_Opower(U_7447),U_7448),U_7449))
| ~ class_Rings_Olinordered__idom(U_7447) ),
inference(clausify,[status(thm)],[f_2073_3]) ).
fof(f_2074_1,plain,
! [V_n,V_m] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| 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) ),
inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1]) ).
fof(f_2074_2,plain,
! [U_7451,U_7450] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7450),U_7451)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2074_1]) ).
fof(f_2074_3,plain,
! [U_7450,U_7451] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7450),U_7451)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2074_2]) ).
cnf(f_2074_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7450),U_7451)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2074_3]) ).
fof(f_2075_1,plain,
! [T_a] :
( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Pls]) ).
fof(f_2075_2,plain,
! [U_7452] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7452),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_7452)
| ~ class_Int_Onumber__ring(U_7452) ),
inference(variable_rename,[status(thm)],[f_2075_1]) ).
fof(f_2075_3,plain,
! [U_7452] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7452),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_7452)
| ~ class_Int_Onumber__ring(U_7452) ),
inference(definitional_conversion,[status(esa)],[f_2075_2]) ).
cnf(f_2075_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7452),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_7452)
| ~ class_Int_Onumber__ring(U_7452) ),
inference(clausify,[status(thm)],[f_2075_3]) ).
fof(f_2076_1,plain,
! [T_a] :
( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J]) ).
fof(f_2076_2,plain,
! [U_7453] :
( c_Groups_Ozero__class_Ozero(U_7453) = hAPP(c_Int_Onumber__class_Onumber__of(U_7453),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_7453) ),
inference(variable_rename,[status(thm)],[f_2076_1]) ).
fof(f_2076_3,plain,
! [U_7453] :
( c_Groups_Ozero__class_Ozero(U_7453) = hAPP(c_Int_Onumber__class_Onumber__of(U_7453),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_7453) ),
inference(definitional_conversion,[status(esa)],[f_2076_2]) ).
cnf(f_2076_4,plain,
( c_Groups_Ozero__class_Ozero(U_7453) = hAPP(c_Int_Onumber__class_Onumber__of(U_7453),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_7453) ),
inference(clausify,[status(thm)],[f_2076_3]) ).
fof(f_2077_1,plain,
! [V_a,T_a] :
( 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
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__numeral__0]) ).
fof(f_2077_2,plain,
! [U_7455,U_7454] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7454),hAPP(c_Int_Onumber__class_Onumber__of(U_7454),c_Int_OPls)),U_7455) = U_7455
| ~ class_Int_Onumber__ring(U_7454) ),
inference(variable_rename,[status(thm)],[f_2077_1]) ).
fof(f_2077_3,plain,
! [U_7454,U_7455] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7454),hAPP(c_Int_Onumber__class_Onumber__of(U_7454),c_Int_OPls)),U_7455) = U_7455
| ~ class_Int_Onumber__ring(U_7454) ),
inference(definitional_conversion,[status(esa)],[f_2077_2]) ).
cnf(f_2077_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7454),hAPP(c_Int_Onumber__class_Onumber__of(U_7454),c_Int_OPls)),U_7455) = U_7455
| ~ class_Int_Onumber__ring(U_7454) ),
inference(clausify,[status(thm)],[f_2077_3]) ).
fof(f_2078_1,plain,
! [V_a,T_a] :
( 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
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right]) ).
fof(f_2078_2,plain,
! [U_7457,U_7456] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7456),U_7457),hAPP(c_Int_Onumber__class_Onumber__of(U_7456),c_Int_OPls)) = U_7457
| ~ class_Int_Onumber__ring(U_7456) ),
inference(variable_rename,[status(thm)],[f_2078_1]) ).
fof(f_2078_3,plain,
! [U_7456,U_7457] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7456),U_7457),hAPP(c_Int_Onumber__class_Onumber__of(U_7456),c_Int_OPls)) = U_7457
| ~ class_Int_Onumber__ring(U_7456) ),
inference(definitional_conversion,[status(esa)],[f_2078_2]) ).
cnf(f_2078_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7456),U_7457),hAPP(c_Int_Onumber__class_Onumber__of(U_7456),c_Int_OPls)) = U_7457
| ~ class_Int_Onumber__ring(U_7456) ),
inference(clausify,[status(thm)],[f_2078_3]) ).
fof(f_2079_1,plain,
! [V_k,T_a] :
( 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))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__sgn]) ).
fof(f_2079_2,plain,
! [U_7459,U_7458] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7458),U_7459) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7458),U_7459),c_Groups_Osgn__class_Osgn(U_7458,U_7459))
| ~ class_Rings_Olinordered__idom(U_7458) ),
inference(variable_rename,[status(thm)],[f_2079_1]) ).
fof(f_2079_3,plain,
! [U_7458,U_7459] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7458),U_7459) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7458),U_7459),c_Groups_Osgn__class_Osgn(U_7458,U_7459))
| ~ class_Rings_Olinordered__idom(U_7458) ),
inference(definitional_conversion,[status(esa)],[f_2079_2]) ).
cnf(f_2079_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7458),U_7459) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7458),U_7459),c_Groups_Osgn__class_Osgn(U_7458,U_7459))
| ~ class_Rings_Olinordered__idom(U_7458) ),
inference(clausify,[status(thm)],[f_2079_3]) ).
fof(f_2080_1,plain,
! [V_x,T_a] :
( 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
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs]) ).
fof(f_2080_2,plain,
! [U_7461,U_7460] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7460),c_Groups_Osgn__class_Osgn(U_7460,U_7461)),hAPP(c_Groups_Oabs__class_Oabs(U_7460),U_7461)) = U_7461
| ~ class_Rings_Olinordered__idom(U_7460) ),
inference(variable_rename,[status(thm)],[f_2080_1]) ).
fof(f_2080_3,plain,
! [U_7460,U_7461] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7460),c_Groups_Osgn__class_Osgn(U_7460,U_7461)),hAPP(c_Groups_Oabs__class_Oabs(U_7460),U_7461)) = U_7461
| ~ class_Rings_Olinordered__idom(U_7460) ),
inference(definitional_conversion,[status(esa)],[f_2080_2]) ).
cnf(f_2080_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7460),c_Groups_Osgn__class_Osgn(U_7460,U_7461)),hAPP(c_Groups_Oabs__class_Oabs(U_7460),U_7461)) = U_7461
| ~ class_Rings_Olinordered__idom(U_7460) ),
inference(clausify,[status(thm)],[f_2080_3]) ).
fof(f_2081_1,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).
fof(f_2081_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_2081_1]) ).
cnf(f_2081_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_2081_2]) ).
fof(f_2082_1,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I113_J]) ).
fof(f_2082_2,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_2082_1]) ).
cnf(f_2082_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(clausify,[status(thm)],[f_2082_2]) ).
fof(f_2083_1,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__Pls]) ).
fof(f_2083_2,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_2083_1]) ).
cnf(f_2083_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2083_2]) ).
fof(f_2084_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_zero__is__num__zero]) ).
fof(f_2084_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_2084_1]) ).
cnf(f_2084_3,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(clausify,[status(thm)],[f_2084_2]) ).
fof(f_2085_1,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I23_J]) ).
fof(f_2085_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2085_1]) ).
cnf(f_2085_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2085_2]) ).
fof(f_2086_1,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I20_J]) ).
fof(f_2086_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(definitional_conversion,[status(esa)],[f_2086_1]) ).
cnf(f_2086_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(clausify,[status(thm)],[f_2086_2]) ).
fof(f_2087_1,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I3_J]) ).
fof(f_2087_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(definitional_conversion,[status(esa)],[f_2087_1]) ).
cnf(f_2087_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(clausify,[status(thm)],[f_2087_2]) ).
fof(f_2088_1,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I6_J]) ).
fof(f_2088_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2088_1]) ).
cnf(f_2088_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2088_2]) ).
fof(f_2089_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__Pls__Min]) ).
fof(f_2089_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_2089_1]) ).
cnf(f_2089_3,plain,
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),
inference(clausify,[status(thm)],[f_2089_2]) ).
fof(f_2090_1,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(fof_nnf,[status(thm)],[fact_not__neg__number__of__Pls]) ).
fof(f_2090_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(definitional_conversion,[status(esa)],[f_2090_1]) ).
cnf(f_2090_3,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(clausify,[status(thm)],[f_2090_2]) ).
fof(f_2091_1,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I5_J]) ).
fof(f_2091_2,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2091_1]) ).
cnf(f_2091_3,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2091_2]) ).
fof(f_2092_1,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I2_J]) ).
fof(f_2092_2,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(definitional_conversion,[status(esa)],[f_2092_1]) ).
cnf(f_2092_3,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(clausify,[status(thm)],[f_2092_2]) ).
fof(f_2093_1,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).
fof(f_2093_2,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2093_1]) ).
cnf(f_2093_3,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(clausify,[status(thm)],[f_2093_2]) ).
fof(f_2094_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult__pos]) ).
fof(f_2094_2,plain,
! [U_7464,U_7463,U_7462] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),hAPP(c_Groups_Oabs__class_Oabs(U_7462),U_7464)),U_7463) = hAPP(c_Groups_Oabs__class_Oabs(U_7462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7462),c_Groups_Ozero__class_Ozero(U_7462)),U_7463))
| ~ class_Rings_Olinordered__idom(U_7462) ),
inference(variable_rename,[status(thm)],[f_2094_1]) ).
fof(f_2094_3,plain,
! [U_7462,U_7463,U_7464] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),hAPP(c_Groups_Oabs__class_Oabs(U_7462),U_7464)),U_7463) = hAPP(c_Groups_Oabs__class_Oabs(U_7462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7462),c_Groups_Ozero__class_Ozero(U_7462)),U_7463))
| ~ class_Rings_Olinordered__idom(U_7462) ),
inference(definitional_conversion,[status(esa)],[f_2094_2]) ).
cnf(f_2094_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),hAPP(c_Groups_Oabs__class_Oabs(U_7462),U_7464)),U_7463) = hAPP(c_Groups_Oabs__class_Oabs(U_7462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7462),c_Groups_Ozero__class_Ozero(U_7462)),U_7463))
| ~ class_Rings_Olinordered__idom(U_7462) ),
inference(clausify,[status(thm)],[f_2094_3]) ).
fof(f_2095_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) )
| ~ class_Rings_Oordered__ring__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__eq__mult]) ).
fof(f_2095_2,plain,
! [U_7467,U_7466,U_7465] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7465),U_7466),U_7467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7465),hAPP(c_Groups_Oabs__class_Oabs(U_7465),U_7466)),hAPP(c_Groups_Oabs__class_Oabs(U_7465),U_7467))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),U_7467),c_Groups_Ozero__class_Ozero(U_7465)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),c_Groups_Ozero__class_Ozero(U_7465)),U_7467)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),U_7466),c_Groups_Ozero__class_Ozero(U_7465)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),c_Groups_Ozero__class_Ozero(U_7465)),U_7466)) )
| ~ class_Rings_Oordered__ring__abs(U_7465) ),
inference(variable_rename,[status(thm)],[f_2095_1]) ).
fof(f_2095_3,plain,
( ! [U_7465,U_7467] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),U_7467),c_Groups_Ozero__class_Ozero(U_7465)))
| ~ sP686(U_7465,U_7467) )
& ! [U_7465,U_7467] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),c_Groups_Ozero__class_Ozero(U_7465)),U_7467))
| ~ sP686(U_7465,U_7467) )
& ! [U_7465,U_7466] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),U_7466),c_Groups_Ozero__class_Ozero(U_7465)))
| ~ sP685(U_7465,U_7466) )
& ! [U_7465,U_7466] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),c_Groups_Ozero__class_Ozero(U_7465)),U_7466))
| ~ sP685(U_7465,U_7466) )
& ! [U_7465,U_7466,U_7467] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7465),U_7466),U_7467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7465),hAPP(c_Groups_Oabs__class_Oabs(U_7465),U_7466)),hAPP(c_Groups_Oabs__class_Oabs(U_7465),U_7467))
| sP686(U_7465,U_7467)
| sP685(U_7465,U_7466)
| ~ class_Rings_Oordered__ring__abs(U_7465) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP685,sP686])],[f_2095_2]) ).
cnf(f_2095_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7465),U_7466),U_7467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7465),hAPP(c_Groups_Oabs__class_Oabs(U_7465),U_7466)),hAPP(c_Groups_Oabs__class_Oabs(U_7465),U_7467))
| sP686(U_7465,U_7467)
| sP685(U_7465,U_7466)
| ~ class_Rings_Oordered__ring__abs(U_7465) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),c_Groups_Ozero__class_Ozero(U_7465)),U_7466))
| ~ sP685(U_7465,U_7466) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),U_7466),c_Groups_Ozero__class_Ozero(U_7465)))
| ~ sP685(U_7465,U_7466) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),c_Groups_Ozero__class_Ozero(U_7465)),U_7467))
| ~ sP686(U_7465,U_7467) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7465),U_7467),c_Groups_Ozero__class_Ozero(U_7465)))
| ~ sP686(U_7465,U_7467) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
fof(f_2096_1,plain,
! [V_b,V_a,T_a] :
( 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))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4]) ).
fof(f_2096_2,plain,
! [U_7470,U_7469,U_7468] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7468),hAPP(c_Groups_Oabs__class_Oabs(U_7468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7468),U_7469),U_7470))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7468),hAPP(c_Groups_Oabs__class_Oabs(U_7468),U_7469)),hAPP(c_Groups_Oabs__class_Oabs(U_7468),U_7470))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7468) ),
inference(variable_rename,[status(thm)],[f_2096_1]) ).
fof(f_2096_3,plain,
! [U_7469,U_7470,U_7468] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7468),hAPP(c_Groups_Oabs__class_Oabs(U_7468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7468),U_7469),U_7470))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7468),hAPP(c_Groups_Oabs__class_Oabs(U_7468),U_7469)),hAPP(c_Groups_Oabs__class_Oabs(U_7468),U_7470))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7468) ),
inference(definitional_conversion,[status(esa)],[f_2096_2]) ).
cnf(f_2096_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7468),hAPP(c_Groups_Oabs__class_Oabs(U_7468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7468),U_7469),U_7470))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7468),hAPP(c_Groups_Oabs__class_Oabs(U_7468),U_7469)),hAPP(c_Groups_Oabs__class_Oabs(U_7468),U_7470))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7468) ),
inference(clausify,[status(thm)],[f_2096_3]) ).
fof(f_2097_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq]) ).
fof(f_2097_2,plain,
! [U_7475,U_7474,U_7473,U_7472,U_7471] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7471),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),U_7472),U_7473)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),U_7474),U_7475)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),U_7472),U_7474))),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),U_7473),U_7475)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7471) ),
inference(variable_rename,[status(thm)],[f_2097_1]) ).
fof(f_2097_3,plain,
! [U_7471,U_7472,U_7473,U_7474,U_7475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7471),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),U_7472),U_7473)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),U_7474),U_7475)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),U_7472),U_7474))),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),U_7473),U_7475)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7471) ),
inference(definitional_conversion,[status(esa)],[f_2097_2]) ).
cnf(f_2097_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7471),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),U_7472),U_7473)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),U_7474),U_7475)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7471),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),U_7472),U_7474))),hAPP(c_Groups_Oabs__class_Oabs(U_7471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7471),U_7473),U_7475)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7471) ),
inference(clausify,[status(thm)],[f_2097_3]) ).
fof(f_2098_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos]) ).
fof(f_2098_2,plain,
! [U_7477,U_7476] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7476),U_7477) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7476),U_7477)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7476),U_7477),c_Groups_Ozero__class_Ozero(U_7476)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7476) ),
inference(variable_rename,[status(thm)],[f_2098_1]) ).
fof(f_2098_3,plain,
! [U_7477,U_7476] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7476),U_7477) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7476),U_7477)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7476),U_7477),c_Groups_Ozero__class_Ozero(U_7476)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7476) ),
inference(definitional_conversion,[status(esa)],[f_2098_2]) ).
cnf(f_2098_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7476),U_7477) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7476),U_7477)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7476),U_7477),c_Groups_Ozero__class_Ozero(U_7476)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7476) ),
inference(clausify,[status(thm)],[f_2098_3]) ).
fof(f_2099_1,plain,
! [V_a,T_a] :
( 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)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero]) ).
fof(f_2099_2,plain,
! [U_7479,U_7478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7478),hAPP(c_Groups_Ouminus__class_Ouminus(U_7478),hAPP(c_Groups_Oabs__class_Oabs(U_7478),U_7479))),c_Groups_Ozero__class_Ozero(U_7478)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7478) ),
inference(variable_rename,[status(thm)],[f_2099_1]) ).
fof(f_2099_3,plain,
! [U_7478,U_7479] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7478),hAPP(c_Groups_Ouminus__class_Ouminus(U_7478),hAPP(c_Groups_Oabs__class_Oabs(U_7478),U_7479))),c_Groups_Ozero__class_Ozero(U_7478)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7478) ),
inference(definitional_conversion,[status(esa)],[f_2099_2]) ).
cnf(f_2099_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7478),hAPP(c_Groups_Ouminus__class_Ouminus(U_7478),hAPP(c_Groups_Oabs__class_Oabs(U_7478),U_7479))),c_Groups_Ozero__class_Ozero(U_7478)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7478) ),
inference(clausify,[status(thm)],[f_2099_3]) ).
fof(f_2100_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__neg]) ).
fof(f_2100_2,plain,
! [U_7481,U_7480] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7480),U_7481) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7480),U_7481)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7480),U_7481),c_Groups_Ozero__class_Ozero(U_7480)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7480) ),
inference(variable_rename,[status(thm)],[f_2100_1]) ).
fof(f_2100_3,plain,
! [U_7480,U_7481] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7480),U_7481) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7480),U_7481)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7480),U_7481),c_Groups_Ozero__class_Ozero(U_7480)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7480) ),
inference(definitional_conversion,[status(esa)],[f_2100_2]) ).
cnf(f_2100_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7480),U_7481) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7480),U_7481)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7480),U_7481),c_Groups_Ozero__class_Ozero(U_7480)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7480) ),
inference(clausify,[status(thm)],[f_2100_3]) ).
fof(f_2101_1,plain,
! [V_a,T_a] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) )
| ~ class_Groups_Oabs__if(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__if]) ).
fof(f_2101_2,plain,
! [U_7483,U_7482] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_7482),U_7483) = U_7483
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7482),U_7483),c_Groups_Ozero__class_Ozero(U_7482))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(U_7482),U_7483) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7482),U_7483)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7482),U_7483),c_Groups_Ozero__class_Ozero(U_7482))) ) )
| ~ class_Groups_Oabs__if(U_7482) ),
inference(variable_rename,[status(thm)],[f_2101_1]) ).
fof(f_2101_3,plain,
( ! [U_7482,U_7483] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7482),U_7483) = U_7483
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7482),U_7483),c_Groups_Ozero__class_Ozero(U_7482)))
| ~ sP687(U_7482,U_7483) )
& ! [U_7482,U_7483] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7482),U_7483) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7482),U_7483)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7482),U_7483),c_Groups_Ozero__class_Ozero(U_7482)))
| ~ sP687(U_7482,U_7483) )
& ! [U_7482,U_7483] :
( sP687(U_7482,U_7483)
| ~ class_Groups_Oabs__if(U_7482) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP687])],[f_2101_2]) ).
cnf(f_2101_4,plain,
( sP687(U_7482,U_7483)
| ~ class_Groups_Oabs__if(U_7482) ),
inference(clausify,[status(thm)],[f_2101_3]) ).
cnf(f_2101_5,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7482),U_7483) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7482),U_7483)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7482),U_7483),c_Groups_Ozero__class_Ozero(U_7482)))
| ~ sP687(U_7482,U_7483) ),
inference(clausify,[status(thm)],[f_2101_3]) ).
cnf(f_2101_6,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7482),U_7483) = U_7483
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7482),U_7483),c_Groups_Ozero__class_Ozero(U_7482)))
| ~ sP687(U_7482,U_7483) ),
inference(clausify,[status(thm)],[f_2101_3]) ).
fof(f_2102_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs]) ).
fof(f_2102_2,plain,
! [U_7486,U_7485,U_7484] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7484),c_Groups_Ozero__class_Ozero(U_7484)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7484),hAPP(c_Groups_Oabs__class_Oabs(U_7484),U_7485)),U_7486)))
| ~ class_Rings_Olinordered__idom(U_7484) ),
inference(variable_rename,[status(thm)],[f_2102_1]) ).
fof(f_2102_3,plain,
! [U_7486,U_7485,U_7484] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7484),c_Groups_Ozero__class_Ozero(U_7484)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7484),hAPP(c_Groups_Oabs__class_Oabs(U_7484),U_7485)),U_7486)))
| ~ class_Rings_Olinordered__idom(U_7484) ),
inference(definitional_conversion,[status(esa)],[f_2102_2]) ).
cnf(f_2102_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7484),c_Groups_Ozero__class_Ozero(U_7484)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7484),hAPP(c_Groups_Oabs__class_Oabs(U_7484),U_7485)),U_7486)))
| ~ class_Rings_Olinordered__idom(U_7484) ),
inference(clausify,[status(thm)],[f_2102_3]) ).
fof(f_2103_1,plain,
! [V_x,V_y,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__div__pos]) ).
fof(f_2103_2,plain,
! [U_7489,U_7488,U_7487] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7487),hAPP(c_Groups_Oabs__class_Oabs(U_7487),U_7489)),U_7488) = hAPP(c_Groups_Oabs__class_Oabs(U_7487),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7487),U_7489),U_7488))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7487),c_Groups_Ozero__class_Ozero(U_7487)),U_7488))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7487) ),
inference(variable_rename,[status(thm)],[f_2103_1]) ).
fof(f_2103_3,plain,
! [U_7487,U_7488,U_7489] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7487),hAPP(c_Groups_Oabs__class_Oabs(U_7487),U_7489)),U_7488) = hAPP(c_Groups_Oabs__class_Oabs(U_7487),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7487),U_7489),U_7488))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7487),c_Groups_Ozero__class_Ozero(U_7487)),U_7488))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7487) ),
inference(definitional_conversion,[status(esa)],[f_2103_2]) ).
cnf(f_2103_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7487),hAPP(c_Groups_Oabs__class_Oabs(U_7487),U_7489)),U_7488) = hAPP(c_Groups_Oabs__class_Oabs(U_7487),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7487),U_7489),U_7488))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7487),c_Groups_Ozero__class_Ozero(U_7487)),U_7488))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7487) ),
inference(clausify,[status(thm)],[f_2103_3]) ).
fof(f_2104_1,plain,
! [T_a] :
( 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)
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__one]) ).
fof(f_2104_2,plain,
! [U_7490] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7490),hAPP(c_Int_Onumber__class_Onumber__of(U_7490),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_7490)
| ~ class_Rings_Olinordered__idom(U_7490)
| ~ class_Int_Onumber__ring(U_7490) ),
inference(variable_rename,[status(thm)],[f_2104_1]) ).
fof(f_2104_3,plain,
! [U_7490] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7490),hAPP(c_Int_Onumber__class_Onumber__of(U_7490),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_7490)
| ~ class_Rings_Olinordered__idom(U_7490)
| ~ class_Int_Onumber__ring(U_7490) ),
inference(definitional_conversion,[status(esa)],[f_2104_2]) ).
cnf(f_2104_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7490),hAPP(c_Int_Onumber__class_Onumber__of(U_7490),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_7490)
| ~ class_Rings_Olinordered__idom(U_7490)
| ~ class_Int_Onumber__ring(U_7490) ),
inference(clausify,[status(thm)],[f_2104_3]) ).
fof(f_2105_1,plain,
! [V_z_2] :
( ( 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)))
| V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff]) ).
fof(f_2105_2,plain,
! [U_7491] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7491)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_7491 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_7491 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7491)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2105_1]) ).
fof(f_2105_3,plain,
( ! [U_7493] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7493)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_7493 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_7492] :
( U_7492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7492)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2105_2]) ).
fof(f_2105_4,plain,
( ! [U_7493] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7493)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_7493 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_7492] :
( U_7492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7492)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_2105_3]) ).
cnf(f_2105_5,plain,
( U_7492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7492)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2105_4]) ).
cnf(f_2105_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7493)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_7493 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2105_4]) ).
fof(f_2106_1,plain,
! [V_i] :
( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zabs__def]) ).
fof(f_2106_2,plain,
! [U_7494] :
( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7494) = U_7494
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7494),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7494) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7494)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7494),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2106_1]) ).
fof(f_2106_3,plain,
( ! [U_7496] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7496) = U_7496
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7496),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7495] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7495) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7495)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2106_2]) ).
fof(f_2106_4,plain,
( ! [U_7496] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7496) = U_7496
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7496),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7495] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7495) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7495)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_2106_3]) ).
cnf(f_2106_5,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7495) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7495)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2106_4]) ).
cnf(f_2106_6,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7496) = U_7496
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7496),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2106_4]) ).
fof(f_2107_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_nat__abs__mult__distrib]) ).
fof(f_2107_2,plain,
! [U_7498,U_7497] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7497),U_7498))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7497))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7498))),
inference(variable_rename,[status(thm)],[f_2107_1]) ).
fof(f_2107_3,plain,
! [U_7497,U_7498] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7497),U_7498))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7497))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7498))),
inference(definitional_conversion,[status(esa)],[f_2107_2]) ).
cnf(f_2107_4,plain,
hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7497),U_7498))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7497))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7498))),
inference(clausify,[status(thm)],[f_2107_3]) ).
fof(f_2108_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(f_2108_2,plain,
! [U_7500,U_7499] : 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),U_7499)),U_7500))),
inference(variable_rename,[status(thm)],[f_2108_1]) ).
fof(f_2108_3,plain,
! [U_7499,U_7500] : 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),U_7499)),U_7500))),
inference(definitional_conversion,[status(esa)],[f_2108_2]) ).
cnf(f_2108_4,plain,
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),U_7499)),U_7500))),
inference(clausify,[status(thm)],[f_2108_3]) ).
fof(f_2109_1,plain,
! [V_x,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__Numeral0]) ).
fof(f_2109_2,plain,
! [U_7502,U_7501] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7501),U_7502),hAPP(c_Int_Onumber__class_Onumber__of(U_7501),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_7501)
| ~ class_Int_Onumber__ring(U_7501)
| ~ class_Fields_Ofield__inverse__zero(U_7501) ),
inference(variable_rename,[status(thm)],[f_2109_1]) ).
fof(f_2109_3,plain,
! [U_7501,U_7502] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7501),U_7502),hAPP(c_Int_Onumber__class_Onumber__of(U_7501),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_7501)
| ~ class_Int_Onumber__ring(U_7501)
| ~ class_Fields_Ofield__inverse__zero(U_7501) ),
inference(definitional_conversion,[status(esa)],[f_2109_2]) ).
cnf(f_2109_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7501),U_7502),hAPP(c_Int_Onumber__class_Onumber__of(U_7501),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_7501)
| ~ class_Int_Onumber__ring(U_7501)
| ~ class_Fields_Ofield__inverse__zero(U_7501) ),
inference(clausify,[status(thm)],[f_2109_3]) ).
fof(f_2110_1,plain,
! [V_v_2] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__0]) ).
fof(f_2110_2,plain,
! [U_7503] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7503) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7503),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7503),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7503) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_2110_1]) ).
fof(f_2110_3,plain,
( ! [U_7505] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7505) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),c_Int_OPls)) )
& ! [U_7504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7504),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7504) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_2110_2]) ).
fof(f_2110_4,plain,
( ! [U_7505] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7505) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),c_Int_OPls)) )
& ! [U_7504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7504),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7504) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_2110_3]) ).
cnf(f_2110_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7504),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7504) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2110_4]) ).
cnf(f_2110_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7505) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2110_4]) ).
fof(f_2111_1,plain,
! [V_v_2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__0__number__of]) ).
fof(f_2111_2,plain,
! [U_7506] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7506)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7506),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7506),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7506) ) ),
inference(variable_rename,[status(thm)],[f_2111_1]) ).
fof(f_2111_3,plain,
( ! [U_7508] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7508)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7508),c_Int_OPls)) )
& ! [U_7507] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7507),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7507) ) ),
inference(miniscope,[status(thm)],[f_2111_2]) ).
fof(f_2111_4,plain,
( ! [U_7508] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7508)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7508),c_Int_OPls)) )
& ! [U_7507] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7507),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7507) ) ),
inference(definitional_conversion,[status(esa)],[f_2111_3]) ).
cnf(f_2111_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7507),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7507) ),
inference(clausify,[status(thm)],[f_2111_4]) ).
cnf(f_2111_6,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7508)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7508),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2111_4]) ).
fof(f_2112_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_number__of2]) ).
fof(f_2112_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_2112_1]) ).
cnf(f_2112_3,plain,
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))),
inference(clausify,[status(thm)],[f_2112_2]) ).
fof(f_2113_1,plain,
! [V_v_H_2,V_v_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__nat__number__of]) ).
fof(f_2113_2,plain,
! [U_7510,U_7509] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7509)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7510)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7509),U_7510))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7510))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7509),U_7510)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7509),U_7510))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7509),U_7510)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7509)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7510))) ) ),
inference(variable_rename,[status(thm)],[f_2113_1]) ).
fof(f_2113_3,plain,
( ! [U_7514,U_7512] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7512)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7514)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7512),U_7514))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7514))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7512),U_7514)) ) )
& ! [U_7513,U_7511] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7511),U_7513))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7511),U_7513)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7511)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7513))) ) ),
inference(miniscope,[status(thm)],[f_2113_2]) ).
fof(f_2113_4,plain,
( ! [U_7514,U_7512] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7514))
| ~ sP689(U_7514,U_7512) )
& ! [U_7514,U_7512] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7512),U_7514))
| ~ sP689(U_7514,U_7512) )
& ! [U_7513,U_7511] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7511),U_7513))
| ~ sP688(U_7513,U_7511) )
& ! [U_7513,U_7511] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7511),U_7513))
| ~ sP688(U_7513,U_7511) )
& ! [U_7514,U_7512] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7512)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7514)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7512),U_7514))
| sP689(U_7514,U_7512) )
& ! [U_7513,U_7511] :
( sP688(U_7513,U_7511)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7511)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7513))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP688,sP689])],[f_2113_3]) ).
cnf(f_2113_5,plain,
( sP688(U_7513,U_7511)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7511)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7513))) ),
inference(clausify,[status(thm)],[f_2113_4]) ).
cnf(f_2113_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7512)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7514)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7512),U_7514))
| sP689(U_7514,U_7512) ),
inference(clausify,[status(thm)],[f_2113_4]) ).
cnf(f_2113_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7511),U_7513))
| ~ sP688(U_7513,U_7511) ),
inference(clausify,[status(thm)],[f_2113_4]) ).
cnf(f_2113_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7511),U_7513))
| ~ sP688(U_7513,U_7511) ),
inference(clausify,[status(thm)],[f_2113_4]) ).
cnf(f_2113_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7512),U_7514))
| ~ sP689(U_7514,U_7512) ),
inference(clausify,[status(thm)],[f_2113_4]) ).
cnf(f_2113_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7514))
| ~ sP689(U_7514,U_7512) ),
inference(clausify,[status(thm)],[f_2113_4]) ).
fof(f_2114_1,plain,
! [V_v_H_2,V_v_2] :
( ( 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)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__nat__number__of]) ).
fof(f_2114_2,plain,
! [U_7516,U_7515] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7515)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7516)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7515),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7515),U_7516)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7515),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7515),U_7516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7515)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7516))) ) ),
inference(variable_rename,[status(thm)],[f_2114_1]) ).
fof(f_2114_3,plain,
( ! [U_7520,U_7518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7518)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7520)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7518),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7518),U_7520)) ) )
& ! [U_7519,U_7517] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7517),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7517),U_7519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7517)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7519))) ) ),
inference(miniscope,[status(thm)],[f_2114_2]) ).
fof(f_2114_4,plain,
( ! [U_7520,U_7518] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7518),c_Int_OPls))
| ~ sP690(U_7520,U_7518) )
& ! [U_7520,U_7518] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7518),U_7520))
| ~ sP690(U_7520,U_7518) )
& ! [U_7520,U_7518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7518)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7520)))
| sP690(U_7520,U_7518) )
& ! [U_7517,U_7519] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7517),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7517),U_7519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7517)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7519))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP690])],[f_2114_3]) ).
cnf(f_2114_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7517),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7517),U_7519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7517)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7519))) ),
inference(clausify,[status(thm)],[f_2114_4]) ).
cnf(f_2114_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7518)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7520)))
| sP690(U_7520,U_7518) ),
inference(clausify,[status(thm)],[f_2114_4]) ).
cnf(f_2114_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7518),U_7520))
| ~ sP690(U_7520,U_7518) ),
inference(clausify,[status(thm)],[f_2114_4]) ).
cnf(f_2114_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7518),c_Int_OPls))
| ~ sP690(U_7520,U_7518) ),
inference(clausify,[status(thm)],[f_2114_4]) ).
fof(f_2115_1,plain,
! [V_x,T_a] :
( ( ( 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)
| 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))) )
& ( 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))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__number__of]) ).
fof(f_2115_2,plain,
! [U_7522,U_7521] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)),c_Groups_Ozero__class_Ozero(U_7521))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)),c_Groups_Ozero__class_Ozero(U_7521))) ) )
| ~ class_Rings_Olinordered__idom(U_7521)
| ~ class_Int_Onumber__ring(U_7521) ),
inference(variable_rename,[status(thm)],[f_2115_1]) ).
fof(f_2115_3,plain,
( ! [U_7522,U_7521] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)),c_Groups_Ozero__class_Ozero(U_7521)))
| ~ sP691(U_7522,U_7521) )
& ! [U_7522,U_7521] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)),c_Groups_Ozero__class_Ozero(U_7521)))
| ~ sP691(U_7522,U_7521) )
& ! [U_7522,U_7521] :
( sP691(U_7522,U_7521)
| ~ class_Rings_Olinordered__idom(U_7521)
| ~ class_Int_Onumber__ring(U_7521) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP691])],[f_2115_2]) ).
cnf(f_2115_4,plain,
( sP691(U_7522,U_7521)
| ~ class_Rings_Olinordered__idom(U_7521)
| ~ class_Int_Onumber__ring(U_7521) ),
inference(clausify,[status(thm)],[f_2115_3]) ).
cnf(f_2115_5,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)),c_Groups_Ozero__class_Ozero(U_7521)))
| ~ sP691(U_7522,U_7521) ),
inference(clausify,[status(thm)],[f_2115_3]) ).
cnf(f_2115_6,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7521),hAPP(c_Int_Onumber__class_Onumber__of(U_7521),U_7522)),c_Groups_Ozero__class_Ozero(U_7521)))
| ~ sP691(U_7522,U_7521) ),
inference(clausify,[status(thm)],[f_2115_3]) ).
fof(f_2116_1,plain,
! [V_n,T_a] :
( 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)
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one]) ).
fof(f_2116_2,plain,
! [U_7524,U_7523] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7523),hAPP(hAPP(c_Power_Opower__class_Opower(U_7523),hAPP(c_Int_Onumber__class_Onumber__of(U_7523),c_Int_OMin)),U_7524)) = c_Groups_Oone__class_Oone(U_7523)
| ~ class_Rings_Olinordered__idom(U_7523)
| ~ class_Int_Onumber__ring(U_7523) ),
inference(variable_rename,[status(thm)],[f_2116_1]) ).
fof(f_2116_3,plain,
! [U_7524,U_7523] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7523),hAPP(hAPP(c_Power_Opower__class_Opower(U_7523),hAPP(c_Int_Onumber__class_Onumber__of(U_7523),c_Int_OMin)),U_7524)) = c_Groups_Oone__class_Oone(U_7523)
| ~ class_Rings_Olinordered__idom(U_7523)
| ~ class_Int_Onumber__ring(U_7523) ),
inference(definitional_conversion,[status(esa)],[f_2116_2]) ).
cnf(f_2116_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7523),hAPP(hAPP(c_Power_Opower__class_Opower(U_7523),hAPP(c_Int_Onumber__class_Onumber__of(U_7523),c_Int_OMin)),U_7524)) = c_Groups_Oone__class_Oone(U_7523)
| ~ class_Rings_Olinordered__idom(U_7523)
| ~ class_Int_Onumber__ring(U_7523) ),
inference(clausify,[status(thm)],[f_2116_3]) ).
fof(f_2117_1,plain,
! [V_n_2,V_x_2] :
( ( 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)))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff]) ).
fof(f_2117_2,plain,
! [U_7526,U_7525] :
( ( 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),U_7525)),U_7526)))
| ( U_7526 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7525 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( U_7526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7525 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),U_7525)),U_7526))) ) ),
inference(variable_rename,[status(thm)],[f_2117_1]) ).
fof(f_2117_3,plain,
( ! [U_7530,U_7528] :
( 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),U_7528)),U_7530)))
| ( U_7530 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7528 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_7529,U_7527] :
( U_7529 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7527 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),U_7527)),U_7529))) ) ),
inference(miniscope,[status(thm)],[f_2117_2]) ).
fof(f_2117_4,plain,
( ! [U_7530,U_7528] :
( U_7530 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP692(U_7530,U_7528) )
& ! [U_7530,U_7528] :
( U_7528 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP692(U_7530,U_7528) )
& ! [U_7530,U_7528] :
( 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),U_7528)),U_7530)))
| sP692(U_7530,U_7528) )
& ! [U_7529,U_7527] :
( U_7529 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7527 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),U_7527)),U_7529))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP692])],[f_2117_3]) ).
cnf(f_2117_5,plain,
( U_7529 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7527 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),U_7527)),U_7529))) ),
inference(clausify,[status(thm)],[f_2117_4]) ).
cnf(f_2117_6,plain,
( 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),U_7528)),U_7530)))
| sP692(U_7530,U_7528) ),
inference(clausify,[status(thm)],[f_2117_4]) ).
cnf(f_2117_7,plain,
( U_7528 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP692(U_7530,U_7528) ),
inference(clausify,[status(thm)],[f_2117_4]) ).
cnf(f_2117_8,plain,
( U_7530 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP692(U_7530,U_7528) ),
inference(clausify,[status(thm)],[f_2117_4]) ).
fof(f_2118_1,plain,
! [V_y_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).
fof(f_2118_2,plain,
! [U_7532,U_7531] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7531),c_Groups_Ozero__class_Ozero(U_7531)),hAPP(c_Int_Onumber__class_Onumber__of(U_7531),U_7532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7532)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7531),c_Groups_Ozero__class_Ozero(U_7531)),hAPP(c_Int_Onumber__class_Onumber__of(U_7531),U_7532))) ) )
| ~ class_Rings_Olinordered__idom(U_7531)
| ~ class_Int_Onumber__ring(U_7531) ),
inference(variable_rename,[status(thm)],[f_2118_1]) ).
fof(f_2118_3,plain,
( ! [U_7532,U_7531] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7531),c_Groups_Ozero__class_Ozero(U_7531)),hAPP(c_Int_Onumber__class_Onumber__of(U_7531),U_7532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7532))
| ~ sP693(U_7532,U_7531) )
& ! [U_7532,U_7531] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7531),c_Groups_Ozero__class_Ozero(U_7531)),hAPP(c_Int_Onumber__class_Onumber__of(U_7531),U_7532)))
| ~ sP693(U_7532,U_7531) )
& ! [U_7532,U_7531] :
( sP693(U_7532,U_7531)
| ~ class_Rings_Olinordered__idom(U_7531)
| ~ class_Int_Onumber__ring(U_7531) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP693])],[f_2118_2]) ).
cnf(f_2118_4,plain,
( sP693(U_7532,U_7531)
| ~ class_Rings_Olinordered__idom(U_7531)
| ~ class_Int_Onumber__ring(U_7531) ),
inference(clausify,[status(thm)],[f_2118_3]) ).
cnf(f_2118_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7531),c_Groups_Ozero__class_Ozero(U_7531)),hAPP(c_Int_Onumber__class_Onumber__of(U_7531),U_7532)))
| ~ sP693(U_7532,U_7531) ),
inference(clausify,[status(thm)],[f_2118_3]) ).
cnf(f_2118_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7531),c_Groups_Ozero__class_Ozero(U_7531)),hAPP(c_Int_Onumber__class_Onumber__of(U_7531),U_7532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7532))
| ~ sP693(U_7532,U_7531) ),
inference(clausify,[status(thm)],[f_2118_3]) ).
fof(f_2119_1,plain,
! [V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I3_J]) ).
fof(f_2119_2,plain,
! [U_7534,U_7533] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7533),hAPP(c_Int_Onumber__class_Onumber__of(U_7533),U_7534)),c_Groups_Ozero__class_Ozero(U_7533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7534),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7534),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7533),hAPP(c_Int_Onumber__class_Onumber__of(U_7533),U_7534)),c_Groups_Ozero__class_Ozero(U_7533))) ) )
| ~ class_Rings_Olinordered__idom(U_7533)
| ~ class_Int_Onumber__ring(U_7533) ),
inference(variable_rename,[status(thm)],[f_2119_1]) ).
fof(f_2119_3,plain,
( ! [U_7534,U_7533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7533),hAPP(c_Int_Onumber__class_Onumber__of(U_7533),U_7534)),c_Groups_Ozero__class_Ozero(U_7533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7534),c_Int_OPls))
| ~ sP694(U_7534,U_7533) )
& ! [U_7534,U_7533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7534),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7533),hAPP(c_Int_Onumber__class_Onumber__of(U_7533),U_7534)),c_Groups_Ozero__class_Ozero(U_7533)))
| ~ sP694(U_7534,U_7533) )
& ! [U_7534,U_7533] :
( sP694(U_7534,U_7533)
| ~ class_Rings_Olinordered__idom(U_7533)
| ~ class_Int_Onumber__ring(U_7533) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP694])],[f_2119_2]) ).
cnf(f_2119_4,plain,
( sP694(U_7534,U_7533)
| ~ class_Rings_Olinordered__idom(U_7533)
| ~ class_Int_Onumber__ring(U_7533) ),
inference(clausify,[status(thm)],[f_2119_3]) ).
cnf(f_2119_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7534),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7533),hAPP(c_Int_Onumber__class_Onumber__of(U_7533),U_7534)),c_Groups_Ozero__class_Ozero(U_7533)))
| ~ sP694(U_7534,U_7533) ),
inference(clausify,[status(thm)],[f_2119_3]) ).
cnf(f_2119_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7533),hAPP(c_Int_Onumber__class_Onumber__of(U_7533),U_7534)),c_Groups_Ozero__class_Ozero(U_7533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7534),c_Int_OPls))
| ~ sP694(U_7534,U_7533) ),
inference(clausify,[status(thm)],[f_2119_3]) ).
fof(f_2120_1,plain,
! [V_y_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).
fof(f_2120_2,plain,
! [U_7536,U_7535] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7535),c_Groups_Ozero__class_Ozero(U_7535)),hAPP(c_Int_Onumber__class_Onumber__of(U_7535),U_7536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7536)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7535),c_Groups_Ozero__class_Ozero(U_7535)),hAPP(c_Int_Onumber__class_Onumber__of(U_7535),U_7536))) ) )
| ~ class_Rings_Olinordered__idom(U_7535)
| ~ class_Int_Onumber__ring(U_7535) ),
inference(variable_rename,[status(thm)],[f_2120_1]) ).
fof(f_2120_3,plain,
( ! [U_7535,U_7536] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7535),c_Groups_Ozero__class_Ozero(U_7535)),hAPP(c_Int_Onumber__class_Onumber__of(U_7535),U_7536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7536))
| ~ sP695(U_7535,U_7536) )
& ! [U_7535,U_7536] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7535),c_Groups_Ozero__class_Ozero(U_7535)),hAPP(c_Int_Onumber__class_Onumber__of(U_7535),U_7536)))
| ~ sP695(U_7535,U_7536) )
& ! [U_7535,U_7536] :
( sP695(U_7535,U_7536)
| ~ class_Rings_Olinordered__idom(U_7535)
| ~ class_Int_Onumber__ring(U_7535) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP695])],[f_2120_2]) ).
cnf(f_2120_4,plain,
( sP695(U_7535,U_7536)
| ~ class_Rings_Olinordered__idom(U_7535)
| ~ class_Int_Onumber__ring(U_7535) ),
inference(clausify,[status(thm)],[f_2120_3]) ).
cnf(f_2120_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7535),c_Groups_Ozero__class_Ozero(U_7535)),hAPP(c_Int_Onumber__class_Onumber__of(U_7535),U_7536)))
| ~ sP695(U_7535,U_7536) ),
inference(clausify,[status(thm)],[f_2120_3]) ).
cnf(f_2120_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7535),c_Groups_Ozero__class_Ozero(U_7535)),hAPP(c_Int_Onumber__class_Onumber__of(U_7535),U_7536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7536))
| ~ sP695(U_7535,U_7536) ),
inference(clausify,[status(thm)],[f_2120_3]) ).
fof(f_2121_1,plain,
! [V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I3_J]) ).
fof(f_2121_2,plain,
! [U_7538,U_7537] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7537),hAPP(c_Int_Onumber__class_Onumber__of(U_7537),U_7538)),c_Groups_Ozero__class_Ozero(U_7537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7537),hAPP(c_Int_Onumber__class_Onumber__of(U_7537),U_7538)),c_Groups_Ozero__class_Ozero(U_7537))) ) )
| ~ class_Rings_Olinordered__idom(U_7537)
| ~ class_Int_Onumber__ring(U_7537) ),
inference(variable_rename,[status(thm)],[f_2121_1]) ).
fof(f_2121_3,plain,
( ! [U_7538,U_7537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7537),hAPP(c_Int_Onumber__class_Onumber__of(U_7537),U_7538)),c_Groups_Ozero__class_Ozero(U_7537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Int_OPls))
| ~ sP696(U_7538,U_7537) )
& ! [U_7538,U_7537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7537),hAPP(c_Int_Onumber__class_Onumber__of(U_7537),U_7538)),c_Groups_Ozero__class_Ozero(U_7537)))
| ~ sP696(U_7538,U_7537) )
& ! [U_7538,U_7537] :
( sP696(U_7538,U_7537)
| ~ class_Rings_Olinordered__idom(U_7537)
| ~ class_Int_Onumber__ring(U_7537) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP696])],[f_2121_2]) ).
cnf(f_2121_4,plain,
( sP696(U_7538,U_7537)
| ~ class_Rings_Olinordered__idom(U_7537)
| ~ class_Int_Onumber__ring(U_7537) ),
inference(clausify,[status(thm)],[f_2121_3]) ).
cnf(f_2121_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7537),hAPP(c_Int_Onumber__class_Onumber__of(U_7537),U_7538)),c_Groups_Ozero__class_Ozero(U_7537)))
| ~ sP696(U_7538,U_7537) ),
inference(clausify,[status(thm)],[f_2121_3]) ).
cnf(f_2121_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7537),hAPP(c_Int_Onumber__class_Onumber__of(U_7537),U_7538)),c_Groups_Ozero__class_Ozero(U_7537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Int_OPls))
| ~ sP696(U_7538,U_7537) ),
inference(clausify,[status(thm)],[f_2121_3]) ).
fof(f_2122_1,plain,
! [V_v_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__0__number__of]) ).
fof(f_2122_2,plain,
! [U_7539] :
( ( 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),U_7539)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7539)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7539))
| ~ 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),U_7539))) ) ),
inference(variable_rename,[status(thm)],[f_2122_1]) ).
fof(f_2122_3,plain,
( ! [U_7541] :
( 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),U_7541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7541)) )
& ! [U_7540] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7540))
| ~ 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),U_7540))) ) ),
inference(miniscope,[status(thm)],[f_2122_2]) ).
fof(f_2122_4,plain,
( ! [U_7541] :
( 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),U_7541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7541)) )
& ! [U_7540] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7540))
| ~ 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),U_7540))) ) ),
inference(definitional_conversion,[status(esa)],[f_2122_3]) ).
cnf(f_2122_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7540))
| ~ 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),U_7540))) ),
inference(clausify,[status(thm)],[f_2122_4]) ).
cnf(f_2122_6,plain,
( 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),U_7541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7541)) ),
inference(clausify,[status(thm)],[f_2122_4]) ).
fof(f_2123_1,plain,
! [V_v_H,V_v] :
( ( ( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__nat__number__of]) ).
fof(f_2123_2,plain,
! [U_7543,U_7542] :
( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7543)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7542),U_7543))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7543),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7543)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7542)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7543),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7542),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7543)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7543)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7542),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2123_1]) ).
fof(f_2123_3,plain,
( ! [U_7547,U_7545] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7547))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7547),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7547),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7545),c_Int_OPls)) )
& ! [U_7546,U_7544] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7544)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7546)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7546)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7544),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2123_2]) ).
fof(f_2123_4,plain,
( ! [U_7547,U_7545] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7547))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7547),c_Int_OPls))
| ~ sP697(U_7547,U_7545) )
& ! [U_7547,U_7545] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7547),c_Int_OPls))
| ~ sP697(U_7547,U_7545) )
& ! [U_7547,U_7545] :
( sP697(U_7547,U_7545)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7545),c_Int_OPls)) )
& ! [U_7544,U_7546] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7544)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7546)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7546)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7544),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP697])],[f_2123_3]) ).
cnf(f_2123_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7544)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7546)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7546)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7544),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2123_4]) ).
cnf(f_2123_6,plain,
( sP697(U_7547,U_7545)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7545),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2123_4]) ).
cnf(f_2123_7,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7547),c_Int_OPls))
| ~ sP697(U_7547,U_7545) ),
inference(clausify,[status(thm)],[f_2123_4]) ).
cnf(f_2123_8,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7547))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7547),c_Int_OPls))
| ~ sP697(U_7547,U_7545) ),
inference(clausify,[status(thm)],[f_2123_4]) ).
fof(f_2124_1,plain,
! [V_k,V_v_H,V_v] :
( ( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__mult__left]) ).
fof(f_2124_2,plain,
! [U_7550,U_7549,U_7548] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7548)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7549)),U_7550)) = 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),U_7548),U_7549))),U_7550)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7548)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7549)),U_7550)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2124_1]) ).
fof(f_2124_3,plain,
( ! [U_7556,U_7554,U_7552] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7554)),U_7556)) = 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),U_7552),U_7554))),U_7556)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7552),c_Int_OPls)) )
& ! [U_7555,U_7553,U_7551] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7553)),U_7555)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2124_2]) ).
fof(f_2124_4,plain,
( ! [U_7552,U_7554,U_7556] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7554)),U_7556)) = 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),U_7552),U_7554))),U_7556)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7552),c_Int_OPls)) )
& ! [U_7551,U_7553,U_7555] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7553)),U_7555)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2124_3]) ).
cnf(f_2124_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7553)),U_7555)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2124_4]) ).
cnf(f_2124_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7554)),U_7556)) = 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),U_7552),U_7554))),U_7556)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7552),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2124_4]) ).
fof(f_2125_1,plain,
! [V_v_H,V_v] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__nat__number__of]) ).
fof(f_2125_2,plain,
! [U_7558,U_7557] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7557)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7558)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7557),U_7558))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7557),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7557)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7558)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7557),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2125_1]) ).
fof(f_2125_3,plain,
( ! [U_7562,U_7560] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7560)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7562)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7560),U_7562))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7560),c_Int_OPls)) )
& ! [U_7561,U_7559] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7559)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7561)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7559),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2125_2]) ).
fof(f_2125_4,plain,
( ! [U_7560,U_7562] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7560)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7562)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7560),U_7562))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7560),c_Int_OPls)) )
& ! [U_7561,U_7559] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7559)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7561)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7559),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2125_3]) ).
cnf(f_2125_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7559)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7561)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7559),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2125_4]) ).
cnf(f_2125_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7560)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7562)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7560),U_7562))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7560),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2125_4]) ).
fof(f_2126_1,plain,
! [V_x_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
| ~ 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)))) )
& ( 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))))
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J]) ).
fof(f_2126_2,plain,
! [U_7564,U_7563] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7563),U_7564) = c_Groups_Ozero__class_Ozero(U_7563)
| ~ c_Int_Oiszero(U_7563,hAPP(c_Int_Onumber__class_Onumber__of(U_7563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7564),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
& ( c_Int_Oiszero(U_7563,hAPP(c_Int_Onumber__class_Onumber__of(U_7563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7564),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7563),U_7564) != c_Groups_Ozero__class_Ozero(U_7563) ) )
| ~ class_Int_Onumber__ring(U_7563) ),
inference(variable_rename,[status(thm)],[f_2126_1]) ).
fof(f_2126_3,plain,
( ! [U_7563,U_7564] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7563),U_7564) = c_Groups_Ozero__class_Ozero(U_7563)
| ~ c_Int_Oiszero(U_7563,hAPP(c_Int_Onumber__class_Onumber__of(U_7563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7564),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ sP698(U_7563,U_7564) )
& ! [U_7563,U_7564] :
( c_Int_Oiszero(U_7563,hAPP(c_Int_Onumber__class_Onumber__of(U_7563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7564),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7563),U_7564) != c_Groups_Ozero__class_Ozero(U_7563)
| ~ sP698(U_7563,U_7564) )
& ! [U_7563,U_7564] :
( sP698(U_7563,U_7564)
| ~ class_Int_Onumber__ring(U_7563) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP698])],[f_2126_2]) ).
cnf(f_2126_4,plain,
( sP698(U_7563,U_7564)
| ~ class_Int_Onumber__ring(U_7563) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_5,plain,
( c_Int_Oiszero(U_7563,hAPP(c_Int_Onumber__class_Onumber__of(U_7563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7564),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7563),U_7564) != c_Groups_Ozero__class_Ozero(U_7563)
| ~ sP698(U_7563,U_7564) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7563),U_7564) = c_Groups_Ozero__class_Ozero(U_7563)
| ~ c_Int_Oiszero(U_7563,hAPP(c_Int_Onumber__class_Onumber__of(U_7563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7564),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ sP698(U_7563,U_7564) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
fof(f_2127_1,plain,
! [V_y_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
| ~ 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)))) )
& ( 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))))
| c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J]) ).
fof(f_2127_2,plain,
! [U_7566,U_7565] :
( ( ( c_Groups_Ozero__class_Ozero(U_7565) = hAPP(c_Int_Onumber__class_Onumber__of(U_7565),U_7566)
| ~ c_Int_Oiszero(U_7565,hAPP(c_Int_Onumber__class_Onumber__of(U_7565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7566)))) )
& ( c_Int_Oiszero(U_7565,hAPP(c_Int_Onumber__class_Onumber__of(U_7565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7566))))
| c_Groups_Ozero__class_Ozero(U_7565) != hAPP(c_Int_Onumber__class_Onumber__of(U_7565),U_7566) ) )
| ~ class_Int_Onumber__ring(U_7565) ),
inference(variable_rename,[status(thm)],[f_2127_1]) ).
fof(f_2127_3,plain,
( ! [U_7566,U_7565] :
( c_Groups_Ozero__class_Ozero(U_7565) = hAPP(c_Int_Onumber__class_Onumber__of(U_7565),U_7566)
| ~ c_Int_Oiszero(U_7565,hAPP(c_Int_Onumber__class_Onumber__of(U_7565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7566))))
| ~ sP699(U_7566,U_7565) )
& ! [U_7566,U_7565] :
( c_Int_Oiszero(U_7565,hAPP(c_Int_Onumber__class_Onumber__of(U_7565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7566))))
| c_Groups_Ozero__class_Ozero(U_7565) != hAPP(c_Int_Onumber__class_Onumber__of(U_7565),U_7566)
| ~ sP699(U_7566,U_7565) )
& ! [U_7566,U_7565] :
( sP699(U_7566,U_7565)
| ~ class_Int_Onumber__ring(U_7565) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP699])],[f_2127_2]) ).
cnf(f_2127_4,plain,
( sP699(U_7566,U_7565)
| ~ class_Int_Onumber__ring(U_7565) ),
inference(clausify,[status(thm)],[f_2127_3]) ).
cnf(f_2127_5,plain,
( c_Int_Oiszero(U_7565,hAPP(c_Int_Onumber__class_Onumber__of(U_7565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7566))))
| c_Groups_Ozero__class_Ozero(U_7565) != hAPP(c_Int_Onumber__class_Onumber__of(U_7565),U_7566)
| ~ sP699(U_7566,U_7565) ),
inference(clausify,[status(thm)],[f_2127_3]) ).
cnf(f_2127_6,plain,
( c_Groups_Ozero__class_Ozero(U_7565) = hAPP(c_Int_Onumber__class_Onumber__of(U_7565),U_7566)
| ~ c_Int_Oiszero(U_7565,hAPP(c_Int_Onumber__class_Onumber__of(U_7565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7566))))
| ~ sP699(U_7566,U_7565) ),
inference(clausify,[status(thm)],[f_2127_3]) ).
fof(f_2128_1,plain,
! [V_v] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__diff__1]) ).
fof(f_2128_2,plain,
! [U_7567] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7567)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7567))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7567),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7567)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7567),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2128_1]) ).
fof(f_2128_3,plain,
( ! [U_7569] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7569)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7569))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7569),c_Int_OPls)) )
& ! [U_7568] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7568)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7568),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2128_2]) ).
fof(f_2128_4,plain,
( ! [U_7569] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7569)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7569))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7569),c_Int_OPls)) )
& ! [U_7568] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7568)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7568),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2128_3]) ).
cnf(f_2128_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7568)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7568),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2128_4]) ).
cnf(f_2128_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7569)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7569))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7569),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2128_4]) ).
fof(f_2129_1,plain,
! [V_w_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__number__of]) ).
fof(f_2129_2,plain,
! [U_7571,U_7570] :
( hBOOL(hAPP(hAPP(c_member(U_7570),hAPP(c_Int_Onumber__class_Onumber__of(U_7570),U_7571)),c_Nat_Osemiring__1__class_ONats(U_7570)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7571))
| ~ class_Int_Onumber__ring(U_7570) ),
inference(variable_rename,[status(thm)],[f_2129_1]) ).
fof(f_2129_3,plain,
! [U_7570,U_7571] :
( hBOOL(hAPP(hAPP(c_member(U_7570),hAPP(c_Int_Onumber__class_Onumber__of(U_7570),U_7571)),c_Nat_Osemiring__1__class_ONats(U_7570)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7571))
| ~ class_Int_Onumber__ring(U_7570) ),
inference(definitional_conversion,[status(esa)],[f_2129_2]) ).
cnf(f_2129_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7570),hAPP(c_Int_Onumber__class_Onumber__of(U_7570),U_7571)),c_Nat_Osemiring__1__class_ONats(U_7570)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7571))
| ~ class_Int_Onumber__ring(U_7570) ),
inference(clausify,[status(thm)],[f_2129_3]) ).
fof(f_2130_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).
fof(f_2130_2,plain,
! [U_7573,U_7572] : c_Nitpick_Oint__lcm(U_7572,U_7573) = 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),U_7572)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7573)))),
inference(variable_rename,[status(thm)],[f_2130_1]) ).
fof(f_2130_3,plain,
! [U_7573,U_7572] : c_Nitpick_Oint__lcm(U_7572,U_7573) = 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),U_7572)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7573)))),
inference(definitional_conversion,[status(esa)],[f_2130_2]) ).
cnf(f_2130_4,plain,
c_Nitpick_Oint__lcm(U_7572,U_7573) = 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),U_7572)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7573)))),
inference(clausify,[status(thm)],[f_2130_3]) ).
fof(f_2131_1,plain,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).
fof(f_2131_2,plain,
! [U_7574] : c_Int_Osucc(c_Int_Opred(U_7574)) = U_7574,
inference(variable_rename,[status(thm)],[f_2131_1]) ).
fof(f_2131_3,plain,
! [U_7574] : c_Int_Osucc(c_Int_Opred(U_7574)) = U_7574,
inference(definitional_conversion,[status(esa)],[f_2131_2]) ).
cnf(f_2131_4,plain,
c_Int_Osucc(c_Int_Opred(U_7574)) = U_7574,
inference(clausify,[status(thm)],[f_2131_3]) ).
fof(f_2132_1,plain,
! [V_z_2,T_b] :
( ( ( c_Int_Oiszero(T_b,V_z_2)
| V_z_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ c_Int_Oiszero(T_b,V_z_2) ) )
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_iszero__def]) ).
fof(f_2132_2,plain,
! [U_7576,U_7575] :
( ( ( c_Int_Oiszero(U_7575,U_7576)
| U_7576 != c_Groups_Ozero__class_Ozero(U_7575) )
& ( U_7576 = c_Groups_Ozero__class_Ozero(U_7575)
| ~ c_Int_Oiszero(U_7575,U_7576) ) )
| ~ class_Rings_Osemiring__1(U_7575) ),
inference(variable_rename,[status(thm)],[f_2132_1]) ).
fof(f_2132_3,plain,
( ! [U_7575,U_7576] :
( c_Int_Oiszero(U_7575,U_7576)
| U_7576 != c_Groups_Ozero__class_Ozero(U_7575)
| ~ sP700(U_7575,U_7576) )
& ! [U_7575,U_7576] :
( U_7576 = c_Groups_Ozero__class_Ozero(U_7575)
| ~ c_Int_Oiszero(U_7575,U_7576)
| ~ sP700(U_7575,U_7576) )
& ! [U_7575,U_7576] :
( sP700(U_7575,U_7576)
| ~ class_Rings_Osemiring__1(U_7575) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP700])],[f_2132_2]) ).
cnf(f_2132_4,plain,
( sP700(U_7575,U_7576)
| ~ class_Rings_Osemiring__1(U_7575) ),
inference(clausify,[status(thm)],[f_2132_3]) ).
cnf(f_2132_5,plain,
( U_7576 = c_Groups_Ozero__class_Ozero(U_7575)
| ~ c_Int_Oiszero(U_7575,U_7576)
| ~ sP700(U_7575,U_7576) ),
inference(clausify,[status(thm)],[f_2132_3]) ).
cnf(f_2132_6,plain,
( c_Int_Oiszero(U_7575,U_7576)
| U_7576 != c_Groups_Ozero__class_Ozero(U_7575)
| ~ sP700(U_7575,U_7576) ),
inference(clausify,[status(thm)],[f_2132_3]) ).
fof(f_2133_1,plain,
! [T_a] :
( c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__0]) ).
fof(f_2133_2,plain,
! [U_7577] :
( c_Int_Oiszero(U_7577,c_Groups_Ozero__class_Ozero(U_7577))
| ~ class_Rings_Osemiring__1(U_7577) ),
inference(variable_rename,[status(thm)],[f_2133_1]) ).
fof(f_2133_3,plain,
! [U_7577] :
( c_Int_Oiszero(U_7577,c_Groups_Ozero__class_Ozero(U_7577))
| ~ class_Rings_Osemiring__1(U_7577) ),
inference(definitional_conversion,[status(esa)],[f_2133_2]) ).
cnf(f_2133_4,plain,
( c_Int_Oiszero(U_7577,c_Groups_Ozero__class_Ozero(U_7577))
| ~ class_Rings_Osemiring__1(U_7577) ),
inference(clausify,[status(thm)],[f_2133_3]) ).
fof(f_2134_1,plain,
! [T_a] :
( ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__iszero__1]) ).
fof(f_2134_2,plain,
! [U_7578] :
( ~ c_Int_Oiszero(U_7578,c_Groups_Oone__class_Oone(U_7578))
| ~ class_Rings_Osemiring__1(U_7578) ),
inference(variable_rename,[status(thm)],[f_2134_1]) ).
fof(f_2134_3,plain,
! [U_7578] :
( ~ c_Int_Oiszero(U_7578,c_Groups_Oone__class_Oone(U_7578))
| ~ class_Rings_Osemiring__1(U_7578) ),
inference(definitional_conversion,[status(esa)],[f_2134_2]) ).
cnf(f_2134_4,plain,
( ~ c_Int_Oiszero(U_7578,c_Groups_Oone__class_Oone(U_7578))
| ~ class_Rings_Osemiring__1(U_7578) ),
inference(clausify,[status(thm)],[f_2134_3]) ).
fof(f_2135_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less]) ).
fof(f_2135_2,plain,
! [U_7580,U_7579] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7579),U_7580))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_7579)),U_7580)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_7579)),U_7580))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7579),U_7580)) ) ),
inference(variable_rename,[status(thm)],[f_2135_1]) ).
fof(f_2135_3,plain,
( ! [U_7584,U_7582] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7582),U_7584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_7582)),U_7584)) )
& ! [U_7583,U_7581] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_7581)),U_7583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7581),U_7583)) ) ),
inference(miniscope,[status(thm)],[f_2135_2]) ).
fof(f_2135_4,plain,
( ! [U_7582,U_7584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7582),U_7584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_7582)),U_7584)) )
& ! [U_7583,U_7581] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_7581)),U_7583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7581),U_7583)) ) ),
inference(definitional_conversion,[status(esa)],[f_2135_3]) ).
cnf(f_2135_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_7581)),U_7583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7581),U_7583)) ),
inference(clausify,[status(thm)],[f_2135_4]) ).
cnf(f_2135_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7582),U_7584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_7582)),U_7584)) ),
inference(clausify,[status(thm)],[f_2135_4]) ).
fof(f_2136_1,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).
fof(f_2136_2,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_2136_1]) ).
cnf(f_2136_3,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(clausify,[status(thm)],[f_2136_2]) ).
fof(f_2137_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_pred__def]) ).
fof(f_2137_2,plain,
! [U_7585] : c_Int_Opred(U_7585) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7585),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_2137_1]) ).
fof(f_2137_3,plain,
! [U_7585] : c_Int_Opred(U_7585) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7585),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_2137_2]) ).
cnf(f_2137_4,plain,
c_Int_Opred(U_7585) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7585),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_2137_3]) ).
fof(f_2138_1,plain,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k),
inference(fof_nnf,[status(thm)],[fact_add__Min__right]) ).
fof(f_2138_2,plain,
! [U_7586] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7586),c_Int_OMin) = c_Int_Opred(U_7586),
inference(variable_rename,[status(thm)],[f_2138_1]) ).
fof(f_2138_3,plain,
! [U_7586] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7586),c_Int_OMin) = c_Int_Opred(U_7586),
inference(definitional_conversion,[status(esa)],[f_2138_2]) ).
cnf(f_2138_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7586),c_Int_OMin) = c_Int_Opred(U_7586),
inference(clausify,[status(thm)],[f_2138_3]) ).
fof(f_2139_1,plain,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k),
inference(fof_nnf,[status(thm)],[fact_add__Min]) ).
fof(f_2139_2,plain,
! [U_7587] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_7587) = c_Int_Opred(U_7587),
inference(variable_rename,[status(thm)],[f_2139_1]) ).
fof(f_2139_3,plain,
! [U_7587] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_7587) = c_Int_Opred(U_7587),
inference(definitional_conversion,[status(esa)],[f_2139_2]) ).
cnf(f_2139_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_7587) = c_Int_Opred(U_7587),
inference(clausify,[status(thm)],[f_2139_3]) ).
fof(f_2140_1,plain,
! [T_a] :
( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0]) ).
fof(f_2140_2,plain,
! [U_7588] :
( c_Int_Oiszero(U_7588,hAPP(c_Int_Onumber__class_Onumber__of(U_7588),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_7588) ),
inference(variable_rename,[status(thm)],[f_2140_1]) ).
fof(f_2140_3,plain,
! [U_7588] :
( c_Int_Oiszero(U_7588,hAPP(c_Int_Onumber__class_Onumber__of(U_7588),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_7588) ),
inference(definitional_conversion,[status(esa)],[f_2140_2]) ).
cnf(f_2140_4,plain,
( c_Int_Oiszero(U_7588,hAPP(c_Int_Onumber__class_Onumber__of(U_7588),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_7588) ),
inference(clausify,[status(thm)],[f_2140_3]) ).
fof(f_2141_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__0]) ).
fof(f_2141_2,plain,
! [U_7589] :
( hBOOL(hAPP(hAPP(c_member(U_7589),c_Groups_Ozero__class_Ozero(U_7589)),c_Nat_Osemiring__1__class_ONats(U_7589)))
| ~ class_Rings_Osemiring__1(U_7589) ),
inference(variable_rename,[status(thm)],[f_2141_1]) ).
fof(f_2141_3,plain,
! [U_7589] :
( hBOOL(hAPP(hAPP(c_member(U_7589),c_Groups_Ozero__class_Ozero(U_7589)),c_Nat_Osemiring__1__class_ONats(U_7589)))
| ~ class_Rings_Osemiring__1(U_7589) ),
inference(definitional_conversion,[status(esa)],[f_2141_2]) ).
cnf(f_2141_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7589),c_Groups_Ozero__class_Ozero(U_7589)),c_Nat_Osemiring__1__class_ONats(U_7589)))
| ~ class_Rings_Osemiring__1(U_7589) ),
inference(clausify,[status(thm)],[f_2141_3]) ).
fof(f_2142_1,plain,
! [V_b_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__add]) ).
fof(f_2142_2,plain,
! [U_7592,U_7591,U_7590] :
( hBOOL(hAPP(hAPP(c_member(U_7590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),U_7591),U_7592)),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7590),U_7592),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7590),U_7591),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ class_Rings_Osemiring__1(U_7590) ),
inference(variable_rename,[status(thm)],[f_2142_1]) ).
fof(f_2142_3,plain,
! [U_7590,U_7591,U_7592] :
( hBOOL(hAPP(hAPP(c_member(U_7590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),U_7591),U_7592)),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7590),U_7592),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7590),U_7591),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ class_Rings_Osemiring__1(U_7590) ),
inference(definitional_conversion,[status(esa)],[f_2142_2]) ).
cnf(f_2142_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),U_7591),U_7592)),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7590),U_7592),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7590),U_7591),c_Nat_Osemiring__1__class_ONats(U_7590)))
| ~ class_Rings_Osemiring__1(U_7590) ),
inference(clausify,[status(thm)],[f_2142_3]) ).
fof(f_2143_1,plain,
! [V_b_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__mult]) ).
fof(f_2143_2,plain,
! [U_7595,U_7594,U_7593] :
( hBOOL(hAPP(hAPP(c_member(U_7593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7593),U_7594),U_7595)),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7595),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7594),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ class_Rings_Osemiring__1(U_7593) ),
inference(variable_rename,[status(thm)],[f_2143_1]) ).
fof(f_2143_3,plain,
! [U_7593,U_7594,U_7595] :
( hBOOL(hAPP(hAPP(c_member(U_7593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7593),U_7594),U_7595)),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7595),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7594),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ class_Rings_Osemiring__1(U_7593) ),
inference(definitional_conversion,[status(esa)],[f_2143_2]) ).
cnf(f_2143_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7593),U_7594),U_7595)),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7595),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7594),c_Nat_Osemiring__1__class_ONats(U_7593)))
| ~ class_Rings_Osemiring__1(U_7593) ),
inference(clausify,[status(thm)],[f_2143_3]) ).
fof(f_2144_1,plain,
! [T_a] :
( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__number__of__Min]) ).
fof(f_2144_2,plain,
! [U_7596] :
( ~ c_Int_Oiszero(U_7596,hAPP(c_Int_Onumber__class_Onumber__of(U_7596),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_7596) ),
inference(variable_rename,[status(thm)],[f_2144_1]) ).
fof(f_2144_3,plain,
! [U_7596] :
( ~ c_Int_Oiszero(U_7596,hAPP(c_Int_Onumber__class_Onumber__of(U_7596),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_7596) ),
inference(definitional_conversion,[status(esa)],[f_2144_2]) ).
cnf(f_2144_4,plain,
( ~ c_Int_Oiszero(U_7596,hAPP(c_Int_Onumber__class_Onumber__of(U_7596),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_7596) ),
inference(clausify,[status(thm)],[f_2144_3]) ).
fof(f_2145_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__1]) ).
fof(f_2145_2,plain,
! [U_7597] :
( hBOOL(hAPP(hAPP(c_member(U_7597),c_Groups_Oone__class_Oone(U_7597)),c_Nat_Osemiring__1__class_ONats(U_7597)))
| ~ class_Rings_Osemiring__1(U_7597) ),
inference(variable_rename,[status(thm)],[f_2145_1]) ).
fof(f_2145_3,plain,
! [U_7597] :
( hBOOL(hAPP(hAPP(c_member(U_7597),c_Groups_Oone__class_Oone(U_7597)),c_Nat_Osemiring__1__class_ONats(U_7597)))
| ~ class_Rings_Osemiring__1(U_7597) ),
inference(definitional_conversion,[status(esa)],[f_2145_2]) ).
cnf(f_2145_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7597),c_Groups_Oone__class_Oone(U_7597)),c_Nat_Osemiring__1__class_ONats(U_7597)))
| ~ class_Rings_Osemiring__1(U_7597) ),
inference(clausify,[status(thm)],[f_2145_3]) ).
fof(f_2146_1,plain,
! [V_n_2,T_b] :
( 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)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats]) ).
fof(f_2146_2,plain,
! [U_7599,U_7598] :
( hBOOL(hAPP(hAPP(c_member(U_7598),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7598),U_7599)),c_Nat_Osemiring__1__class_ONats(U_7598)))
| ~ class_Rings_Osemiring__1(U_7598) ),
inference(variable_rename,[status(thm)],[f_2146_1]) ).
fof(f_2146_3,plain,
! [U_7598,U_7599] :
( hBOOL(hAPP(hAPP(c_member(U_7598),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7598),U_7599)),c_Nat_Osemiring__1__class_ONats(U_7598)))
| ~ class_Rings_Osemiring__1(U_7598) ),
inference(definitional_conversion,[status(esa)],[f_2146_2]) ).
cnf(f_2146_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7598),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7598),U_7599)),c_Nat_Osemiring__1__class_ONats(U_7598)))
| ~ class_Rings_Osemiring__1(U_7598) ),
inference(clausify,[status(thm)],[f_2146_3]) ).
fof(f_2147_1,plain,
! [V_w,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__pred]) ).
fof(f_2147_2,plain,
! [U_7601,U_7600] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7600),c_Int_Opred(U_7601)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7600),hAPP(c_Groups_Ouminus__class_Ouminus(U_7600),c_Groups_Oone__class_Oone(U_7600))),hAPP(c_Int_Onumber__class_Onumber__of(U_7600),U_7601))
| ~ class_Int_Onumber__ring(U_7600) ),
inference(variable_rename,[status(thm)],[f_2147_1]) ).
fof(f_2147_3,plain,
! [U_7600,U_7601] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7600),c_Int_Opred(U_7601)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7600),hAPP(c_Groups_Ouminus__class_Ouminus(U_7600),c_Groups_Oone__class_Oone(U_7600))),hAPP(c_Int_Onumber__class_Onumber__of(U_7600),U_7601))
| ~ class_Int_Onumber__ring(U_7600) ),
inference(definitional_conversion,[status(esa)],[f_2147_2]) ).
cnf(f_2147_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7600),c_Int_Opred(U_7601)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7600),hAPP(c_Groups_Ouminus__class_Ouminus(U_7600),c_Groups_Oone__class_Oone(U_7600))),hAPP(c_Int_Onumber__class_Onumber__of(U_7600),U_7601))
| ~ class_Int_Onumber__ring(U_7600) ),
inference(clausify,[status(thm)],[f_2147_3]) ).
fof(f_2148_1,plain,
! [V_v_2] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0]) ).
fof(f_2148_2,plain,
! [U_7602] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7602))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7602) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7602)))) ) ),
inference(variable_rename,[status(thm)],[f_2148_1]) ).
fof(f_2148_3,plain,
( ! [U_7604] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7604))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7604) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_7603] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7603)))) ) ),
inference(miniscope,[status(thm)],[f_2148_2]) ).
fof(f_2148_4,plain,
( ! [U_7604] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7604))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7604) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_7603] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7603)))) ) ),
inference(definitional_conversion,[status(esa)],[f_2148_3]) ).
cnf(f_2148_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7603)))) ),
inference(clausify,[status(thm)],[f_2148_4]) ).
cnf(f_2148_6,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7604))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7604) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2148_4]) ).
fof(f_2149_1,plain,
! [V_y_2,V_x_2,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)
| ~ 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)))) )
& ( 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))))
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq]) ).
fof(f_2149_2,plain,
! [U_7607,U_7606,U_7605] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7606) = hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7607)
| ~ c_Int_Oiszero(U_7605,hAPP(c_Int_Onumber__class_Onumber__of(U_7605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7606),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7607)))) )
& ( c_Int_Oiszero(U_7605,hAPP(c_Int_Onumber__class_Onumber__of(U_7605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7606),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7607))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7606) != hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7607) ) )
| ~ class_Int_Onumber__ring(U_7605) ),
inference(variable_rename,[status(thm)],[f_2149_1]) ).
fof(f_2149_3,plain,
( ! [U_7606,U_7605,U_7607] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7606) = hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7607)
| ~ c_Int_Oiszero(U_7605,hAPP(c_Int_Onumber__class_Onumber__of(U_7605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7606),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7607))))
| ~ sP701(U_7606,U_7605,U_7607) )
& ! [U_7606,U_7605,U_7607] :
( c_Int_Oiszero(U_7605,hAPP(c_Int_Onumber__class_Onumber__of(U_7605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7606),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7607))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7606) != hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7607)
| ~ sP701(U_7606,U_7605,U_7607) )
& ! [U_7606,U_7605,U_7607] :
( sP701(U_7606,U_7605,U_7607)
| ~ class_Int_Onumber__ring(U_7605) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP701])],[f_2149_2]) ).
cnf(f_2149_4,plain,
( sP701(U_7606,U_7605,U_7607)
| ~ class_Int_Onumber__ring(U_7605) ),
inference(clausify,[status(thm)],[f_2149_3]) ).
cnf(f_2149_5,plain,
( c_Int_Oiszero(U_7605,hAPP(c_Int_Onumber__class_Onumber__of(U_7605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7606),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7607))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7606) != hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7607)
| ~ sP701(U_7606,U_7605,U_7607) ),
inference(clausify,[status(thm)],[f_2149_3]) ).
cnf(f_2149_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7606) = hAPP(c_Int_Onumber__class_Onumber__of(U_7605),U_7607)
| ~ c_Int_Oiszero(U_7605,hAPP(c_Int_Onumber__class_Onumber__of(U_7605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7606),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7607))))
| ~ sP701(U_7606,U_7605,U_7607) ),
inference(clausify,[status(thm)],[f_2149_3]) ).
fof(f_2150_1,plain,
! [V_m,V_v] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of]) ).
fof(f_2150_2,plain,
! [U_7609,U_7608] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7609)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7608)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7609),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7608)) ),
inference(variable_rename,[status(thm)],[f_2150_1]) ).
fof(f_2150_3,plain,
! [U_7608,U_7609] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7609)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7608)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7609),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7608)) ),
inference(definitional_conversion,[status(esa)],[f_2150_2]) ).
cnf(f_2150_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7609)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7608)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7609),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7608)) ),
inference(clausify,[status(thm)],[f_2150_3]) ).
fof(f_2151_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).
fof(f_2151_2,plain,
! [U_7611,U_7610] : c_Nitpick_Onat__lcm(U_7610,U_7611) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7610),U_7611)),c_Nitpick_Onat__gcd(U_7610,U_7611)),
inference(variable_rename,[status(thm)],[f_2151_1]) ).
fof(f_2151_3,plain,
! [U_7610,U_7611] : c_Nitpick_Onat__lcm(U_7610,U_7611) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7610),U_7611)),c_Nitpick_Onat__gcd(U_7610,U_7611)),
inference(definitional_conversion,[status(esa)],[f_2151_2]) ).
cnf(f_2151_4,plain,
c_Nitpick_Onat__lcm(U_7610,U_7611) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7610),U_7611)),c_Nitpick_Onat__gcd(U_7610,U_7611)),
inference(clausify,[status(thm)],[f_2151_3]) ).
fof(f_2152_1,plain,
! [V_x_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
| ~ 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))))) )
& ( 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)))))
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != c_Groups_Oone__class_Oone(T_b) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J]) ).
fof(f_2152_2,plain,
! [U_7613,U_7612] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7612),U_7613) = c_Groups_Oone__class_Oone(U_7612)
| ~ c_Int_Oiszero(U_7612,hAPP(c_Int_Onumber__class_Onumber__of(U_7612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(U_7612,hAPP(c_Int_Onumber__class_Onumber__of(U_7612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7612),U_7613) != c_Groups_Oone__class_Oone(U_7612) ) )
| ~ class_Int_Onumber__ring(U_7612) ),
inference(variable_rename,[status(thm)],[f_2152_1]) ).
fof(f_2152_3,plain,
( ! [U_7613,U_7612] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7612),U_7613) = c_Groups_Oone__class_Oone(U_7612)
| ~ c_Int_Oiszero(U_7612,hAPP(c_Int_Onumber__class_Onumber__of(U_7612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ sP702(U_7613,U_7612) )
& ! [U_7613,U_7612] :
( c_Int_Oiszero(U_7612,hAPP(c_Int_Onumber__class_Onumber__of(U_7612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7612),U_7613) != c_Groups_Oone__class_Oone(U_7612)
| ~ sP702(U_7613,U_7612) )
& ! [U_7613,U_7612] :
( sP702(U_7613,U_7612)
| ~ class_Int_Onumber__ring(U_7612) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP702])],[f_2152_2]) ).
cnf(f_2152_4,plain,
( sP702(U_7613,U_7612)
| ~ class_Int_Onumber__ring(U_7612) ),
inference(clausify,[status(thm)],[f_2152_3]) ).
cnf(f_2152_5,plain,
( c_Int_Oiszero(U_7612,hAPP(c_Int_Onumber__class_Onumber__of(U_7612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7612),U_7613) != c_Groups_Oone__class_Oone(U_7612)
| ~ sP702(U_7613,U_7612) ),
inference(clausify,[status(thm)],[f_2152_3]) ).
cnf(f_2152_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7612),U_7613) = c_Groups_Oone__class_Oone(U_7612)
| ~ c_Int_Oiszero(U_7612,hAPP(c_Int_Onumber__class_Onumber__of(U_7612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ sP702(U_7613,U_7612) ),
inference(clausify,[status(thm)],[f_2152_3]) ).
fof(f_2153_1,plain,
! [V_y_2,T_b] :
( ( ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
| ~ 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)))) )
& ( 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))))
| c_Groups_Oone__class_Oone(T_b) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J]) ).
fof(f_2153_2,plain,
! [U_7615,U_7614] :
( ( ( c_Groups_Oone__class_Oone(U_7614) = hAPP(c_Int_Onumber__class_Onumber__of(U_7614),U_7615)
| ~ c_Int_Oiszero(U_7614,hAPP(c_Int_Onumber__class_Onumber__of(U_7614),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),U_7615)))) )
& ( c_Int_Oiszero(U_7614,hAPP(c_Int_Onumber__class_Onumber__of(U_7614),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),U_7615))))
| c_Groups_Oone__class_Oone(U_7614) != hAPP(c_Int_Onumber__class_Onumber__of(U_7614),U_7615) ) )
| ~ class_Int_Onumber__ring(U_7614) ),
inference(variable_rename,[status(thm)],[f_2153_1]) ).
fof(f_2153_3,plain,
( ! [U_7615,U_7614] :
( c_Groups_Oone__class_Oone(U_7614) = hAPP(c_Int_Onumber__class_Onumber__of(U_7614),U_7615)
| ~ c_Int_Oiszero(U_7614,hAPP(c_Int_Onumber__class_Onumber__of(U_7614),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),U_7615))))
| ~ sP703(U_7615,U_7614) )
& ! [U_7615,U_7614] :
( c_Int_Oiszero(U_7614,hAPP(c_Int_Onumber__class_Onumber__of(U_7614),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),U_7615))))
| c_Groups_Oone__class_Oone(U_7614) != hAPP(c_Int_Onumber__class_Onumber__of(U_7614),U_7615)
| ~ sP703(U_7615,U_7614) )
& ! [U_7615,U_7614] :
( sP703(U_7615,U_7614)
| ~ class_Int_Onumber__ring(U_7614) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP703])],[f_2153_2]) ).
cnf(f_2153_4,plain,
( sP703(U_7615,U_7614)
| ~ class_Int_Onumber__ring(U_7614) ),
inference(clausify,[status(thm)],[f_2153_3]) ).
cnf(f_2153_5,plain,
( c_Int_Oiszero(U_7614,hAPP(c_Int_Onumber__class_Onumber__of(U_7614),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),U_7615))))
| c_Groups_Oone__class_Oone(U_7614) != hAPP(c_Int_Onumber__class_Onumber__of(U_7614),U_7615)
| ~ sP703(U_7615,U_7614) ),
inference(clausify,[status(thm)],[f_2153_3]) ).
cnf(f_2153_6,plain,
( c_Groups_Oone__class_Oone(U_7614) = hAPP(c_Int_Onumber__class_Onumber__of(U_7614),U_7615)
| ~ c_Int_Oiszero(U_7614,hAPP(c_Int_Onumber__class_Onumber__of(U_7614),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),U_7615))))
| ~ sP703(U_7615,U_7614) ),
inference(clausify,[status(thm)],[f_2153_3]) ).
fof(f_2154_1,plain,
! [V_v,T_a] :
( 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))))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J]) ).
fof(f_2154_2,plain,
! [U_7617,U_7616] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7616),hAPP(c_Int_Onumber__class_Onumber__of(U_7616),U_7617)),c_Groups_Oone__class_Oone(U_7616)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7617),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_7616) ),
inference(variable_rename,[status(thm)],[f_2154_1]) ).
fof(f_2154_3,plain,
! [U_7617,U_7616] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7616),hAPP(c_Int_Onumber__class_Onumber__of(U_7616),U_7617)),c_Groups_Oone__class_Oone(U_7616)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7617),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_7616) ),
inference(definitional_conversion,[status(esa)],[f_2154_2]) ).
cnf(f_2154_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7616),hAPP(c_Int_Onumber__class_Onumber__of(U_7616),U_7617)),c_Groups_Oone__class_Oone(U_7616)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7617),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_7616) ),
inference(clausify,[status(thm)],[f_2154_3]) ).
fof(f_2155_1,plain,
! [V_w,T_a] :
( 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)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J]) ).
fof(f_2155_2,plain,
! [U_7619,U_7618] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7618),c_Groups_Oone__class_Oone(U_7618)),hAPP(c_Int_Onumber__class_Onumber__of(U_7618),U_7619)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7618),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),U_7619)))
| ~ class_Int_Onumber__ring(U_7618) ),
inference(variable_rename,[status(thm)],[f_2155_1]) ).
fof(f_2155_3,plain,
! [U_7618,U_7619] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7618),c_Groups_Oone__class_Oone(U_7618)),hAPP(c_Int_Onumber__class_Onumber__of(U_7618),U_7619)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7618),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),U_7619)))
| ~ class_Int_Onumber__ring(U_7618) ),
inference(definitional_conversion,[status(esa)],[f_2155_2]) ).
cnf(f_2155_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7618),c_Groups_Oone__class_Oone(U_7618)),hAPP(c_Int_Onumber__class_Onumber__of(U_7618),U_7619)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7618),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),U_7619)))
| ~ class_Int_Onumber__ring(U_7618) ),
inference(clausify,[status(thm)],[f_2155_3]) ).
fof(f_2156_1,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).
fof(f_2156_2,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_2156_1]) ).
cnf(f_2156_3,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(clausify,[status(thm)],[f_2156_2]) ).
fof(f_2157_1,plain,
! [V_l_2] :
( ( c_Int_OMin = c_Int_OBit1(V_l_2)
| c_Int_OMin != V_l_2 )
& ( c_Int_OMin = V_l_2
| c_Int_OMin != c_Int_OBit1(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J]) ).
fof(f_2157_2,plain,
! [U_7620] :
( ( c_Int_OMin = c_Int_OBit1(U_7620)
| c_Int_OMin != U_7620 )
& ( c_Int_OMin = U_7620
| c_Int_OMin != c_Int_OBit1(U_7620) ) ),
inference(variable_rename,[status(thm)],[f_2157_1]) ).
fof(f_2157_3,plain,
( ! [U_7622] :
( c_Int_OMin = c_Int_OBit1(U_7622)
| c_Int_OMin != U_7622 )
& ! [U_7621] :
( c_Int_OMin = U_7621
| c_Int_OMin != c_Int_OBit1(U_7621) ) ),
inference(miniscope,[status(thm)],[f_2157_2]) ).
fof(f_2157_4,plain,
( ! [U_7622] :
( c_Int_OMin = c_Int_OBit1(U_7622)
| c_Int_OMin != U_7622 )
& ! [U_7621] :
( c_Int_OMin = U_7621
| c_Int_OMin != c_Int_OBit1(U_7621) ) ),
inference(definitional_conversion,[status(esa)],[f_2157_3]) ).
cnf(f_2157_5,plain,
( c_Int_OMin = U_7621
| c_Int_OMin != c_Int_OBit1(U_7621) ),
inference(clausify,[status(thm)],[f_2157_4]) ).
cnf(f_2157_6,plain,
( c_Int_OMin = c_Int_OBit1(U_7622)
| c_Int_OMin != U_7622 ),
inference(clausify,[status(thm)],[f_2157_4]) ).
fof(f_2158_1,plain,
! [V_k_2] :
( ( c_Int_OBit1(V_k_2) = c_Int_OMin
| V_k_2 != c_Int_OMin )
& ( V_k_2 = c_Int_OMin
| c_Int_OBit1(V_k_2) != c_Int_OMin ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J]) ).
fof(f_2158_2,plain,
! [U_7623] :
( ( c_Int_OBit1(U_7623) = c_Int_OMin
| U_7623 != c_Int_OMin )
& ( U_7623 = c_Int_OMin
| c_Int_OBit1(U_7623) != c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[f_2158_1]) ).
fof(f_2158_3,plain,
( ! [U_7625] :
( c_Int_OBit1(U_7625) = c_Int_OMin
| U_7625 != c_Int_OMin )
& ! [U_7624] :
( U_7624 = c_Int_OMin
| c_Int_OBit1(U_7624) != c_Int_OMin ) ),
inference(miniscope,[status(thm)],[f_2158_2]) ).
fof(f_2158_4,plain,
( ! [U_7625] :
( c_Int_OBit1(U_7625) = c_Int_OMin
| U_7625 != c_Int_OMin )
& ! [U_7624] :
( U_7624 = c_Int_OMin
| c_Int_OBit1(U_7624) != c_Int_OMin ) ),
inference(definitional_conversion,[status(esa)],[f_2158_3]) ).
cnf(f_2158_5,plain,
( U_7624 = c_Int_OMin
| c_Int_OBit1(U_7624) != c_Int_OMin ),
inference(clausify,[status(thm)],[f_2158_4]) ).
cnf(f_2158_6,plain,
( c_Int_OBit1(U_7625) = c_Int_OMin
| U_7625 != c_Int_OMin ),
inference(clausify,[status(thm)],[f_2158_4]) ).
fof(f_2159_1,plain,
! [V_l_2,V_k_2] :
( ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
| V_k_2 != V_l_2 )
& ( V_k_2 = V_l_2
| c_Int_OBit1(V_k_2) != c_Int_OBit1(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J]) ).
fof(f_2159_2,plain,
! [U_7627,U_7626] :
( ( c_Int_OBit1(U_7626) = c_Int_OBit1(U_7627)
| U_7626 != U_7627 )
& ( U_7626 = U_7627
| c_Int_OBit1(U_7626) != c_Int_OBit1(U_7627) ) ),
inference(variable_rename,[status(thm)],[f_2159_1]) ).
fof(f_2159_3,plain,
( ! [U_7631,U_7629] :
( c_Int_OBit1(U_7629) = c_Int_OBit1(U_7631)
| U_7629 != U_7631 )
& ! [U_7630,U_7628] :
( U_7628 = U_7630
| c_Int_OBit1(U_7628) != c_Int_OBit1(U_7630) ) ),
inference(miniscope,[status(thm)],[f_2159_2]) ).
fof(f_2159_4,plain,
( ! [U_7629,U_7631] :
( c_Int_OBit1(U_7629) = c_Int_OBit1(U_7631)
| U_7629 != U_7631 )
& ! [U_7628,U_7630] :
( U_7628 = U_7630
| c_Int_OBit1(U_7628) != c_Int_OBit1(U_7630) ) ),
inference(definitional_conversion,[status(esa)],[f_2159_3]) ).
cnf(f_2159_5,plain,
( U_7628 = U_7630
| c_Int_OBit1(U_7628) != c_Int_OBit1(U_7630) ),
inference(clausify,[status(thm)],[f_2159_4]) ).
cnf(f_2159_6,plain,
( c_Int_OBit1(U_7629) = c_Int_OBit1(U_7631)
| U_7629 != U_7631 ),
inference(clausify,[status(thm)],[f_2159_4]) ).
fof(f_2160_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J]) ).
fof(f_2160_2,plain,
! [U_7633,U_7632] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7632)),c_Int_OBit1(U_7633)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7632),U_7633)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7632),U_7633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7632)),c_Int_OBit1(U_7633))) ) ),
inference(variable_rename,[status(thm)],[f_2160_1]) ).
fof(f_2160_3,plain,
( ! [U_7637,U_7635] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7635)),c_Int_OBit1(U_7637)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7635),U_7637)) )
& ! [U_7636,U_7634] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7634)),c_Int_OBit1(U_7636))) ) ),
inference(miniscope,[status(thm)],[f_2160_2]) ).
fof(f_2160_4,plain,
( ! [U_7635,U_7637] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7635)),c_Int_OBit1(U_7637)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7635),U_7637)) )
& ! [U_7636,U_7634] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7634)),c_Int_OBit1(U_7636))) ) ),
inference(definitional_conversion,[status(esa)],[f_2160_3]) ).
cnf(f_2160_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7634)),c_Int_OBit1(U_7636))) ),
inference(clausify,[status(thm)],[f_2160_4]) ).
cnf(f_2160_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7635)),c_Int_OBit1(U_7637)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7635),U_7637)) ),
inference(clausify,[status(thm)],[f_2160_4]) ).
fof(f_2161_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J]) ).
fof(f_2161_2,plain,
! [U_7639,U_7638] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7638)),c_Int_OBit1(U_7639)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7638),U_7639)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7638),U_7639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7638)),c_Int_OBit1(U_7639))) ) ),
inference(variable_rename,[status(thm)],[f_2161_1]) ).
fof(f_2161_3,plain,
( ! [U_7643,U_7641] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7641)),c_Int_OBit1(U_7643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7641),U_7643)) )
& ! [U_7642,U_7640] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7640),U_7642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7640)),c_Int_OBit1(U_7642))) ) ),
inference(miniscope,[status(thm)],[f_2161_2]) ).
fof(f_2161_4,plain,
( ! [U_7641,U_7643] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7641)),c_Int_OBit1(U_7643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7641),U_7643)) )
& ! [U_7642,U_7640] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7640),U_7642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7640)),c_Int_OBit1(U_7642))) ) ),
inference(definitional_conversion,[status(esa)],[f_2161_3]) ).
cnf(f_2161_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7640),U_7642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7640)),c_Int_OBit1(U_7642))) ),
inference(clausify,[status(thm)],[f_2161_4]) ).
cnf(f_2161_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7641)),c_Int_OBit1(U_7643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7641),U_7643)) ),
inference(clausify,[status(thm)],[f_2161_4]) ).
fof(f_2162_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J]) ).
fof(f_2162_2,plain,
! [U_7645,U_7644] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7644)),c_Int_OBit1(U_7645)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7644),U_7645)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7644),U_7645))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7644)),c_Int_OBit1(U_7645))) ) ),
inference(variable_rename,[status(thm)],[f_2162_1]) ).
fof(f_2162_3,plain,
( ! [U_7649,U_7647] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7647)),c_Int_OBit1(U_7649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7647),U_7649)) )
& ! [U_7648,U_7646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7646),U_7648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7646)),c_Int_OBit1(U_7648))) ) ),
inference(miniscope,[status(thm)],[f_2162_2]) ).
fof(f_2162_4,plain,
( ! [U_7647,U_7649] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7647)),c_Int_OBit1(U_7649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7647),U_7649)) )
& ! [U_7648,U_7646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7646),U_7648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7646)),c_Int_OBit1(U_7648))) ) ),
inference(definitional_conversion,[status(esa)],[f_2162_3]) ).
cnf(f_2162_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7646),U_7648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7646)),c_Int_OBit1(U_7648))) ),
inference(clausify,[status(thm)],[f_2162_4]) ).
cnf(f_2162_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7647)),c_Int_OBit1(U_7649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7647),U_7649)) ),
inference(clausify,[status(thm)],[f_2162_4]) ).
fof(f_2163_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J]) ).
fof(f_2163_2,plain,
! [U_7651,U_7650] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7650)),c_Int_OBit1(U_7651)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7650),U_7651)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7650),U_7651))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7650)),c_Int_OBit1(U_7651))) ) ),
inference(variable_rename,[status(thm)],[f_2163_1]) ).
fof(f_2163_3,plain,
( ! [U_7655,U_7653] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7653)),c_Int_OBit1(U_7655)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7653),U_7655)) )
& ! [U_7654,U_7652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7652),U_7654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7652)),c_Int_OBit1(U_7654))) ) ),
inference(miniscope,[status(thm)],[f_2163_2]) ).
fof(f_2163_4,plain,
( ! [U_7653,U_7655] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7653)),c_Int_OBit1(U_7655)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7653),U_7655)) )
& ! [U_7654,U_7652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7652),U_7654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7652)),c_Int_OBit1(U_7654))) ) ),
inference(definitional_conversion,[status(esa)],[f_2163_3]) ).
cnf(f_2163_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7652),U_7654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7652)),c_Int_OBit1(U_7654))) ),
inference(clausify,[status(thm)],[f_2163_4]) ).
cnf(f_2163_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7653)),c_Int_OBit1(U_7655)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7653),U_7655)) ),
inference(clausify,[status(thm)],[f_2163_4]) ).
fof(f_2164_1,plain,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(f_2164_2,plain,
! [U_7656] : c_Int_OPls != c_Int_OBit1(U_7656),
inference(variable_rename,[status(thm)],[f_2164_1]) ).
fof(f_2164_3,plain,
! [U_7656] : c_Int_OPls != c_Int_OBit1(U_7656),
inference(definitional_conversion,[status(esa)],[f_2164_2]) ).
cnf(f_2164_4,plain,
c_Int_OPls != c_Int_OBit1(U_7656),
inference(clausify,[status(thm)],[f_2164_3]) ).
fof(f_2165_1,plain,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(f_2165_2,plain,
! [U_7657] : c_Int_OBit1(U_7657) != c_Int_OPls,
inference(variable_rename,[status(thm)],[f_2165_1]) ).
fof(f_2165_3,plain,
! [U_7657] : c_Int_OBit1(U_7657) != c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2165_2]) ).
cnf(f_2165_4,plain,
c_Int_OBit1(U_7657) != c_Int_OPls,
inference(clausify,[status(thm)],[f_2165_3]) ).
fof(f_2166_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I16_J]) ).
fof(f_2166_2,plain,
! [U_7659,U_7658] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7658)),c_Int_OBit1(U_7659)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7658),U_7659)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7658),U_7659))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7658)),c_Int_OBit1(U_7659))) ) ),
inference(variable_rename,[status(thm)],[f_2166_1]) ).
fof(f_2166_3,plain,
( ! [U_7663,U_7661] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7661)),c_Int_OBit1(U_7663)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7661),U_7663)) )
& ! [U_7662,U_7660] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7660),U_7662))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7660)),c_Int_OBit1(U_7662))) ) ),
inference(miniscope,[status(thm)],[f_2166_2]) ).
fof(f_2166_4,plain,
( ! [U_7661,U_7663] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7661)),c_Int_OBit1(U_7663)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7661),U_7663)) )
& ! [U_7662,U_7660] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7660),U_7662))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7660)),c_Int_OBit1(U_7662))) ) ),
inference(definitional_conversion,[status(esa)],[f_2166_3]) ).
cnf(f_2166_5,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7660),U_7662))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7660)),c_Int_OBit1(U_7662))) ),
inference(clausify,[status(thm)],[f_2166_4]) ).
cnf(f_2166_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7661)),c_Int_OBit1(U_7663)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7661),U_7663)) ),
inference(clausify,[status(thm)],[f_2166_4]) ).
fof(f_2167_1,plain,
! [V_w_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J]) ).
fof(f_2167_2,plain,
! [U_7664] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7664)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7664),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7664),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7664)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2167_1]) ).
fof(f_2167_3,plain,
( ! [U_7666] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7666)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7666),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7665] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7665),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7665)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2167_2]) ).
fof(f_2167_4,plain,
( ! [U_7666] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7666)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7666),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7665] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7665),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7665)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_2167_3]) ).
cnf(f_2167_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7665),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7665)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2167_4]) ).
cnf(f_2167_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7666)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7666),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2167_4]) ).
fof(f_2168_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J]) ).
fof(f_2168_2,plain,
! [U_7667] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7667)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7667)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7667))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7667))) ) ),
inference(variable_rename,[status(thm)],[f_2168_1]) ).
fof(f_2168_3,plain,
( ! [U_7669] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7669)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7669)) )
& ! [U_7668] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7668))) ) ),
inference(miniscope,[status(thm)],[f_2168_2]) ).
fof(f_2168_4,plain,
( ! [U_7669] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7669)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7669)) )
& ! [U_7668] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7668))) ) ),
inference(definitional_conversion,[status(esa)],[f_2168_3]) ).
cnf(f_2168_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7668))) ),
inference(clausify,[status(thm)],[f_2168_4]) ).
cnf(f_2168_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7669)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7669)) ),
inference(clausify,[status(thm)],[f_2168_4]) ).
fof(f_2169_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J]) ).
fof(f_2169_2,plain,
! [U_7670] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7670)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7670),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7670),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7670)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2169_1]) ).
fof(f_2169_3,plain,
( ! [U_7672] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7672)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7672),c_Int_OPls)) )
& ! [U_7671] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7671),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7671)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2169_2]) ).
fof(f_2169_4,plain,
( ! [U_7672] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7672)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7672),c_Int_OPls)) )
& ! [U_7671] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7671),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7671)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2169_3]) ).
cnf(f_2169_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7671),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7671)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2169_4]) ).
cnf(f_2169_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7672)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7672),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2169_4]) ).
fof(f_2170_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Bit1__def]) ).
fof(f_2170_2,plain,
! [U_7673] : c_Int_OBit1(U_7673) = 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)),U_7673)),U_7673),
inference(variable_rename,[status(thm)],[f_2170_1]) ).
fof(f_2170_3,plain,
! [U_7673] : c_Int_OBit1(U_7673) = 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)),U_7673)),U_7673),
inference(definitional_conversion,[status(esa)],[f_2170_2]) ).
cnf(f_2170_4,plain,
c_Int_OBit1(U_7673) = 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)),U_7673)),U_7673),
inference(clausify,[status(thm)],[f_2170_3]) ).
fof(f_2171_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J]) ).
fof(f_2171_2,plain,
! [U_7674] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7674)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_7674)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_7674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7674))) ) ),
inference(variable_rename,[status(thm)],[f_2171_1]) ).
fof(f_2171_3,plain,
( ! [U_7676] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_7676)) )
& ! [U_7675] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_7675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7675))) ) ),
inference(miniscope,[status(thm)],[f_2171_2]) ).
fof(f_2171_4,plain,
( ! [U_7676] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_7676)) )
& ! [U_7675] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_7675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7675))) ) ),
inference(definitional_conversion,[status(esa)],[f_2171_3]) ).
cnf(f_2171_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_7675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7675))) ),
inference(clausify,[status(thm)],[f_2171_4]) ).
cnf(f_2171_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_7676)) ),
inference(clausify,[status(thm)],[f_2171_4]) ).
fof(f_2172_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J]) ).
fof(f_2172_2,plain,
! [U_7677] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7677)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7677),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7677),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7677)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2172_1]) ).
fof(f_2172_3,plain,
( ! [U_7679] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7679)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7679),c_Int_OMin)) )
& ! [U_7678] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7678),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7678)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2172_2]) ).
fof(f_2172_4,plain,
( ! [U_7679] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7679)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7679),c_Int_OMin)) )
& ! [U_7678] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7678),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7678)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2172_3]) ).
cnf(f_2172_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7678),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7678)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2172_4]) ).
cnf(f_2172_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7679)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7679),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2172_4]) ).
fof(f_2173_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J]) ).
fof(f_2173_2,plain,
! [U_7680] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7680)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7680),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7680),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7680)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2173_1]) ).
fof(f_2173_3,plain,
( ! [U_7682] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7682)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7682),c_Int_OMin)) )
& ! [U_7681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7681),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7681)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2173_2]) ).
fof(f_2173_4,plain,
( ! [U_7682] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7682)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7682),c_Int_OMin)) )
& ! [U_7681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7681),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7681)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2173_3]) ).
cnf(f_2173_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7681),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7681)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2173_4]) ).
cnf(f_2173_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7682)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7682),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2173_4]) ).
fof(f_2174_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J]) ).
fof(f_2174_2,plain,
! [U_7683] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7683)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7683)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7683))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7683))) ) ),
inference(variable_rename,[status(thm)],[f_2174_1]) ).
fof(f_2174_3,plain,
( ! [U_7685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7685)) )
& ! [U_7684] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7684))) ) ),
inference(miniscope,[status(thm)],[f_2174_2]) ).
fof(f_2174_4,plain,
( ! [U_7685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7685)) )
& ! [U_7684] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7684))) ) ),
inference(definitional_conversion,[status(esa)],[f_2174_3]) ).
cnf(f_2174_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7684))) ),
inference(clausify,[status(thm)],[f_2174_4]) ).
cnf(f_2174_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7685)) ),
inference(clausify,[status(thm)],[f_2174_4]) ).
fof(f_2175_1,plain,
! [V_w_2] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1]) ).
fof(f_2175_2,plain,
! [U_7686] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7686))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7686))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7686)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7686)))) ) ),
inference(variable_rename,[status(thm)],[f_2175_1]) ).
fof(f_2175_3,plain,
( ! [U_7688] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7688))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7688))) )
& ! [U_7687] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7687)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7687)))) ) ),
inference(miniscope,[status(thm)],[f_2175_2]) ).
fof(f_2175_4,plain,
( ! [U_7688] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7688))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7688))) )
& ! [U_7687] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7687)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7687)))) ) ),
inference(definitional_conversion,[status(esa)],[f_2175_3]) ).
cnf(f_2175_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7687)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7687)))) ),
inference(clausify,[status(thm)],[f_2175_4]) ).
cnf(f_2175_6,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7688))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7688))) ),
inference(clausify,[status(thm)],[f_2175_4]) ).
fof(f_2176_1,plain,
! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I4_J]) ).
fof(f_2176_2,plain,
! [U_7689] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7689))),
inference(variable_rename,[status(thm)],[f_2176_1]) ).
fof(f_2176_3,plain,
! [U_7689] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7689))),
inference(definitional_conversion,[status(esa)],[f_2176_2]) ).
cnf(f_2176_4,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7689))),
inference(clausify,[status(thm)],[f_2176_3]) ).
fof(f_2177_1,plain,
! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I10_J]) ).
fof(f_2177_2,plain,
! [U_7690] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7690)),c_Int_OPls)),
inference(variable_rename,[status(thm)],[f_2177_1]) ).
fof(f_2177_3,plain,
! [U_7690] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7690)),c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2177_2]) ).
cnf(f_2177_4,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7690)),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2177_3]) ).
fof(f_2178_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_minus__Bit1]) ).
fof(f_2178_2,plain,
! [U_7691] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_7691)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7691))),
inference(variable_rename,[status(thm)],[f_2178_1]) ).
fof(f_2178_3,plain,
! [U_7691] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_7691)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7691))),
inference(definitional_conversion,[status(esa)],[f_2178_2]) ).
cnf(f_2178_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_7691)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7691))),
inference(clausify,[status(thm)],[f_2178_3]) ).
fof(f_2179_1,plain,
! [V_k2_2] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I8_J]) ).
fof(f_2179_2,plain,
! [U_7692] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7692)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_7692)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_7692))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7692))) ) ),
inference(variable_rename,[status(thm)],[f_2179_1]) ).
fof(f_2179_3,plain,
( ! [U_7694] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7694)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_7694)) )
& ! [U_7693] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_7693))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7693))) ) ),
inference(miniscope,[status(thm)],[f_2179_2]) ).
fof(f_2179_4,plain,
( ! [U_7694] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7694)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_7694)) )
& ! [U_7693] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_7693))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7693))) ) ),
inference(definitional_conversion,[status(esa)],[f_2179_3]) ).
cnf(f_2179_5,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_7693))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7693))) ),
inference(clausify,[status(thm)],[f_2179_4]) ).
cnf(f_2179_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7694)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_7694)) ),
inference(clausify,[status(thm)],[f_2179_4]) ).
fof(f_2180_1,plain,
! [V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I12_J]) ).
fof(f_2180_2,plain,
! [U_7695] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7695)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7695),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7695),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7695)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2180_1]) ).
fof(f_2180_3,plain,
( ! [U_7697] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7697)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7697),c_Int_OMin)) )
& ! [U_7696] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7696),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7696)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2180_2]) ).
fof(f_2180_4,plain,
( ! [U_7697] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7697)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7697),c_Int_OMin)) )
& ! [U_7696] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7696),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7696)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2180_3]) ).
cnf(f_2180_5,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7696),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7696)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2180_4]) ).
cnf(f_2180_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7697)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7697),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2180_4]) ).
fof(f_2181_1,plain,
! [V_w,T_a] :
( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)))
| ~ class_Int_Oring__char__0(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit1]) ).
fof(f_2181_2,plain,
! [U_7699,U_7698] :
( ~ c_Int_Oiszero(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),c_Int_OBit1(U_7699)))
| ~ class_Int_Oring__char__0(U_7698)
| ~ class_Int_Onumber__ring(U_7698) ),
inference(variable_rename,[status(thm)],[f_2181_1]) ).
fof(f_2181_3,plain,
! [U_7698,U_7699] :
( ~ c_Int_Oiszero(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),c_Int_OBit1(U_7699)))
| ~ class_Int_Oring__char__0(U_7698)
| ~ class_Int_Onumber__ring(U_7698) ),
inference(definitional_conversion,[status(esa)],[f_2181_2]) ).
cnf(f_2181_4,plain,
( ~ c_Int_Oiszero(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),c_Int_OBit1(U_7699)))
| ~ class_Int_Oring__char__0(U_7698)
| ~ class_Int_Onumber__ring(U_7698) ),
inference(clausify,[status(thm)],[f_2181_3]) ).
fof(f_2182_1,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).
fof(f_2182_2,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_2182_1]) ).
cnf(f_2182_3,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(clausify,[status(thm)],[f_2182_2]) ).
fof(f_2183_1,plain,
! [V_w,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Bit1]) ).
fof(f_2183_2,plain,
! [U_7701,U_7700] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7700),c_Int_OBit1(U_7701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7700),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7700),c_Groups_Oone__class_Oone(U_7700)),hAPP(c_Int_Onumber__class_Onumber__of(U_7700),U_7701))),hAPP(c_Int_Onumber__class_Onumber__of(U_7700),U_7701))
| ~ class_Int_Onumber__ring(U_7700) ),
inference(variable_rename,[status(thm)],[f_2183_1]) ).
fof(f_2183_3,plain,
! [U_7700,U_7701] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7700),c_Int_OBit1(U_7701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7700),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7700),c_Groups_Oone__class_Oone(U_7700)),hAPP(c_Int_Onumber__class_Onumber__of(U_7700),U_7701))),hAPP(c_Int_Onumber__class_Onumber__of(U_7700),U_7701))
| ~ class_Int_Onumber__ring(U_7700) ),
inference(definitional_conversion,[status(esa)],[f_2183_2]) ).
cnf(f_2183_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7700),c_Int_OBit1(U_7701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7700),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7700),c_Groups_Oone__class_Oone(U_7700)),hAPP(c_Int_Onumber__class_Onumber__of(U_7700),U_7701))),hAPP(c_Int_Onumber__class_Onumber__of(U_7700),U_7701))
| ~ class_Int_Onumber__ring(U_7700) ),
inference(clausify,[status(thm)],[f_2183_3]) ).
fof(f_2184_1,plain,
! [V_a,T_a] :
( 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
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__numeral__1]) ).
fof(f_2184_2,plain,
! [U_7703,U_7702] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7702),hAPP(c_Int_Onumber__class_Onumber__of(U_7702),c_Int_OBit1(c_Int_OPls))),U_7703) = U_7703
| ~ class_Int_Onumber__ring(U_7702) ),
inference(variable_rename,[status(thm)],[f_2184_1]) ).
fof(f_2184_3,plain,
! [U_7702,U_7703] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7702),hAPP(c_Int_Onumber__class_Onumber__of(U_7702),c_Int_OBit1(c_Int_OPls))),U_7703) = U_7703
| ~ class_Int_Onumber__ring(U_7702) ),
inference(definitional_conversion,[status(esa)],[f_2184_2]) ).
cnf(f_2184_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7702),hAPP(c_Int_Onumber__class_Onumber__of(U_7702),c_Int_OBit1(c_Int_OPls))),U_7703) = U_7703
| ~ class_Int_Onumber__ring(U_7702) ),
inference(clausify,[status(thm)],[f_2184_3]) ).
fof(f_2185_1,plain,
! [V_a,T_a] :
( 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
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right]) ).
fof(f_2185_2,plain,
! [U_7705,U_7704] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7704),U_7705),hAPP(c_Int_Onumber__class_Onumber__of(U_7704),c_Int_OBit1(c_Int_OPls))) = U_7705
| ~ class_Int_Onumber__ring(U_7704) ),
inference(variable_rename,[status(thm)],[f_2185_1]) ).
fof(f_2185_3,plain,
! [U_7704,U_7705] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7704),U_7705),hAPP(c_Int_Onumber__class_Onumber__of(U_7704),c_Int_OBit1(c_Int_OPls))) = U_7705
| ~ class_Int_Onumber__ring(U_7704) ),
inference(definitional_conversion,[status(esa)],[f_2185_2]) ).
cnf(f_2185_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7704),U_7705),hAPP(c_Int_Onumber__class_Onumber__of(U_7704),c_Int_OBit1(c_Int_OPls))) = U_7705
| ~ class_Int_Onumber__ring(U_7704) ),
inference(clausify,[status(thm)],[f_2185_3]) ).
fof(f_2186_1,plain,
! [T_a] :
( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J]) ).
fof(f_2186_2,plain,
! [U_7706] :
( c_Groups_Oone__class_Oone(U_7706) = hAPP(c_Int_Onumber__class_Onumber__of(U_7706),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_7706) ),
inference(variable_rename,[status(thm)],[f_2186_1]) ).
fof(f_2186_3,plain,
! [U_7706] :
( c_Groups_Oone__class_Oone(U_7706) = hAPP(c_Int_Onumber__class_Onumber__of(U_7706),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_7706) ),
inference(definitional_conversion,[status(esa)],[f_2186_2]) ).
cnf(f_2186_4,plain,
( c_Groups_Oone__class_Oone(U_7706) = hAPP(c_Int_Onumber__class_Onumber__of(U_7706),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_7706) ),
inference(clausify,[status(thm)],[f_2186_3]) ).
fof(f_2187_1,plain,
! [T_a] :
( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1]) ).
fof(f_2187_2,plain,
! [U_7707] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7707),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_7707)
| ~ class_Int_Onumber__ring(U_7707) ),
inference(variable_rename,[status(thm)],[f_2187_1]) ).
fof(f_2187_3,plain,
! [U_7707] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7707),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_7707)
| ~ class_Int_Onumber__ring(U_7707) ),
inference(definitional_conversion,[status(esa)],[f_2187_2]) ).
cnf(f_2187_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7707),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_7707)
| ~ class_Int_Onumber__ring(U_7707) ),
inference(clausify,[status(thm)],[f_2187_3]) ).
fof(f_2188_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J]) ).
fof(f_2188_2,plain,
! [U_7708] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7708)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7708),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7708),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7708)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2188_1]) ).
fof(f_2188_3,plain,
( ! [U_7710] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7710)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7710),c_Int_OPls)) )
& ! [U_7709] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7709),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7709)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2188_2]) ).
fof(f_2188_4,plain,
( ! [U_7710] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7710)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7710),c_Int_OPls)) )
& ! [U_7709] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7709),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7709)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2188_3]) ).
cnf(f_2188_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7709),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7709)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2188_4]) ).
cnf(f_2188_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7710)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7710),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2188_4]) ).
fof(f_2189_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J]) ).
fof(f_2189_2,plain,
! [U_7711] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7711)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7711)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7711))) ) ),
inference(variable_rename,[status(thm)],[f_2189_1]) ).
fof(f_2189_3,plain,
( ! [U_7713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7713)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7713)) )
& ! [U_7712] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7712))) ) ),
inference(miniscope,[status(thm)],[f_2189_2]) ).
fof(f_2189_4,plain,
( ! [U_7713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7713)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7713)) )
& ! [U_7712] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7712))) ) ),
inference(definitional_conversion,[status(esa)],[f_2189_3]) ).
cnf(f_2189_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7712))) ),
inference(clausify,[status(thm)],[f_2189_4]) ).
cnf(f_2189_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7713)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7713)) ),
inference(clausify,[status(thm)],[f_2189_4]) ).
fof(f_2190_1,plain,
! [V_x,T_a] :
( 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
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__Numeral1]) ).
fof(f_2190_2,plain,
! [U_7715,U_7714] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7714),U_7715),hAPP(c_Int_Onumber__class_Onumber__of(U_7714),c_Int_OBit1(c_Int_OPls))) = U_7715
| ~ class_Int_Onumber__ring(U_7714)
| ~ class_Fields_Ofield(U_7714) ),
inference(variable_rename,[status(thm)],[f_2190_1]) ).
fof(f_2190_3,plain,
! [U_7714,U_7715] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7714),U_7715),hAPP(c_Int_Onumber__class_Onumber__of(U_7714),c_Int_OBit1(c_Int_OPls))) = U_7715
| ~ class_Int_Onumber__ring(U_7714)
| ~ class_Fields_Ofield(U_7714) ),
inference(definitional_conversion,[status(esa)],[f_2190_2]) ).
cnf(f_2190_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7714),U_7715),hAPP(c_Int_Onumber__class_Onumber__of(U_7714),c_Int_OBit1(c_Int_OPls))) = U_7715
| ~ class_Int_Onumber__ring(U_7714)
| ~ class_Fields_Ofield(U_7714) ),
inference(clausify,[status(thm)],[f_2190_3]) ).
fof(f_2191_1,plain,
! [V_a,T_a] :
( 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
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__numeral__1]) ).
fof(f_2191_2,plain,
! [U_7717,U_7716] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7716),U_7717),hAPP(c_Int_Onumber__class_Onumber__of(U_7716),c_Int_OBit1(c_Int_OPls))) = U_7717
| ~ class_Int_Onumber__ring(U_7716)
| ~ class_Fields_Ofield(U_7716) ),
inference(variable_rename,[status(thm)],[f_2191_1]) ).
fof(f_2191_3,plain,
! [U_7716,U_7717] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7716),U_7717),hAPP(c_Int_Onumber__class_Onumber__of(U_7716),c_Int_OBit1(c_Int_OPls))) = U_7717
| ~ class_Int_Onumber__ring(U_7716)
| ~ class_Fields_Ofield(U_7716) ),
inference(definitional_conversion,[status(esa)],[f_2191_2]) ).
cnf(f_2191_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7716),U_7717),hAPP(c_Int_Onumber__class_Onumber__of(U_7716),c_Int_OBit1(c_Int_OPls))) = U_7717
| ~ class_Int_Onumber__ring(U_7716)
| ~ class_Fields_Ofield(U_7716) ),
inference(clausify,[status(thm)],[f_2191_3]) ).
fof(f_2192_1,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_one__is__num__one]) ).
fof(f_2192_2,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2192_1]) ).
cnf(f_2192_3,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(clausify,[status(thm)],[f_2192_2]) ).
fof(f_2193_1,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_Numeral1__eq1__nat]) ).
fof(f_2193_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(definitional_conversion,[status(esa)],[f_2193_1]) ).
cnf(f_2193_3,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(clausify,[status(thm)],[f_2193_2]) ).
fof(f_2194_1,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat__numeral__1__eq__1]) ).
fof(f_2194_2,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_2194_1]) ).
cnf(f_2194_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2194_2]) ).
fof(f_2195_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I4_J]) ).
fof(f_2195_2,plain,
! [U_7718] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7718)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7718)),
inference(variable_rename,[status(thm)],[f_2195_1]) ).
fof(f_2195_3,plain,
! [U_7718] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7718)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7718)),
inference(definitional_conversion,[status(esa)],[f_2195_2]) ).
cnf(f_2195_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7718)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7718)),
inference(clausify,[status(thm)],[f_2195_3]) ).
fof(f_2196_1,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_minus__Min]) ).
fof(f_2196_2,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_2196_1]) ).
cnf(f_2196_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
inference(clausify,[status(thm)],[f_2196_2]) ).
fof(f_2197_1,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J]) ).
fof(f_2197_2,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(definitional_conversion,[status(esa)],[f_2197_1]) ).
cnf(f_2197_3,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_2197_2]) ).
fof(f_2198_1,plain,
! [T_a] :
( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__iszero__Numeral1]) ).
fof(f_2198_2,plain,
! [U_7719] :
( ~ c_Int_Oiszero(U_7719,hAPP(c_Int_Onumber__class_Onumber__of(U_7719),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7719) ),
inference(variable_rename,[status(thm)],[f_2198_1]) ).
fof(f_2198_3,plain,
! [U_7719] :
( ~ c_Int_Oiszero(U_7719,hAPP(c_Int_Onumber__class_Onumber__of(U_7719),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7719) ),
inference(definitional_conversion,[status(esa)],[f_2198_2]) ).
cnf(f_2198_4,plain,
( ~ c_Int_Oiszero(U_7719,hAPP(c_Int_Onumber__class_Onumber__of(U_7719),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7719) ),
inference(clausify,[status(thm)],[f_2198_3]) ).
fof(f_2199_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__Suc__0]) ).
fof(f_2199_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_2199_1]) ).
cnf(f_2199_3,plain,
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)),
inference(clausify,[status(thm)],[f_2199_2]) ).
fof(f_2200_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_numeral__3__eq__3]) ).
fof(f_2200_2,plain,
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)))),
inference(definitional_conversion,[status(esa)],[f_2200_1]) ).
cnf(f_2200_3,plain,
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)))),
inference(clausify,[status(thm)],[f_2200_2]) ).
fof(f_2201_1,plain,
! [V_a,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_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)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power3__eq__cube]) ).
fof(f_2201_2,plain,
! [U_7721,U_7720] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7720),U_7721),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(U_7720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7720),U_7721),U_7721)),U_7721)
| ~ class_Groups_Omonoid__mult(U_7720) ),
inference(variable_rename,[status(thm)],[f_2201_1]) ).
fof(f_2201_3,plain,
! [U_7720,U_7721] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7720),U_7721),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(U_7720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7720),U_7721),U_7721)),U_7721)
| ~ class_Groups_Omonoid__mult(U_7720) ),
inference(definitional_conversion,[status(esa)],[f_2201_2]) ).
cnf(f_2201_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7720),U_7721),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(U_7720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7720),U_7721),U_7721)),U_7721)
| ~ class_Groups_Omonoid__mult(U_7720) ),
inference(clausify,[status(thm)],[f_2201_3]) ).
fof(f_2202_1,plain,
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))))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).
fof(f_2202_2,plain,
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))))),
inference(definitional_conversion,[status(esa)],[f_2202_1]) ).
cnf(f_2202_3,plain,
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))))),
inference(clausify,[status(thm)],[f_2202_2]) ).
fof(f_2203_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Suc3__eq__add__3]) ).
fof(f_2203_2,plain,
! [U_7722] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7722))) = 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)))),U_7722),
inference(variable_rename,[status(thm)],[f_2203_1]) ).
fof(f_2203_3,plain,
! [U_7722] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7722))) = 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)))),U_7722),
inference(definitional_conversion,[status(esa)],[f_2203_2]) ).
cnf(f_2203_4,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7722))) = 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)))),U_7722),
inference(clausify,[status(thm)],[f_2203_3]) ).
fof(f_2204_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I4_J]) ).
fof(f_2204_2,plain,
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)))),
inference(definitional_conversion,[status(esa)],[f_2204_1]) ).
cnf(f_2204_3,plain,
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)))),
inference(clausify,[status(thm)],[f_2204_2]) ).
fof(f_2205_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I4_J]) ).
fof(f_2205_2,plain,
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)))),
inference(definitional_conversion,[status(esa)],[f_2205_1]) ).
cnf(f_2205_3,plain,
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)))),
inference(clausify,[status(thm)],[f_2205_2]) ).
fof(f_2206_1,plain,
! [V_y_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I2_J]) ).
fof(f_2206_2,plain,
! [U_7724,U_7723] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7723),c_Groups_Oone__class_Oone(U_7723)),hAPP(c_Int_Onumber__class_Onumber__of(U_7723),U_7724)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7724)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7724))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7723),c_Groups_Oone__class_Oone(U_7723)),hAPP(c_Int_Onumber__class_Onumber__of(U_7723),U_7724))) ) )
| ~ class_Rings_Olinordered__idom(U_7723)
| ~ class_Int_Onumber__ring(U_7723) ),
inference(variable_rename,[status(thm)],[f_2206_1]) ).
fof(f_2206_3,plain,
( ! [U_7723,U_7724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7723),c_Groups_Oone__class_Oone(U_7723)),hAPP(c_Int_Onumber__class_Onumber__of(U_7723),U_7724)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7724))
| ~ sP704(U_7723,U_7724) )
& ! [U_7723,U_7724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7724))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7723),c_Groups_Oone__class_Oone(U_7723)),hAPP(c_Int_Onumber__class_Onumber__of(U_7723),U_7724)))
| ~ sP704(U_7723,U_7724) )
& ! [U_7723,U_7724] :
( sP704(U_7723,U_7724)
| ~ class_Rings_Olinordered__idom(U_7723)
| ~ class_Int_Onumber__ring(U_7723) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP704])],[f_2206_2]) ).
cnf(f_2206_4,plain,
( sP704(U_7723,U_7724)
| ~ class_Rings_Olinordered__idom(U_7723)
| ~ class_Int_Onumber__ring(U_7723) ),
inference(clausify,[status(thm)],[f_2206_3]) ).
cnf(f_2206_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7724))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7723),c_Groups_Oone__class_Oone(U_7723)),hAPP(c_Int_Onumber__class_Onumber__of(U_7723),U_7724)))
| ~ sP704(U_7723,U_7724) ),
inference(clausify,[status(thm)],[f_2206_3]) ).
cnf(f_2206_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7723),c_Groups_Oone__class_Oone(U_7723)),hAPP(c_Int_Onumber__class_Onumber__of(U_7723),U_7724)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7724))
| ~ sP704(U_7723,U_7724) ),
inference(clausify,[status(thm)],[f_2206_3]) ).
fof(f_2207_1,plain,
! [V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I4_J]) ).
fof(f_2207_2,plain,
! [U_7726,U_7725] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7725),hAPP(c_Int_Onumber__class_Onumber__of(U_7725),U_7726)),c_Groups_Oone__class_Oone(U_7725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7726),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7726),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7725),hAPP(c_Int_Onumber__class_Onumber__of(U_7725),U_7726)),c_Groups_Oone__class_Oone(U_7725))) ) )
| ~ class_Rings_Olinordered__idom(U_7725)
| ~ class_Int_Onumber__ring(U_7725) ),
inference(variable_rename,[status(thm)],[f_2207_1]) ).
fof(f_2207_3,plain,
( ! [U_7726,U_7725] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7725),hAPP(c_Int_Onumber__class_Onumber__of(U_7725),U_7726)),c_Groups_Oone__class_Oone(U_7725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7726),c_Int_OBit1(c_Int_OPls)))
| ~ sP705(U_7726,U_7725) )
& ! [U_7726,U_7725] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7726),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7725),hAPP(c_Int_Onumber__class_Onumber__of(U_7725),U_7726)),c_Groups_Oone__class_Oone(U_7725)))
| ~ sP705(U_7726,U_7725) )
& ! [U_7726,U_7725] :
( sP705(U_7726,U_7725)
| ~ class_Rings_Olinordered__idom(U_7725)
| ~ class_Int_Onumber__ring(U_7725) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP705])],[f_2207_2]) ).
cnf(f_2207_4,plain,
( sP705(U_7726,U_7725)
| ~ class_Rings_Olinordered__idom(U_7725)
| ~ class_Int_Onumber__ring(U_7725) ),
inference(clausify,[status(thm)],[f_2207_3]) ).
cnf(f_2207_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7726),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7725),hAPP(c_Int_Onumber__class_Onumber__of(U_7725),U_7726)),c_Groups_Oone__class_Oone(U_7725)))
| ~ sP705(U_7726,U_7725) ),
inference(clausify,[status(thm)],[f_2207_3]) ).
cnf(f_2207_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7725),hAPP(c_Int_Onumber__class_Onumber__of(U_7725),U_7726)),c_Groups_Oone__class_Oone(U_7725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7726),c_Int_OBit1(c_Int_OPls)))
| ~ sP705(U_7726,U_7725) ),
inference(clausify,[status(thm)],[f_2207_3]) ).
fof(f_2208_1,plain,
! [V_y_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I2_J]) ).
fof(f_2208_2,plain,
! [U_7728,U_7727] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),c_Groups_Oone__class_Oone(U_7727)),hAPP(c_Int_Onumber__class_Onumber__of(U_7727),U_7728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7728)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),c_Groups_Oone__class_Oone(U_7727)),hAPP(c_Int_Onumber__class_Onumber__of(U_7727),U_7728))) ) )
| ~ class_Rings_Olinordered__idom(U_7727)
| ~ class_Int_Onumber__ring(U_7727) ),
inference(variable_rename,[status(thm)],[f_2208_1]) ).
fof(f_2208_3,plain,
( ! [U_7727,U_7728] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),c_Groups_Oone__class_Oone(U_7727)),hAPP(c_Int_Onumber__class_Onumber__of(U_7727),U_7728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7728))
| ~ sP706(U_7727,U_7728) )
& ! [U_7727,U_7728] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),c_Groups_Oone__class_Oone(U_7727)),hAPP(c_Int_Onumber__class_Onumber__of(U_7727),U_7728)))
| ~ sP706(U_7727,U_7728) )
& ! [U_7727,U_7728] :
( sP706(U_7727,U_7728)
| ~ class_Rings_Olinordered__idom(U_7727)
| ~ class_Int_Onumber__ring(U_7727) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP706])],[f_2208_2]) ).
cnf(f_2208_4,plain,
( sP706(U_7727,U_7728)
| ~ class_Rings_Olinordered__idom(U_7727)
| ~ class_Int_Onumber__ring(U_7727) ),
inference(clausify,[status(thm)],[f_2208_3]) ).
cnf(f_2208_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),c_Groups_Oone__class_Oone(U_7727)),hAPP(c_Int_Onumber__class_Onumber__of(U_7727),U_7728)))
| ~ sP706(U_7727,U_7728) ),
inference(clausify,[status(thm)],[f_2208_3]) ).
cnf(f_2208_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),c_Groups_Oone__class_Oone(U_7727)),hAPP(c_Int_Onumber__class_Onumber__of(U_7727),U_7728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7728))
| ~ sP706(U_7727,U_7728) ),
inference(clausify,[status(thm)],[f_2208_3]) ).
fof(f_2209_1,plain,
! [V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I4_J]) ).
fof(f_2209_2,plain,
! [U_7730,U_7729] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7729),hAPP(c_Int_Onumber__class_Onumber__of(U_7729),U_7730)),c_Groups_Oone__class_Oone(U_7729)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7730),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7730),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7729),hAPP(c_Int_Onumber__class_Onumber__of(U_7729),U_7730)),c_Groups_Oone__class_Oone(U_7729))) ) )
| ~ class_Rings_Olinordered__idom(U_7729)
| ~ class_Int_Onumber__ring(U_7729) ),
inference(variable_rename,[status(thm)],[f_2209_1]) ).
fof(f_2209_3,plain,
( ! [U_7729,U_7730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7729),hAPP(c_Int_Onumber__class_Onumber__of(U_7729),U_7730)),c_Groups_Oone__class_Oone(U_7729)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7730),c_Int_OBit1(c_Int_OPls)))
| ~ sP707(U_7729,U_7730) )
& ! [U_7729,U_7730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7730),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7729),hAPP(c_Int_Onumber__class_Onumber__of(U_7729),U_7730)),c_Groups_Oone__class_Oone(U_7729)))
| ~ sP707(U_7729,U_7730) )
& ! [U_7729,U_7730] :
( sP707(U_7729,U_7730)
| ~ class_Rings_Olinordered__idom(U_7729)
| ~ class_Int_Onumber__ring(U_7729) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP707])],[f_2209_2]) ).
cnf(f_2209_4,plain,
( sP707(U_7729,U_7730)
| ~ class_Rings_Olinordered__idom(U_7729)
| ~ class_Int_Onumber__ring(U_7729) ),
inference(clausify,[status(thm)],[f_2209_3]) ).
cnf(f_2209_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7730),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7729),hAPP(c_Int_Onumber__class_Onumber__of(U_7729),U_7730)),c_Groups_Oone__class_Oone(U_7729)))
| ~ sP707(U_7729,U_7730) ),
inference(clausify,[status(thm)],[f_2209_3]) ).
cnf(f_2209_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7729),hAPP(c_Int_Onumber__class_Onumber__of(U_7729),U_7730)),c_Groups_Oone__class_Oone(U_7729)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7730),c_Int_OBit1(c_Int_OPls)))
| ~ sP707(U_7729,U_7730) ),
inference(clausify,[status(thm)],[f_2209_3]) ).
fof(f_2210_1,plain,
! [V_v,T_a] :
( 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)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__special_I3_J]) ).
fof(f_2210_2,plain,
! [U_7732,U_7731] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7731),hAPP(c_Int_Onumber__class_Onumber__of(U_7731),U_7732)),c_Groups_Oone__class_Oone(U_7731)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7732),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7731) ),
inference(variable_rename,[status(thm)],[f_2210_1]) ).
fof(f_2210_3,plain,
! [U_7731,U_7732] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7731),hAPP(c_Int_Onumber__class_Onumber__of(U_7731),U_7732)),c_Groups_Oone__class_Oone(U_7731)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7732),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7731) ),
inference(definitional_conversion,[status(esa)],[f_2210_2]) ).
cnf(f_2210_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7731),hAPP(c_Int_Onumber__class_Onumber__of(U_7731),U_7732)),c_Groups_Oone__class_Oone(U_7731)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7732),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7731) ),
inference(clausify,[status(thm)],[f_2210_3]) ).
fof(f_2211_1,plain,
! [V_w,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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__special_I2_J]) ).
fof(f_2211_2,plain,
! [U_7734,U_7733] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7733),c_Groups_Oone__class_Oone(U_7733)),hAPP(c_Int_Onumber__class_Onumber__of(U_7733),U_7734)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7734))
| ~ class_Int_Onumber__ring(U_7733) ),
inference(variable_rename,[status(thm)],[f_2211_1]) ).
fof(f_2211_3,plain,
! [U_7733,U_7734] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7733),c_Groups_Oone__class_Oone(U_7733)),hAPP(c_Int_Onumber__class_Onumber__of(U_7733),U_7734)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7734))
| ~ class_Int_Onumber__ring(U_7733) ),
inference(definitional_conversion,[status(esa)],[f_2211_2]) ).
cnf(f_2211_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7733),c_Groups_Oone__class_Oone(U_7733)),hAPP(c_Int_Onumber__class_Onumber__of(U_7733),U_7734)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7734))
| ~ class_Int_Onumber__ring(U_7733) ),
inference(clausify,[status(thm)],[f_2211_3]) ).
fof(f_2212_1,plain,
! [V_m,V_n] :
( 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))))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred]) ).
fof(f_2212_2,plain,
! [U_7736,U_7735] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7736)),U_7735) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7735),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),U_7735)) ),
inference(variable_rename,[status(thm)],[f_2212_1]) ).
fof(f_2212_3,plain,
! [U_7735,U_7736] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7736)),U_7735) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7735),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),U_7735)) ),
inference(definitional_conversion,[status(esa)],[f_2212_2]) ).
cnf(f_2212_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7736)),U_7735) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7735),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),U_7735)) ),
inference(clausify,[status(thm)],[f_2212_3]) ).
fof(f_2213_1,plain,
! [V_x,V_y] :
( ( 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))
| V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(V_x,V_y) = V_x
| V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps]) ).
fof(f_2213_2,plain,
! [U_7738,U_7737] :
( ( c_Nitpick_Onat__gcd(U_7738,U_7737) = c_Nitpick_Onat__gcd(U_7737,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7738,U_7737))
| U_7737 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(U_7738,U_7737) = U_7738
| U_7737 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_2213_1]) ).
fof(f_2213_3,plain,
( ! [U_7742,U_7740] :
( c_Nitpick_Onat__gcd(U_7742,U_7740) = c_Nitpick_Onat__gcd(U_7740,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7742,U_7740))
| U_7740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_7741,U_7739] :
( c_Nitpick_Onat__gcd(U_7741,U_7739) = U_7741
| U_7739 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_2213_2]) ).
fof(f_2213_4,plain,
( ! [U_7742,U_7740] :
( c_Nitpick_Onat__gcd(U_7742,U_7740) = c_Nitpick_Onat__gcd(U_7740,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7742,U_7740))
| U_7740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_7741,U_7739] :
( c_Nitpick_Onat__gcd(U_7741,U_7739) = U_7741
| U_7739 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_2213_3]) ).
cnf(f_2213_5,plain,
( c_Nitpick_Onat__gcd(U_7741,U_7739) = U_7741
| U_7739 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2213_4]) ).
cnf(f_2213_6,plain,
( c_Nitpick_Onat__gcd(U_7742,U_7740) = c_Nitpick_Onat__gcd(U_7740,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7742,U_7740))
| U_7740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2213_4]) ).
fof(f_2214_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).
fof(f_2214_2,plain,
! [U_7744,U_7743] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7743))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7744)) = 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)))),U_7743),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7744)),
inference(variable_rename,[status(thm)],[f_2214_1]) ).
fof(f_2214_3,plain,
! [U_7743,U_7744] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7743))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7744)) = 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)))),U_7743),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7744)),
inference(definitional_conversion,[status(esa)],[f_2214_2]) ).
cnf(f_2214_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7743))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7744)) = 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)))),U_7743),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7744)),
inference(clausify,[status(thm)],[f_2214_3]) ).
fof(f_2215_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).
fof(f_2215_2,plain,
! [U_7746,U_7745] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7745))),U_7746) = 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)))),U_7745),U_7746),
inference(variable_rename,[status(thm)],[f_2215_1]) ).
fof(f_2215_3,plain,
! [U_7745,U_7746] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7745))),U_7746) = 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)))),U_7745),U_7746),
inference(definitional_conversion,[status(esa)],[f_2215_2]) ).
cnf(f_2215_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7745))),U_7746) = 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)))),U_7745),U_7746),
inference(clausify,[status(thm)],[f_2215_3]) ).
fof(f_2216_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).
fof(f_2216_2,plain,
! [U_7748,U_7747] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7747,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7748)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7747,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)))),U_7748)),
inference(variable_rename,[status(thm)],[f_2216_1]) ).
fof(f_2216_3,plain,
! [U_7748,U_7747] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7747,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7748)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7747,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)))),U_7748)),
inference(definitional_conversion,[status(esa)],[f_2216_2]) ).
cnf(f_2216_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7747,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7748)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7747,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)))),U_7748)),
inference(clausify,[status(thm)],[f_2216_3]) ).
fof(f_2217_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).
fof(f_2217_2,plain,
! [U_7750,U_7749] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7749)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7750)) = 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)))),U_7749)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7750)),
inference(variable_rename,[status(thm)],[f_2217_1]) ).
fof(f_2217_3,plain,
! [U_7749,U_7750] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7749)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7750)) = 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)))),U_7749)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7750)),
inference(definitional_conversion,[status(esa)],[f_2217_2]) ).
cnf(f_2217_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7749)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7750)) = 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)))),U_7749)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7750)),
inference(clausify,[status(thm)],[f_2217_3]) ).
fof(f_2218_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Suc__div__eq__add3__div]) ).
fof(f_2218_2,plain,
! [U_7752,U_7751] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7751)))),U_7752) = 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)))),U_7751)),U_7752),
inference(variable_rename,[status(thm)],[f_2218_1]) ).
fof(f_2218_3,plain,
! [U_7751,U_7752] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7751)))),U_7752) = 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)))),U_7751)),U_7752),
inference(definitional_conversion,[status(esa)],[f_2218_2]) ).
cnf(f_2218_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7751)))),U_7752) = 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)))),U_7751)),U_7752),
inference(clausify,[status(thm)],[f_2218_3]) ).
fof(f_2219_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_div__Suc__eq__div__add3]) ).
fof(f_2219_2,plain,
! [U_7754,U_7753] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7754)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),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)))),U_7754)),
inference(variable_rename,[status(thm)],[f_2219_1]) ).
fof(f_2219_3,plain,
! [U_7753,U_7754] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7754)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),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)))),U_7754)),
inference(definitional_conversion,[status(esa)],[f_2219_2]) ).
cnf(f_2219_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7754)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),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)))),U_7754)),
inference(clausify,[status(thm)],[f_2219_3]) ).
fof(f_2220_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).
fof(f_2220_2,plain,
! [U_7756,U_7755] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_7755),U_7756) = 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),U_7755)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7756)))),
inference(variable_rename,[status(thm)],[f_2220_1]) ).
fof(f_2220_3,plain,
! [U_7755,U_7756] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_7755),U_7756) = 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),U_7755)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7756)))),
inference(definitional_conversion,[status(esa)],[f_2220_2]) ).
cnf(f_2220_4,plain,
hAPP(hAPP(c_Nitpick_Oint__gcd,U_7755),U_7756) = 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),U_7755)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7756)))),
inference(clausify,[status(thm)],[f_2220_3]) ).
fof(f_2221_1,plain,
! [V_v,V_w] :
( ( 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))
| 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))) )
& ( 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))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zmod__number__of__Bit1]) ).
fof(f_2221_2,plain,
! [U_7758,U_7757] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7758)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7757))) = 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),U_7758)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7757)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| 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),U_7757))) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7758)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7757))) = 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),U_7758),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7757)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ 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),U_7757))) ) ),
inference(variable_rename,[status(thm)],[f_2221_1]) ).
fof(f_2221_3,plain,
( ! [U_7762,U_7760] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7762)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7760))) = 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),U_7762)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7760)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| 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),U_7760))) )
& ! [U_7761,U_7759] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7761)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7759))) = 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),U_7761),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7759)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ 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),U_7759))) ) ),
inference(miniscope,[status(thm)],[f_2221_2]) ).
fof(f_2221_4,plain,
( ! [U_7760,U_7762] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7762)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7760))) = 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),U_7762)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7760)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| 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),U_7760))) )
& ! [U_7759,U_7761] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7761)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7759))) = 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),U_7761),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7759)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ 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),U_7759))) ) ),
inference(definitional_conversion,[status(esa)],[f_2221_3]) ).
cnf(f_2221_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7761)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7759))) = 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),U_7761),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7759)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ 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),U_7759))) ),
inference(clausify,[status(thm)],[f_2221_4]) ).
cnf(f_2221_6,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7762)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7760))) = 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),U_7762)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7760)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| 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),U_7760))) ),
inference(clausify,[status(thm)],[f_2221_4]) ).
fof(f_2222_1,plain,
! [V_b,V_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__zmod__mult__2]) ).
fof(f_2222_2,plain,
! [U_7764,U_7763] :
( 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)))),U_7764)),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)))),U_7763)) = 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),U_7764),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7763))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7763),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2222_1]) ).
fof(f_2222_3,plain,
! [U_7763,U_7764] :
( 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)))),U_7764)),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)))),U_7763)) = 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),U_7764),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7763))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7763),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2222_2]) ).
cnf(f_2222_4,plain,
( 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)))),U_7764)),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)))),U_7763)) = 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),U_7764),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7763))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7763),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2222_3]) ).
fof(f_2223_1,plain,
! [V_b,V_a] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2]) ).
fof(f_2223_2,plain,
! [U_7766,U_7765] :
( 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)))),U_7766))),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)))),U_7765)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7766),U_7765)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7765)) ),
inference(variable_rename,[status(thm)],[f_2223_1]) ).
fof(f_2223_3,plain,
! [U_7765,U_7766] :
( 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)))),U_7766))),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)))),U_7765)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7766),U_7765)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7765)) ),
inference(definitional_conversion,[status(esa)],[f_2223_2]) ).
cnf(f_2223_4,plain,
( 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)))),U_7766))),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)))),U_7765)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7766),U_7765)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7765)) ),
inference(clausify,[status(thm)],[f_2223_3]) ).
fof(f_2224_1,plain,
! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I50_J]) ).
fof(f_2224_2,plain,
! [U_7768,U_7767] : c_Int_OBit1(U_7767) != c_Int_OBit0(U_7768),
inference(variable_rename,[status(thm)],[f_2224_1]) ).
fof(f_2224_3,plain,
! [U_7767,U_7768] : c_Int_OBit1(U_7767) != c_Int_OBit0(U_7768),
inference(definitional_conversion,[status(esa)],[f_2224_2]) ).
cnf(f_2224_4,plain,
c_Int_OBit1(U_7767) != c_Int_OBit0(U_7768),
inference(clausify,[status(thm)],[f_2224_3]) ).
fof(f_2225_1,plain,
! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I49_J]) ).
fof(f_2225_2,plain,
! [U_7770,U_7769] : c_Int_OBit0(U_7769) != c_Int_OBit1(U_7770),
inference(variable_rename,[status(thm)],[f_2225_1]) ).
fof(f_2225_3,plain,
! [U_7769,U_7770] : c_Int_OBit0(U_7769) != c_Int_OBit1(U_7770),
inference(definitional_conversion,[status(esa)],[f_2225_2]) ).
cnf(f_2225_4,plain,
c_Int_OBit0(U_7769) != c_Int_OBit1(U_7770),
inference(clausify,[status(thm)],[f_2225_3]) ).
fof(f_2226_1,plain,
! [V_k_2] :
( ( c_Int_OBit0(V_k_2) = c_Int_OPls
| V_k_2 != c_Int_OPls )
& ( V_k_2 = c_Int_OPls
| c_Int_OBit0(V_k_2) != c_Int_OPls ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J]) ).
fof(f_2226_2,plain,
! [U_7771] :
( ( c_Int_OBit0(U_7771) = c_Int_OPls
| U_7771 != c_Int_OPls )
& ( U_7771 = c_Int_OPls
| c_Int_OBit0(U_7771) != c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[f_2226_1]) ).
fof(f_2226_3,plain,
( ! [U_7773] :
( c_Int_OBit0(U_7773) = c_Int_OPls
| U_7773 != c_Int_OPls )
& ! [U_7772] :
( U_7772 = c_Int_OPls
| c_Int_OBit0(U_7772) != c_Int_OPls ) ),
inference(miniscope,[status(thm)],[f_2226_2]) ).
fof(f_2226_4,plain,
( ! [U_7773] :
( c_Int_OBit0(U_7773) = c_Int_OPls
| U_7773 != c_Int_OPls )
& ! [U_7772] :
( U_7772 = c_Int_OPls
| c_Int_OBit0(U_7772) != c_Int_OPls ) ),
inference(definitional_conversion,[status(esa)],[f_2226_3]) ).
cnf(f_2226_5,plain,
( U_7772 = c_Int_OPls
| c_Int_OBit0(U_7772) != c_Int_OPls ),
inference(clausify,[status(thm)],[f_2226_4]) ).
cnf(f_2226_6,plain,
( c_Int_OBit0(U_7773) = c_Int_OPls
| U_7773 != c_Int_OPls ),
inference(clausify,[status(thm)],[f_2226_4]) ).
fof(f_2227_1,plain,
! [V_l_2] :
( ( c_Int_OPls = c_Int_OBit0(V_l_2)
| c_Int_OPls != V_l_2 )
& ( c_Int_OPls = V_l_2
| c_Int_OPls != c_Int_OBit0(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J]) ).
fof(f_2227_2,plain,
! [U_7774] :
( ( c_Int_OPls = c_Int_OBit0(U_7774)
| c_Int_OPls != U_7774 )
& ( c_Int_OPls = U_7774
| c_Int_OPls != c_Int_OBit0(U_7774) ) ),
inference(variable_rename,[status(thm)],[f_2227_1]) ).
fof(f_2227_3,plain,
( ! [U_7776] :
( c_Int_OPls = c_Int_OBit0(U_7776)
| c_Int_OPls != U_7776 )
& ! [U_7775] :
( c_Int_OPls = U_7775
| c_Int_OPls != c_Int_OBit0(U_7775) ) ),
inference(miniscope,[status(thm)],[f_2227_2]) ).
fof(f_2227_4,plain,
( ! [U_7776] :
( c_Int_OPls = c_Int_OBit0(U_7776)
| c_Int_OPls != U_7776 )
& ! [U_7775] :
( c_Int_OPls = U_7775
| c_Int_OPls != c_Int_OBit0(U_7775) ) ),
inference(definitional_conversion,[status(esa)],[f_2227_3]) ).
cnf(f_2227_5,plain,
( c_Int_OPls = U_7775
| c_Int_OPls != c_Int_OBit0(U_7775) ),
inference(clausify,[status(thm)],[f_2227_4]) ).
cnf(f_2227_6,plain,
( c_Int_OPls = c_Int_OBit0(U_7776)
| c_Int_OPls != U_7776 ),
inference(clausify,[status(thm)],[f_2227_4]) ).
fof(f_2228_1,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).
fof(f_2228_2,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2228_1]) ).
cnf(f_2228_3,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_2228_2]) ).
fof(f_2229_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J]) ).
fof(f_2229_2,plain,
! [U_7778,U_7777] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7777)),c_Int_OBit0(U_7778)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7777),U_7778)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7777),U_7778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7777)),c_Int_OBit0(U_7778))) ) ),
inference(variable_rename,[status(thm)],[f_2229_1]) ).
fof(f_2229_3,plain,
( ! [U_7782,U_7780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7780)),c_Int_OBit0(U_7782)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7780),U_7782)) )
& ! [U_7781,U_7779] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7779),U_7781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7779)),c_Int_OBit0(U_7781))) ) ),
inference(miniscope,[status(thm)],[f_2229_2]) ).
fof(f_2229_4,plain,
( ! [U_7780,U_7782] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7780)),c_Int_OBit0(U_7782)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7780),U_7782)) )
& ! [U_7781,U_7779] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7779),U_7781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7779)),c_Int_OBit0(U_7781))) ) ),
inference(definitional_conversion,[status(esa)],[f_2229_3]) ).
cnf(f_2229_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7779),U_7781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7779)),c_Int_OBit0(U_7781))) ),
inference(clausify,[status(thm)],[f_2229_4]) ).
cnf(f_2229_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7780)),c_Int_OBit0(U_7782)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7780),U_7782)) ),
inference(clausify,[status(thm)],[f_2229_4]) ).
fof(f_2230_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J]) ).
fof(f_2230_2,plain,
! [U_7784,U_7783] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7783)),c_Int_OBit0(U_7784)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7783),U_7784)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7783),U_7784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7783)),c_Int_OBit0(U_7784))) ) ),
inference(variable_rename,[status(thm)],[f_2230_1]) ).
fof(f_2230_3,plain,
( ! [U_7788,U_7786] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7786)),c_Int_OBit0(U_7788)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7786),U_7788)) )
& ! [U_7787,U_7785] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7785),U_7787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7785)),c_Int_OBit0(U_7787))) ) ),
inference(miniscope,[status(thm)],[f_2230_2]) ).
fof(f_2230_4,plain,
( ! [U_7786,U_7788] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7786)),c_Int_OBit0(U_7788)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7786),U_7788)) )
& ! [U_7787,U_7785] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7785),U_7787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7785)),c_Int_OBit0(U_7787))) ) ),
inference(definitional_conversion,[status(esa)],[f_2230_3]) ).
cnf(f_2230_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7785),U_7787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7785)),c_Int_OBit0(U_7787))) ),
inference(clausify,[status(thm)],[f_2230_4]) ).
cnf(f_2230_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7786)),c_Int_OBit0(U_7788)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7786),U_7788)) ),
inference(clausify,[status(thm)],[f_2230_4]) ).
fof(f_2231_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J]) ).
fof(f_2231_2,plain,
! [U_7790,U_7789] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7789)),c_Int_OBit0(U_7790)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7789),U_7790)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7789),U_7790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7789)),c_Int_OBit0(U_7790))) ) ),
inference(variable_rename,[status(thm)],[f_2231_1]) ).
fof(f_2231_3,plain,
( ! [U_7794,U_7792] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7792)),c_Int_OBit0(U_7794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7792),U_7794)) )
& ! [U_7793,U_7791] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7791),U_7793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7791)),c_Int_OBit0(U_7793))) ) ),
inference(miniscope,[status(thm)],[f_2231_2]) ).
fof(f_2231_4,plain,
( ! [U_7792,U_7794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7792)),c_Int_OBit0(U_7794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7792),U_7794)) )
& ! [U_7793,U_7791] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7791),U_7793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7791)),c_Int_OBit0(U_7793))) ) ),
inference(definitional_conversion,[status(esa)],[f_2231_3]) ).
cnf(f_2231_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7791),U_7793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7791)),c_Int_OBit0(U_7793))) ),
inference(clausify,[status(thm)],[f_2231_4]) ).
cnf(f_2231_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7792)),c_Int_OBit0(U_7794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7792),U_7794)) ),
inference(clausify,[status(thm)],[f_2231_4]) ).
fof(f_2232_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J]) ).
fof(f_2232_2,plain,
! [U_7796,U_7795] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7795)),c_Int_OBit0(U_7796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7795),U_7796)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7795),U_7796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7795)),c_Int_OBit0(U_7796))) ) ),
inference(variable_rename,[status(thm)],[f_2232_1]) ).
fof(f_2232_3,plain,
( ! [U_7800,U_7798] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7798)),c_Int_OBit0(U_7800)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7798),U_7800)) )
& ! [U_7799,U_7797] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7797),U_7799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7797)),c_Int_OBit0(U_7799))) ) ),
inference(miniscope,[status(thm)],[f_2232_2]) ).
fof(f_2232_4,plain,
( ! [U_7798,U_7800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7798)),c_Int_OBit0(U_7800)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7798),U_7800)) )
& ! [U_7799,U_7797] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7797),U_7799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7797)),c_Int_OBit0(U_7799))) ) ),
inference(definitional_conversion,[status(esa)],[f_2232_3]) ).
cnf(f_2232_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7797),U_7799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7797)),c_Int_OBit0(U_7799))) ),
inference(clausify,[status(thm)],[f_2232_4]) ).
cnf(f_2232_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7798)),c_Int_OBit0(U_7800)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7798),U_7800)) ),
inference(clausify,[status(thm)],[f_2232_4]) ).
fof(f_2233_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit0]) ).
fof(f_2233_2,plain,
! [U_7802,U_7801] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7801)),c_Int_OBit0(U_7802)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7801),U_7802)),
inference(variable_rename,[status(thm)],[f_2233_1]) ).
fof(f_2233_3,plain,
! [U_7801,U_7802] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7801)),c_Int_OBit0(U_7802)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7801),U_7802)),
inference(definitional_conversion,[status(esa)],[f_2233_2]) ).
cnf(f_2233_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7801)),c_Int_OBit0(U_7802)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7801),U_7802)),
inference(clausify,[status(thm)],[f_2233_3]) ).
fof(f_2234_1,plain,
! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
inference(fof_nnf,[status(thm)],[fact_Bit0__def]) ).
fof(f_2234_2,plain,
! [U_7803] : c_Int_OBit0(U_7803) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7803),U_7803),
inference(variable_rename,[status(thm)],[f_2234_1]) ).
fof(f_2234_3,plain,
! [U_7803] : c_Int_OBit0(U_7803) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7803),U_7803),
inference(definitional_conversion,[status(esa)],[f_2234_2]) ).
cnf(f_2234_4,plain,
c_Int_OBit0(U_7803) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7803),U_7803),
inference(clausify,[status(thm)],[f_2234_3]) ).
fof(f_2235_1,plain,
! [V_l_2,V_k_2] :
( ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
| V_k_2 != V_l_2 )
& ( V_k_2 = V_l_2
| c_Int_OBit0(V_k_2) != c_Int_OBit0(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J]) ).
fof(f_2235_2,plain,
! [U_7805,U_7804] :
( ( c_Int_OBit0(U_7804) = c_Int_OBit0(U_7805)
| U_7804 != U_7805 )
& ( U_7804 = U_7805
| c_Int_OBit0(U_7804) != c_Int_OBit0(U_7805) ) ),
inference(variable_rename,[status(thm)],[f_2235_1]) ).
fof(f_2235_3,plain,
( ! [U_7809,U_7807] :
( c_Int_OBit0(U_7807) = c_Int_OBit0(U_7809)
| U_7807 != U_7809 )
& ! [U_7808,U_7806] :
( U_7806 = U_7808
| c_Int_OBit0(U_7806) != c_Int_OBit0(U_7808) ) ),
inference(miniscope,[status(thm)],[f_2235_2]) ).
fof(f_2235_4,plain,
( ! [U_7807,U_7809] :
( c_Int_OBit0(U_7807) = c_Int_OBit0(U_7809)
| U_7807 != U_7809 )
& ! [U_7808,U_7806] :
( U_7806 = U_7808
| c_Int_OBit0(U_7806) != c_Int_OBit0(U_7808) ) ),
inference(definitional_conversion,[status(esa)],[f_2235_3]) ).
cnf(f_2235_5,plain,
( U_7806 = U_7808
| c_Int_OBit0(U_7806) != c_Int_OBit0(U_7808) ),
inference(clausify,[status(thm)],[f_2235_4]) ).
cnf(f_2235_6,plain,
( c_Int_OBit0(U_7807) = c_Int_OBit0(U_7809)
| U_7807 != U_7809 ),
inference(clausify,[status(thm)],[f_2235_4]) ).
fof(f_2236_1,plain,
! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(f_2236_2,plain,
! [U_7810] : c_Int_OBit0(U_7810) != c_Int_OMin,
inference(variable_rename,[status(thm)],[f_2236_1]) ).
fof(f_2236_3,plain,
! [U_7810] : c_Int_OBit0(U_7810) != c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_2236_2]) ).
cnf(f_2236_4,plain,
c_Int_OBit0(U_7810) != c_Int_OMin,
inference(clausify,[status(thm)],[f_2236_3]) ).
fof(f_2237_1,plain,
! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(f_2237_2,plain,
! [U_7811] : c_Int_OMin != c_Int_OBit0(U_7811),
inference(variable_rename,[status(thm)],[f_2237_1]) ).
fof(f_2237_3,plain,
! [U_7811] : c_Int_OMin != c_Int_OBit0(U_7811),
inference(definitional_conversion,[status(esa)],[f_2237_2]) ).
cnf(f_2237_4,plain,
c_Int_OMin != c_Int_OBit0(U_7811),
inference(clausify,[status(thm)],[f_2237_3]) ).
fof(f_2238_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_minus__Bit0]) ).
fof(f_2238_2,plain,
! [U_7812] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_7812)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7812)),
inference(variable_rename,[status(thm)],[f_2238_1]) ).
fof(f_2238_3,plain,
! [U_7812] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_7812)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7812)),
inference(definitional_conversion,[status(esa)],[f_2238_2]) ).
cnf(f_2238_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_7812)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7812)),
inference(clausify,[status(thm)],[f_2238_3]) ).
fof(f_2239_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I7_J]) ).
fof(f_2239_2,plain,
! [U_7814,U_7813] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7813)),c_Int_OBit0(U_7814)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7813),U_7814)),
inference(variable_rename,[status(thm)],[f_2239_1]) ).
fof(f_2239_3,plain,
! [U_7813,U_7814] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7813)),c_Int_OBit0(U_7814)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7813),U_7814)),
inference(definitional_conversion,[status(esa)],[f_2239_2]) ).
cnf(f_2239_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7813)),c_Int_OBit0(U_7814)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7813),U_7814)),
inference(clausify,[status(thm)],[f_2239_3]) ).
fof(f_2240_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mult__Bit0]) ).
fof(f_2240_2,plain,
! [U_7816,U_7815] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_7815)),U_7816) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7815),U_7816)),
inference(variable_rename,[status(thm)],[f_2240_1]) ).
fof(f_2240_3,plain,
! [U_7815,U_7816] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_7815)),U_7816) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7815),U_7816)),
inference(definitional_conversion,[status(esa)],[f_2240_2]) ).
cnf(f_2240_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_7815)),U_7816) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7815),U_7816)),
inference(clausify,[status(thm)],[f_2240_3]) ).
fof(f_2241_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I13_J]) ).
fof(f_2241_2,plain,
! [U_7818,U_7817] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7817)),c_Int_OBit0(U_7818)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7817),U_7818)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7817),U_7818))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7817)),c_Int_OBit0(U_7818))) ) ),
inference(variable_rename,[status(thm)],[f_2241_1]) ).
fof(f_2241_3,plain,
( ! [U_7822,U_7820] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7820)),c_Int_OBit0(U_7822)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7820),U_7822)) )
& ! [U_7821,U_7819] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7819),U_7821))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7819)),c_Int_OBit0(U_7821))) ) ),
inference(miniscope,[status(thm)],[f_2241_2]) ).
fof(f_2241_4,plain,
( ! [U_7820,U_7822] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7820)),c_Int_OBit0(U_7822)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7820),U_7822)) )
& ! [U_7821,U_7819] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7819),U_7821))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7819)),c_Int_OBit0(U_7821))) ) ),
inference(definitional_conversion,[status(esa)],[f_2241_3]) ).
cnf(f_2241_5,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7819),U_7821))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7819)),c_Int_OBit0(U_7821))) ),
inference(clausify,[status(thm)],[f_2241_4]) ).
cnf(f_2241_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7820)),c_Int_OBit0(U_7822)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7820),U_7822)) ),
inference(clausify,[status(thm)],[f_2241_4]) ).
fof(f_2242_1,plain,
! [V_w_2] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J]) ).
fof(f_2242_2,plain,
! [U_7823] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7823)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7823),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7823),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7823)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2242_1]) ).
fof(f_2242_3,plain,
( ! [U_7825] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7825)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7825),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7824] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7824),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7824)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2242_2]) ).
fof(f_2242_4,plain,
( ! [U_7825] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7825)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7825),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7824] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7824),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7824)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_2242_3]) ).
cnf(f_2242_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7824),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7824)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2242_4]) ).
cnf(f_2242_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7825)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7825),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2242_4]) ).
fof(f_2243_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J]) ).
fof(f_2243_2,plain,
! [U_7826] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7826)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7826)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7826))) ) ),
inference(variable_rename,[status(thm)],[f_2243_1]) ).
fof(f_2243_3,plain,
( ! [U_7828] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7828)) )
& ! [U_7827] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7827))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7827))) ) ),
inference(miniscope,[status(thm)],[f_2243_2]) ).
fof(f_2243_4,plain,
( ! [U_7828] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7828)) )
& ! [U_7827] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7827))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7827))) ) ),
inference(definitional_conversion,[status(esa)],[f_2243_3]) ).
cnf(f_2243_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7827))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7827))) ),
inference(clausify,[status(thm)],[f_2243_4]) ).
cnf(f_2243_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7828)) ),
inference(clausify,[status(thm)],[f_2243_4]) ).
fof(f_2244_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J]) ).
fof(f_2244_2,plain,
! [U_7829] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7829)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7829),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7829),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7829)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2244_1]) ).
fof(f_2244_3,plain,
( ! [U_7831] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7831)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7831),c_Int_OPls)) )
& ! [U_7830] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7830),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7830)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2244_2]) ).
fof(f_2244_4,plain,
( ! [U_7831] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7831)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7831),c_Int_OPls)) )
& ! [U_7830] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7830),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7830)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2244_3]) ).
cnf(f_2244_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7830),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7830)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2244_4]) ).
cnf(f_2244_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7831)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7831),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2244_4]) ).
fof(f_2245_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J]) ).
fof(f_2245_2,plain,
! [U_7833,U_7832] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7832)),c_Int_OBit1(U_7833)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7832),U_7833)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7832),U_7833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7832)),c_Int_OBit1(U_7833))) ) ),
inference(variable_rename,[status(thm)],[f_2245_1]) ).
fof(f_2245_3,plain,
( ! [U_7837,U_7835] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7835)),c_Int_OBit1(U_7837)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7835),U_7837)) )
& ! [U_7836,U_7834] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7834),U_7836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7834)),c_Int_OBit1(U_7836))) ) ),
inference(miniscope,[status(thm)],[f_2245_2]) ).
fof(f_2245_4,plain,
( ! [U_7835,U_7837] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7835)),c_Int_OBit1(U_7837)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7835),U_7837)) )
& ! [U_7836,U_7834] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7834),U_7836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7834)),c_Int_OBit1(U_7836))) ) ),
inference(definitional_conversion,[status(esa)],[f_2245_3]) ).
cnf(f_2245_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7834),U_7836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7834)),c_Int_OBit1(U_7836))) ),
inference(clausify,[status(thm)],[f_2245_4]) ).
cnf(f_2245_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7835)),c_Int_OBit1(U_7837)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7835),U_7837)) ),
inference(clausify,[status(thm)],[f_2245_4]) ).
fof(f_2246_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J]) ).
fof(f_2246_2,plain,
! [U_7839,U_7838] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7838)),c_Int_OBit1(U_7839)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7838),U_7839)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7838),U_7839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7838)),c_Int_OBit1(U_7839))) ) ),
inference(variable_rename,[status(thm)],[f_2246_1]) ).
fof(f_2246_3,plain,
( ! [U_7843,U_7841] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7841)),c_Int_OBit1(U_7843)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7841),U_7843)) )
& ! [U_7842,U_7840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7840),U_7842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7840)),c_Int_OBit1(U_7842))) ) ),
inference(miniscope,[status(thm)],[f_2246_2]) ).
fof(f_2246_4,plain,
( ! [U_7841,U_7843] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7841)),c_Int_OBit1(U_7843)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7841),U_7843)) )
& ! [U_7842,U_7840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7840),U_7842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7840)),c_Int_OBit1(U_7842))) ) ),
inference(definitional_conversion,[status(esa)],[f_2246_3]) ).
cnf(f_2246_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7840),U_7842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7840)),c_Int_OBit1(U_7842))) ),
inference(clausify,[status(thm)],[f_2246_4]) ).
cnf(f_2246_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7841)),c_Int_OBit1(U_7843)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7841),U_7843)) ),
inference(clausify,[status(thm)],[f_2246_4]) ).
fof(f_2247_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J]) ).
fof(f_2247_2,plain,
! [U_7844] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7844)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7844),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7844),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7844)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2247_1]) ).
fof(f_2247_3,plain,
( ! [U_7846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7846)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7846),c_Int_OPls)) )
& ! [U_7845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7845),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7845)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2247_2]) ).
fof(f_2247_4,plain,
( ! [U_7846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7846)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7846),c_Int_OPls)) )
& ! [U_7845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7845),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7845)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2247_3]) ).
cnf(f_2247_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7845),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7845)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2247_4]) ).
cnf(f_2247_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7846)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7846),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2247_4]) ).
fof(f_2248_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J]) ).
fof(f_2248_2,plain,
! [U_7847] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7847)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7847))) ) ),
inference(variable_rename,[status(thm)],[f_2248_1]) ).
fof(f_2248_3,plain,
( ! [U_7849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7849)) )
& ! [U_7848] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7848))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7848))) ) ),
inference(miniscope,[status(thm)],[f_2248_2]) ).
fof(f_2248_4,plain,
( ! [U_7849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7849)) )
& ! [U_7848] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7848))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7848))) ) ),
inference(definitional_conversion,[status(esa)],[f_2248_3]) ).
cnf(f_2248_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7848))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7848))) ),
inference(clausify,[status(thm)],[f_2248_4]) ).
cnf(f_2248_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7849)) ),
inference(clausify,[status(thm)],[f_2248_4]) ).
fof(f_2249_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J]) ).
fof(f_2249_2,plain,
! [U_7851,U_7850] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7850)),c_Int_OBit0(U_7851)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7850),U_7851)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7850),U_7851))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7850)),c_Int_OBit0(U_7851))) ) ),
inference(variable_rename,[status(thm)],[f_2249_1]) ).
fof(f_2249_3,plain,
( ! [U_7855,U_7853] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7853)),c_Int_OBit0(U_7855)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7853),U_7855)) )
& ! [U_7854,U_7852] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7852),U_7854))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7852)),c_Int_OBit0(U_7854))) ) ),
inference(miniscope,[status(thm)],[f_2249_2]) ).
fof(f_2249_4,plain,
( ! [U_7853,U_7855] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7853)),c_Int_OBit0(U_7855)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7853),U_7855)) )
& ! [U_7854,U_7852] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7852),U_7854))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7852)),c_Int_OBit0(U_7854))) ) ),
inference(definitional_conversion,[status(esa)],[f_2249_3]) ).
cnf(f_2249_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7852),U_7854))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7852)),c_Int_OBit0(U_7854))) ),
inference(clausify,[status(thm)],[f_2249_4]) ).
cnf(f_2249_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7853)),c_Int_OBit0(U_7855)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7853),U_7855)) ),
inference(clausify,[status(thm)],[f_2249_4]) ).
fof(f_2250_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J]) ).
fof(f_2250_2,plain,
! [U_7857,U_7856] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7856)),c_Int_OBit0(U_7857)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7856),U_7857)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7856),U_7857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7856)),c_Int_OBit0(U_7857))) ) ),
inference(variable_rename,[status(thm)],[f_2250_1]) ).
fof(f_2250_3,plain,
( ! [U_7861,U_7859] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7859)),c_Int_OBit0(U_7861)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7859),U_7861)) )
& ! [U_7860,U_7858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7858),U_7860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7858)),c_Int_OBit0(U_7860))) ) ),
inference(miniscope,[status(thm)],[f_2250_2]) ).
fof(f_2250_4,plain,
( ! [U_7861,U_7859] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7859)),c_Int_OBit0(U_7861)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7859),U_7861)) )
& ! [U_7860,U_7858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7858),U_7860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7858)),c_Int_OBit0(U_7860))) ) ),
inference(definitional_conversion,[status(esa)],[f_2250_3]) ).
cnf(f_2250_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7858),U_7860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7858)),c_Int_OBit0(U_7860))) ),
inference(clausify,[status(thm)],[f_2250_4]) ).
cnf(f_2250_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7859)),c_Int_OBit0(U_7861)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7859),U_7861)) ),
inference(clausify,[status(thm)],[f_2250_4]) ).
fof(f_2251_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit0]) ).
fof(f_2251_2,plain,
! [U_7863,U_7862] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7862)),c_Int_OBit0(U_7863)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7862),U_7863)),
inference(variable_rename,[status(thm)],[f_2251_1]) ).
fof(f_2251_3,plain,
! [U_7863,U_7862] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7862)),c_Int_OBit0(U_7863)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7862),U_7863)),
inference(definitional_conversion,[status(esa)],[f_2251_2]) ).
cnf(f_2251_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7862)),c_Int_OBit0(U_7863)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7862),U_7863)),
inference(clausify,[status(thm)],[f_2251_3]) ).
fof(f_2252_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit1]) ).
fof(f_2252_2,plain,
! [U_7865,U_7864] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7864)),c_Int_OBit1(U_7865)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7864),U_7865)),
inference(variable_rename,[status(thm)],[f_2252_1]) ).
fof(f_2252_3,plain,
! [U_7864,U_7865] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7864)),c_Int_OBit1(U_7865)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7864),U_7865)),
inference(definitional_conversion,[status(esa)],[f_2252_2]) ).
cnf(f_2252_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7864)),c_Int_OBit1(U_7865)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7864),U_7865)),
inference(clausify,[status(thm)],[f_2252_3]) ).
fof(f_2253_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I3_J]) ).
fof(f_2253_2,plain,
! [U_7866] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7866)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_7866)),
inference(variable_rename,[status(thm)],[f_2253_1]) ).
fof(f_2253_3,plain,
! [U_7866] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7866)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_7866)),
inference(definitional_conversion,[status(esa)],[f_2253_2]) ).
cnf(f_2253_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7866)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_7866)),
inference(clausify,[status(thm)],[f_2253_3]) ).
fof(f_2254_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I10_J]) ).
fof(f_2254_2,plain,
! [U_7868,U_7867] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7867)),c_Int_OBit1(U_7868)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7867),U_7868)),
inference(variable_rename,[status(thm)],[f_2254_1]) ).
fof(f_2254_3,plain,
! [U_7867,U_7868] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7867)),c_Int_OBit1(U_7868)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7867),U_7868)),
inference(definitional_conversion,[status(esa)],[f_2254_2]) ).
cnf(f_2254_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7867)),c_Int_OBit1(U_7868)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7867),U_7868)),
inference(clausify,[status(thm)],[f_2254_3]) ).
fof(f_2255_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I9_J]) ).
fof(f_2255_2,plain,
! [U_7870,U_7869] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7869)),c_Int_OBit0(U_7870)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7869),U_7870)),
inference(variable_rename,[status(thm)],[f_2255_1]) ).
fof(f_2255_3,plain,
! [U_7869,U_7870] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7869)),c_Int_OBit0(U_7870)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7869),U_7870)),
inference(definitional_conversion,[status(esa)],[f_2255_2]) ).
cnf(f_2255_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7869)),c_Int_OBit0(U_7870)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7869),U_7870)),
inference(clausify,[status(thm)],[f_2255_3]) ).
fof(f_2256_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J]) ).
fof(f_2256_2,plain,
! [U_7871] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7871)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7871),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7871),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7871)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2256_1]) ).
fof(f_2256_3,plain,
( ! [U_7873] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7873)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7873),c_Int_OMin)) )
& ! [U_7872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7872),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7872)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2256_2]) ).
fof(f_2256_4,plain,
( ! [U_7873] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7873)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7873),c_Int_OMin)) )
& ! [U_7872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7872),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7872)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2256_3]) ).
cnf(f_2256_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7872),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7872)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2256_4]) ).
cnf(f_2256_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7873)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7873),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2256_4]) ).
fof(f_2257_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J]) ).
fof(f_2257_2,plain,
! [U_7874] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7874)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7874)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7874))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7874))) ) ),
inference(variable_rename,[status(thm)],[f_2257_1]) ).
fof(f_2257_3,plain,
( ! [U_7876] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7876)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7876)) )
& ! [U_7875] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7875))) ) ),
inference(miniscope,[status(thm)],[f_2257_2]) ).
fof(f_2257_4,plain,
( ! [U_7876] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7876)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7876)) )
& ! [U_7875] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7875))) ) ),
inference(definitional_conversion,[status(esa)],[f_2257_3]) ).
cnf(f_2257_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7875))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7875))) ),
inference(clausify,[status(thm)],[f_2257_4]) ).
cnf(f_2257_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7876)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7876)) ),
inference(clausify,[status(thm)],[f_2257_4]) ).
fof(f_2258_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_zdiv__number__of__Bit0]) ).
fof(f_2258_2,plain,
! [U_7878,U_7877] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7877))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7878))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7877)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7878)),
inference(variable_rename,[status(thm)],[f_2258_1]) ).
fof(f_2258_3,plain,
! [U_7877,U_7878] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7877))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7878))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7877)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7878)),
inference(definitional_conversion,[status(esa)],[f_2258_2]) ).
cnf(f_2258_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7877))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7878))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7877)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7878)),
inference(clausify,[status(thm)],[f_2258_3]) ).
fof(f_2259_1,plain,
! [V_w_2] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0]) ).
fof(f_2259_2,plain,
! [U_7879] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7879))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7879))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7879)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7879)))) ) ),
inference(variable_rename,[status(thm)],[f_2259_1]) ).
fof(f_2259_3,plain,
( ! [U_7881] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7881))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7881))) )
& ! [U_7880] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7880)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7880)))) ) ),
inference(miniscope,[status(thm)],[f_2259_2]) ).
fof(f_2259_4,plain,
( ! [U_7881] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7881))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7881))) )
& ! [U_7880] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7880)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7880)))) ) ),
inference(definitional_conversion,[status(esa)],[f_2259_3]) ).
cnf(f_2259_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7880)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7880)))) ),
inference(clausify,[status(thm)],[f_2259_4]) ).
cnf(f_2259_6,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7881))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7881))) ),
inference(clausify,[status(thm)],[f_2259_4]) ).
fof(f_2260_1,plain,
! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
inference(fof_nnf,[status(thm)],[fact_pred__Bit0]) ).
fof(f_2260_2,plain,
! [U_7882] : c_Int_Opred(c_Int_OBit0(U_7882)) = c_Int_OBit1(c_Int_Opred(U_7882)),
inference(variable_rename,[status(thm)],[f_2260_1]) ).
fof(f_2260_3,plain,
! [U_7882] : c_Int_Opred(c_Int_OBit0(U_7882)) = c_Int_OBit1(c_Int_Opred(U_7882)),
inference(definitional_conversion,[status(esa)],[f_2260_2]) ).
cnf(f_2260_4,plain,
c_Int_Opred(c_Int_OBit0(U_7882)) = c_Int_OBit1(c_Int_Opred(U_7882)),
inference(clausify,[status(thm)],[f_2260_3]) ).
fof(f_2261_1,plain,
! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
inference(fof_nnf,[status(thm)],[fact_pred__Bit1]) ).
fof(f_2261_2,plain,
! [U_7883] : c_Int_Opred(c_Int_OBit1(U_7883)) = c_Int_OBit0(U_7883),
inference(variable_rename,[status(thm)],[f_2261_1]) ).
fof(f_2261_3,plain,
! [U_7883] : c_Int_Opred(c_Int_OBit1(U_7883)) = c_Int_OBit0(U_7883),
inference(definitional_conversion,[status(esa)],[f_2261_2]) ).
cnf(f_2261_4,plain,
c_Int_Opred(c_Int_OBit1(U_7883)) = c_Int_OBit0(U_7883),
inference(clausify,[status(thm)],[f_2261_3]) ).
fof(f_2262_1,plain,
! [V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I9_J]) ).
fof(f_2262_2,plain,
! [U_7884] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7884)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7884),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7884),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7884)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2262_1]) ).
fof(f_2262_3,plain,
( ! [U_7886] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7886)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7886),c_Int_OPls)) )
& ! [U_7885] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7885),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7885)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2262_2]) ).
fof(f_2262_4,plain,
( ! [U_7886] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7886)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7886),c_Int_OPls)) )
& ! [U_7885] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7885),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7885)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2262_3]) ).
cnf(f_2262_5,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7885),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7885)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2262_4]) ).
cnf(f_2262_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7886)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_7886),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2262_4]) ).
fof(f_2263_1,plain,
! [V_k2_2] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I3_J]) ).
fof(f_2263_2,plain,
! [U_7887] :
( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7887)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_7887)) )
& ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_7887))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7887))) ) ),
inference(variable_rename,[status(thm)],[f_2263_1]) ).
fof(f_2263_3,plain,
( ! [U_7889] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7889)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_7889)) )
& ! [U_7888] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_7888))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7888))) ) ),
inference(miniscope,[status(thm)],[f_2263_2]) ).
fof(f_2263_4,plain,
( ! [U_7889] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7889)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_7889)) )
& ! [U_7888] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_7888))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7888))) ) ),
inference(definitional_conversion,[status(esa)],[f_2263_3]) ).
cnf(f_2263_5,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_7888))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7888))) ),
inference(clausify,[status(thm)],[f_2263_4]) ).
cnf(f_2263_6,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7889)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_7889)) ),
inference(clausify,[status(thm)],[f_2263_4]) ).
fof(f_2264_1,plain,
! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I15_J]) ).
fof(f_2264_2,plain,
! [U_7891,U_7890] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7890)),c_Int_OBit0(U_7891))),
inference(variable_rename,[status(thm)],[f_2264_1]) ).
fof(f_2264_3,plain,
! [U_7890,U_7891] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7890)),c_Int_OBit0(U_7891))),
inference(definitional_conversion,[status(esa)],[f_2264_2]) ).
cnf(f_2264_4,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_7890)),c_Int_OBit0(U_7891))),
inference(clausify,[status(thm)],[f_2264_3]) ).
fof(f_2265_1,plain,
! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I14_J]) ).
fof(f_2265_2,plain,
! [U_7893,U_7892] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7892)),c_Int_OBit1(U_7893))),
inference(variable_rename,[status(thm)],[f_2265_1]) ).
fof(f_2265_3,plain,
! [U_7892,U_7893] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7892)),c_Int_OBit1(U_7893))),
inference(definitional_conversion,[status(esa)],[f_2265_2]) ).
cnf(f_2265_4,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7892)),c_Int_OBit1(U_7893))),
inference(clausify,[status(thm)],[f_2265_3]) ).
fof(f_2266_1,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).
fof(f_2266_2,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(definitional_conversion,[status(esa)],[f_2266_1]) ).
cnf(f_2266_3,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(clausify,[status(thm)],[f_2266_2]) ).
fof(f_2267_1,plain,
! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I11_J]) ).
fof(f_2267_2,plain,
! [U_7894] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7894)),c_Int_OMin)),
inference(variable_rename,[status(thm)],[f_2267_1]) ).
fof(f_2267_3,plain,
! [U_7894] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7894)),c_Int_OMin)),
inference(definitional_conversion,[status(esa)],[f_2267_2]) ).
cnf(f_2267_4,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_7894)),c_Int_OMin)),
inference(clausify,[status(thm)],[f_2267_3]) ).
fof(f_2268_1,plain,
! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))),
inference(fof_nnf,[status(thm)],[fact_eq__int__code_I7_J]) ).
fof(f_2268_2,plain,
! [U_7895] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7895))),
inference(variable_rename,[status(thm)],[f_2268_1]) ).
fof(f_2268_3,plain,
! [U_7895] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7895))),
inference(definitional_conversion,[status(esa)],[f_2268_2]) ).
cnf(f_2268_4,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7895))),
inference(clausify,[status(thm)],[f_2268_3]) ).
fof(f_2269_1,plain,
! [V_w_2,T_b] :
( ( ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
& ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) ) )
| ~ class_Int_Oring__char__0(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0]) ).
fof(f_2269_2,plain,
! [U_7897,U_7896] :
( ( ( c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),c_Int_OBit0(U_7897)))
| ~ c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),U_7897)) )
& ( c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),U_7897))
| ~ c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),c_Int_OBit0(U_7897))) ) )
| ~ class_Int_Oring__char__0(U_7896)
| ~ class_Int_Onumber__ring(U_7896) ),
inference(variable_rename,[status(thm)],[f_2269_1]) ).
fof(f_2269_3,plain,
( ! [U_7896,U_7897] :
( c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),c_Int_OBit0(U_7897)))
| ~ c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),U_7897))
| ~ sP708(U_7896,U_7897) )
& ! [U_7896,U_7897] :
( c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),U_7897))
| ~ c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),c_Int_OBit0(U_7897)))
| ~ sP708(U_7896,U_7897) )
& ! [U_7896,U_7897] :
( sP708(U_7896,U_7897)
| ~ class_Int_Oring__char__0(U_7896)
| ~ class_Int_Onumber__ring(U_7896) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP708])],[f_2269_2]) ).
cnf(f_2269_4,plain,
( sP708(U_7896,U_7897)
| ~ class_Int_Oring__char__0(U_7896)
| ~ class_Int_Onumber__ring(U_7896) ),
inference(clausify,[status(thm)],[f_2269_3]) ).
cnf(f_2269_5,plain,
( c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),U_7897))
| ~ c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),c_Int_OBit0(U_7897)))
| ~ sP708(U_7896,U_7897) ),
inference(clausify,[status(thm)],[f_2269_3]) ).
cnf(f_2269_6,plain,
( c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),c_Int_OBit0(U_7897)))
| ~ c_Int_Oiszero(U_7896,hAPP(c_Int_Onumber__class_Onumber__of(U_7896),U_7897))
| ~ sP708(U_7896,U_7897) ),
inference(clausify,[status(thm)],[f_2269_3]) ).
fof(f_2270_1,plain,
! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
inference(fof_nnf,[status(thm)],[fact_succ__Bit1]) ).
fof(f_2270_2,plain,
! [U_7898] : c_Int_Osucc(c_Int_OBit1(U_7898)) = c_Int_OBit0(c_Int_Osucc(U_7898)),
inference(variable_rename,[status(thm)],[f_2270_1]) ).
fof(f_2270_3,plain,
! [U_7898] : c_Int_Osucc(c_Int_OBit1(U_7898)) = c_Int_OBit0(c_Int_Osucc(U_7898)),
inference(definitional_conversion,[status(esa)],[f_2270_2]) ).
cnf(f_2270_4,plain,
c_Int_Osucc(c_Int_OBit1(U_7898)) = c_Int_OBit0(c_Int_Osucc(U_7898)),
inference(clausify,[status(thm)],[f_2270_3]) ).
fof(f_2271_1,plain,
! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
inference(fof_nnf,[status(thm)],[fact_succ__Bit0]) ).
fof(f_2271_2,plain,
! [U_7899] : c_Int_Osucc(c_Int_OBit0(U_7899)) = c_Int_OBit1(U_7899),
inference(variable_rename,[status(thm)],[f_2271_1]) ).
fof(f_2271_3,plain,
! [U_7899] : c_Int_Osucc(c_Int_OBit0(U_7899)) = c_Int_OBit1(U_7899),
inference(definitional_conversion,[status(esa)],[f_2271_2]) ).
cnf(f_2271_4,plain,
c_Int_Osucc(c_Int_OBit0(U_7899)) = c_Int_OBit1(U_7899),
inference(clausify,[status(thm)],[f_2271_3]) ).
fof(f_2272_1,plain,
! [V_w,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Bit0]) ).
fof(f_2272_2,plain,
! [U_7901,U_7900] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7900),c_Int_OBit0(U_7901)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7900),c_Groups_Ozero__class_Ozero(U_7900)),hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))),hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))
| ~ class_Int_Onumber__ring(U_7900) ),
inference(variable_rename,[status(thm)],[f_2272_1]) ).
fof(f_2272_3,plain,
! [U_7900,U_7901] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7900),c_Int_OBit0(U_7901)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7900),c_Groups_Ozero__class_Ozero(U_7900)),hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))),hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))
| ~ class_Int_Onumber__ring(U_7900) ),
inference(definitional_conversion,[status(esa)],[f_2272_2]) ).
cnf(f_2272_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7900),c_Int_OBit0(U_7901)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7900),c_Groups_Ozero__class_Ozero(U_7900)),hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))),hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))
| ~ class_Int_Onumber__ring(U_7900) ),
inference(clausify,[status(thm)],[f_2272_3]) ).
fof(f_2273_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J]) ).
fof(f_2273_2,plain,
! [U_7903,U_7902] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7902)),c_Int_OBit1(U_7903)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7902),U_7903)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7902),U_7903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7902)),c_Int_OBit1(U_7903))) ) ),
inference(variable_rename,[status(thm)],[f_2273_1]) ).
fof(f_2273_3,plain,
( ! [U_7907,U_7905] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7905)),c_Int_OBit1(U_7907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7905),U_7907)) )
& ! [U_7906,U_7904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7904),U_7906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7904)),c_Int_OBit1(U_7906))) ) ),
inference(miniscope,[status(thm)],[f_2273_2]) ).
fof(f_2273_4,plain,
( ! [U_7907,U_7905] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7905)),c_Int_OBit1(U_7907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7905),U_7907)) )
& ! [U_7906,U_7904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7904),U_7906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7904)),c_Int_OBit1(U_7906))) ) ),
inference(definitional_conversion,[status(esa)],[f_2273_3]) ).
cnf(f_2273_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7904),U_7906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7904)),c_Int_OBit1(U_7906))) ),
inference(clausify,[status(thm)],[f_2273_4]) ).
cnf(f_2273_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7905)),c_Int_OBit1(U_7907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7905),U_7907)) ),
inference(clausify,[status(thm)],[f_2273_4]) ).
fof(f_2274_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J]) ).
fof(f_2274_2,plain,
! [U_7909,U_7908] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7908)),c_Int_OBit1(U_7909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7908),U_7909)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7908),U_7909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7908)),c_Int_OBit1(U_7909))) ) ),
inference(variable_rename,[status(thm)],[f_2274_1]) ).
fof(f_2274_3,plain,
( ! [U_7913,U_7911] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7911)),c_Int_OBit1(U_7913)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7911),U_7913)) )
& ! [U_7912,U_7910] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7910),U_7912))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7910)),c_Int_OBit1(U_7912))) ) ),
inference(miniscope,[status(thm)],[f_2274_2]) ).
fof(f_2274_4,plain,
( ! [U_7911,U_7913] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7911)),c_Int_OBit1(U_7913)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7911),U_7913)) )
& ! [U_7912,U_7910] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7910),U_7912))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7910)),c_Int_OBit1(U_7912))) ) ),
inference(definitional_conversion,[status(esa)],[f_2274_3]) ).
cnf(f_2274_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7910),U_7912))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7910)),c_Int_OBit1(U_7912))) ),
inference(clausify,[status(thm)],[f_2274_4]) ).
cnf(f_2274_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7911)),c_Int_OBit1(U_7913)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7911),U_7913)) ),
inference(clausify,[status(thm)],[f_2274_4]) ).
fof(f_2275_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J]) ).
fof(f_2275_2,plain,
! [U_7915,U_7914] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7914)),c_Int_OBit0(U_7915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7914),U_7915)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7914),U_7915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7914)),c_Int_OBit0(U_7915))) ) ),
inference(variable_rename,[status(thm)],[f_2275_1]) ).
fof(f_2275_3,plain,
( ! [U_7919,U_7917] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7917)),c_Int_OBit0(U_7919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7917),U_7919)) )
& ! [U_7918,U_7916] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7916),U_7918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7916)),c_Int_OBit0(U_7918))) ) ),
inference(miniscope,[status(thm)],[f_2275_2]) ).
fof(f_2275_4,plain,
( ! [U_7917,U_7919] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7917)),c_Int_OBit0(U_7919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7917),U_7919)) )
& ! [U_7918,U_7916] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7916),U_7918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7916)),c_Int_OBit0(U_7918))) ) ),
inference(definitional_conversion,[status(esa)],[f_2275_3]) ).
cnf(f_2275_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7916),U_7918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7916)),c_Int_OBit0(U_7918))) ),
inference(clausify,[status(thm)],[f_2275_4]) ).
cnf(f_2275_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7917)),c_Int_OBit0(U_7919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7917),U_7919)) ),
inference(clausify,[status(thm)],[f_2275_4]) ).
fof(f_2276_1,plain,
! [V_k2_2,V_k1_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J]) ).
fof(f_2276_2,plain,
! [U_7921,U_7920] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7920)),c_Int_OBit0(U_7921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7920),U_7921)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7920),U_7921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7920)),c_Int_OBit0(U_7921))) ) ),
inference(variable_rename,[status(thm)],[f_2276_1]) ).
fof(f_2276_3,plain,
( ! [U_7925,U_7923] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7923)),c_Int_OBit0(U_7925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7923),U_7925)) )
& ! [U_7924,U_7922] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7922),U_7924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7922)),c_Int_OBit0(U_7924))) ) ),
inference(miniscope,[status(thm)],[f_2276_2]) ).
fof(f_2276_4,plain,
( ! [U_7923,U_7925] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7923)),c_Int_OBit0(U_7925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7923),U_7925)) )
& ! [U_7924,U_7922] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7922),U_7924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7922)),c_Int_OBit0(U_7924))) ) ),
inference(definitional_conversion,[status(esa)],[f_2276_3]) ).
cnf(f_2276_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7922),U_7924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7922)),c_Int_OBit0(U_7924))) ),
inference(clausify,[status(thm)],[f_2276_4]) ).
cnf(f_2276_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7923)),c_Int_OBit0(U_7925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7923),U_7925)) ),
inference(clausify,[status(thm)],[f_2276_4]) ).
fof(f_2277_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_card__UNIV__bool]) ).
fof(f_2277_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_2277_1]) ).
cnf(f_2277_3,plain,
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))),
inference(clausify,[status(thm)],[f_2277_2]) ).
fof(f_2278_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_mult__Bit1]) ).
fof(f_2278_2,plain,
! [U_7927,U_7926] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_7926)),U_7927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7926),U_7927))),U_7927),
inference(variable_rename,[status(thm)],[f_2278_1]) ).
fof(f_2278_3,plain,
! [U_7926,U_7927] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_7926)),U_7927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7926),U_7927))),U_7927),
inference(definitional_conversion,[status(esa)],[f_2278_2]) ).
cnf(f_2278_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_7926)),U_7927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7926),U_7927))),U_7927),
inference(clausify,[status(thm)],[f_2278_3]) ).
fof(f_2279_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J]) ).
fof(f_2279_2,plain,
! [U_7928] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7928)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7928)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7928))) ) ),
inference(variable_rename,[status(thm)],[f_2279_1]) ).
fof(f_2279_3,plain,
( ! [U_7930] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7930)) )
& ! [U_7929] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7929))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7929))) ) ),
inference(miniscope,[status(thm)],[f_2279_2]) ).
fof(f_2279_4,plain,
( ! [U_7930] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7930)) )
& ! [U_7929] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7929))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7929))) ) ),
inference(definitional_conversion,[status(esa)],[f_2279_3]) ).
cnf(f_2279_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7929))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7929))) ),
inference(clausify,[status(thm)],[f_2279_4]) ).
cnf(f_2279_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7930)) ),
inference(clausify,[status(thm)],[f_2279_4]) ).
fof(f_2280_1,plain,
! [V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J]) ).
fof(f_2280_2,plain,
! [U_7931] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7931)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7931),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7931),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7931)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2280_1]) ).
fof(f_2280_3,plain,
( ! [U_7933] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7933)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7933),c_Int_OMin)) )
& ! [U_7932] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7932),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7932)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2280_2]) ).
fof(f_2280_4,plain,
( ! [U_7933] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7933)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7933),c_Int_OMin)) )
& ! [U_7932] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7932),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7932)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2280_3]) ).
cnf(f_2280_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7932),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7932)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2280_4]) ).
cnf(f_2280_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7933)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7933),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2280_4]) ).
fof(f_2281_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I5_J]) ).
fof(f_2281_2,plain,
! [U_7934] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7934)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7934)),
inference(variable_rename,[status(thm)],[f_2281_1]) ).
fof(f_2281_3,plain,
! [U_7934] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7934)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7934)),
inference(definitional_conversion,[status(esa)],[f_2281_2]) ).
cnf(f_2281_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7934)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7934)),
inference(clausify,[status(thm)],[f_2281_3]) ).
fof(f_2282_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I6_J]) ).
fof(f_2282_2,plain,
! [U_7935] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7935)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7935)),
inference(variable_rename,[status(thm)],[f_2282_1]) ).
fof(f_2282_3,plain,
! [U_7935] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7935)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7935)),
inference(definitional_conversion,[status(esa)],[f_2282_2]) ).
cnf(f_2282_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7935)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7935)),
inference(clausify,[status(thm)],[f_2282_3]) ).
fof(f_2283_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I8_J]) ).
fof(f_2283_2,plain,
! [U_7937,U_7936] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7936)),c_Int_OBit1(U_7937)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_7936)),U_7937)),
inference(variable_rename,[status(thm)],[f_2283_1]) ).
fof(f_2283_3,plain,
! [U_7936,U_7937] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7936)),c_Int_OBit1(U_7937)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_7936)),U_7937)),
inference(definitional_conversion,[status(esa)],[f_2283_2]) ).
cnf(f_2283_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7936)),c_Int_OBit1(U_7937)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_7936)),U_7937)),
inference(clausify,[status(thm)],[f_2283_3]) ).
fof(f_2284_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit1]) ).
fof(f_2284_2,plain,
! [U_7939,U_7938] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7938)),c_Int_OBit1(U_7939)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7938),c_Int_Osucc(U_7939))),
inference(variable_rename,[status(thm)],[f_2284_1]) ).
fof(f_2284_3,plain,
! [U_7938,U_7939] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7938)),c_Int_OBit1(U_7939)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7938),c_Int_Osucc(U_7939))),
inference(definitional_conversion,[status(esa)],[f_2284_2]) ).
cnf(f_2284_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7938)),c_Int_OBit1(U_7939)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7938),c_Int_Osucc(U_7939))),
inference(clausify,[status(thm)],[f_2284_3]) ).
fof(f_2285_1,plain,
! [V_w,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0]) ).
fof(f_2285_2,plain,
! [U_7941,U_7940] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7940),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7940),c_Groups_Oone__class_Oone(U_7940)),c_Groups_Oone__class_Oone(U_7940))),hAPP(c_Int_Onumber__class_Onumber__of(U_7940),U_7941)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7940),c_Int_OBit0(U_7941))
| ~ class_Int_Onumber__ring(U_7940) ),
inference(variable_rename,[status(thm)],[f_2285_1]) ).
fof(f_2285_3,plain,
! [U_7940,U_7941] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7940),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7940),c_Groups_Oone__class_Oone(U_7940)),c_Groups_Oone__class_Oone(U_7940))),hAPP(c_Int_Onumber__class_Onumber__of(U_7940),U_7941)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7940),c_Int_OBit0(U_7941))
| ~ class_Int_Onumber__ring(U_7940) ),
inference(definitional_conversion,[status(esa)],[f_2285_2]) ).
cnf(f_2285_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7940),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7940),c_Groups_Oone__class_Oone(U_7940)),c_Groups_Oone__class_Oone(U_7940))),hAPP(c_Int_Onumber__class_Onumber__of(U_7940),U_7941)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7940),c_Int_OBit0(U_7941))
| ~ class_Int_Onumber__ring(U_7940) ),
inference(clausify,[status(thm)],[f_2285_3]) ).
fof(f_2286_1,plain,
! [V_n] :
( ( 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))))
& 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)))) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_number__of1]) ).
fof(f_2286_2,plain,
! [U_7942] :
( ( 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(U_7942))))
& 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(U_7942)))) )
| ~ 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),U_7942))) ),
inference(variable_rename,[status(thm)],[f_2286_1]) ).
fof(f_2286_3,plain,
( ! [U_7942] :
( 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(U_7942))))
| ~ sP709(U_7942) )
& ! [U_7942] :
( 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(U_7942))))
| ~ sP709(U_7942) )
& ! [U_7942] :
( sP709(U_7942)
| ~ 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),U_7942))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP709])],[f_2286_2]) ).
cnf(f_2286_4,plain,
( sP709(U_7942)
| ~ 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),U_7942))) ),
inference(clausify,[status(thm)],[f_2286_3]) ).
cnf(f_2286_5,plain,
( 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(U_7942))))
| ~ sP709(U_7942) ),
inference(clausify,[status(thm)],[f_2286_3]) ).
cnf(f_2286_6,plain,
( 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(U_7942))))
| ~ sP709(U_7942) ),
inference(clausify,[status(thm)],[f_2286_3]) ).
fof(f_2287_1,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J]) ).
fof(f_2287_2,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(definitional_conversion,[status(esa)],[f_2287_1]) ).
cnf(f_2287_3,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_2287_2]) ).
fof(f_2288_1,plain,
! [V_z,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__2__right]) ).
fof(f_2288_2,plain,
! [U_7944,U_7943] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7943),U_7944),hAPP(c_Int_Onumber__class_Onumber__of(U_7943),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7943),U_7944),U_7944)
| ~ class_Int_Onumber__ring(U_7943) ),
inference(variable_rename,[status(thm)],[f_2288_1]) ).
fof(f_2288_3,plain,
! [U_7943,U_7944] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7943),U_7944),hAPP(c_Int_Onumber__class_Onumber__of(U_7943),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7943),U_7944),U_7944)
| ~ class_Int_Onumber__ring(U_7943) ),
inference(definitional_conversion,[status(esa)],[f_2288_2]) ).
cnf(f_2288_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7943),U_7944),hAPP(c_Int_Onumber__class_Onumber__of(U_7943),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7943),U_7944),U_7944)
| ~ class_Int_Onumber__ring(U_7943) ),
inference(clausify,[status(thm)],[f_2288_3]) ).
fof(f_2289_1,plain,
! [V_z,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_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__2]) ).
fof(f_2289_2,plain,
! [U_7946,U_7945] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7945),hAPP(c_Int_Onumber__class_Onumber__of(U_7945),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7945),U_7946),U_7946)
| ~ class_Int_Onumber__ring(U_7945) ),
inference(variable_rename,[status(thm)],[f_2289_1]) ).
fof(f_2289_3,plain,
! [U_7945,U_7946] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7945),hAPP(c_Int_Onumber__class_Onumber__of(U_7945),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7945),U_7946),U_7946)
| ~ class_Int_Onumber__ring(U_7945) ),
inference(definitional_conversion,[status(esa)],[f_2289_2]) ).
cnf(f_2289_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7945),hAPP(c_Int_Onumber__class_Onumber__of(U_7945),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7945),U_7946),U_7946)
| ~ class_Int_Onumber__ring(U_7945) ),
inference(clausify,[status(thm)],[f_2289_3]) ).
fof(f_2290_1,plain,
! [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),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two]) ).
fof(f_2290_2,plain,
! [U_7947] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7947),c_Groups_Oone__class_Oone(U_7947)),c_Groups_Oone__class_Oone(U_7947)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7947),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7947) ),
inference(variable_rename,[status(thm)],[f_2290_1]) ).
fof(f_2290_3,plain,
! [U_7947] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7947),c_Groups_Oone__class_Oone(U_7947)),c_Groups_Oone__class_Oone(U_7947)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7947),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7947) ),
inference(definitional_conversion,[status(esa)],[f_2290_2]) ).
cnf(f_2290_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7947),c_Groups_Oone__class_Oone(U_7947)),c_Groups_Oone__class_Oone(U_7947)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7947),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_7947) ),
inference(clausify,[status(thm)],[f_2290_3]) ).
fof(f_2291_1,plain,
! [T_a] :
( 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)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__power2]) ).
fof(f_2291_2,plain,
! [U_7948] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7948),c_Groups_Ozero__class_Ozero(U_7948)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7948)
| ~ class_Rings_Osemiring__1(U_7948) ),
inference(variable_rename,[status(thm)],[f_2291_1]) ).
fof(f_2291_3,plain,
! [U_7948] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7948),c_Groups_Ozero__class_Ozero(U_7948)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7948)
| ~ class_Rings_Osemiring__1(U_7948) ),
inference(definitional_conversion,[status(esa)],[f_2291_2]) ).
cnf(f_2291_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7948),c_Groups_Ozero__class_Ozero(U_7948)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7948)
| ~ class_Rings_Osemiring__1(U_7948) ),
inference(clausify,[status(thm)],[f_2291_3]) ).
fof(f_2292_1,plain,
! [V_a_2,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)))) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = 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)))) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__eq__power2]) ).
fof(f_2292_2,plain,
! [U_7950,U_7949] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7949),U_7950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7949)
| U_7950 != c_Groups_Ozero__class_Ozero(U_7949) )
& ( U_7950 = c_Groups_Ozero__class_Ozero(U_7949)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7949),U_7950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_7949) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_7949) ),
inference(variable_rename,[status(thm)],[f_2292_1]) ).
fof(f_2292_3,plain,
( ! [U_7949,U_7950] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7949),U_7950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7949)
| U_7950 != c_Groups_Ozero__class_Ozero(U_7949)
| ~ sP710(U_7949,U_7950) )
& ! [U_7949,U_7950] :
( U_7950 = c_Groups_Ozero__class_Ozero(U_7949)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7949),U_7950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_7949)
| ~ sP710(U_7949,U_7950) )
& ! [U_7949,U_7950] :
( sP710(U_7949,U_7950)
| ~ class_Rings_Oring__1__no__zero__divisors(U_7949) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP710])],[f_2292_2]) ).
cnf(f_2292_4,plain,
( sP710(U_7949,U_7950)
| ~ class_Rings_Oring__1__no__zero__divisors(U_7949) ),
inference(clausify,[status(thm)],[f_2292_3]) ).
cnf(f_2292_5,plain,
( U_7950 = c_Groups_Ozero__class_Ozero(U_7949)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7949),U_7950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_7949)
| ~ sP710(U_7949,U_7950) ),
inference(clausify,[status(thm)],[f_2292_3]) ).
cnf(f_2292_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7949),U_7950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7949)
| U_7950 != c_Groups_Ozero__class_Ozero(U_7949)
| ~ sP710(U_7949,U_7950) ),
inference(clausify,[status(thm)],[f_2292_3]) ).
fof(f_2293_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I115_J]) ).
fof(f_2293_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_2293_1]) ).
cnf(f_2293_3,plain,
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))),
inference(clausify,[status(thm)],[f_2293_2]) ).
fof(f_2294_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_numeral__2__eq__2]) ).
fof(f_2294_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_2294_1]) ).
cnf(f_2294_3,plain,
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))),
inference(clausify,[status(thm)],[f_2294_2]) ).
fof(f_2295_1,plain,
! [V_x,T_a] :
( 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))))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(f_2295_2,plain,
! [U_7952,U_7951] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7951),U_7952),U_7952) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7951),U_7952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(U_7951) ),
inference(variable_rename,[status(thm)],[f_2295_1]) ).
fof(f_2295_3,plain,
! [U_7951,U_7952] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7951),U_7952),U_7952) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7951),U_7952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(U_7951) ),
inference(definitional_conversion,[status(esa)],[f_2295_2]) ).
cnf(f_2295_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7951),U_7952),U_7952) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7951),U_7952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(U_7951) ),
inference(clausify,[status(thm)],[f_2295_3]) ).
fof(f_2296_1,plain,
! [V_a,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_Groups_Otimes__class_Otimes(T_a),V_a),V_a)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__square]) ).
fof(f_2296_2,plain,
! [U_7954,U_7953] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7953),U_7954),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(U_7953),U_7954),U_7954)
| ~ class_Groups_Omonoid__mult(U_7953) ),
inference(variable_rename,[status(thm)],[f_2296_1]) ).
fof(f_2296_3,plain,
! [U_7953,U_7954] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7953),U_7954),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(U_7953),U_7954),U_7954)
| ~ class_Groups_Omonoid__mult(U_7953) ),
inference(definitional_conversion,[status(esa)],[f_2296_2]) ).
cnf(f_2296_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7953),U_7954),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(U_7953),U_7954),U_7954)
| ~ class_Groups_Omonoid__mult(U_7953) ),
inference(clausify,[status(thm)],[f_2296_3]) ).
fof(f_2297_1,plain,
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))))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).
fof(f_2297_2,plain,
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))))),
inference(definitional_conversion,[status(esa)],[f_2297_1]) ).
cnf(f_2297_3,plain,
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))))),
inference(clausify,[status(thm)],[f_2297_2]) ).
fof(f_2298_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__2__eq__Suc_H]) ).
fof(f_2298_2,plain,
! [U_7955] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7955),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,U_7955)),
inference(variable_rename,[status(thm)],[f_2298_1]) ).
fof(f_2298_3,plain,
! [U_7955] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7955),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,U_7955)),
inference(definitional_conversion,[status(esa)],[f_2298_2]) ).
cnf(f_2298_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7955),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,U_7955)),
inference(clausify,[status(thm)],[f_2298_3]) ).
fof(f_2299_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_add__2__eq__Suc]) ).
fof(f_2299_2,plain,
! [U_7956] : 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)))),U_7956) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7956)),
inference(variable_rename,[status(thm)],[f_2299_1]) ).
fof(f_2299_3,plain,
! [U_7956] : 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)))),U_7956) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7956)),
inference(definitional_conversion,[status(esa)],[f_2299_2]) ).
cnf(f_2299_4,plain,
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)))),U_7956) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7956)),
inference(clausify,[status(thm)],[f_2299_3]) ).
fof(f_2300_1,plain,
! [T_a] :
( 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)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__power2]) ).
fof(f_2300_2,plain,
! [U_7957] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7957),c_Groups_Oone__class_Oone(U_7957)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7957)
| ~ class_Rings_Osemiring__1(U_7957) ),
inference(variable_rename,[status(thm)],[f_2300_1]) ).
fof(f_2300_3,plain,
! [U_7957] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7957),c_Groups_Oone__class_Oone(U_7957)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7957)
| ~ class_Rings_Osemiring__1(U_7957) ),
inference(definitional_conversion,[status(esa)],[f_2300_2]) ).
cnf(f_2300_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7957),c_Groups_Oone__class_Oone(U_7957)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7957)
| ~ class_Rings_Osemiring__1(U_7957) ),
inference(clausify,[status(thm)],[f_2300_3]) ).
fof(f_2301_1,plain,
! [V_a,T_a] :
( 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))))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__minus]) ).
fof(f_2301_2,plain,
! [U_7959,U_7958] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),hAPP(c_Groups_Ouminus__class_Ouminus(U_7958),U_7959)),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(U_7958),U_7959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_7958) ),
inference(variable_rename,[status(thm)],[f_2301_1]) ).
fof(f_2301_3,plain,
! [U_7958,U_7959] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),hAPP(c_Groups_Ouminus__class_Ouminus(U_7958),U_7959)),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(U_7958),U_7959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_7958) ),
inference(definitional_conversion,[status(esa)],[f_2301_2]) ).
cnf(f_2301_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),hAPP(c_Groups_Ouminus__class_Ouminus(U_7958),U_7959)),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(U_7958),U_7959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_7958) ),
inference(clausify,[status(thm)],[f_2301_3]) ).
fof(f_2302_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__mult__2__right]) ).
fof(f_2302_2,plain,
! [U_7960] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7960),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),U_7960),U_7960),
inference(variable_rename,[status(thm)],[f_2302_1]) ).
fof(f_2302_3,plain,
! [U_7960] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7960),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),U_7960),U_7960),
inference(definitional_conversion,[status(esa)],[f_2302_2]) ).
cnf(f_2302_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7960),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),U_7960),U_7960),
inference(clausify,[status(thm)],[f_2302_3]) ).
fof(f_2303_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__mult__2]) ).
fof(f_2303_2,plain,
! [U_7961] : 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)))),U_7961) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7961),U_7961),
inference(variable_rename,[status(thm)],[f_2303_1]) ).
fof(f_2303_3,plain,
! [U_7961] : 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)))),U_7961) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7961),U_7961),
inference(definitional_conversion,[status(esa)],[f_2303_2]) ).
cnf(f_2303_4,plain,
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)))),U_7961) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7961),U_7961),
inference(clausify,[status(thm)],[f_2303_3]) ).
fof(f_2304_1,plain,
! [V_n,V_a,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)) = 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))))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__even__eq]) ).
fof(f_2304_2,plain,
! [U_7964,U_7963,U_7962] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),U_7963),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)))),U_7964)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),U_7963),U_7964)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_7962) ),
inference(variable_rename,[status(thm)],[f_2304_1]) ).
fof(f_2304_3,plain,
! [U_7962,U_7963,U_7964] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),U_7963),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)))),U_7964)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),U_7963),U_7964)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_7962) ),
inference(definitional_conversion,[status(esa)],[f_2304_2]) ).
cnf(f_2304_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),U_7963),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)))),U_7964)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),hAPP(hAPP(c_Power_Opower__class_Opower(U_7962),U_7963),U_7964)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_7962) ),
inference(clausify,[status(thm)],[f_2304_3]) ).
fof(f_2305_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I3_J]) ).
fof(f_2305_2,plain,
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)))),
inference(definitional_conversion,[status(esa)],[f_2305_1]) ).
cnf(f_2305_3,plain,
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)))),
inference(clausify,[status(thm)],[f_2305_2]) ).
fof(f_2306_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I3_J]) ).
fof(f_2306_2,plain,
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)))),
inference(definitional_conversion,[status(esa)],[f_2306_1]) ).
cnf(f_2306_3,plain,
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)))),
inference(clausify,[status(thm)],[f_2306_2]) ).
fof(f_2307_1,plain,
! [V_a,T_a] :
( 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))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__abs]) ).
fof(f_2307_2,plain,
! [U_7966,U_7965] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7965),hAPP(c_Groups_Oabs__class_Oabs(U_7965),U_7966)),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(U_7965),U_7966),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7965) ),
inference(variable_rename,[status(thm)],[f_2307_1]) ).
fof(f_2307_3,plain,
! [U_7965,U_7966] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7965),hAPP(c_Groups_Oabs__class_Oabs(U_7965),U_7966)),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(U_7965),U_7966),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7965) ),
inference(definitional_conversion,[status(esa)],[f_2307_2]) ).
cnf(f_2307_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7965),hAPP(c_Groups_Oabs__class_Oabs(U_7965),U_7966)),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(U_7965),U_7966),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7965) ),
inference(clausify,[status(thm)],[f_2307_3]) ).
fof(f_2308_1,plain,
! [V_a,T_a] :
( 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))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__power2]) ).
fof(f_2308_2,plain,
! [U_7968,U_7967] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7967),hAPP(hAPP(c_Power_Opower__class_Opower(U_7967),U_7968),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(U_7967),U_7968),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7967) ),
inference(variable_rename,[status(thm)],[f_2308_1]) ).
fof(f_2308_3,plain,
! [U_7967,U_7968] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7967),hAPP(hAPP(c_Power_Opower__class_Opower(U_7967),U_7968),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(U_7967),U_7968),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7967) ),
inference(definitional_conversion,[status(esa)],[f_2308_2]) ).
cnf(f_2308_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7967),hAPP(hAPP(c_Power_Opower__class_Opower(U_7967),U_7968),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(U_7967),U_7968),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7967) ),
inference(clausify,[status(thm)],[f_2308_3]) ).
fof(f_2309_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_nat__1__add__1]) ).
fof(f_2309_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_2309_1]) ).
cnf(f_2309_3,plain,
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))),
inference(clausify,[status(thm)],[f_2309_2]) ).
fof(f_2310_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_mod2__Suc__Suc]) ).
fof(f_2310_2,plain,
! [U_7969] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7969)),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,U_7969,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[f_2310_1]) ).
fof(f_2310_3,plain,
! [U_7969] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7969)),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,U_7969,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(definitional_conversion,[status(esa)],[f_2310_2]) ).
cnf(f_2310_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7969)),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,U_7969,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_2310_3]) ).
fof(f_2311_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_div2__Suc__Suc]) ).
fof(f_2311_2,plain,
! [U_7970] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7970))),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),U_7970),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(variable_rename,[status(thm)],[f_2311_1]) ).
fof(f_2311_3,plain,
! [U_7970] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7970))),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),U_7970),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(definitional_conversion,[status(esa)],[f_2311_2]) ).
cnf(f_2311_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7970))),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),U_7970),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_2311_3]) ).
fof(f_2312_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_zmod__number__of__Bit0]) ).
fof(f_2312_2,plain,
! [U_7972,U_7971] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7971)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7972))) = 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),U_7971),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7972))),
inference(variable_rename,[status(thm)],[f_2312_1]) ).
fof(f_2312_3,plain,
! [U_7971,U_7972] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7971)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7972))) = 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),U_7971),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7972))),
inference(definitional_conversion,[status(esa)],[f_2312_2]) ).
cnf(f_2312_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7971)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7972))) = 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),U_7971),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7972))),
inference(clausify,[status(thm)],[f_2312_3]) ).
fof(f_2313_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_add__self__div__2]) ).
fof(f_2313_2,plain,
! [U_7973] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7973),U_7973)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_7973,
inference(variable_rename,[status(thm)],[f_2313_1]) ).
fof(f_2313_3,plain,
! [U_7973] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7973),U_7973)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_7973,
inference(definitional_conversion,[status(esa)],[f_2313_2]) ).
cnf(f_2313_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7973),U_7973)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_7973,
inference(clausify,[status(thm)],[f_2313_3]) ).
fof(f_2314_1,plain,
! [V_r,T_a] :
( 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))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_half__gt__zero]) ).
fof(f_2314_2,plain,
! [U_7975,U_7974] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7974),c_Groups_Ozero__class_Ozero(U_7974)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7974),U_7975),hAPP(c_Int_Onumber__class_Onumber__of(U_7974),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7974),c_Groups_Ozero__class_Ozero(U_7974)),U_7975))
| ~ class_Int_Onumber__ring(U_7974)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7974) ),
inference(variable_rename,[status(thm)],[f_2314_1]) ).
fof(f_2314_3,plain,
! [U_7974,U_7975] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7974),c_Groups_Ozero__class_Ozero(U_7974)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7974),U_7975),hAPP(c_Int_Onumber__class_Onumber__of(U_7974),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7974),c_Groups_Ozero__class_Ozero(U_7974)),U_7975))
| ~ class_Int_Onumber__ring(U_7974)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7974) ),
inference(definitional_conversion,[status(esa)],[f_2314_2]) ).
cnf(f_2314_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7974),c_Groups_Ozero__class_Ozero(U_7974)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7974),U_7975),hAPP(c_Int_Onumber__class_Onumber__of(U_7974),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7974),c_Groups_Ozero__class_Ozero(U_7974)),U_7975))
| ~ class_Int_Onumber__ring(U_7974)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7974) ),
inference(clausify,[status(thm)],[f_2314_3]) ).
fof(f_2315_1,plain,
! [V_r_2,T_b] :
( ( ( 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))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2))
| ~ 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)))))) ) )
| ~ class_Int_Onumber__ring(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff]) ).
fof(f_2315_2,plain,
! [U_7977,U_7976] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7976),U_7977),hAPP(c_Int_Onumber__class_Onumber__of(U_7976),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),U_7977)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),U_7977))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7976),U_7977),hAPP(c_Int_Onumber__class_Onumber__of(U_7976),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Int_Onumber__ring(U_7976)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7976) ),
inference(variable_rename,[status(thm)],[f_2315_1]) ).
fof(f_2315_3,plain,
( ! [U_7976,U_7977] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7976),U_7977),hAPP(c_Int_Onumber__class_Onumber__of(U_7976),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),U_7977))
| ~ sP711(U_7976,U_7977) )
& ! [U_7976,U_7977] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),U_7977))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7976),U_7977),hAPP(c_Int_Onumber__class_Onumber__of(U_7976),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP711(U_7976,U_7977) )
& ! [U_7976,U_7977] :
( sP711(U_7976,U_7977)
| ~ class_Int_Onumber__ring(U_7976)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7976) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP711])],[f_2315_2]) ).
cnf(f_2315_4,plain,
( sP711(U_7976,U_7977)
| ~ class_Int_Onumber__ring(U_7976)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7976) ),
inference(clausify,[status(thm)],[f_2315_3]) ).
cnf(f_2315_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),U_7977))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7976),U_7977),hAPP(c_Int_Onumber__class_Onumber__of(U_7976),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP711(U_7976,U_7977) ),
inference(clausify,[status(thm)],[f_2315_3]) ).
cnf(f_2315_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7976),U_7977),hAPP(c_Int_Onumber__class_Onumber__of(U_7976),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),U_7977))
| ~ sP711(U_7976,U_7977) ),
inference(clausify,[status(thm)],[f_2315_3]) ).
fof(f_2316_1,plain,
! [V_a,T_a] :
( 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))))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power2]) ).
fof(f_2316_2,plain,
! [U_7979,U_7978] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7978),c_Groups_Ozero__class_Ozero(U_7978)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7978),U_7979),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_7978) ),
inference(variable_rename,[status(thm)],[f_2316_1]) ).
fof(f_2316_3,plain,
! [U_7979,U_7978] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7978),c_Groups_Ozero__class_Ozero(U_7978)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7978),U_7979),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_7978) ),
inference(definitional_conversion,[status(esa)],[f_2316_2]) ).
cnf(f_2316_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7978),c_Groups_Ozero__class_Ozero(U_7978)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7978),U_7979),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_7978) ),
inference(clausify,[status(thm)],[f_2316_3]) ).
fof(f_2317_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ 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))))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le]) ).
fof(f_2317_2,plain,
! [U_7982,U_7981,U_7980] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),U_7981),U_7982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),c_Groups_Ozero__class_Ozero(U_7980)),U_7982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),hAPP(hAPP(c_Power_Opower__class_Opower(U_7980),U_7981),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(U_7980),U_7982),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_7980) ),
inference(variable_rename,[status(thm)],[f_2317_1]) ).
fof(f_2317_3,plain,
! [U_7980,U_7981,U_7982] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),U_7981),U_7982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),c_Groups_Ozero__class_Ozero(U_7980)),U_7982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),hAPP(hAPP(c_Power_Opower__class_Opower(U_7980),U_7981),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(U_7980),U_7982),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_7980) ),
inference(definitional_conversion,[status(esa)],[f_2317_2]) ).
cnf(f_2317_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),U_7981),U_7982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),c_Groups_Ozero__class_Ozero(U_7980)),U_7982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7980),hAPP(hAPP(c_Power_Opower__class_Opower(U_7980),U_7981),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(U_7980),U_7982),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_7980) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
fof(f_2318_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),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)))) != 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))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq]) ).
fof(f_2318_2,plain,
! [U_7985,U_7984,U_7983] :
( U_7984 = U_7985
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7983),c_Groups_Ozero__class_Ozero(U_7983)),U_7985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7983),c_Groups_Ozero__class_Ozero(U_7983)),U_7984))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7983),U_7984),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(U_7983),U_7985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_7983) ),
inference(variable_rename,[status(thm)],[f_2318_1]) ).
fof(f_2318_3,plain,
! [U_7985,U_7983,U_7984] :
( U_7984 = U_7985
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7983),c_Groups_Ozero__class_Ozero(U_7983)),U_7985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7983),c_Groups_Ozero__class_Ozero(U_7983)),U_7984))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7983),U_7984),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(U_7983),U_7985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_7983) ),
inference(definitional_conversion,[status(esa)],[f_2318_2]) ).
cnf(f_2318_4,plain,
( U_7984 = U_7985
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7983),c_Groups_Ozero__class_Ozero(U_7983)),U_7985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7983),c_Groups_Ozero__class_Ozero(U_7983)),U_7984))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7983),U_7984),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(U_7983),U_7985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_7983) ),
inference(clausify,[status(thm)],[f_2318_3]) ).
fof(f_2319_1,plain,
! [V_a,T_a] :
( ~ 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)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__less__0]) ).
fof(f_2319_2,plain,
! [U_7987,U_7986] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7986),hAPP(hAPP(c_Power_Opower__class_Opower(U_7986),U_7987),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_7986)))
| ~ class_Rings_Olinordered__idom(U_7986) ),
inference(variable_rename,[status(thm)],[f_2319_1]) ).
fof(f_2319_3,plain,
! [U_7987,U_7986] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7986),hAPP(hAPP(c_Power_Opower__class_Opower(U_7986),U_7987),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_7986)))
| ~ class_Rings_Olinordered__idom(U_7986) ),
inference(definitional_conversion,[status(esa)],[f_2319_2]) ).
cnf(f_2319_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7986),hAPP(hAPP(c_Power_Opower__class_Opower(U_7986),U_7987),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_7986)))
| ~ class_Rings_Olinordered__idom(U_7986) ),
inference(clausify,[status(thm)],[f_2319_3]) ).
fof(f_2320_1,plain,
! [V_a_2,T_b] :
( ( ( 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))))))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
| ~ 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)))))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power2]) ).
fof(f_2320_2,plain,
! [U_7989,U_7988] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7988),U_7989),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_7989 = c_Groups_Ozero__class_Ozero(U_7988) )
& ( U_7989 != c_Groups_Ozero__class_Ozero(U_7988)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7988),U_7989),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(U_7988) ),
inference(variable_rename,[status(thm)],[f_2320_1]) ).
fof(f_2320_3,plain,
( ! [U_7989,U_7988] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7988),U_7989),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_7989 = c_Groups_Ozero__class_Ozero(U_7988)
| ~ sP712(U_7989,U_7988) )
& ! [U_7989,U_7988] :
( U_7989 != c_Groups_Ozero__class_Ozero(U_7988)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7988),U_7989),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP712(U_7989,U_7988) )
& ! [U_7989,U_7988] :
( sP712(U_7989,U_7988)
| ~ class_Rings_Olinordered__idom(U_7988) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP712])],[f_2320_2]) ).
cnf(f_2320_4,plain,
( sP712(U_7989,U_7988)
| ~ class_Rings_Olinordered__idom(U_7988) ),
inference(clausify,[status(thm)],[f_2320_3]) ).
cnf(f_2320_5,plain,
( U_7989 != c_Groups_Ozero__class_Ozero(U_7988)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7988),U_7989),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP712(U_7989,U_7988) ),
inference(clausify,[status(thm)],[f_2320_3]) ).
cnf(f_2320_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7988),U_7989),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_7989 = c_Groups_Ozero__class_Ozero(U_7988)
| ~ sP712(U_7989,U_7988) ),
inference(clausify,[status(thm)],[f_2320_3]) ).
fof(f_2321_1,plain,
! [V_y_2,V_x_2,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)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = 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))))) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff]) ).
fof(f_2321_2,plain,
! [U_7992,U_7991,U_7990] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7990),hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),U_7991),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(U_7990),U_7992),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_7990)
| U_7992 != c_Groups_Ozero__class_Ozero(U_7990)
| U_7991 != c_Groups_Ozero__class_Ozero(U_7990) )
& ( ( U_7992 = c_Groups_Ozero__class_Ozero(U_7990)
& U_7991 = c_Groups_Ozero__class_Ozero(U_7990) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7990),hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),U_7991),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(U_7990),U_7992),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_7990) ) )
| ~ class_Rings_Olinordered__idom(U_7990) ),
inference(variable_rename,[status(thm)],[f_2321_1]) ).
fof(f_2321_3,plain,
( ! [U_7991,U_7992,U_7990] :
( U_7992 = c_Groups_Ozero__class_Ozero(U_7990)
| ~ sP713(U_7991,U_7992,U_7990) )
& ! [U_7991,U_7992,U_7990] :
( U_7991 = c_Groups_Ozero__class_Ozero(U_7990)
| ~ sP713(U_7991,U_7992,U_7990) )
& ! [U_7991,U_7992,U_7990] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7990),hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),U_7991),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(U_7990),U_7992),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_7990)
| U_7992 != c_Groups_Ozero__class_Ozero(U_7990)
| U_7991 != c_Groups_Ozero__class_Ozero(U_7990)
| ~ sP714(U_7991,U_7992,U_7990) )
& ! [U_7991,U_7992,U_7990] :
( sP713(U_7991,U_7992,U_7990)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7990),hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),U_7991),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(U_7990),U_7992),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_7990)
| ~ sP714(U_7991,U_7992,U_7990) )
& ! [U_7991,U_7992,U_7990] :
( sP714(U_7991,U_7992,U_7990)
| ~ class_Rings_Olinordered__idom(U_7990) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP713,sP714])],[f_2321_2]) ).
cnf(f_2321_4,plain,
( sP714(U_7991,U_7992,U_7990)
| ~ class_Rings_Olinordered__idom(U_7990) ),
inference(clausify,[status(thm)],[f_2321_3]) ).
cnf(f_2321_5,plain,
( sP713(U_7991,U_7992,U_7990)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7990),hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),U_7991),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(U_7990),U_7992),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_7990)
| ~ sP714(U_7991,U_7992,U_7990) ),
inference(clausify,[status(thm)],[f_2321_3]) ).
cnf(f_2321_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7990),hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),U_7991),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(U_7990),U_7992),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_7990)
| U_7992 != c_Groups_Ozero__class_Ozero(U_7990)
| U_7991 != c_Groups_Ozero__class_Ozero(U_7990)
| ~ sP714(U_7991,U_7992,U_7990) ),
inference(clausify,[status(thm)],[f_2321_3]) ).
cnf(f_2321_7,plain,
( U_7991 = c_Groups_Ozero__class_Ozero(U_7990)
| ~ sP713(U_7991,U_7992,U_7990) ),
inference(clausify,[status(thm)],[f_2321_3]) ).
cnf(f_2321_8,plain,
( U_7992 = c_Groups_Ozero__class_Ozero(U_7990)
| ~ sP713(U_7991,U_7992,U_7990) ),
inference(clausify,[status(thm)],[f_2321_3]) ).
fof(f_2322_1,plain,
! [V_w,T_b] :
( 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))
| ~ class_Int_Onumber(T_b)
| ~ class_Groups_Omonoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of]) ).
fof(f_2322_2,plain,
! [U_7994,U_7993] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7993),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994)),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(U_7993),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994)),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994))
| ~ class_Int_Onumber(U_7993)
| ~ class_Groups_Omonoid__mult(U_7993) ),
inference(variable_rename,[status(thm)],[f_2322_1]) ).
fof(f_2322_3,plain,
! [U_7994,U_7993] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7993),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994)),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(U_7993),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994)),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994))
| ~ class_Int_Onumber(U_7993)
| ~ class_Groups_Omonoid__mult(U_7993) ),
inference(definitional_conversion,[status(esa)],[f_2322_2]) ).
cnf(f_2322_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7993),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994)),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(U_7993),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994)),hAPP(c_Int_Onumber__class_Onumber__of(U_7993),U_7994))
| ~ class_Int_Onumber(U_7993)
| ~ class_Groups_Omonoid__mult(U_7993) ),
inference(clausify,[status(thm)],[f_2322_3]) ).
fof(f_2323_1,plain,
! [V_n] :
( V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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))))) ),
inference(fof_nnf,[status(thm)],[fact_less__2__cases]) ).
fof(f_2323_2,plain,
! [U_7995] :
( U_7995 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_7995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(variable_rename,[status(thm)],[f_2323_1]) ).
fof(f_2323_3,plain,
! [U_7995] :
( U_7995 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_7995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(definitional_conversion,[status(esa)],[f_2323_2]) ).
cnf(f_2323_4,plain,
( U_7995 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_7995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(clausify,[status(thm)],[f_2323_3]) ).
fof(f_2324_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_nat__2]) ).
fof(f_2324_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_2324_1]) ).
cnf(f_2324_3,plain,
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))),
inference(clausify,[status(thm)],[f_2324_2]) ).
fof(f_2325_1,plain,
! [V_a_2,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)))) = c_Groups_Oone__class_Oone(T_b)
| ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
& V_a_2 != c_Groups_Oone__class_Oone(T_b) ) )
& ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| V_a_2 = c_Groups_Oone__class_Oone(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)))) != c_Groups_Oone__class_Oone(T_b) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff]) ).
fof(f_2325_2,plain,
! [U_7997,U_7996] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7996)
| ( U_7997 != hAPP(c_Groups_Ouminus__class_Ouminus(U_7996),c_Groups_Oone__class_Oone(U_7996))
& U_7997 != c_Groups_Oone__class_Oone(U_7996) ) )
& ( U_7997 = hAPP(c_Groups_Ouminus__class_Ouminus(U_7996),c_Groups_Oone__class_Oone(U_7996))
| U_7997 = c_Groups_Oone__class_Oone(U_7996)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_7996) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_7996) ),
inference(variable_rename,[status(thm)],[f_2325_1]) ).
fof(f_2325_3,plain,
( ! [U_7996,U_7997] :
( U_7997 != hAPP(c_Groups_Ouminus__class_Ouminus(U_7996),c_Groups_Oone__class_Oone(U_7996))
| ~ sP715(U_7996,U_7997) )
& ! [U_7996,U_7997] :
( U_7997 != c_Groups_Oone__class_Oone(U_7996)
| ~ sP715(U_7996,U_7997) )
& ! [U_7996,U_7997] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7996)
| sP715(U_7996,U_7997)
| ~ sP716(U_7996,U_7997) )
& ! [U_7996,U_7997] :
( U_7997 = hAPP(c_Groups_Ouminus__class_Ouminus(U_7996),c_Groups_Oone__class_Oone(U_7996))
| U_7997 = c_Groups_Oone__class_Oone(U_7996)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_7996)
| ~ sP716(U_7996,U_7997) )
& ! [U_7996,U_7997] :
( sP716(U_7996,U_7997)
| ~ class_Rings_Oring__1__no__zero__divisors(U_7996) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP715,sP716])],[f_2325_2]) ).
cnf(f_2325_4,plain,
( sP716(U_7996,U_7997)
| ~ class_Rings_Oring__1__no__zero__divisors(U_7996) ),
inference(clausify,[status(thm)],[f_2325_3]) ).
cnf(f_2325_5,plain,
( U_7997 = hAPP(c_Groups_Ouminus__class_Ouminus(U_7996),c_Groups_Oone__class_Oone(U_7996))
| U_7997 = c_Groups_Oone__class_Oone(U_7996)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_7996)
| ~ sP716(U_7996,U_7997) ),
inference(clausify,[status(thm)],[f_2325_3]) ).
cnf(f_2325_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7996)
| sP715(U_7996,U_7997)
| ~ sP716(U_7996,U_7997) ),
inference(clausify,[status(thm)],[f_2325_3]) ).
cnf(f_2325_7,plain,
( U_7997 != c_Groups_Oone__class_Oone(U_7996)
| ~ sP715(U_7996,U_7997) ),
inference(clausify,[status(thm)],[f_2325_3]) ).
cnf(f_2325_8,plain,
( U_7997 != hAPP(c_Groups_Ouminus__class_Ouminus(U_7996),c_Groups_Oone__class_Oone(U_7996))
| ~ sP715(U_7996,U_7997) ),
inference(clausify,[status(thm)],[f_2325_3]) ).
fof(f_2326_1,plain,
! [V_n,V_x,T_a] :
( 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_2326_2,plain,
! [U_8000,U_7999,U_7998] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),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)))),U_8000)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7998),hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),U_8000)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),U_8000))
| ~ class_Rings_Ocomm__semiring__1(U_7998) ),
inference(variable_rename,[status(thm)],[f_2326_1]) ).
fof(f_2326_3,plain,
! [U_8000,U_7998,U_7999] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),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)))),U_8000)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7998),hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),U_8000)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),U_8000))
| ~ class_Rings_Ocomm__semiring__1(U_7998) ),
inference(definitional_conversion,[status(esa)],[f_2326_2]) ).
cnf(f_2326_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),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)))),U_8000)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7998),hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),U_8000)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7998),U_7999),U_8000))
| ~ class_Rings_Ocomm__semiring__1(U_7998) ),
inference(clausify,[status(thm)],[f_2326_3]) ).
fof(f_2327_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__minus__even]) ).
fof(f_2327_2,plain,
! [U_8003,U_8002,U_8001] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8001),hAPP(c_Groups_Ouminus__class_Ouminus(U_8001),U_8002)),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)))),U_8003)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8001),U_8002),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)))),U_8003))
| ~ class_Rings_Oring__1(U_8001) ),
inference(variable_rename,[status(thm)],[f_2327_1]) ).
fof(f_2327_3,plain,
! [U_8001,U_8002,U_8003] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8001),hAPP(c_Groups_Ouminus__class_Ouminus(U_8001),U_8002)),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)))),U_8003)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8001),U_8002),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)))),U_8003))
| ~ class_Rings_Oring__1(U_8001) ),
inference(definitional_conversion,[status(esa)],[f_2327_2]) ).
cnf(f_2327_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8001),hAPP(c_Groups_Ouminus__class_Ouminus(U_8001),U_8002)),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)))),U_8003)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8001),U_8002),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)))),U_8003))
| ~ class_Rings_Oring__1(U_8001) ),
inference(clausify,[status(thm)],[f_2327_3]) ).
fof(f_2328_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ 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))))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less]) ).
fof(f_2328_2,plain,
! [U_8006,U_8005,U_8004] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8004),U_8005),U_8006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8004),c_Groups_Ozero__class_Ozero(U_8004)),U_8006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8004),hAPP(hAPP(c_Power_Opower__class_Opower(U_8004),U_8005),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(U_8004),U_8006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_8004) ),
inference(variable_rename,[status(thm)],[f_2328_1]) ).
fof(f_2328_3,plain,
! [U_8004,U_8005,U_8006] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8004),U_8005),U_8006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8004),c_Groups_Ozero__class_Ozero(U_8004)),U_8006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8004),hAPP(hAPP(c_Power_Opower__class_Opower(U_8004),U_8005),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(U_8004),U_8006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_8004) ),
inference(definitional_conversion,[status(esa)],[f_2328_2]) ).
cnf(f_2328_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8004),U_8005),U_8006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8004),c_Groups_Ozero__class_Ozero(U_8004)),U_8006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8004),hAPP(hAPP(c_Power_Opower__class_Opower(U_8004),U_8005),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(U_8004),U_8006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_8004) ),
inference(clausify,[status(thm)],[f_2328_3]) ).
fof(f_2329_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ~ 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))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff]) ).
fof(f_2329_2,plain,
! [U_8009,U_8008,U_8007] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8007),hAPP(hAPP(c_Power_Opower__class_Opower(U_8007),U_8008),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(U_8007),U_8009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8007)))
| U_8009 != c_Groups_Ozero__class_Ozero(U_8007)
| U_8008 != c_Groups_Ozero__class_Ozero(U_8007) )
& ( ( U_8009 = c_Groups_Ozero__class_Ozero(U_8007)
& U_8008 = c_Groups_Ozero__class_Ozero(U_8007) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8007),hAPP(hAPP(c_Power_Opower__class_Opower(U_8007),U_8008),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(U_8007),U_8009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8007))) ) )
| ~ class_Rings_Olinordered__idom(U_8007) ),
inference(variable_rename,[status(thm)],[f_2329_1]) ).
fof(f_2329_3,plain,
( ! [U_8008,U_8007,U_8009] :
( U_8009 = c_Groups_Ozero__class_Ozero(U_8007)
| ~ sP717(U_8008,U_8007,U_8009) )
& ! [U_8008,U_8007,U_8009] :
( U_8008 = c_Groups_Ozero__class_Ozero(U_8007)
| ~ sP717(U_8008,U_8007,U_8009) )
& ! [U_8008,U_8007,U_8009] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8007),hAPP(hAPP(c_Power_Opower__class_Opower(U_8007),U_8008),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(U_8007),U_8009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8007)))
| U_8009 != c_Groups_Ozero__class_Ozero(U_8007)
| U_8008 != c_Groups_Ozero__class_Ozero(U_8007)
| ~ sP718(U_8008,U_8007,U_8009) )
& ! [U_8008,U_8007,U_8009] :
( sP717(U_8008,U_8007,U_8009)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8007),hAPP(hAPP(c_Power_Opower__class_Opower(U_8007),U_8008),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(U_8007),U_8009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8007)))
| ~ sP718(U_8008,U_8007,U_8009) )
& ! [U_8008,U_8007,U_8009] :
( sP718(U_8008,U_8007,U_8009)
| ~ class_Rings_Olinordered__idom(U_8007) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP717,sP718])],[f_2329_2]) ).
cnf(f_2329_4,plain,
( sP718(U_8008,U_8007,U_8009)
| ~ class_Rings_Olinordered__idom(U_8007) ),
inference(clausify,[status(thm)],[f_2329_3]) ).
cnf(f_2329_5,plain,
( sP717(U_8008,U_8007,U_8009)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8007),hAPP(hAPP(c_Power_Opower__class_Opower(U_8007),U_8008),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(U_8007),U_8009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8007)))
| ~ sP718(U_8008,U_8007,U_8009) ),
inference(clausify,[status(thm)],[f_2329_3]) ).
cnf(f_2329_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8007),hAPP(hAPP(c_Power_Opower__class_Opower(U_8007),U_8008),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(U_8007),U_8009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8007)))
| U_8009 != c_Groups_Ozero__class_Ozero(U_8007)
| U_8008 != c_Groups_Ozero__class_Ozero(U_8007)
| ~ sP718(U_8008,U_8007,U_8009) ),
inference(clausify,[status(thm)],[f_2329_3]) ).
cnf(f_2329_7,plain,
( U_8008 = c_Groups_Ozero__class_Ozero(U_8007)
| ~ sP717(U_8008,U_8007,U_8009) ),
inference(clausify,[status(thm)],[f_2329_3]) ).
cnf(f_2329_8,plain,
( U_8009 = c_Groups_Ozero__class_Ozero(U_8007)
| ~ sP717(U_8008,U_8007,U_8009) ),
inference(clausify,[status(thm)],[f_2329_3]) ).
fof(f_2330_1,plain,
! [V_y,V_x,T_a] :
( 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)))))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero]) ).
fof(f_2330_2,plain,
! [U_8012,U_8011,U_8010] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8010),c_Groups_Ozero__class_Ozero(U_8010)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8010),hAPP(hAPP(c_Power_Opower__class_Opower(U_8010),U_8011),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(U_8010),U_8012),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_8010) ),
inference(variable_rename,[status(thm)],[f_2330_1]) ).
fof(f_2330_3,plain,
! [U_8010,U_8011,U_8012] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8010),c_Groups_Ozero__class_Ozero(U_8010)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8010),hAPP(hAPP(c_Power_Opower__class_Opower(U_8010),U_8011),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(U_8010),U_8012),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_8010) ),
inference(definitional_conversion,[status(esa)],[f_2330_2]) ).
cnf(f_2330_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8010),c_Groups_Ozero__class_Ozero(U_8010)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8010),hAPP(hAPP(c_Power_Opower__class_Opower(U_8010),U_8011),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(U_8010),U_8012),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_8010) ),
inference(clausify,[status(thm)],[f_2330_3]) ).
fof(f_2331_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( 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)))))))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
| ~ 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))))))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff]) ).
fof(f_2331_2,plain,
! [U_8015,U_8014,U_8013] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8013),c_Groups_Ozero__class_Ozero(U_8013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8013),hAPP(hAPP(c_Power_Opower__class_Opower(U_8013),U_8014),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(U_8013),U_8015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ( U_8015 = c_Groups_Ozero__class_Ozero(U_8013)
& U_8014 = c_Groups_Ozero__class_Ozero(U_8013) ) )
& ( U_8015 != c_Groups_Ozero__class_Ozero(U_8013)
| U_8014 != c_Groups_Ozero__class_Ozero(U_8013)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8013),c_Groups_Ozero__class_Ozero(U_8013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8013),hAPP(hAPP(c_Power_Opower__class_Opower(U_8013),U_8014),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(U_8013),U_8015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
| ~ class_Rings_Olinordered__idom(U_8013) ),
inference(variable_rename,[status(thm)],[f_2331_1]) ).
fof(f_2331_3,plain,
( ! [U_8015,U_8014,U_8013] :
( U_8015 = c_Groups_Ozero__class_Ozero(U_8013)
| ~ sP719(U_8015,U_8014,U_8013) )
& ! [U_8015,U_8014,U_8013] :
( U_8014 = c_Groups_Ozero__class_Ozero(U_8013)
| ~ sP719(U_8015,U_8014,U_8013) )
& ! [U_8015,U_8014,U_8013] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8013),c_Groups_Ozero__class_Ozero(U_8013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8013),hAPP(hAPP(c_Power_Opower__class_Opower(U_8013),U_8014),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(U_8013),U_8015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| sP719(U_8015,U_8014,U_8013)
| ~ sP720(U_8015,U_8014,U_8013) )
& ! [U_8015,U_8014,U_8013] :
( U_8015 != c_Groups_Ozero__class_Ozero(U_8013)
| U_8014 != c_Groups_Ozero__class_Ozero(U_8013)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8013),c_Groups_Ozero__class_Ozero(U_8013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8013),hAPP(hAPP(c_Power_Opower__class_Opower(U_8013),U_8014),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(U_8013),U_8015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ sP720(U_8015,U_8014,U_8013) )
& ! [U_8015,U_8014,U_8013] :
( sP720(U_8015,U_8014,U_8013)
| ~ class_Rings_Olinordered__idom(U_8013) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP719,sP720])],[f_2331_2]) ).
cnf(f_2331_4,plain,
( sP720(U_8015,U_8014,U_8013)
| ~ class_Rings_Olinordered__idom(U_8013) ),
inference(clausify,[status(thm)],[f_2331_3]) ).
cnf(f_2331_5,plain,
( U_8015 != c_Groups_Ozero__class_Ozero(U_8013)
| U_8014 != c_Groups_Ozero__class_Ozero(U_8013)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8013),c_Groups_Ozero__class_Ozero(U_8013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8013),hAPP(hAPP(c_Power_Opower__class_Opower(U_8013),U_8014),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(U_8013),U_8015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ sP720(U_8015,U_8014,U_8013) ),
inference(clausify,[status(thm)],[f_2331_3]) ).
cnf(f_2331_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8013),c_Groups_Ozero__class_Ozero(U_8013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8013),hAPP(hAPP(c_Power_Opower__class_Opower(U_8013),U_8014),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(U_8013),U_8015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| sP719(U_8015,U_8014,U_8013)
| ~ sP720(U_8015,U_8014,U_8013) ),
inference(clausify,[status(thm)],[f_2331_3]) ).
cnf(f_2331_7,plain,
( U_8014 = c_Groups_Ozero__class_Ozero(U_8013)
| ~ sP719(U_8015,U_8014,U_8013) ),
inference(clausify,[status(thm)],[f_2331_3]) ).
cnf(f_2331_8,plain,
( U_8015 = c_Groups_Ozero__class_Ozero(U_8013)
| ~ sP719(U_8015,U_8014,U_8013) ),
inference(clausify,[status(thm)],[f_2331_3]) ).
fof(f_2332_1,plain,
! [V_y,V_x,T_a] :
( ~ 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)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__sum__power2__lt__zero]) ).
fof(f_2332_2,plain,
! [U_8018,U_8017,U_8016] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8016),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8016),hAPP(hAPP(c_Power_Opower__class_Opower(U_8016),U_8017),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(U_8016),U_8018),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8016)))
| ~ class_Rings_Olinordered__idom(U_8016) ),
inference(variable_rename,[status(thm)],[f_2332_1]) ).
fof(f_2332_3,plain,
! [U_8018,U_8017,U_8016] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8016),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8016),hAPP(hAPP(c_Power_Opower__class_Opower(U_8016),U_8017),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(U_8016),U_8018),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8016)))
| ~ class_Rings_Olinordered__idom(U_8016) ),
inference(definitional_conversion,[status(esa)],[f_2332_2]) ).
cnf(f_2332_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8016),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8016),hAPP(hAPP(c_Power_Opower__class_Opower(U_8016),U_8017),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(U_8016),U_8018),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8016)))
| ~ class_Rings_Olinordered__idom(U_8016) ),
inference(clausify,[status(thm)],[f_2332_3]) ).
fof(f_2333_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__sum]) ).
fof(f_2333_2,plain,
! [U_8021,U_8020,U_8019] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8019),U_8020),U_8021)),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(U_8019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8019),hAPP(hAPP(c_Power_Opower__class_Opower(U_8019),U_8020),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(U_8019),U_8021),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(U_8019),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8019),hAPP(c_Int_Onumber__class_Onumber__of(U_8019),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8020)),U_8021))
| ~ class_Int_Onumber__ring(U_8019) ),
inference(variable_rename,[status(thm)],[f_2333_1]) ).
fof(f_2333_3,plain,
! [U_8019,U_8020,U_8021] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8019),U_8020),U_8021)),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(U_8019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8019),hAPP(hAPP(c_Power_Opower__class_Opower(U_8019),U_8020),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(U_8019),U_8021),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(U_8019),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8019),hAPP(c_Int_Onumber__class_Onumber__of(U_8019),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8020)),U_8021))
| ~ class_Int_Onumber__ring(U_8019) ),
inference(definitional_conversion,[status(esa)],[f_2333_2]) ).
cnf(f_2333_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8019),U_8020),U_8021)),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(U_8019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8019),hAPP(hAPP(c_Power_Opower__class_Opower(U_8019),U_8020),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(U_8019),U_8021),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(U_8019),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8019),hAPP(c_Int_Onumber__class_Onumber__of(U_8019),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8020)),U_8021))
| ~ class_Int_Onumber__ring(U_8019) ),
inference(clausify,[status(thm)],[f_2333_3]) ).
fof(f_2334_1,plain,
! [V_n,V_a,T_a] :
( 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))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H]) ).
fof(f_2334_2,plain,
! [U_8024,U_8023,U_8022] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8022),c_Groups_Ozero__class_Ozero(U_8022)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8022),U_8023),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)))),U_8024))))
| ~ class_Rings_Olinordered__idom(U_8022) ),
inference(variable_rename,[status(thm)],[f_2334_1]) ).
fof(f_2334_3,plain,
! [U_8022,U_8023,U_8024] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8022),c_Groups_Ozero__class_Ozero(U_8022)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8022),U_8023),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)))),U_8024))))
| ~ class_Rings_Olinordered__idom(U_8022) ),
inference(definitional_conversion,[status(esa)],[f_2334_2]) ).
cnf(f_2334_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8022),c_Groups_Ozero__class_Ozero(U_8022)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8022),U_8023),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)))),U_8024))))
| ~ class_Rings_Olinordered__idom(U_8022) ),
inference(clausify,[status(thm)],[f_2334_3]) ).
fof(f_2335_1,plain,
! [V_n,V_a,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))) = 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)))))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__odd__eq]) ).
fof(f_2335_2,plain,
! [U_8027,U_8026,U_8025] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),U_8026),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)))),U_8027))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8025),U_8026),hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),U_8026),U_8027)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_8025) ),
inference(variable_rename,[status(thm)],[f_2335_1]) ).
fof(f_2335_3,plain,
! [U_8025,U_8026,U_8027] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),U_8026),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)))),U_8027))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8025),U_8026),hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),U_8026),U_8027)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_8025) ),
inference(definitional_conversion,[status(esa)],[f_2335_2]) ).
cnf(f_2335_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),U_8026),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)))),U_8027))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8025),U_8026),hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),hAPP(hAPP(c_Power_Opower__class_Opower(U_8025),U_8026),U_8027)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_8025) ),
inference(clausify,[status(thm)],[f_2335_3]) ).
fof(f_2336_1,plain,
! [V_n,V_x,T_a] :
( 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)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J]) ).
fof(f_2336_2,plain,
! [U_8030,U_8029,U_8028] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),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)))),U_8030))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8028),U_8029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8028),hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),U_8030)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),U_8030)))
| ~ class_Rings_Ocomm__semiring__1(U_8028) ),
inference(variable_rename,[status(thm)],[f_2336_1]) ).
fof(f_2336_3,plain,
! [U_8028,U_8029,U_8030] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),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)))),U_8030))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8028),U_8029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8028),hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),U_8030)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),U_8030)))
| ~ class_Rings_Ocomm__semiring__1(U_8028) ),
inference(definitional_conversion,[status(esa)],[f_2336_2]) ).
cnf(f_2336_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),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)))),U_8030))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8028),U_8029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8028),hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),U_8030)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8028),U_8029),U_8030)))
| ~ class_Rings_Ocomm__semiring__1(U_8028) ),
inference(clausify,[status(thm)],[f_2336_3]) ).
fof(f_2337_1,plain,
! [V_n,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))),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)
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__minus1__even]) ).
fof(f_2337_2,plain,
! [U_8032,U_8031] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8031),hAPP(c_Groups_Ouminus__class_Ouminus(U_8031),c_Groups_Oone__class_Oone(U_8031))),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)))),U_8032)) = c_Groups_Oone__class_Oone(U_8031)
| ~ class_Rings_Oring__1(U_8031) ),
inference(variable_rename,[status(thm)],[f_2337_1]) ).
fof(f_2337_3,plain,
! [U_8031,U_8032] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8031),hAPP(c_Groups_Ouminus__class_Ouminus(U_8031),c_Groups_Oone__class_Oone(U_8031))),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)))),U_8032)) = c_Groups_Oone__class_Oone(U_8031)
| ~ class_Rings_Oring__1(U_8031) ),
inference(definitional_conversion,[status(esa)],[f_2337_2]) ).
cnf(f_2337_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8031),hAPP(c_Groups_Ouminus__class_Ouminus(U_8031),c_Groups_Oone__class_Oone(U_8031))),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)))),U_8032)) = c_Groups_Oone__class_Oone(U_8031)
| ~ class_Rings_Oring__1(U_8031) ),
inference(clausify,[status(thm)],[f_2337_3]) ).
fof(f_2338_1,plain,
! [V_v,V_w] :
( ( 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))
| 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))) )
& ( 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))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__number__of__Bit1]) ).
fof(f_2338_2,plain,
! [U_8034,U_8033] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8034))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8033))) = 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),U_8034)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8033))
| 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),U_8033))) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8034))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8033))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8034)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8033))
| ~ 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),U_8033))) ) ),
inference(variable_rename,[status(thm)],[f_2338_1]) ).
fof(f_2338_3,plain,
( ! [U_8038,U_8036] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8038))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8036))) = 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),U_8038)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8036))
| 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),U_8036))) )
& ! [U_8037,U_8035] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8037))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8035))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8037)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8035))
| ~ 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),U_8035))) ) ),
inference(miniscope,[status(thm)],[f_2338_2]) ).
fof(f_2338_4,plain,
( ! [U_8036,U_8038] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8038))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8036))) = 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),U_8038)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8036))
| 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),U_8036))) )
& ! [U_8037,U_8035] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8037))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8035))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8037)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8035))
| ~ 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),U_8035))) ) ),
inference(definitional_conversion,[status(esa)],[f_2338_3]) ).
cnf(f_2338_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8037))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8035))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8037)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8035))
| ~ 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),U_8035))) ),
inference(clausify,[status(thm)],[f_2338_4]) ).
cnf(f_2338_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8038))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8036))) = 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),U_8038)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8036))
| 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),U_8036))) ),
inference(clausify,[status(thm)],[f_2338_4]) ).
fof(f_2339_1,plain,
! [V_m_2] :
( ( 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))))))
| 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) )
& ( 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)
| ~ 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)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_mod2__gr__0]) ).
fof(f_2339_2,plain,
! [U_8039] :
( ( 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,U_8039,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,U_8039,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) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8039,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)
| ~ 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,U_8039,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(variable_rename,[status(thm)],[f_2339_1]) ).
fof(f_2339_3,plain,
( ! [U_8041] :
( 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,U_8041,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,U_8041,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) )
& ! [U_8040] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8040,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)
| ~ 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,U_8040,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(miniscope,[status(thm)],[f_2339_2]) ).
fof(f_2339_4,plain,
( ! [U_8041] :
( 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,U_8041,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,U_8041,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) )
& ! [U_8040] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8040,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)
| ~ 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,U_8040,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(definitional_conversion,[status(esa)],[f_2339_3]) ).
cnf(f_2339_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8040,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)
| ~ 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,U_8040,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(clausify,[status(thm)],[f_2339_4]) ).
cnf(f_2339_6,plain,
( 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,U_8041,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,U_8041,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) ),
inference(clausify,[status(thm)],[f_2339_4]) ).
fof(f_2340_1,plain,
! [V_n] :
( 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))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__2__gt__zero]) ).
fof(f_2340_2,plain,
! [U_8042] :
( 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),U_8042),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_8042)) ),
inference(variable_rename,[status(thm)],[f_2340_1]) ).
fof(f_2340_3,plain,
! [U_8042] :
( 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),U_8042),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_8042)) ),
inference(definitional_conversion,[status(esa)],[f_2340_2]) ).
cnf(f_2340_4,plain,
( 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),U_8042),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_8042)) ),
inference(clausify,[status(thm)],[f_2340_3]) ).
fof(f_2341_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__diff]) ).
fof(f_2341_2,plain,
! [U_8045,U_8044,U_8043] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8043),U_8044),U_8045)),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(U_8043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8043),hAPP(hAPP(c_Power_Opower__class_Opower(U_8043),U_8044),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(U_8043),U_8045),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(U_8043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8043),hAPP(c_Int_Onumber__class_Onumber__of(U_8043),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8044)),U_8045))
| ~ class_Int_Onumber__ring(U_8043) ),
inference(variable_rename,[status(thm)],[f_2341_1]) ).
fof(f_2341_3,plain,
! [U_8043,U_8044,U_8045] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8043),U_8044),U_8045)),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(U_8043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8043),hAPP(hAPP(c_Power_Opower__class_Opower(U_8043),U_8044),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(U_8043),U_8045),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(U_8043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8043),hAPP(c_Int_Onumber__class_Onumber__of(U_8043),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8044)),U_8045))
| ~ class_Int_Onumber__ring(U_8043) ),
inference(definitional_conversion,[status(esa)],[f_2341_2]) ).
cnf(f_2341_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8043),U_8044),U_8045)),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(U_8043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8043),hAPP(hAPP(c_Power_Opower__class_Opower(U_8043),U_8044),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(U_8043),U_8045),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(U_8043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8043),hAPP(c_Int_Onumber__class_Onumber__of(U_8043),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8044)),U_8045))
| ~ class_Int_Onumber__ring(U_8043) ),
inference(clausify,[status(thm)],[f_2341_3]) ).
fof(f_2342_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ 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)))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le]) ).
fof(f_2342_2,plain,
! [U_8048,U_8047,U_8046] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),U_8047))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8046),U_8047),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)))),U_8048)))))
| ~ class_Rings_Olinordered__idom(U_8046) ),
inference(variable_rename,[status(thm)],[f_2342_1]) ).
fof(f_2342_3,plain,
! [U_8047,U_8046,U_8048] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),U_8047))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8046),U_8047),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)))),U_8048)))))
| ~ class_Rings_Olinordered__idom(U_8046) ),
inference(definitional_conversion,[status(esa)],[f_2342_2]) ).
cnf(f_2342_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),U_8047))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8046),U_8047),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)))),U_8048)))))
| ~ class_Rings_Olinordered__idom(U_8046) ),
inference(clausify,[status(thm)],[f_2342_3]) ).
fof(f_2343_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero]) ).
fof(f_2343_2,plain,
! [U_8051,U_8050,U_8049] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8049),hAPP(hAPP(c_Power_Opower__class_Opower(U_8049),U_8050),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)))),U_8051)))),c_Groups_Ozero__class_Ozero(U_8049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8049),U_8050),c_Groups_Ozero__class_Ozero(U_8049)))
| ~ class_Rings_Olinordered__idom(U_8049) ),
inference(variable_rename,[status(thm)],[f_2343_1]) ).
fof(f_2343_3,plain,
! [U_8049,U_8050,U_8051] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8049),hAPP(hAPP(c_Power_Opower__class_Opower(U_8049),U_8050),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)))),U_8051)))),c_Groups_Ozero__class_Ozero(U_8049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8049),U_8050),c_Groups_Ozero__class_Ozero(U_8049)))
| ~ class_Rings_Olinordered__idom(U_8049) ),
inference(definitional_conversion,[status(esa)],[f_2343_2]) ).
cnf(f_2343_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8049),hAPP(hAPP(c_Power_Opower__class_Opower(U_8049),U_8050),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)))),U_8051)))),c_Groups_Ozero__class_Ozero(U_8049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8049),U_8050),c_Groups_Ozero__class_Ozero(U_8049)))
| ~ class_Rings_Olinordered__idom(U_8049) ),
inference(clausify,[status(thm)],[f_2343_3]) ).
fof(f_2344_1,plain,
! [V_n,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))),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))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__minus1__odd]) ).
fof(f_2344_2,plain,
! [U_8053,U_8052] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8052),hAPP(c_Groups_Ouminus__class_Ouminus(U_8052),c_Groups_Oone__class_Oone(U_8052))),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)))),U_8053))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8052),c_Groups_Oone__class_Oone(U_8052))
| ~ class_Rings_Oring__1(U_8052) ),
inference(variable_rename,[status(thm)],[f_2344_1]) ).
fof(f_2344_3,plain,
! [U_8052,U_8053] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8052),hAPP(c_Groups_Ouminus__class_Ouminus(U_8052),c_Groups_Oone__class_Oone(U_8052))),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)))),U_8053))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8052),c_Groups_Oone__class_Oone(U_8052))
| ~ class_Rings_Oring__1(U_8052) ),
inference(definitional_conversion,[status(esa)],[f_2344_2]) ).
cnf(f_2344_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8052),hAPP(c_Groups_Ouminus__class_Ouminus(U_8052),c_Groups_Oone__class_Oone(U_8052))),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)))),U_8053))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8052),c_Groups_Oone__class_Oone(U_8052))
| ~ class_Rings_Oring__1(U_8052) ),
inference(clausify,[status(thm)],[f_2344_3]) ).
fof(f_2345_1,plain,
! [V_n,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__m1__even]) ).
fof(f_2345_2,plain,
! [U_8055,U_8054] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8054),hAPP(c_Int_Onumber__class_Onumber__of(U_8054),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)))),U_8055)) = c_Groups_Oone__class_Oone(U_8054)
| ~ class_Int_Onumber__ring(U_8054) ),
inference(variable_rename,[status(thm)],[f_2345_1]) ).
fof(f_2345_3,plain,
! [U_8054,U_8055] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8054),hAPP(c_Int_Onumber__class_Onumber__of(U_8054),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)))),U_8055)) = c_Groups_Oone__class_Oone(U_8054)
| ~ class_Int_Onumber__ring(U_8054) ),
inference(definitional_conversion,[status(esa)],[f_2345_2]) ).
cnf(f_2345_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8054),hAPP(c_Int_Onumber__class_Onumber__of(U_8054),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)))),U_8055)) = c_Groups_Oone__class_Oone(U_8054)
| ~ class_Int_Onumber__ring(U_8054) ),
inference(clausify,[status(thm)],[f_2345_3]) ).
fof(f_2346_1,plain,
! [V_n,T_a] :
( 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)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__m1__odd]) ).
fof(f_2346_2,plain,
! [U_8057,U_8056] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8056),hAPP(c_Int_Onumber__class_Onumber__of(U_8056),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)))),U_8057))) = hAPP(c_Int_Onumber__class_Onumber__of(U_8056),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_8056) ),
inference(variable_rename,[status(thm)],[f_2346_1]) ).
fof(f_2346_3,plain,
! [U_8056,U_8057] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8056),hAPP(c_Int_Onumber__class_Onumber__of(U_8056),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)))),U_8057))) = hAPP(c_Int_Onumber__class_Onumber__of(U_8056),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_8056) ),
inference(definitional_conversion,[status(esa)],[f_2346_2]) ).
cnf(f_2346_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8056),hAPP(c_Int_Onumber__class_Onumber__of(U_8056),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)))),U_8057))) = hAPP(c_Int_Onumber__class_Onumber__of(U_8056),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_8056) ),
inference(clausify,[status(thm)],[f_2346_3]) ).
fof(f_2347_1,plain,
! [V_n] :
( 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))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__n__div__2__gt__zero]) ).
fof(f_2347_2,plain,
! [U_8058] :
( 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),U_8058),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))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8058)) ),
inference(variable_rename,[status(thm)],[f_2347_1]) ).
fof(f_2347_3,plain,
! [U_8058] :
( 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),U_8058),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))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8058)) ),
inference(definitional_conversion,[status(esa)],[f_2347_2]) ).
cnf(f_2347_4,plain,
( 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),U_8058),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))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8058)) ),
inference(clausify,[status(thm)],[f_2347_3]) ).
fof(f_2348_1,plain,
! [V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__double]) ).
fof(f_2348_2,plain,
! [U_8060,U_8059] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),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)))),U_8060))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),hAPP(c_Int_Onat,U_8060))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),hAPP(c_Int_Onat,U_8060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8060))
| ~ class_Rings_Osemiring__1(U_8059) ),
inference(variable_rename,[status(thm)],[f_2348_1]) ).
fof(f_2348_3,plain,
! [U_8059,U_8060] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),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)))),U_8060))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),hAPP(c_Int_Onat,U_8060))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),hAPP(c_Int_Onat,U_8060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8060))
| ~ class_Rings_Osemiring__1(U_8059) ),
inference(definitional_conversion,[status(esa)],[f_2348_2]) ).
cnf(f_2348_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),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)))),U_8060))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),hAPP(c_Int_Onat,U_8060))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8059),hAPP(c_Int_Onat,U_8060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8060))
| ~ class_Rings_Osemiring__1(U_8059) ),
inference(clausify,[status(thm)],[f_2348_3]) ).
fof(f_2349_1,plain,
! [V_b,V_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2]) ).
fof(f_2349_2,plain,
! [U_8062,U_8061] :
( 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)))),U_8062)),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)))),U_8061)) = 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,U_8062,U_8061)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8061)) ),
inference(variable_rename,[status(thm)],[f_2349_1]) ).
fof(f_2349_3,plain,
! [U_8061,U_8062] :
( 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)))),U_8062)),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)))),U_8061)) = 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,U_8062,U_8061)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8061)) ),
inference(definitional_conversion,[status(esa)],[f_2349_2]) ).
cnf(f_2349_4,plain,
( 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)))),U_8062)),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)))),U_8061)) = 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,U_8062,U_8061)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8061)) ),
inference(clausify,[status(thm)],[f_2349_3]) ).
fof(f_2350_1,plain,
! [V_b,V_a] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2]) ).
fof(f_2350_2,plain,
! [U_8064,U_8063] :
( 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)))),U_8064))),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)))),U_8063)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8064),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8063)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2350_1]) ).
fof(f_2350_3,plain,
! [U_8063,U_8064] :
( 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)))),U_8064))),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)))),U_8063)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8064),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8063)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2350_2]) ).
cnf(f_2350_4,plain,
( 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)))),U_8064))),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)))),U_8063)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8064),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8063)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2350_3]) ).
fof(f_2351_1,plain,
! [V_k] :
( ( ( ( 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))
| 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) )
& ( 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))))))
| 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) ) )
| V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(fof_nnf,[status(thm)],[fact_int__of__code]) ).
fof(f_2351_2,plain,
! [U_8065] :
( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_8065) = 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),U_8065),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))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8065,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) )
& ( hAPP(c_Code__Numeral_Oint__of,U_8065) = 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),U_8065),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8065,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) ) )
| U_8065 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_Code__Numeral_Oint__of,U_8065) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_8065 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_2351_1]) ).
fof(f_2351_3,plain,
( ! [U_8067] :
( ( ( hAPP(c_Code__Numeral_Oint__of,U_8067) = 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),U_8067),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))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8067,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) )
& ( hAPP(c_Code__Numeral_Oint__of,U_8067) = 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),U_8067),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8067,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) ) )
| U_8067 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_8066] :
( hAPP(c_Code__Numeral_Oint__of,U_8066) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_8066 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_2351_2]) ).
fof(f_2351_4,plain,
( ! [U_8067] :
( hAPP(c_Code__Numeral_Oint__of,U_8067) = 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),U_8067),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))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8067,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)
| ~ sP721(U_8067) )
& ! [U_8067] :
( hAPP(c_Code__Numeral_Oint__of,U_8067) = 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),U_8067),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8067,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)
| ~ sP721(U_8067) )
& ! [U_8067] :
( sP721(U_8067)
| U_8067 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_8066] :
( hAPP(c_Code__Numeral_Oint__of,U_8066) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_8066 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP721])],[f_2351_3]) ).
cnf(f_2351_5,plain,
( hAPP(c_Code__Numeral_Oint__of,U_8066) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_8066 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2351_4]) ).
cnf(f_2351_6,plain,
( sP721(U_8067)
| U_8067 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2351_4]) ).
cnf(f_2351_7,plain,
( hAPP(c_Code__Numeral_Oint__of,U_8067) = 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),U_8067),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8067,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)
| ~ sP721(U_8067) ),
inference(clausify,[status(thm)],[f_2351_4]) ).
cnf(f_2351_8,plain,
( hAPP(c_Code__Numeral_Oint__of,U_8067) = 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),U_8067),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))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8067,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)
| ~ sP721(U_8067) ),
inference(clausify,[status(thm)],[f_2351_4]) ).
fof(f_2352_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_one__code__numeral__code]) ).
fof(f_2352_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_2352_1]) ).
cnf(f_2352_3,plain,
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)),
inference(clausify,[status(thm)],[f_2352_2]) ).
fof(f_2353_1,plain,
! [V_k_2,V_f_2,V_n_2] :
( ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
| ~ 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))
| ? [B_i] :
( ~ 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)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_int__val__lemma]) ).
fof(f_2353_2,plain,
! [U_8072,U_8071,U_8070] :
( ? [U_8069] :
( hAPP(U_8071,U_8069) = U_8072
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8069),U_8070)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8072),hAPP(U_8071,U_8070)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8071,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8072))
| ? [U_8068] :
( ~ 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(U_8071,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8068),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8071,U_8068)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8068),U_8070)) ) ),
inference(variable_rename,[status(thm)],[f_2353_1]) ).
fof(f_2353_3,plain,
! [U_8072,U_8071,U_8070] :
( ? [U_8069] :
( hAPP(U_8071,U_8069) = U_8072
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8069),U_8070)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8072),hAPP(U_8071,U_8070)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8071,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8072))
| ( ~ 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(U_8071,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK208(U_8072,U_8071,U_8070)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8071,sK208(U_8072,U_8071,U_8070))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK208(U_8072,U_8071,U_8070)),U_8070)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_8068,sK208(U_8072,U_8071,U_8070))],[f_2353_2]) ).
fof(f_2353_4,plain,
! [U_8072,U_8071,U_8070] :
( ( hAPP(U_8071,sK209(U_8072,U_8071,U_8070)) = U_8072
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK209(U_8072,U_8071,U_8070)),U_8070)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8072),hAPP(U_8071,U_8070)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8071,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8072))
| ( ~ 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(U_8071,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK208(U_8072,U_8071,U_8070)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8071,sK208(U_8072,U_8071,U_8070))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK208(U_8072,U_8071,U_8070)),U_8070)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_8069,sK209(U_8072,U_8071,U_8070))],[f_2353_3]) ).
fof(f_2353_5,plain,
( ! [U_8071,U_8072,U_8070] :
( hAPP(U_8071,sK209(U_8072,U_8071,U_8070)) = U_8072
| ~ sP723(U_8071,U_8072,U_8070) )
& ! [U_8071,U_8072,U_8070] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK209(U_8072,U_8071,U_8070)),U_8070))
| ~ sP723(U_8071,U_8072,U_8070) )
& ! [U_8071,U_8072,U_8070] :
( ~ 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(U_8071,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK208(U_8072,U_8071,U_8070)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8071,sK208(U_8072,U_8071,U_8070))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP722(U_8071,U_8072,U_8070) )
& ! [U_8071,U_8072,U_8070] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK208(U_8072,U_8071,U_8070)),U_8070))
| ~ sP722(U_8071,U_8072,U_8070) )
& ! [U_8071,U_8072,U_8070] :
( sP723(U_8071,U_8072,U_8070)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8072),hAPP(U_8071,U_8070)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8071,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8072))
| sP722(U_8071,U_8072,U_8070) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP722,sP723])],[f_2353_4]) ).
cnf(f_2353_6,plain,
( sP723(U_8071,U_8072,U_8070)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8072),hAPP(U_8071,U_8070)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8071,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8072))
| sP722(U_8071,U_8072,U_8070) ),
inference(clausify,[status(thm)],[f_2353_5]) ).
cnf(f_2353_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK208(U_8072,U_8071,U_8070)),U_8070))
| ~ sP722(U_8071,U_8072,U_8070) ),
inference(clausify,[status(thm)],[f_2353_5]) ).
cnf(f_2353_8,plain,
( ~ 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(U_8071,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK208(U_8072,U_8071,U_8070)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8071,sK208(U_8072,U_8071,U_8070))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP722(U_8071,U_8072,U_8070) ),
inference(clausify,[status(thm)],[f_2353_5]) ).
cnf(f_2353_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK209(U_8072,U_8071,U_8070)),U_8070))
| ~ sP723(U_8071,U_8072,U_8070) ),
inference(clausify,[status(thm)],[f_2353_5]) ).
cnf(f_2353_10,plain,
( hAPP(U_8071,sK209(U_8072,U_8071,U_8070)) = U_8072
| ~ sP723(U_8071,U_8072,U_8070) ),
inference(clausify,[status(thm)],[f_2353_5]) ).
fof(f_2354_1,plain,
! [V_k_2,V_f_2,V_n_2] :
( ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
| ~ 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))
| ? [B_i] :
( ~ 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)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat0__intermed__int__val]) ).
fof(f_2354_2,plain,
! [U_8077,U_8076,U_8075] :
( ? [U_8074] :
( hAPP(U_8076,U_8074) = U_8077
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8074),U_8075)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8077),hAPP(U_8076,U_8075)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8077))
| ? [U_8073] :
( ~ 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(U_8076,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8073),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8076,U_8073)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8073),U_8075)) ) ),
inference(variable_rename,[status(thm)],[f_2354_1]) ).
fof(f_2354_3,plain,
! [U_8077,U_8076,U_8075] :
( ? [U_8074] :
( hAPP(U_8076,U_8074) = U_8077
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8074),U_8075)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8077),hAPP(U_8076,U_8075)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8077))
| ( ~ 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(U_8076,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK210(U_8077,U_8076,U_8075)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8076,sK210(U_8077,U_8076,U_8075))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK210(U_8077,U_8076,U_8075)),U_8075)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_8073,sK210(U_8077,U_8076,U_8075))],[f_2354_2]) ).
fof(f_2354_4,plain,
! [U_8077,U_8076,U_8075] :
( ( hAPP(U_8076,sK211(U_8077,U_8076,U_8075)) = U_8077
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK211(U_8077,U_8076,U_8075)),U_8075)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8077),hAPP(U_8076,U_8075)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8077))
| ( ~ 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(U_8076,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK210(U_8077,U_8076,U_8075)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8076,sK210(U_8077,U_8076,U_8075))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK210(U_8077,U_8076,U_8075)),U_8075)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_8074,sK211(U_8077,U_8076,U_8075))],[f_2354_3]) ).
fof(f_2354_5,plain,
( ! [U_8075,U_8076,U_8077] :
( hAPP(U_8076,sK211(U_8077,U_8076,U_8075)) = U_8077
| ~ sP725(U_8075,U_8076,U_8077) )
& ! [U_8075,U_8076,U_8077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK211(U_8077,U_8076,U_8075)),U_8075))
| ~ sP725(U_8075,U_8076,U_8077) )
& ! [U_8075,U_8076,U_8077] :
( ~ 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(U_8076,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK210(U_8077,U_8076,U_8075)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8076,sK210(U_8077,U_8076,U_8075))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP724(U_8075,U_8076,U_8077) )
& ! [U_8075,U_8076,U_8077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK210(U_8077,U_8076,U_8075)),U_8075))
| ~ sP724(U_8075,U_8076,U_8077) )
& ! [U_8075,U_8076,U_8077] :
( sP725(U_8075,U_8076,U_8077)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8077),hAPP(U_8076,U_8075)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8077))
| sP724(U_8075,U_8076,U_8077) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP724,sP725])],[f_2354_4]) ).
cnf(f_2354_6,plain,
( sP725(U_8075,U_8076,U_8077)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8077),hAPP(U_8076,U_8075)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8077))
| sP724(U_8075,U_8076,U_8077) ),
inference(clausify,[status(thm)],[f_2354_5]) ).
cnf(f_2354_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK210(U_8077,U_8076,U_8075)),U_8075))
| ~ sP724(U_8075,U_8076,U_8077) ),
inference(clausify,[status(thm)],[f_2354_5]) ).
cnf(f_2354_8,plain,
( ~ 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(U_8076,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK210(U_8077,U_8076,U_8075)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8076,sK210(U_8077,U_8076,U_8075))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP724(U_8075,U_8076,U_8077) ),
inference(clausify,[status(thm)],[f_2354_5]) ).
cnf(f_2354_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK211(U_8077,U_8076,U_8075)),U_8075))
| ~ sP725(U_8075,U_8076,U_8077) ),
inference(clausify,[status(thm)],[f_2354_5]) ).
cnf(f_2354_10,plain,
( hAPP(U_8076,sK211(U_8077,U_8076,U_8075)) = U_8077
| ~ sP725(U_8075,U_8076,U_8077) ),
inference(clausify,[status(thm)],[f_2354_5]) ).
fof(f_2355_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_code__numeral__zero__minus__one]) ).
fof(f_2355_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_2355_1]) ).
cnf(f_2355_3,plain,
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),
inference(clausify,[status(thm)],[f_2355_2]) ).
fof(f_2356_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_zero__code__numeral__code]) ).
fof(f_2356_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_2356_1]) ).
cnf(f_2356_3,plain,
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),
inference(clausify,[status(thm)],[f_2356_2]) ).
fof(f_2357_1,plain,
! [V_n,V_i] :
( ( 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))
| V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n
| V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code]) ).
fof(f_2357_2,plain,
! [U_8079,U_8078] :
( ( c_Code__Numeral_Onat__of__aux(U_8078,U_8079) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8078),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_8079))
| U_8078 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( c_Code__Numeral_Onat__of__aux(U_8078,U_8079) = U_8079
| U_8078 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_2357_1]) ).
fof(f_2357_3,plain,
( ! [U_8083,U_8081] :
( c_Code__Numeral_Onat__of__aux(U_8081,U_8083) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8081),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_8083))
| U_8081 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_8082,U_8080] :
( c_Code__Numeral_Onat__of__aux(U_8080,U_8082) = U_8082
| U_8080 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_2357_2]) ).
fof(f_2357_4,plain,
( ! [U_8081,U_8083] :
( c_Code__Numeral_Onat__of__aux(U_8081,U_8083) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8081),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_8083))
| U_8081 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_8080,U_8082] :
( c_Code__Numeral_Onat__of__aux(U_8080,U_8082) = U_8082
| U_8080 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(definitional_conversion,[status(esa)],[f_2357_3]) ).
cnf(f_2357_5,plain,
( c_Code__Numeral_Onat__of__aux(U_8080,U_8082) = U_8082
| U_8080 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2357_4]) ).
cnf(f_2357_6,plain,
( c_Code__Numeral_Onat__of__aux(U_8081,U_8083) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8081),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_8083))
| U_8081 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2357_4]) ).
fof(f_2358_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I1_J]) ).
fof(f_2358_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_2358_1]) ).
cnf(f_2358_3,plain,
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),
inference(clausify,[status(thm)],[f_2358_2]) ).
fof(f_2359_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I3_J]) ).
fof(f_2359_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_2359_1]) ).
cnf(f_2359_3,plain,
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),
inference(clausify,[status(thm)],[f_2359_2]) ).
fof(f_2360_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).
fof(f_2360_2,plain,
! [U_8086,U_8085,U_8084] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8084,U_8085,U_8086,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_8085,
inference(variable_rename,[status(thm)],[f_2360_1]) ).
fof(f_2360_3,plain,
! [U_8084,U_8085,U_8086] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8084,U_8085,U_8086,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_8085,
inference(definitional_conversion,[status(esa)],[f_2360_2]) ).
cnf(f_2360_4,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8084,U_8085,U_8086,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_8085,
inference(clausify,[status(thm)],[f_2360_3]) ).
fof(f_2361_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I4_J]) ).
fof(f_2361_2,plain,
! [U_8087] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8087)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_8087)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2361_1]) ).
fof(f_2361_3,plain,
! [U_8087] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8087)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_8087)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2361_2]) ).
cnf(f_2361_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8087)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_8087)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2361_3]) ).
fof(f_2362_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I2_J]) ).
fof(f_2362_2,plain,
! [U_8088] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_8088)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_8088)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2362_1]) ).
fof(f_2362_3,plain,
! [U_8088] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_8088)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_8088)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2362_2]) ).
cnf(f_2362_4,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_8088)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_8088)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2362_3]) ).
fof(f_2363_1,plain,
! [V_y,V_n,V_x] :
( ? [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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) ),
inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma]) ).
fof(f_2363_2,plain,
! [U_8092,U_8091,U_8090] :
( ? [U_8089] : U_8090 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8091),U_8089))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8092),U_8090))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8090,U_8091) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8092,U_8091) ),
inference(variable_rename,[status(thm)],[f_2363_1]) ).
fof(f_2363_3,plain,
! [U_8092,U_8091,U_8090] :
( U_8090 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8091),sK212(U_8092,U_8091,U_8090)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8092),U_8090))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8090,U_8091) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8092,U_8091) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_8089,sK212(U_8092,U_8091,U_8090))],[f_2363_2]) ).
fof(f_2363_4,plain,
! [U_8090,U_8091,U_8092] :
( U_8090 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8091),sK212(U_8092,U_8091,U_8090)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8092),U_8090))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8090,U_8091) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8092,U_8091) ),
inference(definitional_conversion,[status(esa)],[f_2363_3]) ).
cnf(f_2363_5,plain,
( U_8090 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8091),sK212(U_8092,U_8091,U_8090)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8092),U_8090))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8090,U_8091) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8092,U_8091) ),
inference(clausify,[status(thm)],[f_2363_4]) ).
fof(f_2364_1,plain,
! [V_i_2,V_Pa_2,V_p_2] :
( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
| ~ hBOOL(hAPP(V_Pa_2,V_i_2))
| ? [B_i] :
( ~ hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))
& hBOOL(hAPP(V_Pa_2,B_i))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mod__induct__0]) ).
fof(f_2364_2,plain,
! [U_8096,U_8095,U_8094] :
( hBOOL(hAPP(U_8095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8096),U_8094))
| ~ hBOOL(hAPP(U_8095,U_8096))
| ? [U_8093] :
( ~ hBOOL(hAPP(U_8095,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8093),U_8094)))
& hBOOL(hAPP(U_8095,U_8093))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8093),U_8094)) ) ),
inference(variable_rename,[status(thm)],[f_2364_1]) ).
fof(f_2364_3,plain,
! [U_8096,U_8095,U_8094] :
( hBOOL(hAPP(U_8095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8096),U_8094))
| ~ hBOOL(hAPP(U_8095,U_8096))
| ( ~ hBOOL(hAPP(U_8095,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK213(U_8096,U_8095,U_8094)),U_8094)))
& hBOOL(hAPP(U_8095,sK213(U_8096,U_8095,U_8094)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK213(U_8096,U_8095,U_8094)),U_8094)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_8093,sK213(U_8096,U_8095,U_8094))],[f_2364_2]) ).
fof(f_2364_4,plain,
( ! [U_8094,U_8095,U_8096] :
( ~ hBOOL(hAPP(U_8095,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK213(U_8096,U_8095,U_8094)),U_8094)))
| ~ sP726(U_8094,U_8095,U_8096) )
& ! [U_8094,U_8095,U_8096] :
( hBOOL(hAPP(U_8095,sK213(U_8096,U_8095,U_8094)))
| ~ sP726(U_8094,U_8095,U_8096) )
& ! [U_8094,U_8095,U_8096] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK213(U_8096,U_8095,U_8094)),U_8094))
| ~ sP726(U_8094,U_8095,U_8096) )
& ! [U_8094,U_8095,U_8096] :
( hBOOL(hAPP(U_8095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8096),U_8094))
| ~ hBOOL(hAPP(U_8095,U_8096))
| sP726(U_8094,U_8095,U_8096) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP726])],[f_2364_3]) ).
cnf(f_2364_5,plain,
( hBOOL(hAPP(U_8095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8096),U_8094))
| ~ hBOOL(hAPP(U_8095,U_8096))
| sP726(U_8094,U_8095,U_8096) ),
inference(clausify,[status(thm)],[f_2364_4]) ).
cnf(f_2364_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK213(U_8096,U_8095,U_8094)),U_8094))
| ~ sP726(U_8094,U_8095,U_8096) ),
inference(clausify,[status(thm)],[f_2364_4]) ).
cnf(f_2364_7,plain,
( hBOOL(hAPP(U_8095,sK213(U_8096,U_8095,U_8094)))
| ~ sP726(U_8094,U_8095,U_8096) ),
inference(clausify,[status(thm)],[f_2364_4]) ).
cnf(f_2364_8,plain,
( ~ hBOOL(hAPP(U_8095,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK213(U_8096,U_8095,U_8094)),U_8094)))
| ~ sP726(U_8094,U_8095,U_8096) ),
inference(clausify,[status(thm)],[f_2364_4]) ).
fof(f_2365_1,plain,
! [V_code__numeral_H_2,V_code__numeral_2] :
( ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
| V_code__numeral_2 != V_code__numeral_H_2 )
& ( V_code__numeral_2 = V_code__numeral_H_2
| c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject]) ).
fof(f_2365_2,plain,
! [U_8098,U_8097] :
( ( c_Code__Numeral_OSuc__code__numeral(U_8097) = c_Code__Numeral_OSuc__code__numeral(U_8098)
| U_8097 != U_8098 )
& ( U_8097 = U_8098
| c_Code__Numeral_OSuc__code__numeral(U_8097) != c_Code__Numeral_OSuc__code__numeral(U_8098) ) ),
inference(variable_rename,[status(thm)],[f_2365_1]) ).
fof(f_2365_3,plain,
( ! [U_8102,U_8100] :
( c_Code__Numeral_OSuc__code__numeral(U_8100) = c_Code__Numeral_OSuc__code__numeral(U_8102)
| U_8100 != U_8102 )
& ! [U_8101,U_8099] :
( U_8099 = U_8101
| c_Code__Numeral_OSuc__code__numeral(U_8099) != c_Code__Numeral_OSuc__code__numeral(U_8101) ) ),
inference(miniscope,[status(thm)],[f_2365_2]) ).
fof(f_2365_4,plain,
( ! [U_8100,U_8102] :
( c_Code__Numeral_OSuc__code__numeral(U_8100) = c_Code__Numeral_OSuc__code__numeral(U_8102)
| U_8100 != U_8102 )
& ! [U_8099,U_8101] :
( U_8099 = U_8101
| c_Code__Numeral_OSuc__code__numeral(U_8099) != c_Code__Numeral_OSuc__code__numeral(U_8101) ) ),
inference(definitional_conversion,[status(esa)],[f_2365_3]) ).
cnf(f_2365_5,plain,
( U_8099 = U_8101
| c_Code__Numeral_OSuc__code__numeral(U_8099) != c_Code__Numeral_OSuc__code__numeral(U_8101) ),
inference(clausify,[status(thm)],[f_2365_4]) ).
cnf(f_2365_6,plain,
( c_Code__Numeral_OSuc__code__numeral(U_8100) = c_Code__Numeral_OSuc__code__numeral(U_8102)
| U_8100 != U_8102 ),
inference(clausify,[status(thm)],[f_2365_4]) ).
fof(f_2366_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).
fof(f_2366_2,plain,
! [U_8103] : c_Code__Numeral_OSuc__code__numeral(U_8103) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(variable_rename,[status(thm)],[f_2366_1]) ).
fof(f_2366_3,plain,
! [U_8103] : c_Code__Numeral_OSuc__code__numeral(U_8103) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(definitional_conversion,[status(esa)],[f_2366_2]) ).
cnf(f_2366_4,plain,
c_Code__Numeral_OSuc__code__numeral(U_8103) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_2366_3]) ).
fof(f_2367_1,plain,
! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).
fof(f_2367_2,plain,
! [U_8104] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_8104),
inference(variable_rename,[status(thm)],[f_2367_1]) ).
fof(f_2367_3,plain,
! [U_8104] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_8104),
inference(definitional_conversion,[status(esa)],[f_2367_2]) ).
cnf(f_2367_4,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_8104),
inference(clausify,[status(thm)],[f_2367_3]) ).
fof(f_2368_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).
fof(f_2368_2,plain,
! [U_8108,U_8107,U_8106,U_8105] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8105,U_8106,U_8107,c_Code__Numeral_OSuc__code__numeral(U_8108)) = hAPP(U_8107,U_8108),
inference(variable_rename,[status(thm)],[f_2368_1]) ).
fof(f_2368_3,plain,
! [U_8107,U_8105,U_8106,U_8108] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8105,U_8106,U_8107,c_Code__Numeral_OSuc__code__numeral(U_8108)) = hAPP(U_8107,U_8108),
inference(definitional_conversion,[status(esa)],[f_2368_2]) ).
cnf(f_2368_4,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8105,U_8106,U_8107,c_Code__Numeral_OSuc__code__numeral(U_8108)) = hAPP(U_8107,U_8108),
inference(clausify,[status(thm)],[f_2368_3]) ).
fof(f_2369_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).
fof(f_2369_2,plain,
! [U_8109] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8109)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_8109,
inference(variable_rename,[status(thm)],[f_2369_1]) ).
fof(f_2369_3,plain,
! [U_8109] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8109)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_8109,
inference(definitional_conversion,[status(esa)],[f_2369_2]) ).
cnf(f_2369_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8109)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_8109,
inference(clausify,[status(thm)],[f_2369_3]) ).
fof(f_2370_1,plain,
! [V_k_2,V_f_2,V_n_2,V_m_2] :
( ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| ? [B_i] :
( ~ 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)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__intermed__int__val]) ).
fof(f_2370_2,plain,
! [U_8115,U_8114,U_8113,U_8112] :
( ? [U_8111] :
( hAPP(U_8114,U_8111) = U_8115
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8111),U_8113))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),U_8111)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8115),hAPP(U_8114,U_8113)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8114,U_8112)),U_8115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8112),U_8113))
| ? [U_8110] :
( ~ 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(U_8114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8110),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8114,U_8110)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8110),U_8113))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),U_8110)) ) ),
inference(variable_rename,[status(thm)],[f_2370_1]) ).
fof(f_2370_3,plain,
! [U_8115,U_8114,U_8113,U_8112] :
( ? [U_8111] :
( hAPP(U_8114,U_8111) = U_8115
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8111),U_8113))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),U_8111)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8115),hAPP(U_8114,U_8113)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8114,U_8112)),U_8115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8112),U_8113))
| ( ~ 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(U_8114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK214(U_8115,U_8114,U_8113,U_8112)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8114,sK214(U_8115,U_8114,U_8113,U_8112))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK214(U_8115,U_8114,U_8113,U_8112)),U_8113))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),sK214(U_8115,U_8114,U_8113,U_8112))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_8110,sK214(U_8115,U_8114,U_8113,U_8112))],[f_2370_2]) ).
fof(f_2370_4,plain,
! [U_8115,U_8114,U_8113,U_8112] :
( ( hAPP(U_8114,sK215(U_8115,U_8114,U_8113,U_8112)) = U_8115
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK215(U_8115,U_8114,U_8113,U_8112)),U_8113))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),sK215(U_8115,U_8114,U_8113,U_8112))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8115),hAPP(U_8114,U_8113)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8114,U_8112)),U_8115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8112),U_8113))
| ( ~ 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(U_8114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK214(U_8115,U_8114,U_8113,U_8112)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8114,sK214(U_8115,U_8114,U_8113,U_8112))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK214(U_8115,U_8114,U_8113,U_8112)),U_8113))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),sK214(U_8115,U_8114,U_8113,U_8112))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_8111,sK215(U_8115,U_8114,U_8113,U_8112))],[f_2370_3]) ).
fof(f_2370_5,plain,
( ! [U_8112,U_8113,U_8114,U_8115] :
( hAPP(U_8114,sK215(U_8115,U_8114,U_8113,U_8112)) = U_8115
| ~ sP728(U_8112,U_8113,U_8114,U_8115) )
& ! [U_8112,U_8113,U_8114,U_8115] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK215(U_8115,U_8114,U_8113,U_8112)),U_8113))
| ~ sP728(U_8112,U_8113,U_8114,U_8115) )
& ! [U_8112,U_8113,U_8114,U_8115] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),sK215(U_8115,U_8114,U_8113,U_8112)))
| ~ sP728(U_8112,U_8113,U_8114,U_8115) )
& ! [U_8112,U_8113,U_8114,U_8115] :
( ~ 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(U_8114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK214(U_8115,U_8114,U_8113,U_8112)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8114,sK214(U_8115,U_8114,U_8113,U_8112))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP727(U_8112,U_8113,U_8114,U_8115) )
& ! [U_8112,U_8113,U_8114,U_8115] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK214(U_8115,U_8114,U_8113,U_8112)),U_8113))
| ~ sP727(U_8112,U_8113,U_8114,U_8115) )
& ! [U_8112,U_8113,U_8114,U_8115] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),sK214(U_8115,U_8114,U_8113,U_8112)))
| ~ sP727(U_8112,U_8113,U_8114,U_8115) )
& ! [U_8112,U_8113,U_8114,U_8115] :
( sP728(U_8112,U_8113,U_8114,U_8115)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8115),hAPP(U_8114,U_8113)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8114,U_8112)),U_8115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8112),U_8113))
| sP727(U_8112,U_8113,U_8114,U_8115) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP727,sP728])],[f_2370_4]) ).
cnf(f_2370_6,plain,
( sP728(U_8112,U_8113,U_8114,U_8115)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8115),hAPP(U_8114,U_8113)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8114,U_8112)),U_8115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8112),U_8113))
| sP727(U_8112,U_8113,U_8114,U_8115) ),
inference(clausify,[status(thm)],[f_2370_5]) ).
cnf(f_2370_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),sK214(U_8115,U_8114,U_8113,U_8112)))
| ~ sP727(U_8112,U_8113,U_8114,U_8115) ),
inference(clausify,[status(thm)],[f_2370_5]) ).
cnf(f_2370_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK214(U_8115,U_8114,U_8113,U_8112)),U_8113))
| ~ sP727(U_8112,U_8113,U_8114,U_8115) ),
inference(clausify,[status(thm)],[f_2370_5]) ).
cnf(f_2370_9,plain,
( ~ 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(U_8114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK214(U_8115,U_8114,U_8113,U_8112)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8114,sK214(U_8115,U_8114,U_8113,U_8112))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP727(U_8112,U_8113,U_8114,U_8115) ),
inference(clausify,[status(thm)],[f_2370_5]) ).
cnf(f_2370_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8112),sK215(U_8115,U_8114,U_8113,U_8112)))
| ~ sP728(U_8112,U_8113,U_8114,U_8115) ),
inference(clausify,[status(thm)],[f_2370_5]) ).
cnf(f_2370_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK215(U_8115,U_8114,U_8113,U_8112)),U_8113))
| ~ sP728(U_8112,U_8113,U_8114,U_8115) ),
inference(clausify,[status(thm)],[f_2370_5]) ).
cnf(f_2370_12,plain,
( hAPP(U_8114,sK215(U_8115,U_8114,U_8113,U_8112)) = U_8115
| ~ sP728(U_8112,U_8113,U_8114,U_8115) ),
inference(clausify,[status(thm)],[f_2370_5]) ).
fof(f_2371_1,plain,
! [V_i,V_b] :
( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
| 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))) )
& ( c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
& ~ 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))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_log_Osimps]) ).
fof(f_2371_2,plain,
! [U_8117,U_8116] :
( ( c_Random_Olog(U_8116,U_8117) = 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(U_8116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8117),U_8116)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8117),U_8116))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8116),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ( c_Random_Olog(U_8116,U_8117) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8117),U_8116))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8116),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(variable_rename,[status(thm)],[f_2371_1]) ).
fof(f_2371_3,plain,
( ! [U_8121,U_8119] :
( c_Random_Olog(U_8119,U_8121) = 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(U_8119,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8121),U_8119)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8121),U_8119))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8119),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ! [U_8120,U_8118] :
( c_Random_Olog(U_8118,U_8120) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8120),U_8118))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8118),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(miniscope,[status(thm)],[f_2371_2]) ).
fof(f_2371_4,plain,
( ! [U_8118,U_8120] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8120),U_8118))
| ~ sP729(U_8118,U_8120) )
& ! [U_8118,U_8120] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8118),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| ~ sP729(U_8118,U_8120) )
& ! [U_8121,U_8119] :
( c_Random_Olog(U_8119,U_8121) = 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(U_8119,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8121),U_8119)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8121),U_8119))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8119),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ! [U_8118,U_8120] :
( c_Random_Olog(U_8118,U_8120) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| sP729(U_8118,U_8120) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP729])],[f_2371_3]) ).
cnf(f_2371_5,plain,
( c_Random_Olog(U_8118,U_8120) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| sP729(U_8118,U_8120) ),
inference(clausify,[status(thm)],[f_2371_4]) ).
cnf(f_2371_6,plain,
( c_Random_Olog(U_8119,U_8121) = 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(U_8119,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8121),U_8119)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8121),U_8119))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8119),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
inference(clausify,[status(thm)],[f_2371_4]) ).
cnf(f_2371_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8118),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| ~ sP729(U_8118,U_8120) ),
inference(clausify,[status(thm)],[f_2371_4]) ).
cnf(f_2371_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8120),U_8118))
| ~ sP729(U_8118,U_8120) ),
inference(clausify,[status(thm)],[f_2371_4]) ).
fof(f_2372_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__div__decomp]) ).
fof(f_2372_2,plain,
! [U_8124,U_8123,U_8122] :
( U_8123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8122),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8122),U_8123),U_8124)),U_8124)),c_Divides_Odiv__class_Omod(U_8122,U_8123,U_8124))
| ~ class_Divides_Osemiring__div(U_8122) ),
inference(variable_rename,[status(thm)],[f_2372_1]) ).
fof(f_2372_3,plain,
! [U_8124,U_8123,U_8122] :
( U_8123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8122),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8122),U_8123),U_8124)),U_8124)),c_Divides_Odiv__class_Omod(U_8122,U_8123,U_8124))
| ~ class_Divides_Osemiring__div(U_8122) ),
inference(definitional_conversion,[status(esa)],[f_2372_2]) ).
cnf(f_2372_4,plain,
( U_8123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8122),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8122),U_8123),U_8124)),U_8124)),c_Divides_Odiv__class_Omod(U_8122,U_8123,U_8124))
| ~ class_Divides_Osemiring__div(U_8122) ),
inference(clausify,[status(thm)],[f_2372_3]) ).
fof(f_2373_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__pos]) ).
fof(f_2373_2,plain,
! [U_8129,U_8128,U_8127,U_8126] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8127,U_8126),U_8129),U_8128)))
| ? [U_8125] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),hAPP(U_8129,U_8125)))
& hBOOL(hAPP(hAPP(c_member(U_8127),U_8125),U_8128)) )
| ~ class_Rings_Olinordered__semidom(U_8126) ),
inference(variable_rename,[status(thm)],[f_2373_1]) ).
fof(f_2373_3,plain,
! [U_8129,U_8128,U_8127,U_8126] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8127,U_8126),U_8129),U_8128)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),hAPP(U_8129,sK216(U_8129,U_8128,U_8127,U_8126))))
& hBOOL(hAPP(hAPP(c_member(U_8127),sK216(U_8129,U_8128,U_8127,U_8126)),U_8128)) )
| ~ class_Rings_Olinordered__semidom(U_8126) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_8125,sK216(U_8129,U_8128,U_8127,U_8126))],[f_2373_2]) ).
fof(f_2373_4,plain,
( ! [U_8126,U_8127,U_8128,U_8129] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),hAPP(U_8129,sK216(U_8129,U_8128,U_8127,U_8126))))
| ~ sP730(U_8126,U_8127,U_8128,U_8129) )
& ! [U_8126,U_8127,U_8128,U_8129] :
( hBOOL(hAPP(hAPP(c_member(U_8127),sK216(U_8129,U_8128,U_8127,U_8126)),U_8128))
| ~ sP730(U_8126,U_8127,U_8128,U_8129) )
& ! [U_8126,U_8127,U_8128,U_8129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8127,U_8126),U_8129),U_8128)))
| sP730(U_8126,U_8127,U_8128,U_8129)
| ~ class_Rings_Olinordered__semidom(U_8126) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP730])],[f_2373_3]) ).
cnf(f_2373_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8127,U_8126),U_8129),U_8128)))
| sP730(U_8126,U_8127,U_8128,U_8129)
| ~ class_Rings_Olinordered__semidom(U_8126) ),
inference(clausify,[status(thm)],[f_2373_4]) ).
cnf(f_2373_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8127),sK216(U_8129,U_8128,U_8127,U_8126)),U_8128))
| ~ sP730(U_8126,U_8127,U_8128,U_8129) ),
inference(clausify,[status(thm)],[f_2373_4]) ).
cnf(f_2373_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),hAPP(U_8129,sK216(U_8129,U_8128,U_8127,U_8126))))
| ~ sP730(U_8126,U_8127,U_8128,U_8129) ),
inference(clausify,[status(thm)],[f_2373_4]) ).
fof(f_2374_1,plain,
! [V_r,V_l,V_k] :
( ( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) ) ),
inference(fof_nnf,[status(thm)],[fact_minus__shift__def]) ).
fof(f_2374_2,plain,
! [U_8132,U_8131,U_8130] :
( ( c_Random_Ominus__shift(U_8132,U_8130,U_8131) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8130),U_8131)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8130),U_8131)) )
& ( c_Random_Ominus__shift(U_8132,U_8130,U_8131) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8132),U_8130)),U_8131)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8130),U_8131)) ) ),
inference(variable_rename,[status(thm)],[f_2374_1]) ).
fof(f_2374_3,plain,
( ! [U_8138,U_8136,U_8134] :
( c_Random_Ominus__shift(U_8138,U_8134,U_8136) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8134),U_8136)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8134),U_8136)) )
& ! [U_8137,U_8135,U_8133] :
( c_Random_Ominus__shift(U_8137,U_8133,U_8135) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8137),U_8133)),U_8135)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8133),U_8135)) ) ),
inference(miniscope,[status(thm)],[f_2374_2]) ).
fof(f_2374_4,plain,
( ! [U_8136,U_8134,U_8138] :
( c_Random_Ominus__shift(U_8138,U_8134,U_8136) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8134),U_8136)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8134),U_8136)) )
& ! [U_8137,U_8135,U_8133] :
( c_Random_Ominus__shift(U_8137,U_8133,U_8135) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8137),U_8133)),U_8135)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8133),U_8135)) ) ),
inference(definitional_conversion,[status(esa)],[f_2374_3]) ).
cnf(f_2374_5,plain,
( c_Random_Ominus__shift(U_8137,U_8133,U_8135) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8137),U_8133)),U_8135)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8133),U_8135)) ),
inference(clausify,[status(thm)],[f_2374_4]) ).
cnf(f_2374_6,plain,
( c_Random_Ominus__shift(U_8138,U_8134,U_8136) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8134),U_8136)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8134),U_8136)) ),
inference(clausify,[status(thm)],[f_2374_4]) ).
fof(f_2375_1,plain,
! [V_k,V_v] :
( ( 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))
| V_v = V_k )
& ( c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| V_v != V_k ) ),
inference(fof_nnf,[status(thm)],[fact_inc__shift__def]) ).
fof(f_2375_2,plain,
! [U_8140,U_8139] :
( ( c_Random_Oinc__shift(U_8139,U_8140) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8140),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_8139 = U_8140 )
& ( c_Random_Oinc__shift(U_8139,U_8140) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_8139 != U_8140 ) ),
inference(variable_rename,[status(thm)],[f_2375_1]) ).
fof(f_2375_3,plain,
( ! [U_8144,U_8142] :
( c_Random_Oinc__shift(U_8142,U_8144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8144),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_8142 = U_8144 )
& ! [U_8143,U_8141] :
( c_Random_Oinc__shift(U_8141,U_8143) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_8141 != U_8143 ) ),
inference(miniscope,[status(thm)],[f_2375_2]) ).
fof(f_2375_4,plain,
( ! [U_8142,U_8144] :
( c_Random_Oinc__shift(U_8142,U_8144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8144),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_8142 = U_8144 )
& ! [U_8143,U_8141] :
( c_Random_Oinc__shift(U_8141,U_8143) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_8141 != U_8143 ) ),
inference(definitional_conversion,[status(esa)],[f_2375_3]) ).
cnf(f_2375_5,plain,
( c_Random_Oinc__shift(U_8141,U_8143) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_8141 != U_8143 ),
inference(clausify,[status(thm)],[f_2375_4]) ).
cnf(f_2375_6,plain,
( c_Random_Oinc__shift(U_8142,U_8144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8144),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_8142 = U_8144 ),
inference(clausify,[status(thm)],[f_2375_4]) ).
fof(f_2376_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__nonneg]) ).
fof(f_2376_2,plain,
! [U_8149,U_8148,U_8147,U_8146] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8146),c_Groups_Ozero__class_Ozero(U_8146)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8147,U_8146),U_8149),U_8148)))
| ? [U_8145] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8146),c_Groups_Ozero__class_Ozero(U_8146)),hAPP(U_8149,U_8145)))
& hBOOL(hAPP(hAPP(c_member(U_8147),U_8145),U_8148)) )
| ~ class_Rings_Olinordered__semidom(U_8146) ),
inference(variable_rename,[status(thm)],[f_2376_1]) ).
fof(f_2376_3,plain,
! [U_8149,U_8148,U_8147,U_8146] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8146),c_Groups_Ozero__class_Ozero(U_8146)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8147,U_8146),U_8149),U_8148)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8146),c_Groups_Ozero__class_Ozero(U_8146)),hAPP(U_8149,sK217(U_8149,U_8148,U_8147,U_8146))))
& hBOOL(hAPP(hAPP(c_member(U_8147),sK217(U_8149,U_8148,U_8147,U_8146)),U_8148)) )
| ~ class_Rings_Olinordered__semidom(U_8146) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_8145,sK217(U_8149,U_8148,U_8147,U_8146))],[f_2376_2]) ).
fof(f_2376_4,plain,
( ! [U_8146,U_8147,U_8148,U_8149] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8146),c_Groups_Ozero__class_Ozero(U_8146)),hAPP(U_8149,sK217(U_8149,U_8148,U_8147,U_8146))))
| ~ sP731(U_8146,U_8147,U_8148,U_8149) )
& ! [U_8146,U_8147,U_8148,U_8149] :
( hBOOL(hAPP(hAPP(c_member(U_8147),sK217(U_8149,U_8148,U_8147,U_8146)),U_8148))
| ~ sP731(U_8146,U_8147,U_8148,U_8149) )
& ! [U_8146,U_8147,U_8148,U_8149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8146),c_Groups_Ozero__class_Ozero(U_8146)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8147,U_8146),U_8149),U_8148)))
| sP731(U_8146,U_8147,U_8148,U_8149)
| ~ class_Rings_Olinordered__semidom(U_8146) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP731])],[f_2376_3]) ).
cnf(f_2376_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8146),c_Groups_Ozero__class_Ozero(U_8146)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8147,U_8146),U_8149),U_8148)))
| sP731(U_8146,U_8147,U_8148,U_8149)
| ~ class_Rings_Olinordered__semidom(U_8146) ),
inference(clausify,[status(thm)],[f_2376_4]) ).
cnf(f_2376_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8147),sK217(U_8149,U_8148,U_8147,U_8146)),U_8148))
| ~ sP731(U_8146,U_8147,U_8148,U_8149) ),
inference(clausify,[status(thm)],[f_2376_4]) ).
cnf(f_2376_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8146),c_Groups_Ozero__class_Ozero(U_8146)),hAPP(U_8149,sK217(U_8149,U_8148,U_8147,U_8146))))
| ~ sP731(U_8146,U_8147,U_8148,U_8149) ),
inference(clausify,[status(thm)],[f_2376_4]) ).
fof(f_2377_1,plain,
! [V_Pa_2,V_F_2,T_b] :
( hBOOL(hAPP(V_Pa_2,V_F_2))
| ? [B_x,B_F] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F)))
& hBOOL(hAPP(V_Pa_2,B_F))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
| ~ hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__induct]) ).
fof(f_2377_2,plain,
! [U_8154,U_8153,U_8152] :
( hBOOL(hAPP(U_8154,U_8153))
| ? [U_8151,U_8150] :
( ~ hBOOL(hAPP(U_8154,hAPP(hAPP(c_Set_Oinsert(U_8152),U_8151),U_8150)))
& hBOOL(hAPP(U_8154,U_8150))
& ~ hBOOL(hAPP(hAPP(c_member(U_8152),U_8151),U_8150))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),U_8150)) )
| ~ hBOOL(hAPP(U_8154,c_Orderings_Obot__class_Obot(tc_fun(U_8152,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),U_8153)) ),
inference(variable_rename,[status(thm)],[f_2377_1]) ).
fof(f_2377_3,plain,
! [U_8154,U_8153,U_8152] :
( hBOOL(hAPP(U_8154,U_8153))
| ? [U_8150] :
( ~ hBOOL(hAPP(U_8154,hAPP(hAPP(c_Set_Oinsert(U_8152),sK218(U_8154,U_8153,U_8152)),U_8150)))
& hBOOL(hAPP(U_8154,U_8150))
& ~ hBOOL(hAPP(hAPP(c_member(U_8152),sK218(U_8154,U_8153,U_8152)),U_8150))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),U_8150)) )
| ~ hBOOL(hAPP(U_8154,c_Orderings_Obot__class_Obot(tc_fun(U_8152,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),U_8153)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_8151,sK218(U_8154,U_8153,U_8152))],[f_2377_2]) ).
fof(f_2377_4,plain,
! [U_8154,U_8153,U_8152] :
( hBOOL(hAPP(U_8154,U_8153))
| ( ~ hBOOL(hAPP(U_8154,hAPP(hAPP(c_Set_Oinsert(U_8152),sK218(U_8154,U_8153,U_8152)),sK219(U_8154,U_8153,U_8152))))
& hBOOL(hAPP(U_8154,sK219(U_8154,U_8153,U_8152)))
& ~ hBOOL(hAPP(hAPP(c_member(U_8152),sK218(U_8154,U_8153,U_8152)),sK219(U_8154,U_8153,U_8152)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),sK219(U_8154,U_8153,U_8152))) )
| ~ hBOOL(hAPP(U_8154,c_Orderings_Obot__class_Obot(tc_fun(U_8152,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),U_8153)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_8150,sK219(U_8154,U_8153,U_8152))],[f_2377_3]) ).
fof(f_2377_5,plain,
( ! [U_8152,U_8153,U_8154] :
( ~ hBOOL(hAPP(U_8154,hAPP(hAPP(c_Set_Oinsert(U_8152),sK218(U_8154,U_8153,U_8152)),sK219(U_8154,U_8153,U_8152))))
| ~ sP732(U_8152,U_8153,U_8154) )
& ! [U_8152,U_8153,U_8154] :
( hBOOL(hAPP(U_8154,sK219(U_8154,U_8153,U_8152)))
| ~ sP732(U_8152,U_8153,U_8154) )
& ! [U_8152,U_8153,U_8154] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8152),sK218(U_8154,U_8153,U_8152)),sK219(U_8154,U_8153,U_8152)))
| ~ sP732(U_8152,U_8153,U_8154) )
& ! [U_8152,U_8153,U_8154] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),sK219(U_8154,U_8153,U_8152)))
| ~ sP732(U_8152,U_8153,U_8154) )
& ! [U_8152,U_8153,U_8154] :
( hBOOL(hAPP(U_8154,U_8153))
| sP732(U_8152,U_8153,U_8154)
| ~ hBOOL(hAPP(U_8154,c_Orderings_Obot__class_Obot(tc_fun(U_8152,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),U_8153)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP732])],[f_2377_4]) ).
cnf(f_2377_6,plain,
( hBOOL(hAPP(U_8154,U_8153))
| sP732(U_8152,U_8153,U_8154)
| ~ hBOOL(hAPP(U_8154,c_Orderings_Obot__class_Obot(tc_fun(U_8152,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),U_8153)) ),
inference(clausify,[status(thm)],[f_2377_5]) ).
cnf(f_2377_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8152),sK219(U_8154,U_8153,U_8152)))
| ~ sP732(U_8152,U_8153,U_8154) ),
inference(clausify,[status(thm)],[f_2377_5]) ).
cnf(f_2377_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8152),sK218(U_8154,U_8153,U_8152)),sK219(U_8154,U_8153,U_8152)))
| ~ sP732(U_8152,U_8153,U_8154) ),
inference(clausify,[status(thm)],[f_2377_5]) ).
cnf(f_2377_9,plain,
( hBOOL(hAPP(U_8154,sK219(U_8154,U_8153,U_8152)))
| ~ sP732(U_8152,U_8153,U_8154) ),
inference(clausify,[status(thm)],[f_2377_5]) ).
cnf(f_2377_10,plain,
( ~ hBOOL(hAPP(U_8154,hAPP(hAPP(c_Set_Oinsert(U_8152),sK218(U_8154,U_8153,U_8152)),sK219(U_8154,U_8153,U_8152))))
| ~ sP732(U_8152,U_8153,U_8154) ),
inference(clausify,[status(thm)],[f_2377_5]) ).
fof(f_2378_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__antimono]) ).
fof(f_2378_2,plain,
! [U_8157,U_8156,U_8155] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),hAPP(c_Finite__Set_Ofold1(U_8155,c_Orderings_Oord__class_Omin(U_8155)),U_8157)),hAPP(c_Finite__Set_Ofold1(U_8155,c_Orderings_Oord__class_Omin(U_8155)),U_8156)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8155),U_8157))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8155,tc_HOL_Obool)),U_8156),U_8157))
| U_8156 = c_Orderings_Obot__class_Obot(tc_fun(U_8155,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_8155) ),
inference(variable_rename,[status(thm)],[f_2378_1]) ).
fof(f_2378_3,plain,
! [U_8157,U_8155,U_8156] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),hAPP(c_Finite__Set_Ofold1(U_8155,c_Orderings_Oord__class_Omin(U_8155)),U_8157)),hAPP(c_Finite__Set_Ofold1(U_8155,c_Orderings_Oord__class_Omin(U_8155)),U_8156)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8155),U_8157))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8155,tc_HOL_Obool)),U_8156),U_8157))
| U_8156 = c_Orderings_Obot__class_Obot(tc_fun(U_8155,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_8155) ),
inference(definitional_conversion,[status(esa)],[f_2378_2]) ).
cnf(f_2378_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),hAPP(c_Finite__Set_Ofold1(U_8155,c_Orderings_Oord__class_Omin(U_8155)),U_8157)),hAPP(c_Finite__Set_Ofold1(U_8155,c_Orderings_Oord__class_Omin(U_8155)),U_8156)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8155),U_8157))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8155,tc_HOL_Obool)),U_8156),U_8157))
| U_8156 = c_Orderings_Obot__class_Obot(tc_fun(U_8155,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_8155) ),
inference(clausify,[status(thm)],[f_2378_3]) ).
fof(f_2379_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ? [B_e] :
( ~ 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)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) )
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__le__epsilon]) ).
fof(f_2379_2,plain,
! [U_8161,U_8160,U_8159] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8159),U_8160),U_8161))
| ? [U_8158] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8159),U_8160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8159),U_8161),U_8158)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),c_Groups_Ozero__class_Ozero(U_8159)),U_8158)) )
| ~ class_Fields_Olinordered__field(U_8159) ),
inference(variable_rename,[status(thm)],[f_2379_1]) ).
fof(f_2379_3,plain,
! [U_8161,U_8160,U_8159] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8159),U_8160),U_8161))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8159),U_8160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8159),U_8161),sK220(U_8161,U_8160,U_8159))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),c_Groups_Ozero__class_Ozero(U_8159)),sK220(U_8161,U_8160,U_8159))) )
| ~ class_Fields_Olinordered__field(U_8159) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_8158,sK220(U_8161,U_8160,U_8159))],[f_2379_2]) ).
fof(f_2379_4,plain,
( ! [U_8159,U_8160,U_8161] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8159),U_8160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8159),U_8161),sK220(U_8161,U_8160,U_8159))))
| ~ sP733(U_8159,U_8160,U_8161) )
& ! [U_8159,U_8160,U_8161] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),c_Groups_Ozero__class_Ozero(U_8159)),sK220(U_8161,U_8160,U_8159)))
| ~ sP733(U_8159,U_8160,U_8161) )
& ! [U_8159,U_8160,U_8161] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8159),U_8160),U_8161))
| sP733(U_8159,U_8160,U_8161)
| ~ class_Fields_Olinordered__field(U_8159) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP733])],[f_2379_3]) ).
cnf(f_2379_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8159),U_8160),U_8161))
| sP733(U_8159,U_8160,U_8161)
| ~ class_Fields_Olinordered__field(U_8159) ),
inference(clausify,[status(thm)],[f_2379_4]) ).
cnf(f_2379_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),c_Groups_Ozero__class_Ozero(U_8159)),sK220(U_8161,U_8160,U_8159)))
| ~ sP733(U_8159,U_8160,U_8161) ),
inference(clausify,[status(thm)],[f_2379_4]) ).
cnf(f_2379_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8159),U_8160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8159),U_8161),sK220(U_8161,U_8160,U_8159))))
| ~ sP733(U_8159,U_8160,U_8161) ),
inference(clausify,[status(thm)],[f_2379_4]) ).
fof(f_2380_1,plain,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[fact_subtract__code__numeral__def]) ).
fof(f_2380_2,plain,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(definitional_conversion,[status(esa)],[f_2380_1]) ).
cnf(f_2380_3,plain,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_2380_2]) ).
fof(f_2381_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_minus__code__numeral__code]) ).
fof(f_2381_2,plain,
! [U_8163,U_8162] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8162),U_8163) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_8162),U_8163),
inference(variable_rename,[status(thm)],[f_2381_1]) ).
fof(f_2381_3,plain,
! [U_8162,U_8163] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8162),U_8163) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_8162),U_8163),
inference(definitional_conversion,[status(esa)],[f_2381_2]) ).
cnf(f_2381_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8162),U_8163) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_8162),U_8163),
inference(clausify,[status(thm)],[f_2381_3]) ).
fof(f_2382_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_min__0R]) ).
fof(f_2382_2,plain,
! [U_8164] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8164),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_2382_1]) ).
fof(f_2382_3,plain,
! [U_8164] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8164),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_2382_2]) ).
cnf(f_2382_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8164),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2382_3]) ).
fof(f_2383_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_min__0L]) ).
fof(f_2383_2,plain,
! [U_8165] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8165) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_2383_1]) ).
fof(f_2383_3,plain,
! [U_8165] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8165) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_2383_2]) ).
cnf(f_2383_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8165) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2383_3]) ).
fof(f_2384_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf]) ).
fof(f_2384_2,plain,
! [U_8166] :
( c_Finite__Set_Ofun__left__comm__idem(U_8166,U_8166,c_Orderings_Oord__class_Omin(U_8166))
| ~ class_Orderings_Olinorder(U_8166) ),
inference(variable_rename,[status(thm)],[f_2384_1]) ).
fof(f_2384_3,plain,
! [U_8166] :
( c_Finite__Set_Ofun__left__comm__idem(U_8166,U_8166,c_Orderings_Oord__class_Omin(U_8166))
| ~ class_Orderings_Olinorder(U_8166) ),
inference(definitional_conversion,[status(esa)],[f_2384_2]) ).
cnf(f_2384_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_8166,U_8166,c_Orderings_Oord__class_Omin(U_8166))
| ~ class_Orderings_Olinorder(U_8166) ),
inference(clausify,[status(thm)],[f_2384_3]) ).
fof(f_2385_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_min__Suc__Suc]) ).
fof(f_2385_2,plain,
! [U_8168,U_8167] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8167)),hAPP(c_Nat_OSuc,U_8168)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8167),U_8168)),
inference(variable_rename,[status(thm)],[f_2385_1]) ).
fof(f_2385_3,plain,
! [U_8167,U_8168] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8167)),hAPP(c_Nat_OSuc,U_8168)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8167),U_8168)),
inference(definitional_conversion,[status(esa)],[f_2385_2]) ).
cnf(f_2385_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8167)),hAPP(c_Nat_OSuc,U_8168)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8167),U_8168)),
inference(clausify,[status(thm)],[f_2385_3]) ).
fof(f_2386_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oidem]) ).
fof(f_2386_2,plain,
! [U_8170,U_8169] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8169),U_8170),U_8170) = U_8170
| ~ class_Orderings_Olinorder(U_8169) ),
inference(variable_rename,[status(thm)],[f_2386_1]) ).
fof(f_2386_3,plain,
! [U_8169,U_8170] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8169),U_8170),U_8170) = U_8170
| ~ class_Orderings_Olinorder(U_8169) ),
inference(definitional_conversion,[status(esa)],[f_2386_2]) ).
cnf(f_2386_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8169),U_8170),U_8170) = U_8170
| ~ class_Orderings_Olinorder(U_8169) ),
inference(clausify,[status(thm)],[f_2386_3]) ).
fof(f_2387_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem]) ).
fof(f_2387_2,plain,
! [U_8172,U_8171] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8171),U_8172),U_8172) = U_8172
| ~ class_Orderings_Olinorder(U_8171) ),
inference(variable_rename,[status(thm)],[f_2387_1]) ).
fof(f_2387_3,plain,
! [U_8171,U_8172] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8171),U_8172),U_8172) = U_8172
| ~ class_Orderings_Olinorder(U_8171) ),
inference(definitional_conversion,[status(esa)],[f_2387_2]) ).
cnf(f_2387_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8171),U_8172),U_8172) = U_8172
| ~ class_Orderings_Olinorder(U_8171) ),
inference(clausify,[status(thm)],[f_2387_3]) ).
fof(f_2388_1,plain,
! [V_b,V_a,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_b),V_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute]) ).
fof(f_2388_2,plain,
! [U_8175,U_8174,U_8173] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8173),U_8174),U_8175) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8173),U_8175),U_8174)
| ~ class_Orderings_Olinorder(U_8173) ),
inference(variable_rename,[status(thm)],[f_2388_1]) ).
fof(f_2388_3,plain,
! [U_8173,U_8174,U_8175] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8173),U_8174),U_8175) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8173),U_8175),U_8174)
| ~ class_Orderings_Olinorder(U_8173) ),
inference(definitional_conversion,[status(esa)],[f_2388_2]) ).
cnf(f_2388_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8173),U_8174),U_8175) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8173),U_8175),U_8174)
| ~ class_Orderings_Olinorder(U_8173) ),
inference(clausify,[status(thm)],[f_2388_3]) ).
fof(f_2389_1,plain,
! [V_y,V_x,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_y),V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute]) ).
fof(f_2389_2,plain,
! [U_8178,U_8177,U_8176] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8176),U_8177),U_8178) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8176),U_8178),U_8177)
| ~ class_Orderings_Olinorder(U_8176) ),
inference(variable_rename,[status(thm)],[f_2389_1]) ).
fof(f_2389_3,plain,
! [U_8176,U_8177,U_8178] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8176),U_8177),U_8178) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8176),U_8178),U_8177)
| ~ class_Orderings_Olinorder(U_8176) ),
inference(definitional_conversion,[status(esa)],[f_2389_2]) ).
cnf(f_2389_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8176),U_8177),U_8178) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8176),U_8178),U_8177)
| ~ class_Orderings_Olinorder(U_8176) ),
inference(clausify,[status(thm)],[f_2389_3]) ).
fof(f_2390_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem]) ).
fof(f_2390_2,plain,
! [U_8181,U_8180,U_8179] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),U_8181)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),U_8181)
| ~ class_Orderings_Olinorder(U_8179) ),
inference(variable_rename,[status(thm)],[f_2390_1]) ).
fof(f_2390_3,plain,
! [U_8179,U_8180,U_8181] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),U_8181)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),U_8181)
| ~ class_Orderings_Olinorder(U_8179) ),
inference(definitional_conversion,[status(esa)],[f_2390_2]) ).
cnf(f_2390_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),U_8181)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8179),U_8180),U_8181)
| ~ class_Orderings_Olinorder(U_8179) ),
inference(clausify,[status(thm)],[f_2390_3]) ).
fof(f_2391_1,plain,
! [V_y,V_x,T_a] :
( 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)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem]) ).
fof(f_2391_2,plain,
! [U_8184,U_8183,U_8182] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),U_8184)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),U_8184)
| ~ class_Orderings_Olinorder(U_8182) ),
inference(variable_rename,[status(thm)],[f_2391_1]) ).
fof(f_2391_3,plain,
! [U_8182,U_8183,U_8184] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),U_8184)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),U_8184)
| ~ class_Orderings_Olinorder(U_8182) ),
inference(definitional_conversion,[status(esa)],[f_2391_2]) ).
cnf(f_2391_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),U_8184)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8182),U_8183),U_8184)
| ~ class_Orderings_Olinorder(U_8182) ),
inference(clausify,[status(thm)],[f_2391_3]) ).
fof(f_2392_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute]) ).
fof(f_2392_2,plain,
! [U_8188,U_8187,U_8186,U_8185] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8186),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8187),U_8188)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8187),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8186),U_8188))
| ~ class_Orderings_Olinorder(U_8185) ),
inference(variable_rename,[status(thm)],[f_2392_1]) ).
fof(f_2392_3,plain,
! [U_8185,U_8186,U_8187,U_8188] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8186),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8187),U_8188)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8187),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8186),U_8188))
| ~ class_Orderings_Olinorder(U_8185) ),
inference(definitional_conversion,[status(esa)],[f_2392_2]) ).
cnf(f_2392_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8186),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8187),U_8188)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8187),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8185),U_8186),U_8188))
| ~ class_Orderings_Olinorder(U_8185) ),
inference(clausify,[status(thm)],[f_2392_3]) ).
fof(f_2393_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute]) ).
fof(f_2393_2,plain,
! [U_8192,U_8191,U_8190,U_8189] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8190),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8191),U_8192)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8191),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8190),U_8192))
| ~ class_Orderings_Olinorder(U_8189) ),
inference(variable_rename,[status(thm)],[f_2393_1]) ).
fof(f_2393_3,plain,
! [U_8189,U_8190,U_8191,U_8192] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8190),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8191),U_8192)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8191),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8190),U_8192))
| ~ class_Orderings_Olinorder(U_8189) ),
inference(definitional_conversion,[status(esa)],[f_2393_2]) ).
cnf(f_2393_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8190),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8191),U_8192)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8191),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8189),U_8190),U_8192))
| ~ class_Orderings_Olinorder(U_8189) ),
inference(clausify,[status(thm)],[f_2393_3]) ).
fof(f_2394_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc]) ).
fof(f_2394_2,plain,
! [U_8196,U_8195,U_8194,U_8193] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8194),U_8195)),U_8196) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8194),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8195),U_8196))
| ~ class_Orderings_Olinorder(U_8193) ),
inference(variable_rename,[status(thm)],[f_2394_1]) ).
fof(f_2394_3,plain,
! [U_8193,U_8194,U_8195,U_8196] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8194),U_8195)),U_8196) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8194),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8195),U_8196))
| ~ class_Orderings_Olinorder(U_8193) ),
inference(definitional_conversion,[status(esa)],[f_2394_2]) ).
cnf(f_2394_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8194),U_8195)),U_8196) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8194),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8193),U_8195),U_8196))
| ~ class_Orderings_Olinorder(U_8193) ),
inference(clausify,[status(thm)],[f_2394_3]) ).
fof(f_2395_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc]) ).
fof(f_2395_2,plain,
! [U_8200,U_8199,U_8198,U_8197] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8198),U_8199)),U_8200) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8198),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8199),U_8200))
| ~ class_Orderings_Olinorder(U_8197) ),
inference(variable_rename,[status(thm)],[f_2395_1]) ).
fof(f_2395_3,plain,
! [U_8197,U_8198,U_8199,U_8200] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8198),U_8199)),U_8200) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8198),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8199),U_8200))
| ~ class_Orderings_Olinorder(U_8197) ),
inference(definitional_conversion,[status(esa)],[f_2395_2]) ).
cnf(f_2395_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8198),U_8199)),U_8200) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8198),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8197),U_8199),U_8200))
| ~ class_Orderings_Olinorder(U_8197) ),
inference(clausify,[status(thm)],[f_2395_3]) ).
fof(f_2396_1,plain,
! [T_b] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__min]) ).
fof(f_2396_2,plain,
! [U_8201] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_8201) = c_Orderings_Oord__class_Omin(U_8201)
| ~ class_Orderings_Olinorder(U_8201)
| ~ class_Lattices_Osemilattice__inf(U_8201) ),
inference(variable_rename,[status(thm)],[f_2396_1]) ).
fof(f_2396_3,plain,
! [U_8201] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_8201) = c_Orderings_Oord__class_Omin(U_8201)
| ~ class_Orderings_Olinorder(U_8201)
| ~ class_Lattices_Osemilattice__inf(U_8201) ),
inference(definitional_conversion,[status(esa)],[f_2396_2]) ).
cnf(f_2396_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_8201) = c_Orderings_Oord__class_Omin(U_8201)
| ~ class_Orderings_Olinorder(U_8201)
| ~ class_Lattices_Osemilattice__inf(U_8201) ),
inference(clausify,[status(thm)],[f_2396_3]) ).
fof(f_2397_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_min__diff]) ).
fof(f_2397_2,plain,
! [U_8204,U_8203,U_8202] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8202),U_8203)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8204),U_8203)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8202),U_8204)),U_8203),
inference(variable_rename,[status(thm)],[f_2397_1]) ).
fof(f_2397_3,plain,
! [U_8202,U_8203,U_8204] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8202),U_8203)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8204),U_8203)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8202),U_8204)),U_8203),
inference(definitional_conversion,[status(esa)],[f_2397_2]) ).
cnf(f_2397_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8202),U_8203)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8204),U_8203)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8202),U_8204)),U_8203),
inference(clausify,[status(thm)],[f_2397_3]) ).
fof(f_2398_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left]) ).
fof(f_2398_2,plain,
! [U_8208,U_8207,U_8206,U_8205] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8205),U_8206),U_8207)),U_8208) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),U_8206),U_8208)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),U_8207),U_8208))
| ~ class_Groups_Oordered__ab__group__add(U_8205) ),
inference(variable_rename,[status(thm)],[f_2398_1]) ).
fof(f_2398_3,plain,
! [U_8205,U_8206,U_8207,U_8208] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8205),U_8206),U_8207)),U_8208) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),U_8206),U_8208)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),U_8207),U_8208))
| ~ class_Groups_Oordered__ab__group__add(U_8205) ),
inference(definitional_conversion,[status(esa)],[f_2398_2]) ).
cnf(f_2398_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8205),U_8206),U_8207)),U_8208) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),U_8206),U_8208)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8205),U_8207),U_8208))
| ~ class_Groups_Oordered__ab__group__add(U_8205) ),
inference(clausify,[status(thm)],[f_2398_3]) ).
fof(f_2399_1,plain,
! [V_b,V_a,V_x,T_a] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) )
| ~ 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)))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infE]) ).
fof(f_2399_2,plain,
! [U_8212,U_8211,U_8210,U_8209] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),U_8212))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),U_8211)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8209),U_8211),U_8212)))
| ~ class_Orderings_Olinorder(U_8209) ),
inference(variable_rename,[status(thm)],[f_2399_1]) ).
fof(f_2399_3,plain,
( ! [U_8209,U_8210,U_8211,U_8212] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),U_8212))
| ~ sP734(U_8209,U_8210,U_8211,U_8212) )
& ! [U_8209,U_8210,U_8211,U_8212] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),U_8211))
| ~ sP734(U_8209,U_8210,U_8211,U_8212) )
& ! [U_8209,U_8210,U_8211,U_8212] :
( sP734(U_8209,U_8210,U_8211,U_8212)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8209),U_8211),U_8212)))
| ~ class_Orderings_Olinorder(U_8209) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP734])],[f_2399_2]) ).
cnf(f_2399_4,plain,
( sP734(U_8209,U_8210,U_8211,U_8212)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8209),U_8211),U_8212)))
| ~ class_Orderings_Olinorder(U_8209) ),
inference(clausify,[status(thm)],[f_2399_3]) ).
cnf(f_2399_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),U_8211))
| ~ sP734(U_8209,U_8210,U_8211,U_8212) ),
inference(clausify,[status(thm)],[f_2399_3]) ).
cnf(f_2399_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8209),U_8210),U_8212))
| ~ sP734(U_8209,U_8210,U_8211,U_8212) ),
inference(clausify,[status(thm)],[f_2399_3]) ).
fof(f_2400_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono]) ).
fof(f_2400_2,plain,
! [U_8217,U_8216,U_8215,U_8214,U_8213] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8213),U_8214),U_8216)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8213),U_8215),U_8217)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),U_8216),U_8217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),U_8214),U_8215))
| ~ class_Orderings_Olinorder(U_8213) ),
inference(variable_rename,[status(thm)],[f_2400_1]) ).
fof(f_2400_3,plain,
! [U_8214,U_8213,U_8215,U_8216,U_8217] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8213),U_8214),U_8216)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8213),U_8215),U_8217)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),U_8216),U_8217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),U_8214),U_8215))
| ~ class_Orderings_Olinorder(U_8213) ),
inference(definitional_conversion,[status(esa)],[f_2400_2]) ).
cnf(f_2400_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8213),U_8214),U_8216)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8213),U_8215),U_8217)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),U_8216),U_8217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8213),U_8214),U_8215))
| ~ class_Orderings_Olinorder(U_8213) ),
inference(clausify,[status(thm)],[f_2400_3]) ).
fof(f_2401_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest]) ).
fof(f_2401_2,plain,
! [U_8221,U_8220,U_8219,U_8218] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8218),U_8220),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),U_8221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),U_8220))
| ~ class_Orderings_Olinorder(U_8218) ),
inference(variable_rename,[status(thm)],[f_2401_1]) ).
fof(f_2401_3,plain,
! [U_8218,U_8219,U_8220,U_8221] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8218),U_8220),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),U_8221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),U_8220))
| ~ class_Orderings_Olinorder(U_8218) ),
inference(definitional_conversion,[status(esa)],[f_2401_2]) ).
cnf(f_2401_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8218),U_8220),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),U_8221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8218),U_8219),U_8220))
| ~ class_Orderings_Olinorder(U_8218) ),
inference(clausify,[status(thm)],[f_2401_3]) ).
fof(f_2402_1,plain,
! [V_b,V_a,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI]) ).
fof(f_2402_2,plain,
! [U_8225,U_8224,U_8223,U_8222] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8222),U_8224),U_8225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),U_8225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),U_8224))
| ~ class_Orderings_Olinorder(U_8222) ),
inference(variable_rename,[status(thm)],[f_2402_1]) ).
fof(f_2402_3,plain,
! [U_8222,U_8223,U_8224,U_8225] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8222),U_8224),U_8225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),U_8225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),U_8224))
| ~ class_Orderings_Olinorder(U_8222) ),
inference(definitional_conversion,[status(esa)],[f_2402_2]) ).
cnf(f_2402_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8222),U_8224),U_8225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),U_8225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8222),U_8223),U_8224))
| ~ class_Orderings_Olinorder(U_8222) ),
inference(clausify,[status(thm)],[f_2402_3]) ).
fof(f_2403_1,plain,
! [V_x,V_y,T_a] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2]) ).
fof(f_2403_2,plain,
! [U_8228,U_8227,U_8226] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8226),U_8228),U_8227) = U_8227
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8226),U_8227),U_8228))
| ~ class_Orderings_Olinorder(U_8226) ),
inference(variable_rename,[status(thm)],[f_2403_1]) ).
fof(f_2403_3,plain,
! [U_8226,U_8227,U_8228] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8226),U_8228),U_8227) = U_8227
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8226),U_8227),U_8228))
| ~ class_Orderings_Olinorder(U_8226) ),
inference(definitional_conversion,[status(esa)],[f_2403_2]) ).
cnf(f_2403_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8226),U_8228),U_8227) = U_8227
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8226),U_8227),U_8228))
| ~ class_Orderings_Olinorder(U_8226) ),
inference(clausify,[status(thm)],[f_2403_3]) ).
fof(f_2404_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1]) ).
fof(f_2404_2,plain,
! [U_8231,U_8230,U_8229] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8229),U_8230),U_8231) = U_8230
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8229),U_8230),U_8231))
| ~ class_Orderings_Olinorder(U_8229) ),
inference(variable_rename,[status(thm)],[f_2404_1]) ).
fof(f_2404_3,plain,
! [U_8229,U_8230,U_8231] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8229),U_8230),U_8231) = U_8230
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8229),U_8230),U_8231))
| ~ class_Orderings_Olinorder(U_8229) ),
inference(definitional_conversion,[status(esa)],[f_2404_2]) ).
cnf(f_2404_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8229),U_8230),U_8231) = U_8230
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8229),U_8230),U_8231))
| ~ class_Orderings_Olinorder(U_8229) ),
inference(clausify,[status(thm)],[f_2404_3]) ).
fof(f_2405_1,plain,
! [V_a,V_x,V_b,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2]) ).
fof(f_2405_2,plain,
! [U_8235,U_8234,U_8233,U_8232] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8232),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8232),U_8235),U_8233)),U_8234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8232),U_8233),U_8234))
| ~ class_Orderings_Olinorder(U_8232) ),
inference(variable_rename,[status(thm)],[f_2405_1]) ).
fof(f_2405_3,plain,
! [U_8232,U_8233,U_8234,U_8235] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8232),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8232),U_8235),U_8233)),U_8234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8232),U_8233),U_8234))
| ~ class_Orderings_Olinorder(U_8232) ),
inference(definitional_conversion,[status(esa)],[f_2405_2]) ).
cnf(f_2405_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8232),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8232),U_8235),U_8233)),U_8234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8232),U_8233),U_8234))
| ~ class_Orderings_Olinorder(U_8232) ),
inference(clausify,[status(thm)],[f_2405_3]) ).
fof(f_2406_1,plain,
! [V_b,V_x,V_a,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1]) ).
fof(f_2406_2,plain,
! [U_8239,U_8238,U_8237,U_8236] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8236),U_8237),U_8239)),U_8238))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8236),U_8237),U_8238))
| ~ class_Orderings_Olinorder(U_8236) ),
inference(variable_rename,[status(thm)],[f_2406_1]) ).
fof(f_2406_3,plain,
! [U_8236,U_8237,U_8238,U_8239] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8236),U_8237),U_8239)),U_8238))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8236),U_8237),U_8238))
| ~ class_Orderings_Olinorder(U_8236) ),
inference(definitional_conversion,[status(esa)],[f_2406_2]) ).
cnf(f_2406_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8236),U_8237),U_8239)),U_8238))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8236),U_8237),U_8238))
| ~ class_Orderings_Olinorder(U_8236) ),
inference(clausify,[status(thm)],[f_2406_3]) ).
fof(f_2407_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff]) ).
fof(f_2407_2,plain,
! [U_8243,U_8242,U_8241,U_8240] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8240),U_8242),U_8243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8243))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8242)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8243))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8242)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8240),U_8242),U_8243))) ) )
| ~ class_Orderings_Olinorder(U_8240) ),
inference(variable_rename,[status(thm)],[f_2407_1]) ).
fof(f_2407_3,plain,
( ! [U_8240,U_8241,U_8242,U_8243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8243))
| ~ sP735(U_8240,U_8241,U_8242,U_8243) )
& ! [U_8240,U_8241,U_8242,U_8243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8242))
| ~ sP735(U_8240,U_8241,U_8242,U_8243) )
& ! [U_8240,U_8241,U_8242,U_8243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8240),U_8242),U_8243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8243))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8242))
| ~ sP736(U_8240,U_8241,U_8242,U_8243) )
& ! [U_8240,U_8241,U_8242,U_8243] :
( sP735(U_8240,U_8241,U_8242,U_8243)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8240),U_8242),U_8243)))
| ~ sP736(U_8240,U_8241,U_8242,U_8243) )
& ! [U_8240,U_8241,U_8242,U_8243] :
( sP736(U_8240,U_8241,U_8242,U_8243)
| ~ class_Orderings_Olinorder(U_8240) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP735,sP736])],[f_2407_2]) ).
cnf(f_2407_4,plain,
( sP736(U_8240,U_8241,U_8242,U_8243)
| ~ class_Orderings_Olinorder(U_8240) ),
inference(clausify,[status(thm)],[f_2407_3]) ).
cnf(f_2407_5,plain,
( sP735(U_8240,U_8241,U_8242,U_8243)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8240),U_8242),U_8243)))
| ~ sP736(U_8240,U_8241,U_8242,U_8243) ),
inference(clausify,[status(thm)],[f_2407_3]) ).
cnf(f_2407_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8240),U_8242),U_8243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8243))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8242))
| ~ sP736(U_8240,U_8241,U_8242,U_8243) ),
inference(clausify,[status(thm)],[f_2407_3]) ).
cnf(f_2407_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8242))
| ~ sP735(U_8240,U_8241,U_8242,U_8243) ),
inference(clausify,[status(thm)],[f_2407_3]) ).
cnf(f_2407_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8240),U_8241),U_8243))
| ~ sP735(U_8240,U_8241,U_8242,U_8243) ),
inference(clausify,[status(thm)],[f_2407_3]) ).
fof(f_2408_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) != V_x_2 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf]) ).
fof(f_2408_2,plain,
! [U_8246,U_8245,U_8244] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8244),U_8245),U_8246))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8244),U_8245),U_8246) != U_8245 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8244),U_8245),U_8246) = U_8245
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8244),U_8245),U_8246)) ) )
| ~ class_Orderings_Olinorder(U_8244) ),
inference(variable_rename,[status(thm)],[f_2408_1]) ).
fof(f_2408_3,plain,
( ! [U_8246,U_8244,U_8245] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8244),U_8245),U_8246))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8244),U_8245),U_8246) != U_8245
| ~ sP737(U_8246,U_8244,U_8245) )
& ! [U_8246,U_8244,U_8245] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8244),U_8245),U_8246) = U_8245
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8244),U_8245),U_8246))
| ~ sP737(U_8246,U_8244,U_8245) )
& ! [U_8246,U_8244,U_8245] :
( sP737(U_8246,U_8244,U_8245)
| ~ class_Orderings_Olinorder(U_8244) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP737])],[f_2408_2]) ).
cnf(f_2408_4,plain,
( sP737(U_8246,U_8244,U_8245)
| ~ class_Orderings_Olinorder(U_8244) ),
inference(clausify,[status(thm)],[f_2408_3]) ).
cnf(f_2408_5,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8244),U_8245),U_8246) = U_8245
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8244),U_8245),U_8246))
| ~ sP737(U_8246,U_8244,U_8245) ),
inference(clausify,[status(thm)],[f_2408_3]) ).
cnf(f_2408_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8244),U_8245),U_8246))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8244),U_8245),U_8246) != U_8245
| ~ sP737(U_8246,U_8244,U_8245) ),
inference(clausify,[status(thm)],[f_2408_3]) ).
fof(f_2409_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2]) ).
fof(f_2409_2,plain,
! [U_8249,U_8248,U_8247] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8247),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8247),U_8248),U_8249)),U_8249))
| ~ class_Orderings_Olinorder(U_8247) ),
inference(variable_rename,[status(thm)],[f_2409_1]) ).
fof(f_2409_3,plain,
! [U_8248,U_8247,U_8249] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8247),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8247),U_8248),U_8249)),U_8249))
| ~ class_Orderings_Olinorder(U_8247) ),
inference(definitional_conversion,[status(esa)],[f_2409_2]) ).
cnf(f_2409_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8247),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8247),U_8248),U_8249)),U_8249))
| ~ class_Orderings_Olinorder(U_8247) ),
inference(clausify,[status(thm)],[f_2409_3]) ).
fof(f_2410_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1]) ).
fof(f_2410_2,plain,
! [U_8252,U_8251,U_8250] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8250),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8250),U_8251),U_8252)),U_8251))
| ~ class_Orderings_Olinorder(U_8250) ),
inference(variable_rename,[status(thm)],[f_2410_1]) ).
fof(f_2410_3,plain,
! [U_8250,U_8251,U_8252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8250),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8250),U_8251),U_8252)),U_8251))
| ~ class_Orderings_Olinorder(U_8250) ),
inference(definitional_conversion,[status(esa)],[f_2410_2]) ).
cnf(f_2410_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8250),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8250),U_8251),U_8252)),U_8251))
| ~ class_Orderings_Olinorder(U_8250) ),
inference(clausify,[status(thm)],[f_2410_3]) ).
fof(f_2411_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( 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))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
| ~ 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)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj]) ).
fof(f_2411_2,plain,
! [U_8256,U_8255,U_8254,U_8253] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8253),U_8254),U_8255)),U_8256))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8255),U_8256))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8254),U_8256)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8255),U_8256))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8254),U_8256))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8253),U_8254),U_8255)),U_8256)) ) )
| ~ class_Orderings_Olinorder(U_8253) ),
inference(variable_rename,[status(thm)],[f_2411_1]) ).
fof(f_2411_3,plain,
( ! [U_8253,U_8254,U_8255,U_8256] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8255),U_8256))
| ~ sP738(U_8253,U_8254,U_8255,U_8256) )
& ! [U_8253,U_8254,U_8255,U_8256] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8254),U_8256))
| ~ sP738(U_8253,U_8254,U_8255,U_8256) )
& ! [U_8253,U_8254,U_8255,U_8256] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8253),U_8254),U_8255)),U_8256))
| sP738(U_8253,U_8254,U_8255,U_8256)
| ~ sP739(U_8253,U_8254,U_8255,U_8256) )
& ! [U_8253,U_8254,U_8255,U_8256] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8255),U_8256))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8254),U_8256))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8253),U_8254),U_8255)),U_8256))
| ~ sP739(U_8253,U_8254,U_8255,U_8256) )
& ! [U_8253,U_8254,U_8255,U_8256] :
( sP739(U_8253,U_8254,U_8255,U_8256)
| ~ class_Orderings_Olinorder(U_8253) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP738,sP739])],[f_2411_2]) ).
cnf(f_2411_4,plain,
( sP739(U_8253,U_8254,U_8255,U_8256)
| ~ class_Orderings_Olinorder(U_8253) ),
inference(clausify,[status(thm)],[f_2411_3]) ).
cnf(f_2411_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8255),U_8256))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8254),U_8256))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8253),U_8254),U_8255)),U_8256))
| ~ sP739(U_8253,U_8254,U_8255,U_8256) ),
inference(clausify,[status(thm)],[f_2411_3]) ).
cnf(f_2411_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8253),U_8254),U_8255)),U_8256))
| sP738(U_8253,U_8254,U_8255,U_8256)
| ~ sP739(U_8253,U_8254,U_8255,U_8256) ),
inference(clausify,[status(thm)],[f_2411_3]) ).
cnf(f_2411_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8254),U_8256))
| ~ sP738(U_8253,U_8254,U_8255,U_8256) ),
inference(clausify,[status(thm)],[f_2411_3]) ).
cnf(f_2411_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8253),U_8255),U_8256))
| ~ sP738(U_8253,U_8254,U_8255,U_8256) ),
inference(clausify,[status(thm)],[f_2411_3]) ).
fof(f_2412_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left]) ).
fof(f_2412_2,plain,
! [U_8260,U_8259,U_8258,U_8257] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8257),U_8258),U_8259)),U_8260) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),U_8258),U_8260)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),U_8259),U_8260))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8257) ),
inference(variable_rename,[status(thm)],[f_2412_1]) ).
fof(f_2412_3,plain,
! [U_8258,U_8260,U_8257,U_8259] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8257),U_8258),U_8259)),U_8260) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),U_8258),U_8260)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),U_8259),U_8260))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8257) ),
inference(definitional_conversion,[status(esa)],[f_2412_2]) ).
cnf(f_2412_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8257),U_8258),U_8259)),U_8260) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),U_8258),U_8260)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8257),U_8259),U_8260))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8257) ),
inference(clausify,[status(thm)],[f_2412_3]) ).
fof(f_2413_1,plain,
! [V_a,V_x,V_b,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2]) ).
fof(f_2413_2,plain,
! [U_8264,U_8263,U_8262,U_8261] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8261),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8261),U_8264),U_8262)),U_8263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8261),U_8262),U_8263))
| ~ class_Orderings_Olinorder(U_8261) ),
inference(variable_rename,[status(thm)],[f_2413_1]) ).
fof(f_2413_3,plain,
! [U_8261,U_8262,U_8263,U_8264] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8261),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8261),U_8264),U_8262)),U_8263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8261),U_8262),U_8263))
| ~ class_Orderings_Olinorder(U_8261) ),
inference(definitional_conversion,[status(esa)],[f_2413_2]) ).
cnf(f_2413_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8261),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8261),U_8264),U_8262)),U_8263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8261),U_8262),U_8263))
| ~ class_Orderings_Olinorder(U_8261) ),
inference(clausify,[status(thm)],[f_2413_3]) ).
fof(f_2414_1,plain,
! [V_b,V_x,V_a,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1]) ).
fof(f_2414_2,plain,
! [U_8268,U_8267,U_8266,U_8265] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8265),U_8266),U_8268)),U_8267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),U_8266),U_8267))
| ~ class_Orderings_Olinorder(U_8265) ),
inference(variable_rename,[status(thm)],[f_2414_1]) ).
fof(f_2414_3,plain,
! [U_8265,U_8266,U_8267,U_8268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8265),U_8266),U_8268)),U_8267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),U_8266),U_8267))
| ~ class_Orderings_Olinorder(U_8265) ),
inference(definitional_conversion,[status(esa)],[f_2414_2]) ).
cnf(f_2414_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8265),U_8266),U_8268)),U_8267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),U_8266),U_8267))
| ~ class_Orderings_Olinorder(U_8265) ),
inference(clausify,[status(thm)],[f_2414_3]) ).
fof(f_2415_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( 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))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
| ~ 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)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj]) ).
fof(f_2415_2,plain,
! [U_8272,U_8271,U_8270,U_8269] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8269),U_8270),U_8271)),U_8272))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8271),U_8272))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8270),U_8272)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8271),U_8272))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8270),U_8272))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8269),U_8270),U_8271)),U_8272)) ) )
| ~ class_Orderings_Olinorder(U_8269) ),
inference(variable_rename,[status(thm)],[f_2415_1]) ).
fof(f_2415_3,plain,
( ! [U_8269,U_8270,U_8271,U_8272] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8271),U_8272))
| ~ sP740(U_8269,U_8270,U_8271,U_8272) )
& ! [U_8269,U_8270,U_8271,U_8272] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8270),U_8272))
| ~ sP740(U_8269,U_8270,U_8271,U_8272) )
& ! [U_8269,U_8270,U_8271,U_8272] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8269),U_8270),U_8271)),U_8272))
| sP740(U_8269,U_8270,U_8271,U_8272)
| ~ sP741(U_8269,U_8270,U_8271,U_8272) )
& ! [U_8269,U_8270,U_8271,U_8272] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8271),U_8272))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8270),U_8272))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8269),U_8270),U_8271)),U_8272))
| ~ sP741(U_8269,U_8270,U_8271,U_8272) )
& ! [U_8269,U_8270,U_8271,U_8272] :
( sP741(U_8269,U_8270,U_8271,U_8272)
| ~ class_Orderings_Olinorder(U_8269) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP740,sP741])],[f_2415_2]) ).
cnf(f_2415_4,plain,
( sP741(U_8269,U_8270,U_8271,U_8272)
| ~ class_Orderings_Olinorder(U_8269) ),
inference(clausify,[status(thm)],[f_2415_3]) ).
cnf(f_2415_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8271),U_8272))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8270),U_8272))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8269),U_8270),U_8271)),U_8272))
| ~ sP741(U_8269,U_8270,U_8271,U_8272) ),
inference(clausify,[status(thm)],[f_2415_3]) ).
cnf(f_2415_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8269),U_8270),U_8271)),U_8272))
| sP740(U_8269,U_8270,U_8271,U_8272)
| ~ sP741(U_8269,U_8270,U_8271,U_8272) ),
inference(clausify,[status(thm)],[f_2415_3]) ).
cnf(f_2415_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8270),U_8272))
| ~ sP740(U_8269,U_8270,U_8271,U_8272) ),
inference(clausify,[status(thm)],[f_2415_3]) ).
cnf(f_2415_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8269),U_8271),U_8272))
| ~ sP740(U_8269,U_8270,U_8271,U_8272) ),
inference(clausify,[status(thm)],[f_2415_3]) ).
fof(f_2416_1,plain,
! [V_y_2,V_x_2,V_z_2,T_b] :
( ( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) )
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj]) ).
fof(f_2416_2,plain,
! [U_8276,U_8275,U_8274,U_8273] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8273),U_8275),U_8276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8275)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8276))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8275)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8273),U_8275),U_8276))) ) )
| ~ class_Orderings_Olinorder(U_8273) ),
inference(variable_rename,[status(thm)],[f_2416_1]) ).
fof(f_2416_3,plain,
( ! [U_8276,U_8274,U_8275,U_8273] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8276))
| ~ sP742(U_8276,U_8274,U_8275,U_8273) )
& ! [U_8276,U_8274,U_8275,U_8273] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8275))
| ~ sP742(U_8276,U_8274,U_8275,U_8273) )
& ! [U_8276,U_8274,U_8275,U_8273] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8273),U_8275),U_8276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8275))
| ~ sP743(U_8276,U_8274,U_8275,U_8273) )
& ! [U_8276,U_8274,U_8275,U_8273] :
( sP742(U_8276,U_8274,U_8275,U_8273)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8273),U_8275),U_8276)))
| ~ sP743(U_8276,U_8274,U_8275,U_8273) )
& ! [U_8276,U_8274,U_8275,U_8273] :
( sP743(U_8276,U_8274,U_8275,U_8273)
| ~ class_Orderings_Olinorder(U_8273) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP742,sP743])],[f_2416_2]) ).
cnf(f_2416_4,plain,
( sP743(U_8276,U_8274,U_8275,U_8273)
| ~ class_Orderings_Olinorder(U_8273) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
cnf(f_2416_5,plain,
( sP742(U_8276,U_8274,U_8275,U_8273)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8273),U_8275),U_8276)))
| ~ sP743(U_8276,U_8274,U_8275,U_8273) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
cnf(f_2416_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8273),U_8275),U_8276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8275))
| ~ sP743(U_8276,U_8274,U_8275,U_8273) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
cnf(f_2416_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8275))
| ~ sP742(U_8276,U_8274,U_8275,U_8273) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
cnf(f_2416_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8273),U_8274),U_8276))
| ~ sP742(U_8276,U_8274,U_8275,U_8273) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
fof(f_2417_1,plain,
! [V_v,V_u,T_b] :
( ( ( 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)
| 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))) )
& ( 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)
| ~ 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))) ) )
| ~ class_Orderings_Oord(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__number__of]) ).
fof(f_2417_2,plain,
! [U_8279,U_8278,U_8277] :
( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279))) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279))) ) )
| ~ class_Orderings_Oord(U_8277)
| ~ class_Int_Onumber(U_8277) ),
inference(variable_rename,[status(thm)],[f_2417_1]) ).
fof(f_2417_3,plain,
( ! [U_8278,U_8279,U_8277] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)))
| ~ sP744(U_8278,U_8279,U_8277) )
& ! [U_8278,U_8279,U_8277] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)))
| ~ sP744(U_8278,U_8279,U_8277) )
& ! [U_8278,U_8279,U_8277] :
( sP744(U_8278,U_8279,U_8277)
| ~ class_Orderings_Oord(U_8277)
| ~ class_Int_Onumber(U_8277) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP744])],[f_2417_2]) ).
cnf(f_2417_4,plain,
( sP744(U_8278,U_8279,U_8277)
| ~ class_Orderings_Oord(U_8277)
| ~ class_Int_Onumber(U_8277) ),
inference(clausify,[status(thm)],[f_2417_3]) ).
cnf(f_2417_5,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)))
| ~ sP744(U_8278,U_8279,U_8277) ),
inference(clausify,[status(thm)],[f_2417_3]) ).
cnf(f_2417_6,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8277),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8278)),hAPP(c_Int_Onumber__class_Onumber__of(U_8277),U_8279)))
| ~ sP744(U_8278,U_8279,U_8277) ),
inference(clausify,[status(thm)],[f_2417_3]) ).
fof(f_2418_1,plain,
! [V_a_2,V_b_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert]) ).
fof(f_2418_2,plain,
! [U_8283,U_8282,U_8281,U_8280] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_8280,U_8280,c_Orderings_Oord__class_Omin(U_8280)),U_8282),hAPP(hAPP(c_Set_Oinsert(U_8280),U_8283),U_8281)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8280),U_8283),hAPP(hAPP(c_Finite__Set_Ofold(U_8280,U_8280,c_Orderings_Oord__class_Omin(U_8280)),U_8282),U_8281))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8280),U_8281))
| ~ class_Orderings_Olinorder(U_8280) ),
inference(variable_rename,[status(thm)],[f_2418_1]) ).
fof(f_2418_3,plain,
! [U_8282,U_8283,U_8280,U_8281] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_8280,U_8280,c_Orderings_Oord__class_Omin(U_8280)),U_8282),hAPP(hAPP(c_Set_Oinsert(U_8280),U_8283),U_8281)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8280),U_8283),hAPP(hAPP(c_Finite__Set_Ofold(U_8280,U_8280,c_Orderings_Oord__class_Omin(U_8280)),U_8282),U_8281))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8280),U_8281))
| ~ class_Orderings_Olinorder(U_8280) ),
inference(definitional_conversion,[status(esa)],[f_2418_2]) ).
cnf(f_2418_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_8280,U_8280,c_Orderings_Oord__class_Omin(U_8280)),U_8282),hAPP(hAPP(c_Set_Oinsert(U_8280),U_8283),U_8281)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8280),U_8283),hAPP(hAPP(c_Finite__Set_Ofold(U_8280,U_8280,c_Orderings_Oord__class_Omin(U_8280)),U_8282),U_8281))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8280),U_8281))
| ~ class_Orderings_Olinorder(U_8280) ),
inference(clausify,[status(thm)],[f_2418_3]) ).
fof(f_2419_1,plain,
! [V_d_2,V_b_2,V_a_2,T_b] :
( 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))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1]) ).
fof(f_2419_2,plain,
! [U_8287,U_8286,U_8285,U_8284] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8284,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8284,U_8285,U_8286)),hAPP(c_SetInterval_Oord__class_OatMost(U_8284),U_8287)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8284,U_8285,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8284),U_8286),U_8287))
| ~ class_Orderings_Olinorder(U_8284) ),
inference(variable_rename,[status(thm)],[f_2419_1]) ).
fof(f_2419_3,plain,
! [U_8284,U_8285,U_8286,U_8287] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8284,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8284,U_8285,U_8286)),hAPP(c_SetInterval_Oord__class_OatMost(U_8284),U_8287)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8284,U_8285,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8284),U_8286),U_8287))
| ~ class_Orderings_Olinorder(U_8284) ),
inference(definitional_conversion,[status(esa)],[f_2419_2]) ).
cnf(f_2419_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8284,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8284,U_8285,U_8286)),hAPP(c_SetInterval_Oord__class_OatMost(U_8284),U_8287)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8284,U_8285,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8284),U_8286),U_8287))
| ~ class_Orderings_Olinorder(U_8284) ),
inference(clausify,[status(thm)],[f_2419_3]) ).
fof(f_2420_1,plain,
! [V_d_2,V_ca_2,V_b_2,T_b] :
( 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1]) ).
fof(f_2420_2,plain,
! [U_8291,U_8290,U_8289,U_8288] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8288),U_8289)),c_SetInterval_Oord__class_OatLeastAtMost(U_8288,U_8290,U_8291)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8288,U_8290,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8288),U_8289),U_8291))
| ~ class_Orderings_Olinorder(U_8288) ),
inference(variable_rename,[status(thm)],[f_2420_1]) ).
fof(f_2420_3,plain,
! [U_8288,U_8289,U_8290,U_8291] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8288),U_8289)),c_SetInterval_Oord__class_OatLeastAtMost(U_8288,U_8290,U_8291)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8288,U_8290,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8288),U_8289),U_8291))
| ~ class_Orderings_Olinorder(U_8288) ),
inference(definitional_conversion,[status(esa)],[f_2420_2]) ).
cnf(f_2420_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8288),U_8289)),c_SetInterval_Oord__class_OatLeastAtMost(U_8288,U_8290,U_8291)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8288,U_8290,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8288),U_8289),U_8291))
| ~ class_Orderings_Olinorder(U_8288) ),
inference(clausify,[status(thm)],[f_2420_3]) ).
fof(f_2421_1,plain,
! [V_b_2,V_a_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf]) ).
fof(f_2421_2,plain,
! [U_8295,U_8294,U_8293,U_8292] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8292),hAPP(hAPP(c_Finite__Set_Ofold(U_8292,U_8292,c_Orderings_Oord__class_Omin(U_8292)),U_8295),U_8293)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8292),U_8294),U_8295)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8292),U_8294),U_8293))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8292),U_8293))
| ~ class_Orderings_Olinorder(U_8292) ),
inference(variable_rename,[status(thm)],[f_2421_1]) ).
fof(f_2421_3,plain,
! [U_8292,U_8293,U_8294,U_8295] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8292),hAPP(hAPP(c_Finite__Set_Ofold(U_8292,U_8292,c_Orderings_Oord__class_Omin(U_8292)),U_8295),U_8293)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8292),U_8294),U_8295)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8292),U_8294),U_8293))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8292),U_8293))
| ~ class_Orderings_Olinorder(U_8292) ),
inference(definitional_conversion,[status(esa)],[f_2421_2]) ).
cnf(f_2421_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8292),hAPP(hAPP(c_Finite__Set_Ofold(U_8292,U_8292,c_Orderings_Oord__class_Omin(U_8292)),U_8295),U_8293)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8292),U_8294),U_8295)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8292),U_8294),U_8293))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8292),U_8293))
| ~ class_Orderings_Olinorder(U_8292) ),
inference(clausify,[status(thm)],[f_2421_3]) ).
fof(f_2422_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI]) ).
fof(f_2422_2,plain,
! [U_8298,U_8297,U_8296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8296),hAPP(c_Finite__Set_Ofold1(U_8296,c_Orderings_Oord__class_Omin(U_8296)),U_8297)),U_8298))
| ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8296),U_8297))
| ~ class_Orderings_Olinorder(U_8296) ),
inference(variable_rename,[status(thm)],[f_2422_1]) ).
fof(f_2422_3,plain,
! [U_8297,U_8296,U_8298] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8296),hAPP(c_Finite__Set_Ofold1(U_8296,c_Orderings_Oord__class_Omin(U_8296)),U_8297)),U_8298))
| ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8296),U_8297))
| ~ class_Orderings_Olinorder(U_8296) ),
inference(definitional_conversion,[status(esa)],[f_2422_2]) ).
cnf(f_2422_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8296),hAPP(c_Finite__Set_Ofold1(U_8296,c_Orderings_Oord__class_Omin(U_8296)),U_8297)),U_8298))
| ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8296),U_8297))
| ~ class_Orderings_Olinorder(U_8296) ),
inference(clausify,[status(thm)],[f_2422_3]) ).
fof(f_2423_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Obelow__fold1__iff]) ).
fof(f_2423_2,plain,
! [U_8303,U_8302,U_8301] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),hAPP(c_Finite__Set_Ofold1(U_8301,c_Orderings_Oord__class_Omin(U_8301)),U_8302)))
| ? [U_8300] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),U_8300))
& hBOOL(hAPP(hAPP(c_member(U_8301),U_8300),U_8302)) ) )
& ( ! [U_8299] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),U_8299))
| ~ hBOOL(hAPP(hAPP(c_member(U_8301),U_8299),U_8302)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),hAPP(c_Finite__Set_Ofold1(U_8301,c_Orderings_Oord__class_Omin(U_8301)),U_8302))) ) )
| U_8302 = c_Orderings_Obot__class_Obot(tc_fun(U_8301,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8301),U_8302))
| ~ class_Orderings_Olinorder(U_8301) ),
inference(variable_rename,[status(thm)],[f_2423_1]) ).
fof(f_2423_3,plain,
! [U_8303,U_8302,U_8301] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),hAPP(c_Finite__Set_Ofold1(U_8301,c_Orderings_Oord__class_Omin(U_8301)),U_8302)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),sK221(U_8303,U_8302,U_8301)))
& hBOOL(hAPP(hAPP(c_member(U_8301),sK221(U_8303,U_8302,U_8301)),U_8302)) ) )
& ( ! [U_8299] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),U_8299))
| ~ hBOOL(hAPP(hAPP(c_member(U_8301),U_8299),U_8302)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),hAPP(c_Finite__Set_Ofold1(U_8301,c_Orderings_Oord__class_Omin(U_8301)),U_8302))) ) )
| U_8302 = c_Orderings_Obot__class_Obot(tc_fun(U_8301,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8301),U_8302))
| ~ class_Orderings_Olinorder(U_8301) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_8300,sK221(U_8303,U_8302,U_8301))],[f_2423_2]) ).
fof(f_2423_4,plain,
( ! [U_8301,U_8302,U_8303] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),sK221(U_8303,U_8302,U_8301)))
| ~ sP745(U_8301,U_8302,U_8303) )
& ! [U_8301,U_8302,U_8303] :
( hBOOL(hAPP(hAPP(c_member(U_8301),sK221(U_8303,U_8302,U_8301)),U_8302))
| ~ sP745(U_8301,U_8302,U_8303) )
& ! [U_8299,U_8301,U_8302,U_8303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),hAPP(c_Finite__Set_Ofold1(U_8301,c_Orderings_Oord__class_Omin(U_8301)),U_8302)))
| sP745(U_8301,U_8302,U_8303)
| ~ sP746(U_8299,U_8301,U_8302,U_8303) )
& ! [U_8299,U_8301,U_8302,U_8303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),U_8299))
| ~ hBOOL(hAPP(hAPP(c_member(U_8301),U_8299),U_8302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),hAPP(c_Finite__Set_Ofold1(U_8301,c_Orderings_Oord__class_Omin(U_8301)),U_8302)))
| ~ sP746(U_8299,U_8301,U_8302,U_8303) )
& ! [U_8299,U_8301,U_8302,U_8303] :
( sP746(U_8299,U_8301,U_8302,U_8303)
| U_8302 = c_Orderings_Obot__class_Obot(tc_fun(U_8301,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8301),U_8302))
| ~ class_Orderings_Olinorder(U_8301) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP745,sP746])],[f_2423_3]) ).
cnf(f_2423_5,plain,
( sP746(U_8299,U_8301,U_8302,U_8303)
| U_8302 = c_Orderings_Obot__class_Obot(tc_fun(U_8301,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8301),U_8302))
| ~ class_Orderings_Olinorder(U_8301) ),
inference(clausify,[status(thm)],[f_2423_4]) ).
cnf(f_2423_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),U_8299))
| ~ hBOOL(hAPP(hAPP(c_member(U_8301),U_8299),U_8302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),hAPP(c_Finite__Set_Ofold1(U_8301,c_Orderings_Oord__class_Omin(U_8301)),U_8302)))
| ~ sP746(U_8299,U_8301,U_8302,U_8303) ),
inference(clausify,[status(thm)],[f_2423_4]) ).
cnf(f_2423_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),hAPP(c_Finite__Set_Ofold1(U_8301,c_Orderings_Oord__class_Omin(U_8301)),U_8302)))
| sP745(U_8301,U_8302,U_8303)
| ~ sP746(U_8299,U_8301,U_8302,U_8303) ),
inference(clausify,[status(thm)],[f_2423_4]) ).
cnf(f_2423_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_8301),sK221(U_8303,U_8302,U_8301)),U_8302))
| ~ sP745(U_8301,U_8302,U_8303) ),
inference(clausify,[status(thm)],[f_2423_4]) ).
cnf(f_2423_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8301),U_8303),sK221(U_8303,U_8302,U_8301)))
| ~ sP745(U_8301,U_8302,U_8303) ),
inference(clausify,[status(thm)],[f_2423_4]) ).
fof(f_2424_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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)) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__below__iff]) ).
fof(f_2424_2,plain,
! [U_8308,U_8307,U_8306] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),hAPP(c_Finite__Set_Ofold1(U_8306,c_Orderings_Oord__class_Omin(U_8306)),U_8307)),U_8308))
| ! [U_8305] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),U_8305),U_8308))
| ~ hBOOL(hAPP(hAPP(c_member(U_8306),U_8305),U_8307)) ) )
& ( ? [U_8304] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),U_8304),U_8308))
& hBOOL(hAPP(hAPP(c_member(U_8306),U_8304),U_8307)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),hAPP(c_Finite__Set_Ofold1(U_8306,c_Orderings_Oord__class_Omin(U_8306)),U_8307)),U_8308)) ) )
| U_8307 = c_Orderings_Obot__class_Obot(tc_fun(U_8306,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8306),U_8307))
| ~ class_Orderings_Olinorder(U_8306) ),
inference(variable_rename,[status(thm)],[f_2424_1]) ).
fof(f_2424_3,plain,
! [U_8308,U_8307,U_8306] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),hAPP(c_Finite__Set_Ofold1(U_8306,c_Orderings_Oord__class_Omin(U_8306)),U_8307)),U_8308))
| ! [U_8305] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),U_8305),U_8308))
| ~ hBOOL(hAPP(hAPP(c_member(U_8306),U_8305),U_8307)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),sK222(U_8308,U_8307,U_8306)),U_8308))
& hBOOL(hAPP(hAPP(c_member(U_8306),sK222(U_8308,U_8307,U_8306)),U_8307)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),hAPP(c_Finite__Set_Ofold1(U_8306,c_Orderings_Oord__class_Omin(U_8306)),U_8307)),U_8308)) ) )
| U_8307 = c_Orderings_Obot__class_Obot(tc_fun(U_8306,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8306),U_8307))
| ~ class_Orderings_Olinorder(U_8306) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_8304,sK222(U_8308,U_8307,U_8306))],[f_2424_2]) ).
fof(f_2424_4,plain,
( ! [U_8306,U_8307,U_8308] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),sK222(U_8308,U_8307,U_8306)),U_8308))
| ~ sP747(U_8306,U_8307,U_8308) )
& ! [U_8306,U_8307,U_8308] :
( hBOOL(hAPP(hAPP(c_member(U_8306),sK222(U_8308,U_8307,U_8306)),U_8307))
| ~ sP747(U_8306,U_8307,U_8308) )
& ! [U_8306,U_8307,U_8308,U_8305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),hAPP(c_Finite__Set_Ofold1(U_8306,c_Orderings_Oord__class_Omin(U_8306)),U_8307)),U_8308))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),U_8305),U_8308))
| ~ hBOOL(hAPP(hAPP(c_member(U_8306),U_8305),U_8307))
| ~ sP748(U_8306,U_8307,U_8308,U_8305) )
& ! [U_8306,U_8307,U_8308,U_8305] :
( sP747(U_8306,U_8307,U_8308)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),hAPP(c_Finite__Set_Ofold1(U_8306,c_Orderings_Oord__class_Omin(U_8306)),U_8307)),U_8308))
| ~ sP748(U_8306,U_8307,U_8308,U_8305) )
& ! [U_8306,U_8307,U_8308,U_8305] :
( sP748(U_8306,U_8307,U_8308,U_8305)
| U_8307 = c_Orderings_Obot__class_Obot(tc_fun(U_8306,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8306),U_8307))
| ~ class_Orderings_Olinorder(U_8306) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP747,sP748])],[f_2424_3]) ).
cnf(f_2424_5,plain,
( sP748(U_8306,U_8307,U_8308,U_8305)
| U_8307 = c_Orderings_Obot__class_Obot(tc_fun(U_8306,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8306),U_8307))
| ~ class_Orderings_Olinorder(U_8306) ),
inference(clausify,[status(thm)],[f_2424_4]) ).
cnf(f_2424_6,plain,
( sP747(U_8306,U_8307,U_8308)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),hAPP(c_Finite__Set_Ofold1(U_8306,c_Orderings_Oord__class_Omin(U_8306)),U_8307)),U_8308))
| ~ sP748(U_8306,U_8307,U_8308,U_8305) ),
inference(clausify,[status(thm)],[f_2424_4]) ).
cnf(f_2424_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),hAPP(c_Finite__Set_Ofold1(U_8306,c_Orderings_Oord__class_Omin(U_8306)),U_8307)),U_8308))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),U_8305),U_8308))
| ~ hBOOL(hAPP(hAPP(c_member(U_8306),U_8305),U_8307))
| ~ sP748(U_8306,U_8307,U_8308,U_8305) ),
inference(clausify,[status(thm)],[f_2424_4]) ).
cnf(f_2424_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_8306),sK222(U_8308,U_8307,U_8306)),U_8307))
| ~ sP747(U_8306,U_8307,U_8308) ),
inference(clausify,[status(thm)],[f_2424_4]) ).
cnf(f_2424_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8306),sK222(U_8308,U_8307,U_8306)),U_8308))
| ~ sP747(U_8306,U_8307,U_8308) ),
inference(clausify,[status(thm)],[f_2424_4]) ).
fof(f_2425_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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)) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__strict__below__iff]) ).
fof(f_2425_2,plain,
! [U_8313,U_8312,U_8311] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),hAPP(c_Finite__Set_Ofold1(U_8311,c_Orderings_Oord__class_Omin(U_8311)),U_8312)),U_8313))
| ! [U_8310] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),U_8310),U_8313))
| ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8310),U_8312)) ) )
& ( ? [U_8309] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),U_8309),U_8313))
& hBOOL(hAPP(hAPP(c_member(U_8311),U_8309),U_8312)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),hAPP(c_Finite__Set_Ofold1(U_8311,c_Orderings_Oord__class_Omin(U_8311)),U_8312)),U_8313)) ) )
| U_8312 = c_Orderings_Obot__class_Obot(tc_fun(U_8311,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8311),U_8312))
| ~ class_Orderings_Olinorder(U_8311) ),
inference(variable_rename,[status(thm)],[f_2425_1]) ).
fof(f_2425_3,plain,
! [U_8313,U_8312,U_8311] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),hAPP(c_Finite__Set_Ofold1(U_8311,c_Orderings_Oord__class_Omin(U_8311)),U_8312)),U_8313))
| ! [U_8310] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),U_8310),U_8313))
| ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8310),U_8312)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),sK223(U_8313,U_8312,U_8311)),U_8313))
& hBOOL(hAPP(hAPP(c_member(U_8311),sK223(U_8313,U_8312,U_8311)),U_8312)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),hAPP(c_Finite__Set_Ofold1(U_8311,c_Orderings_Oord__class_Omin(U_8311)),U_8312)),U_8313)) ) )
| U_8312 = c_Orderings_Obot__class_Obot(tc_fun(U_8311,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8311),U_8312))
| ~ class_Orderings_Olinorder(U_8311) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_8309,sK223(U_8313,U_8312,U_8311))],[f_2425_2]) ).
fof(f_2425_4,plain,
( ! [U_8312,U_8311,U_8313] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),sK223(U_8313,U_8312,U_8311)),U_8313))
| ~ sP749(U_8312,U_8311,U_8313) )
& ! [U_8312,U_8311,U_8313] :
( hBOOL(hAPP(hAPP(c_member(U_8311),sK223(U_8313,U_8312,U_8311)),U_8312))
| ~ sP749(U_8312,U_8311,U_8313) )
& ! [U_8312,U_8310,U_8311,U_8313] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),hAPP(c_Finite__Set_Ofold1(U_8311,c_Orderings_Oord__class_Omin(U_8311)),U_8312)),U_8313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),U_8310),U_8313))
| ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8310),U_8312))
| ~ sP750(U_8312,U_8310,U_8311,U_8313) )
& ! [U_8312,U_8310,U_8311,U_8313] :
( sP749(U_8312,U_8311,U_8313)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),hAPP(c_Finite__Set_Ofold1(U_8311,c_Orderings_Oord__class_Omin(U_8311)),U_8312)),U_8313))
| ~ sP750(U_8312,U_8310,U_8311,U_8313) )
& ! [U_8312,U_8310,U_8311,U_8313] :
( sP750(U_8312,U_8310,U_8311,U_8313)
| U_8312 = c_Orderings_Obot__class_Obot(tc_fun(U_8311,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8311),U_8312))
| ~ class_Orderings_Olinorder(U_8311) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP749,sP750])],[f_2425_3]) ).
cnf(f_2425_5,plain,
( sP750(U_8312,U_8310,U_8311,U_8313)
| U_8312 = c_Orderings_Obot__class_Obot(tc_fun(U_8311,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8311),U_8312))
| ~ class_Orderings_Olinorder(U_8311) ),
inference(clausify,[status(thm)],[f_2425_4]) ).
cnf(f_2425_6,plain,
( sP749(U_8312,U_8311,U_8313)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),hAPP(c_Finite__Set_Ofold1(U_8311,c_Orderings_Oord__class_Omin(U_8311)),U_8312)),U_8313))
| ~ sP750(U_8312,U_8310,U_8311,U_8313) ),
inference(clausify,[status(thm)],[f_2425_4]) ).
cnf(f_2425_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),hAPP(c_Finite__Set_Ofold1(U_8311,c_Orderings_Oord__class_Omin(U_8311)),U_8312)),U_8313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),U_8310),U_8313))
| ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8310),U_8312))
| ~ sP750(U_8312,U_8310,U_8311,U_8313) ),
inference(clausify,[status(thm)],[f_2425_4]) ).
cnf(f_2425_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_8311),sK223(U_8313,U_8312,U_8311)),U_8312))
| ~ sP749(U_8312,U_8311,U_8313) ),
inference(clausify,[status(thm)],[f_2425_4]) ).
cnf(f_2425_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8311),sK223(U_8313,U_8312,U_8311)),U_8313))
| ~ sP749(U_8312,U_8311,U_8313) ),
inference(clausify,[status(thm)],[f_2425_4]) ).
fof(f_2426_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff]) ).
fof(f_2426_2,plain,
! [U_8318,U_8317,U_8316] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),hAPP(c_Finite__Set_Ofold1(U_8316,c_Orderings_Oord__class_Omin(U_8316)),U_8317)))
| ? [U_8315] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),U_8315))
& hBOOL(hAPP(hAPP(c_member(U_8316),U_8315),U_8317)) ) )
& ( ! [U_8314] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),U_8314))
| ~ hBOOL(hAPP(hAPP(c_member(U_8316),U_8314),U_8317)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),hAPP(c_Finite__Set_Ofold1(U_8316,c_Orderings_Oord__class_Omin(U_8316)),U_8317))) ) )
| U_8317 = c_Orderings_Obot__class_Obot(tc_fun(U_8316,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8316),U_8317))
| ~ class_Orderings_Olinorder(U_8316) ),
inference(variable_rename,[status(thm)],[f_2426_1]) ).
fof(f_2426_3,plain,
! [U_8318,U_8317,U_8316] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),hAPP(c_Finite__Set_Ofold1(U_8316,c_Orderings_Oord__class_Omin(U_8316)),U_8317)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),sK224(U_8318,U_8317,U_8316)))
& hBOOL(hAPP(hAPP(c_member(U_8316),sK224(U_8318,U_8317,U_8316)),U_8317)) ) )
& ( ! [U_8314] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),U_8314))
| ~ hBOOL(hAPP(hAPP(c_member(U_8316),U_8314),U_8317)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),hAPP(c_Finite__Set_Ofold1(U_8316,c_Orderings_Oord__class_Omin(U_8316)),U_8317))) ) )
| U_8317 = c_Orderings_Obot__class_Obot(tc_fun(U_8316,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8316),U_8317))
| ~ class_Orderings_Olinorder(U_8316) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_8315,sK224(U_8318,U_8317,U_8316))],[f_2426_2]) ).
fof(f_2426_4,plain,
( ! [U_8316,U_8317,U_8318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),sK224(U_8318,U_8317,U_8316)))
| ~ sP751(U_8316,U_8317,U_8318) )
& ! [U_8316,U_8317,U_8318] :
( hBOOL(hAPP(hAPP(c_member(U_8316),sK224(U_8318,U_8317,U_8316)),U_8317))
| ~ sP751(U_8316,U_8317,U_8318) )
& ! [U_8316,U_8314,U_8317,U_8318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),hAPP(c_Finite__Set_Ofold1(U_8316,c_Orderings_Oord__class_Omin(U_8316)),U_8317)))
| sP751(U_8316,U_8317,U_8318)
| ~ sP752(U_8316,U_8314,U_8317,U_8318) )
& ! [U_8316,U_8314,U_8317,U_8318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),U_8314))
| ~ hBOOL(hAPP(hAPP(c_member(U_8316),U_8314),U_8317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),hAPP(c_Finite__Set_Ofold1(U_8316,c_Orderings_Oord__class_Omin(U_8316)),U_8317)))
| ~ sP752(U_8316,U_8314,U_8317,U_8318) )
& ! [U_8316,U_8314,U_8317,U_8318] :
( sP752(U_8316,U_8314,U_8317,U_8318)
| U_8317 = c_Orderings_Obot__class_Obot(tc_fun(U_8316,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8316),U_8317))
| ~ class_Orderings_Olinorder(U_8316) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP751,sP752])],[f_2426_3]) ).
cnf(f_2426_5,plain,
( sP752(U_8316,U_8314,U_8317,U_8318)
| U_8317 = c_Orderings_Obot__class_Obot(tc_fun(U_8316,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8316),U_8317))
| ~ class_Orderings_Olinorder(U_8316) ),
inference(clausify,[status(thm)],[f_2426_4]) ).
cnf(f_2426_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),U_8314))
| ~ hBOOL(hAPP(hAPP(c_member(U_8316),U_8314),U_8317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),hAPP(c_Finite__Set_Ofold1(U_8316,c_Orderings_Oord__class_Omin(U_8316)),U_8317)))
| ~ sP752(U_8316,U_8314,U_8317,U_8318) ),
inference(clausify,[status(thm)],[f_2426_4]) ).
cnf(f_2426_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),hAPP(c_Finite__Set_Ofold1(U_8316,c_Orderings_Oord__class_Omin(U_8316)),U_8317)))
| sP751(U_8316,U_8317,U_8318)
| ~ sP752(U_8316,U_8314,U_8317,U_8318) ),
inference(clausify,[status(thm)],[f_2426_4]) ).
cnf(f_2426_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_8316),sK224(U_8318,U_8317,U_8316)),U_8317))
| ~ sP751(U_8316,U_8317,U_8318) ),
inference(clausify,[status(thm)],[f_2426_4]) ).
cnf(f_2426_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8316),U_8318),sK224(U_8318,U_8317,U_8316)))
| ~ sP751(U_8316,U_8317,U_8318) ),
inference(clausify,[status(thm)],[f_2426_4]) ).
fof(f_2427_1,plain,
! [T_b] :
( c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b))
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__ord__min]) ).
fof(f_2427_2,plain,
! [U_8319] :
( c_Orderings_Oord__class_Omin(U_8319) = c_Orderings_Oord_Omin(U_8319,c_Orderings_Oord__class_Oless__eq(U_8319))
| ~ class_Orderings_Oord(U_8319) ),
inference(variable_rename,[status(thm)],[f_2427_1]) ).
fof(f_2427_3,plain,
! [U_8319] :
( c_Orderings_Oord__class_Omin(U_8319) = c_Orderings_Oord_Omin(U_8319,c_Orderings_Oord__class_Oless__eq(U_8319))
| ~ class_Orderings_Oord(U_8319) ),
inference(definitional_conversion,[status(esa)],[f_2427_2]) ).
cnf(f_2427_4,plain,
( c_Orderings_Oord__class_Omin(U_8319) = c_Orderings_Oord_Omin(U_8319,c_Orderings_Oord__class_Oless__eq(U_8319))
| ~ class_Orderings_Oord(U_8319) ),
inference(clausify,[status(thm)],[f_2427_3]) ).
fof(f_2428_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oremove]) ).
fof(f_2428_2,plain,
! [U_8322,U_8321,U_8320] :
( ( ( c_Big__Operators_Olinorder__class_OMin(U_8320,U_8321) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8320),U_8322),c_Big__Operators_Olinorder__class_OMin(U_8320,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(U_8320,U_8321) = U_8322
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8320),U_8322),U_8321))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8320),U_8321))
| ~ class_Orderings_Olinorder(U_8320) ),
inference(variable_rename,[status(thm)],[f_2428_1]) ).
fof(f_2428_3,plain,
( ! [U_8321,U_8320,U_8322] :
( c_Big__Operators_Olinorder__class_OMin(U_8320,U_8321) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8320),U_8322),c_Big__Operators_Olinorder__class_OMin(U_8320,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool))
| ~ sP753(U_8321,U_8320,U_8322) )
& ! [U_8321,U_8320,U_8322] :
( c_Big__Operators_Olinorder__class_OMin(U_8320,U_8321) = U_8322
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool))
| ~ sP753(U_8321,U_8320,U_8322) )
& ! [U_8321,U_8320,U_8322] :
( sP753(U_8321,U_8320,U_8322)
| ~ hBOOL(hAPP(hAPP(c_member(U_8320),U_8322),U_8321))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8320),U_8321))
| ~ class_Orderings_Olinorder(U_8320) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP753])],[f_2428_2]) ).
cnf(f_2428_4,plain,
( sP753(U_8321,U_8320,U_8322)
| ~ hBOOL(hAPP(hAPP(c_member(U_8320),U_8322),U_8321))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8320),U_8321))
| ~ class_Orderings_Olinorder(U_8320) ),
inference(clausify,[status(thm)],[f_2428_3]) ).
cnf(f_2428_5,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8320,U_8321) = U_8322
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool))
| ~ sP753(U_8321,U_8320,U_8322) ),
inference(clausify,[status(thm)],[f_2428_3]) ).
cnf(f_2428_6,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8320,U_8321) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8320),U_8322),c_Big__Operators_Olinorder__class_OMin(U_8320,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8320,tc_HOL_Obool)),U_8321),hAPP(hAPP(c_Set_Oinsert(U_8320),U_8322),c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8320,tc_HOL_Obool))
| ~ sP753(U_8321,U_8320,U_8322) ),
inference(clausify,[status(thm)],[f_2428_3]) ).
fof(f_2429_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove]) ).
fof(f_2429_2,plain,
! [U_8325,U_8324,U_8323] :
( ( ( c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),U_8324) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8323),U_8325),c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),U_8324) = U_8325
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8323),U_8325),U_8324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8324))
| ~ class_Orderings_Olinorder(U_8323) ),
inference(variable_rename,[status(thm)],[f_2429_1]) ).
fof(f_2429_3,plain,
( ! [U_8324,U_8325,U_8323] :
( c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),U_8324) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8323),U_8325),c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool))
| ~ sP754(U_8324,U_8325,U_8323) )
& ! [U_8324,U_8325,U_8323] :
( c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),U_8324) = U_8325
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool))
| ~ sP754(U_8324,U_8325,U_8323) )
& ! [U_8324,U_8325,U_8323] :
( sP754(U_8324,U_8325,U_8323)
| ~ hBOOL(hAPP(hAPP(c_member(U_8323),U_8325),U_8324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8324))
| ~ class_Orderings_Olinorder(U_8323) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP754])],[f_2429_2]) ).
cnf(f_2429_4,plain,
( sP754(U_8324,U_8325,U_8323)
| ~ hBOOL(hAPP(hAPP(c_member(U_8323),U_8325),U_8324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8324))
| ~ class_Orderings_Olinorder(U_8323) ),
inference(clausify,[status(thm)],[f_2429_3]) ).
cnf(f_2429_5,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),U_8324) = U_8325
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool))
| ~ sP754(U_8324,U_8325,U_8323) ),
inference(clausify,[status(thm)],[f_2429_3]) ).
cnf(f_2429_6,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),U_8324) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8323),U_8325),c_Big__Operators_Olattice_OInf__fin(U_8323,c_Orderings_Oord__class_Omin(U_8323),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8323,tc_HOL_Obool)),U_8324),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8325),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool))
| ~ sP754(U_8324,U_8325,U_8323) ),
inference(clausify,[status(thm)],[f_2429_3]) ).
fof(f_2430_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold_H]) ).
fof(f_2430_2,plain,
! [U_8328,U_8327,U_8326] :
( c_Big__Operators_Olinorder__class_OMin(U_8326,hAPP(hAPP(c_Set_Oinsert(U_8326),U_8328),U_8327)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8326,U_8326,c_Orderings_Oord__class_Omin(U_8326)),U_8328),U_8327)
| hBOOL(hAPP(hAPP(c_member(U_8326),U_8328),U_8327))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8326),U_8327))
| ~ class_Orderings_Olinorder(U_8326) ),
inference(variable_rename,[status(thm)],[f_2430_1]) ).
fof(f_2430_3,plain,
! [U_8328,U_8327,U_8326] :
( c_Big__Operators_Olinorder__class_OMin(U_8326,hAPP(hAPP(c_Set_Oinsert(U_8326),U_8328),U_8327)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8326,U_8326,c_Orderings_Oord__class_Omin(U_8326)),U_8328),U_8327)
| hBOOL(hAPP(hAPP(c_member(U_8326),U_8328),U_8327))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8326),U_8327))
| ~ class_Orderings_Olinorder(U_8326) ),
inference(definitional_conversion,[status(esa)],[f_2430_2]) ).
cnf(f_2430_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8326,hAPP(hAPP(c_Set_Oinsert(U_8326),U_8328),U_8327)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8326,U_8326,c_Orderings_Oord__class_Omin(U_8326)),U_8328),U_8327)
| hBOOL(hAPP(hAPP(c_member(U_8326),U_8328),U_8327))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8326),U_8327))
| ~ class_Orderings_Olinorder(U_8326) ),
inference(clausify,[status(thm)],[f_2430_3]) ).
fof(f_2431_1,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_inf__nat__def]) ).
fof(f_2431_2,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_2431_1]) ).
cnf(f_2431_3,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2431_2]) ).
fof(f_2432_1,plain,
! [V_x_2,T_b] :
( 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
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Osingleton]) ).
fof(f_2432_2,plain,
! [U_8330,U_8329] :
( c_Big__Operators_Olinorder__class_OMin(U_8329,hAPP(hAPP(c_Set_Oinsert(U_8329),U_8330),c_Orderings_Obot__class_Obot(tc_fun(U_8329,tc_HOL_Obool)))) = U_8330
| ~ class_Orderings_Olinorder(U_8329) ),
inference(variable_rename,[status(thm)],[f_2432_1]) ).
fof(f_2432_3,plain,
! [U_8329,U_8330] :
( c_Big__Operators_Olinorder__class_OMin(U_8329,hAPP(hAPP(c_Set_Oinsert(U_8329),U_8330),c_Orderings_Obot__class_Obot(tc_fun(U_8329,tc_HOL_Obool)))) = U_8330
| ~ class_Orderings_Olinorder(U_8329) ),
inference(definitional_conversion,[status(esa)],[f_2432_2]) ).
cnf(f_2432_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8329,hAPP(hAPP(c_Set_Oinsert(U_8329),U_8330),c_Orderings_Obot__class_Obot(tc_fun(U_8329,tc_HOL_Obool)))) = U_8330
| ~ class_Orderings_Olinorder(U_8329) ),
inference(clausify,[status(thm)],[f_2432_3]) ).
fof(f_2433_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem]) ).
fof(f_2433_2,plain,
! [U_8333,U_8332,U_8331] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8331),U_8333),c_Big__Operators_Olattice_OInf__fin(U_8331,c_Orderings_Oord__class_Omin(U_8331),U_8332)) = c_Big__Operators_Olattice_OInf__fin(U_8331,c_Orderings_Oord__class_Omin(U_8331),U_8332)
| ~ hBOOL(hAPP(hAPP(c_member(U_8331),U_8333),U_8332))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8331),U_8332))
| ~ class_Orderings_Olinorder(U_8331) ),
inference(variable_rename,[status(thm)],[f_2433_1]) ).
fof(f_2433_3,plain,
! [U_8331,U_8332,U_8333] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8331),U_8333),c_Big__Operators_Olattice_OInf__fin(U_8331,c_Orderings_Oord__class_Omin(U_8331),U_8332)) = c_Big__Operators_Olattice_OInf__fin(U_8331,c_Orderings_Oord__class_Omin(U_8331),U_8332)
| ~ hBOOL(hAPP(hAPP(c_member(U_8331),U_8333),U_8332))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8331),U_8332))
| ~ class_Orderings_Olinorder(U_8331) ),
inference(definitional_conversion,[status(esa)],[f_2433_2]) ).
cnf(f_2433_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8331),U_8333),c_Big__Operators_Olattice_OInf__fin(U_8331,c_Orderings_Oord__class_Omin(U_8331),U_8332)) = c_Big__Operators_Olattice_OInf__fin(U_8331,c_Orderings_Oord__class_Omin(U_8331),U_8332)
| ~ hBOOL(hAPP(hAPP(c_member(U_8331),U_8333),U_8332))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8331),U_8332))
| ~ class_Orderings_Olinorder(U_8331) ),
inference(clausify,[status(thm)],[f_2433_3]) ).
fof(f_2434_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__le]) ).
fof(f_2434_2,plain,
! [U_8336,U_8335,U_8334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8334),c_Big__Operators_Olinorder__class_OMin(U_8334,U_8335)),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8334),U_8336),U_8335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8334),U_8335))
| ~ class_Orderings_Olinorder(U_8334) ),
inference(variable_rename,[status(thm)],[f_2434_1]) ).
fof(f_2434_3,plain,
! [U_8334,U_8335,U_8336] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8334),c_Big__Operators_Olinorder__class_OMin(U_8334,U_8335)),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8334),U_8336),U_8335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8334),U_8335))
| ~ class_Orderings_Olinorder(U_8334) ),
inference(definitional_conversion,[status(esa)],[f_2434_2]) ).
cnf(f_2434_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8334),c_Big__Operators_Olinorder__class_OMin(U_8334,U_8335)),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8334),U_8336),U_8335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8334),U_8335))
| ~ class_Orderings_Olinorder(U_8334) ),
inference(clausify,[status(thm)],[f_2434_3]) ).
fof(f_2435_1,plain,
! [V_x_2,T_b] :
( 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
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton]) ).
fof(f_2435_2,plain,
! [U_8338,U_8337] :
( c_Big__Operators_Olattice_OInf__fin(U_8337,c_Orderings_Oord__class_Omin(U_8337),hAPP(hAPP(c_Set_Oinsert(U_8337),U_8338),c_Orderings_Obot__class_Obot(tc_fun(U_8337,tc_HOL_Obool)))) = U_8338
| ~ class_Orderings_Olinorder(U_8337) ),
inference(variable_rename,[status(thm)],[f_2435_1]) ).
fof(f_2435_3,plain,
! [U_8337,U_8338] :
( c_Big__Operators_Olattice_OInf__fin(U_8337,c_Orderings_Oord__class_Omin(U_8337),hAPP(hAPP(c_Set_Oinsert(U_8337),U_8338),c_Orderings_Obot__class_Obot(tc_fun(U_8337,tc_HOL_Obool)))) = U_8338
| ~ class_Orderings_Olinorder(U_8337) ),
inference(definitional_conversion,[status(esa)],[f_2435_2]) ).
cnf(f_2435_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8337,c_Orderings_Oord__class_Omin(U_8337),hAPP(hAPP(c_Set_Oinsert(U_8337),U_8338),c_Orderings_Obot__class_Obot(tc_fun(U_8337,tc_HOL_Obool)))) = U_8338
| ~ class_Orderings_Olinorder(U_8337) ),
inference(clausify,[status(thm)],[f_2435_3]) ).
fof(f_2436_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__in]) ).
fof(f_2436_2,plain,
! [U_8340,U_8339] :
( hBOOL(hAPP(hAPP(c_member(U_8339),c_Big__Operators_Olinorder__class_OMin(U_8339,U_8340)),U_8340))
| U_8340 = c_Orderings_Obot__class_Obot(tc_fun(U_8339,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8339),U_8340))
| ~ class_Orderings_Olinorder(U_8339) ),
inference(variable_rename,[status(thm)],[f_2436_1]) ).
fof(f_2436_3,plain,
! [U_8339,U_8340] :
( hBOOL(hAPP(hAPP(c_member(U_8339),c_Big__Operators_Olinorder__class_OMin(U_8339,U_8340)),U_8340))
| U_8340 = c_Orderings_Obot__class_Obot(tc_fun(U_8339,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8339),U_8340))
| ~ class_Orderings_Olinorder(U_8339) ),
inference(definitional_conversion,[status(esa)],[f_2436_2]) ).
cnf(f_2436_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8339),c_Big__Operators_Olinorder__class_OMin(U_8339,U_8340)),U_8340))
| U_8340 = c_Orderings_Obot__class_Obot(tc_fun(U_8339,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8339),U_8340))
| ~ class_Orderings_Olinorder(U_8339) ),
inference(clausify,[status(thm)],[f_2436_3]) ).
fof(f_2437_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem]) ).
fof(f_2437_2,plain,
! [U_8343,U_8342,U_8341] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8341),U_8343),c_Big__Operators_Olinorder__class_OMin(U_8341,U_8342)) = c_Big__Operators_Olinorder__class_OMin(U_8341,U_8342)
| ~ hBOOL(hAPP(hAPP(c_member(U_8341),U_8343),U_8342))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8341),U_8342))
| ~ class_Orderings_Olinorder(U_8341) ),
inference(variable_rename,[status(thm)],[f_2437_1]) ).
fof(f_2437_3,plain,
! [U_8342,U_8341,U_8343] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8341),U_8343),c_Big__Operators_Olinorder__class_OMin(U_8341,U_8342)) = c_Big__Operators_Olinorder__class_OMin(U_8341,U_8342)
| ~ hBOOL(hAPP(hAPP(c_member(U_8341),U_8343),U_8342))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8341),U_8342))
| ~ class_Orderings_Olinorder(U_8341) ),
inference(definitional_conversion,[status(esa)],[f_2437_2]) ).
cnf(f_2437_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8341),U_8343),c_Big__Operators_Olinorder__class_OMin(U_8341,U_8342)) = c_Big__Operators_Olinorder__class_OMin(U_8341,U_8342)
| ~ hBOOL(hAPP(hAPP(c_member(U_8341),U_8343),U_8342))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8341),U_8342))
| ~ class_Orderings_Olinorder(U_8341) ),
inference(clausify,[status(thm)],[f_2437_3]) ).
fof(f_2438_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq]) ).
fof(f_2438_2,plain,
! [U_8345,U_8344] :
( c_Big__Operators_Olattice_OInf__fin(U_8344,c_Orderings_Oord__class_Omin(U_8344),U_8345) = hAPP(c_Finite__Set_Ofold1(U_8344,c_Orderings_Oord__class_Omin(U_8344)),U_8345)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8344),U_8345))
| ~ class_Orderings_Olinorder(U_8344) ),
inference(variable_rename,[status(thm)],[f_2438_1]) ).
fof(f_2438_3,plain,
! [U_8344,U_8345] :
( c_Big__Operators_Olattice_OInf__fin(U_8344,c_Orderings_Oord__class_Omin(U_8344),U_8345) = hAPP(c_Finite__Set_Ofold1(U_8344,c_Orderings_Oord__class_Omin(U_8344)),U_8345)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8344),U_8345))
| ~ class_Orderings_Olinorder(U_8344) ),
inference(definitional_conversion,[status(esa)],[f_2438_2]) ).
cnf(f_2438_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8344,c_Orderings_Oord__class_Omin(U_8344),U_8345) = hAPP(c_Finite__Set_Ofold1(U_8344,c_Orderings_Oord__class_Omin(U_8344)),U_8345)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8344),U_8345))
| ~ class_Orderings_Olinorder(U_8344) ),
inference(clausify,[status(thm)],[f_2438_3]) ).
fof(f_2439_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_OF__eq]) ).
fof(f_2439_2,plain,
! [U_8347,U_8346] :
( c_Big__Operators_Olinorder__class_OMin(U_8346,U_8347) = hAPP(c_Finite__Set_Ofold1(U_8346,c_Orderings_Oord__class_Omin(U_8346)),U_8347)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8346),U_8347))
| ~ class_Orderings_Olinorder(U_8346) ),
inference(variable_rename,[status(thm)],[f_2439_1]) ).
fof(f_2439_3,plain,
! [U_8346,U_8347] :
( c_Big__Operators_Olinorder__class_OMin(U_8346,U_8347) = hAPP(c_Finite__Set_Ofold1(U_8346,c_Orderings_Oord__class_Omin(U_8346)),U_8347)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8346),U_8347))
| ~ class_Orderings_Olinorder(U_8346) ),
inference(definitional_conversion,[status(esa)],[f_2439_2]) ).
cnf(f_2439_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8346,U_8347) = hAPP(c_Finite__Set_Ofold1(U_8346,c_Orderings_Oord__class_Omin(U_8346)),U_8347)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8346),U_8347))
| ~ class_Orderings_Olinorder(U_8346) ),
inference(clausify,[status(thm)],[f_2439_3]) ).
fof(f_2440_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem]) ).
fof(f_2440_2,plain,
! [U_8350,U_8349,U_8348] :
( c_Big__Operators_Olattice_OInf__fin(U_8348,c_Orderings_Oord__class_Omin(U_8348),hAPP(hAPP(c_Set_Oinsert(U_8348),U_8350),U_8349)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8348),U_8350),c_Big__Operators_Olattice_OInf__fin(U_8348,c_Orderings_Oord__class_Omin(U_8348),U_8349))
| U_8349 = c_Orderings_Obot__class_Obot(tc_fun(U_8348,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8348),U_8349))
| ~ class_Orderings_Olinorder(U_8348) ),
inference(variable_rename,[status(thm)],[f_2440_1]) ).
fof(f_2440_3,plain,
! [U_8348,U_8349,U_8350] :
( c_Big__Operators_Olattice_OInf__fin(U_8348,c_Orderings_Oord__class_Omin(U_8348),hAPP(hAPP(c_Set_Oinsert(U_8348),U_8350),U_8349)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8348),U_8350),c_Big__Operators_Olattice_OInf__fin(U_8348,c_Orderings_Oord__class_Omin(U_8348),U_8349))
| U_8349 = c_Orderings_Obot__class_Obot(tc_fun(U_8348,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8348),U_8349))
| ~ class_Orderings_Olinorder(U_8348) ),
inference(definitional_conversion,[status(esa)],[f_2440_2]) ).
cnf(f_2440_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8348,c_Orderings_Oord__class_Omin(U_8348),hAPP(hAPP(c_Set_Oinsert(U_8348),U_8350),U_8349)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8348),U_8350),c_Big__Operators_Olattice_OInf__fin(U_8348,c_Orderings_Oord__class_Omin(U_8348),U_8349))
| U_8349 = c_Orderings_Obot__class_Obot(tc_fun(U_8348,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8348),U_8349))
| ~ class_Orderings_Olinorder(U_8348) ),
inference(clausify,[status(thm)],[f_2440_3]) ).
fof(f_2441_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem]) ).
fof(f_2441_2,plain,
! [U_8353,U_8352,U_8351] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8351),c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8353)),c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8352)) = c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8352)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8351,tc_HOL_Obool)),U_8353),U_8352))
| U_8353 = c_Orderings_Obot__class_Obot(tc_fun(U_8351,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8351),U_8352))
| ~ class_Orderings_Olinorder(U_8351) ),
inference(variable_rename,[status(thm)],[f_2441_1]) ).
fof(f_2441_3,plain,
! [U_8351,U_8352,U_8353] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8351),c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8353)),c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8352)) = c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8352)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8351,tc_HOL_Obool)),U_8353),U_8352))
| U_8353 = c_Orderings_Obot__class_Obot(tc_fun(U_8351,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8351),U_8352))
| ~ class_Orderings_Olinorder(U_8351) ),
inference(definitional_conversion,[status(esa)],[f_2441_2]) ).
cnf(f_2441_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8351),c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8353)),c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8352)) = c_Big__Operators_Olattice_OInf__fin(U_8351,c_Orderings_Oord__class_Omin(U_8351),U_8352)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8351,tc_HOL_Obool)),U_8353),U_8352))
| U_8353 = c_Orderings_Obot__class_Obot(tc_fun(U_8351,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8351),U_8352))
| ~ class_Orderings_Olinorder(U_8351) ),
inference(clausify,[status(thm)],[f_2441_3]) ).
fof(f_2442_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem]) ).
fof(f_2442_2,plain,
! [U_8356,U_8355,U_8354] :
( c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8354,tc_HOL_Obool)),U_8355),U_8356)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8354),c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),U_8355)),c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),U_8356))
| U_8356 = c_Orderings_Obot__class_Obot(tc_fun(U_8354,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8354),U_8356))
| U_8355 = c_Orderings_Obot__class_Obot(tc_fun(U_8354,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8354),U_8355))
| ~ class_Orderings_Olinorder(U_8354) ),
inference(variable_rename,[status(thm)],[f_2442_1]) ).
fof(f_2442_3,plain,
! [U_8355,U_8354,U_8356] :
( c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8354,tc_HOL_Obool)),U_8355),U_8356)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8354),c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),U_8355)),c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),U_8356))
| U_8356 = c_Orderings_Obot__class_Obot(tc_fun(U_8354,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8354),U_8356))
| U_8355 = c_Orderings_Obot__class_Obot(tc_fun(U_8354,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8354),U_8355))
| ~ class_Orderings_Olinorder(U_8354) ),
inference(definitional_conversion,[status(esa)],[f_2442_2]) ).
cnf(f_2442_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8354,tc_HOL_Obool)),U_8355),U_8356)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8354),c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),U_8355)),c_Big__Operators_Olattice_OInf__fin(U_8354,c_Orderings_Oord__class_Omin(U_8354),U_8356))
| U_8356 = c_Orderings_Obot__class_Obot(tc_fun(U_8354,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8354),U_8356))
| U_8355 = c_Orderings_Obot__class_Obot(tc_fun(U_8354,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8354),U_8355))
| ~ class_Orderings_Olinorder(U_8354) ),
inference(clausify,[status(thm)],[f_2442_3]) ).
fof(f_2443_1,plain,
! [V_N_2,V_M_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__antimono]) ).
fof(f_2443_2,plain,
! [U_8359,U_8358,U_8357] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8357),c_Big__Operators_Olinorder__class_OMin(U_8357,U_8359)),c_Big__Operators_Olinorder__class_OMin(U_8357,U_8358)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8357),U_8359))
| U_8358 = c_Orderings_Obot__class_Obot(tc_fun(U_8357,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8357,tc_HOL_Obool)),U_8358),U_8359))
| ~ class_Orderings_Olinorder(U_8357) ),
inference(variable_rename,[status(thm)],[f_2443_1]) ).
fof(f_2443_3,plain,
! [U_8359,U_8358,U_8357] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8357),c_Big__Operators_Olinorder__class_OMin(U_8357,U_8359)),c_Big__Operators_Olinorder__class_OMin(U_8357,U_8358)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8357),U_8359))
| U_8358 = c_Orderings_Obot__class_Obot(tc_fun(U_8357,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8357,tc_HOL_Obool)),U_8358),U_8359))
| ~ class_Orderings_Olinorder(U_8357) ),
inference(definitional_conversion,[status(esa)],[f_2443_2]) ).
cnf(f_2443_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8357),c_Big__Operators_Olinorder__class_OMin(U_8357,U_8359)),c_Big__Operators_Olinorder__class_OMin(U_8357,U_8358)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8357),U_8359))
| U_8358 = c_Orderings_Obot__class_Obot(tc_fun(U_8357,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8357,tc_HOL_Obool)),U_8358),U_8359))
| ~ class_Orderings_Olinorder(U_8357) ),
inference(clausify,[status(thm)],[f_2443_3]) ).
fof(f_2444_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H]) ).
fof(f_2444_2,plain,
! [U_8362,U_8361,U_8360] :
( c_Big__Operators_Olattice_OInf__fin(U_8360,c_Orderings_Oord__class_Omin(U_8360),hAPP(hAPP(c_Set_Oinsert(U_8360),U_8362),U_8361)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8360,U_8360,c_Orderings_Oord__class_Omin(U_8360)),U_8362),U_8361)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8360),U_8361))
| ~ class_Orderings_Olinorder(U_8360) ),
inference(variable_rename,[status(thm)],[f_2444_1]) ).
fof(f_2444_3,plain,
! [U_8361,U_8362,U_8360] :
( c_Big__Operators_Olattice_OInf__fin(U_8360,c_Orderings_Oord__class_Omin(U_8360),hAPP(hAPP(c_Set_Oinsert(U_8360),U_8362),U_8361)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8360,U_8360,c_Orderings_Oord__class_Omin(U_8360)),U_8362),U_8361)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8360),U_8361))
| ~ class_Orderings_Olinorder(U_8360) ),
inference(definitional_conversion,[status(esa)],[f_2444_2]) ).
cnf(f_2444_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8360,c_Orderings_Oord__class_Omin(U_8360),hAPP(hAPP(c_Set_Oinsert(U_8360),U_8362),U_8361)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8360,U_8360,c_Orderings_Oord__class_Omin(U_8360)),U_8362),U_8361)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8360),U_8361))
| ~ class_Orderings_Olinorder(U_8360) ),
inference(clausify,[status(thm)],[f_2444_3]) ).
fof(f_2445_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__insert]) ).
fof(f_2445_2,plain,
! [U_8365,U_8364,U_8363] :
( c_Big__Operators_Olinorder__class_OMin(U_8363,hAPP(hAPP(c_Set_Oinsert(U_8363),U_8365),U_8364)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8363),U_8365),c_Big__Operators_Olinorder__class_OMin(U_8363,U_8364))
| U_8364 = c_Orderings_Obot__class_Obot(tc_fun(U_8363,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8363),U_8364))
| ~ class_Orderings_Olinorder(U_8363) ),
inference(variable_rename,[status(thm)],[f_2445_1]) ).
fof(f_2445_3,plain,
! [U_8363,U_8364,U_8365] :
( c_Big__Operators_Olinorder__class_OMin(U_8363,hAPP(hAPP(c_Set_Oinsert(U_8363),U_8365),U_8364)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8363),U_8365),c_Big__Operators_Olinorder__class_OMin(U_8363,U_8364))
| U_8364 = c_Orderings_Obot__class_Obot(tc_fun(U_8363,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8363),U_8364))
| ~ class_Orderings_Olinorder(U_8363) ),
inference(definitional_conversion,[status(esa)],[f_2445_2]) ).
cnf(f_2445_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8363,hAPP(hAPP(c_Set_Oinsert(U_8363),U_8365),U_8364)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8363),U_8365),c_Big__Operators_Olinorder__class_OMin(U_8363,U_8364))
| U_8364 = c_Orderings_Obot__class_Obot(tc_fun(U_8363,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8363),U_8364))
| ~ class_Orderings_Olinorder(U_8363) ),
inference(clausify,[status(thm)],[f_2445_3]) ).
fof(f_2446_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem]) ).
fof(f_2446_2,plain,
! [U_8368,U_8367,U_8366] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8366),c_Big__Operators_Olinorder__class_OMin(U_8366,U_8368)),c_Big__Operators_Olinorder__class_OMin(U_8366,U_8367)) = c_Big__Operators_Olinorder__class_OMin(U_8366,U_8367)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8366,tc_HOL_Obool)),U_8368),U_8367))
| U_8368 = c_Orderings_Obot__class_Obot(tc_fun(U_8366,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8366),U_8367))
| ~ class_Orderings_Olinorder(U_8366) ),
inference(variable_rename,[status(thm)],[f_2446_1]) ).
fof(f_2446_3,plain,
! [U_8366,U_8367,U_8368] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8366),c_Big__Operators_Olinorder__class_OMin(U_8366,U_8368)),c_Big__Operators_Olinorder__class_OMin(U_8366,U_8367)) = c_Big__Operators_Olinorder__class_OMin(U_8366,U_8367)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8366,tc_HOL_Obool)),U_8368),U_8367))
| U_8368 = c_Orderings_Obot__class_Obot(tc_fun(U_8366,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8366),U_8367))
| ~ class_Orderings_Olinorder(U_8366) ),
inference(definitional_conversion,[status(esa)],[f_2446_2]) ).
cnf(f_2446_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8366),c_Big__Operators_Olinorder__class_OMin(U_8366,U_8368)),c_Big__Operators_Olinorder__class_OMin(U_8366,U_8367)) = c_Big__Operators_Olinorder__class_OMin(U_8366,U_8367)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8366,tc_HOL_Obool)),U_8368),U_8367))
| U_8368 = c_Orderings_Obot__class_Obot(tc_fun(U_8366,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8366),U_8367))
| ~ class_Orderings_Olinorder(U_8366) ),
inference(clausify,[status(thm)],[f_2446_3]) ).
fof(f_2447_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__Un]) ).
fof(f_2447_2,plain,
! [U_8371,U_8370,U_8369] :
( c_Big__Operators_Olinorder__class_OMin(U_8369,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8369,tc_HOL_Obool)),U_8370),U_8371)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8369),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8370)),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8371))
| U_8371 = c_Orderings_Obot__class_Obot(tc_fun(U_8369,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8369),U_8371))
| U_8370 = c_Orderings_Obot__class_Obot(tc_fun(U_8369,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8369),U_8370))
| ~ class_Orderings_Olinorder(U_8369) ),
inference(variable_rename,[status(thm)],[f_2447_1]) ).
fof(f_2447_3,plain,
! [U_8369,U_8370,U_8371] :
( c_Big__Operators_Olinorder__class_OMin(U_8369,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8369,tc_HOL_Obool)),U_8370),U_8371)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8369),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8370)),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8371))
| U_8371 = c_Orderings_Obot__class_Obot(tc_fun(U_8369,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8369),U_8371))
| U_8370 = c_Orderings_Obot__class_Obot(tc_fun(U_8369,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8369),U_8370))
| ~ class_Orderings_Olinorder(U_8369) ),
inference(definitional_conversion,[status(esa)],[f_2447_2]) ).
cnf(f_2447_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8369,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8369,tc_HOL_Obool)),U_8370),U_8371)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8369),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8370)),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8371))
| U_8371 = c_Orderings_Obot__class_Obot(tc_fun(U_8369,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8369),U_8371))
| U_8370 = c_Orderings_Obot__class_Obot(tc_fun(U_8369,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8369),U_8370))
| ~ class_Orderings_Olinorder(U_8369) ),
inference(clausify,[status(thm)],[f_2447_3]) ).
fof(f_2448_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H]) ).
fof(f_2448_2,plain,
! [U_8374,U_8373,U_8372] :
( c_Big__Operators_Olinorder__class_OMin(U_8372,hAPP(hAPP(c_Set_Oinsert(U_8372),U_8374),U_8373)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8372,U_8372,c_Orderings_Oord__class_Omin(U_8372)),U_8374),U_8373)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8372),U_8373))
| ~ class_Orderings_Olinorder(U_8372) ),
inference(variable_rename,[status(thm)],[f_2448_1]) ).
fof(f_2448_3,plain,
! [U_8372,U_8374,U_8373] :
( c_Big__Operators_Olinorder__class_OMin(U_8372,hAPP(hAPP(c_Set_Oinsert(U_8372),U_8374),U_8373)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8372,U_8372,c_Orderings_Oord__class_Omin(U_8372)),U_8374),U_8373)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8372),U_8373))
| ~ class_Orderings_Olinorder(U_8372) ),
inference(definitional_conversion,[status(esa)],[f_2448_2]) ).
cnf(f_2448_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8372,hAPP(hAPP(c_Set_Oinsert(U_8372),U_8374),U_8373)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8372,U_8372,c_Orderings_Oord__class_Omin(U_8372)),U_8374),U_8373)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8372),U_8373))
| ~ class_Orderings_Olinorder(U_8372) ),
inference(clausify,[status(thm)],[f_2448_3]) ).
fof(f_2449_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).
fof(f_2449_2,plain,
! [U_8377,U_8376,U_8375] :
( c_Big__Operators_Olattice_OInf__fin(U_8375,c_Orderings_Oord__class_Omin(U_8375),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),U_8376)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8375),U_8377),c_Big__Operators_Olattice_OInf__fin(U_8375,c_Orderings_Oord__class_Omin(U_8375),U_8376))
| U_8376 = c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8375),U_8377),U_8376))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8375),U_8376))
| ~ class_Orderings_Olinorder(U_8375) ),
inference(variable_rename,[status(thm)],[f_2449_1]) ).
fof(f_2449_3,plain,
! [U_8375,U_8376,U_8377] :
( c_Big__Operators_Olattice_OInf__fin(U_8375,c_Orderings_Oord__class_Omin(U_8375),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),U_8376)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8375),U_8377),c_Big__Operators_Olattice_OInf__fin(U_8375,c_Orderings_Oord__class_Omin(U_8375),U_8376))
| U_8376 = c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8375),U_8377),U_8376))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8375),U_8376))
| ~ class_Orderings_Olinorder(U_8375) ),
inference(definitional_conversion,[status(esa)],[f_2449_2]) ).
cnf(f_2449_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8375,c_Orderings_Oord__class_Omin(U_8375),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),U_8376)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8375),U_8377),c_Big__Operators_Olattice_OInf__fin(U_8375,c_Orderings_Oord__class_Omin(U_8375),U_8376))
| U_8376 = c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8375),U_8377),U_8376))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8375),U_8376))
| ~ class_Orderings_Olinorder(U_8375) ),
inference(clausify,[status(thm)],[f_2449_3]) ).
fof(f_2450_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( 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
| 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)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove]) ).
fof(f_2450_2,plain,
! [U_8380,U_8379,U_8378] :
( ( ( c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),U_8379)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8378),U_8380),c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),U_8379)) = U_8380
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8378),U_8379))
| ~ class_Orderings_Olinorder(U_8378) ),
inference(variable_rename,[status(thm)],[f_2450_1]) ).
fof(f_2450_3,plain,
( ! [U_8379,U_8378,U_8380] :
( c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),U_8379)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8378),U_8380),c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))
| ~ sP755(U_8379,U_8378,U_8380) )
& ! [U_8379,U_8378,U_8380] :
( c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),U_8379)) = U_8380
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))
| ~ sP755(U_8379,U_8378,U_8380) )
& ! [U_8379,U_8378,U_8380] :
( sP755(U_8379,U_8378,U_8380)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8378),U_8379))
| ~ class_Orderings_Olinorder(U_8378) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP755])],[f_2450_2]) ).
cnf(f_2450_4,plain,
( sP755(U_8379,U_8378,U_8380)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8378),U_8379))
| ~ class_Orderings_Olinorder(U_8378) ),
inference(clausify,[status(thm)],[f_2450_3]) ).
cnf(f_2450_5,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),U_8379)) = U_8380
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))
| ~ sP755(U_8379,U_8378,U_8380) ),
inference(clausify,[status(thm)],[f_2450_3]) ).
cnf(f_2450_6,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),U_8379)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8378),U_8380),c_Big__Operators_Olattice_OInf__fin(U_8378,c_Orderings_Oord__class_Omin(U_8378),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))
| ~ sP755(U_8379,U_8378,U_8380) ),
inference(clausify,[status(thm)],[f_2450_3]) ).
fof(f_2451_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter]) ).
fof(f_2451_2,plain,
! [U_8383,U_8382,U_8381] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8381),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383))),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8381),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),U_8382)),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),U_8383))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383) = c_Orderings_Obot__class_Obot(tc_fun(U_8381,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8381),U_8383))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8381),U_8382))
| ~ class_Orderings_Olinorder(U_8381) ),
inference(variable_rename,[status(thm)],[f_2451_1]) ).
fof(f_2451_3,plain,
! [U_8381,U_8382,U_8383] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8381),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383))),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8381),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),U_8382)),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),U_8383))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383) = c_Orderings_Obot__class_Obot(tc_fun(U_8381,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8381),U_8383))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8381),U_8382))
| ~ class_Orderings_Olinorder(U_8381) ),
inference(definitional_conversion,[status(esa)],[f_2451_2]) ).
cnf(f_2451_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8381),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383))),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8381),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),U_8382)),c_Big__Operators_Olattice_OInf__fin(U_8381,c_Orderings_Oord__class_Omin(U_8381),U_8383))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8381,tc_HOL_Obool)),U_8382),U_8383) = c_Orderings_Obot__class_Obot(tc_fun(U_8381,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8381),U_8383))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8381),U_8382))
| ~ class_Orderings_Olinorder(U_8381) ),
inference(clausify,[status(thm)],[f_2451_3]) ).
fof(f_2452_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint]) ).
fof(f_2452_2,plain,
! [U_8386,U_8385,U_8384] :
( c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8384,tc_HOL_Obool)),U_8385),U_8386)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8384),c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),U_8385)),c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),U_8386))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8384,tc_HOL_Obool)),U_8385),U_8386) != c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| U_8386 = c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8384),U_8386))
| U_8385 = c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8384),U_8385))
| ~ class_Orderings_Olinorder(U_8384) ),
inference(variable_rename,[status(thm)],[f_2452_1]) ).
fof(f_2452_3,plain,
! [U_8385,U_8386,U_8384] :
( c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8384,tc_HOL_Obool)),U_8385),U_8386)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8384),c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),U_8385)),c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),U_8386))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8384,tc_HOL_Obool)),U_8385),U_8386) != c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| U_8386 = c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8384),U_8386))
| U_8385 = c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8384),U_8385))
| ~ class_Orderings_Olinorder(U_8384) ),
inference(definitional_conversion,[status(esa)],[f_2452_2]) ).
cnf(f_2452_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8384,tc_HOL_Obool)),U_8385),U_8386)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8384),c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),U_8385)),c_Big__Operators_Olattice_OInf__fin(U_8384,c_Orderings_Oord__class_Omin(U_8384),U_8386))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8384,tc_HOL_Obool)),U_8385),U_8386) != c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| U_8386 = c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8384),U_8386))
| U_8385 = c_Orderings_Obot__class_Obot(tc_fun(U_8384,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8384),U_8385))
| ~ class_Orderings_Olinorder(U_8384) ),
inference(clausify,[status(thm)],[f_2452_3]) ).
fof(f_2453_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).
fof(f_2453_2,plain,
! [U_8389,U_8388,U_8387] :
( c_Big__Operators_Olattice_OInf__fin(U_8387,c_Orderings_Oord__class_Omin(U_8387),hAPP(hAPP(c_Set_Oinsert(U_8387),U_8389),U_8388)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8387,U_8387,c_Orderings_Oord__class_Omin(U_8387)),U_8389),U_8388)
| hBOOL(hAPP(hAPP(c_member(U_8387),U_8389),U_8388))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8387),U_8388))
| ~ class_Orderings_Olinorder(U_8387) ),
inference(variable_rename,[status(thm)],[f_2453_1]) ).
fof(f_2453_3,plain,
! [U_8388,U_8387,U_8389] :
( c_Big__Operators_Olattice_OInf__fin(U_8387,c_Orderings_Oord__class_Omin(U_8387),hAPP(hAPP(c_Set_Oinsert(U_8387),U_8389),U_8388)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8387,U_8387,c_Orderings_Oord__class_Omin(U_8387)),U_8389),U_8388)
| hBOOL(hAPP(hAPP(c_member(U_8387),U_8389),U_8388))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8387),U_8388))
| ~ class_Orderings_Olinorder(U_8387) ),
inference(definitional_conversion,[status(esa)],[f_2453_2]) ).
cnf(f_2453_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8387,c_Orderings_Oord__class_Omin(U_8387),hAPP(hAPP(c_Set_Oinsert(U_8387),U_8389),U_8388)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8387,U_8387,c_Orderings_Oord__class_Omin(U_8387)),U_8389),U_8388)
| hBOOL(hAPP(hAPP(c_member(U_8387),U_8389),U_8388))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8387),U_8388))
| ~ class_Orderings_Olinorder(U_8387) ),
inference(clausify,[status(thm)],[f_2453_3]) ).
fof(f_2454_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oinsert]) ).
fof(f_2454_2,plain,
! [U_8392,U_8391,U_8390] :
( c_Big__Operators_Olinorder__class_OMin(U_8390,hAPP(hAPP(c_Set_Oinsert(U_8390),U_8392),U_8391)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8390),U_8392),c_Big__Operators_Olinorder__class_OMin(U_8390,U_8391))
| U_8391 = c_Orderings_Obot__class_Obot(tc_fun(U_8390,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8390),U_8392),U_8391))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8390),U_8391))
| ~ class_Orderings_Olinorder(U_8390) ),
inference(variable_rename,[status(thm)],[f_2454_1]) ).
fof(f_2454_3,plain,
! [U_8390,U_8391,U_8392] :
( c_Big__Operators_Olinorder__class_OMin(U_8390,hAPP(hAPP(c_Set_Oinsert(U_8390),U_8392),U_8391)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8390),U_8392),c_Big__Operators_Olinorder__class_OMin(U_8390,U_8391))
| U_8391 = c_Orderings_Obot__class_Obot(tc_fun(U_8390,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8390),U_8392),U_8391))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8390),U_8391))
| ~ class_Orderings_Olinorder(U_8390) ),
inference(definitional_conversion,[status(esa)],[f_2454_2]) ).
cnf(f_2454_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8390,hAPP(hAPP(c_Set_Oinsert(U_8390),U_8392),U_8391)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8390),U_8392),c_Big__Operators_Olinorder__class_OMin(U_8390,U_8391))
| U_8391 = c_Orderings_Obot__class_Obot(tc_fun(U_8390,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8390),U_8392),U_8391))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8390),U_8391))
| ~ class_Orderings_Olinorder(U_8390) ),
inference(clausify,[status(thm)],[f_2454_3]) ).
fof(f_2455_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove]) ).
fof(f_2455_2,plain,
! [U_8395,U_8394,U_8393] :
( ( ( c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),U_8394)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8393),U_8395),c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),U_8394)) = U_8395
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8393),U_8394))
| ~ class_Orderings_Olinorder(U_8393) ),
inference(variable_rename,[status(thm)],[f_2455_1]) ).
fof(f_2455_3,plain,
( ! [U_8393,U_8394,U_8395] :
( c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),U_8394)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8393),U_8395),c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool))
| ~ sP756(U_8393,U_8394,U_8395) )
& ! [U_8393,U_8394,U_8395] :
( c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),U_8394)) = U_8395
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool))
| ~ sP756(U_8393,U_8394,U_8395) )
& ! [U_8393,U_8394,U_8395] :
( sP756(U_8393,U_8394,U_8395)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8393),U_8394))
| ~ class_Orderings_Olinorder(U_8393) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP756])],[f_2455_2]) ).
cnf(f_2455_4,plain,
( sP756(U_8393,U_8394,U_8395)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8393),U_8394))
| ~ class_Orderings_Olinorder(U_8393) ),
inference(clausify,[status(thm)],[f_2455_3]) ).
cnf(f_2455_5,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),U_8394)) = U_8395
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool))
| ~ sP756(U_8393,U_8394,U_8395) ),
inference(clausify,[status(thm)],[f_2455_3]) ).
cnf(f_2455_6,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),U_8394)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8393),U_8395),c_Big__Operators_Olinorder__class_OMin(U_8393,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8393,tc_HOL_Obool)),U_8394),hAPP(hAPP(c_Set_Oinsert(U_8393),U_8395),c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8393,tc_HOL_Obool))
| ~ sP756(U_8393,U_8394,U_8395) ),
inference(clausify,[status(thm)],[f_2455_3]) ).
fof(f_2456_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter]) ).
fof(f_2456_2,plain,
! [U_8398,U_8397,U_8396] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8396),c_Big__Operators_Olinorder__class_OMin(U_8396,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398))),c_Big__Operators_Olinorder__class_OMin(U_8396,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8396),c_Big__Operators_Olinorder__class_OMin(U_8396,U_8397)),c_Big__Operators_Olinorder__class_OMin(U_8396,U_8398))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398) = c_Orderings_Obot__class_Obot(tc_fun(U_8396,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8396),U_8398))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8396),U_8397))
| ~ class_Orderings_Olinorder(U_8396) ),
inference(variable_rename,[status(thm)],[f_2456_1]) ).
fof(f_2456_3,plain,
! [U_8398,U_8397,U_8396] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8396),c_Big__Operators_Olinorder__class_OMin(U_8396,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398))),c_Big__Operators_Olinorder__class_OMin(U_8396,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8396),c_Big__Operators_Olinorder__class_OMin(U_8396,U_8397)),c_Big__Operators_Olinorder__class_OMin(U_8396,U_8398))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398) = c_Orderings_Obot__class_Obot(tc_fun(U_8396,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8396),U_8398))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8396),U_8397))
| ~ class_Orderings_Olinorder(U_8396) ),
inference(definitional_conversion,[status(esa)],[f_2456_2]) ).
cnf(f_2456_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8396),c_Big__Operators_Olinorder__class_OMin(U_8396,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398))),c_Big__Operators_Olinorder__class_OMin(U_8396,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8396),c_Big__Operators_Olinorder__class_OMin(U_8396,U_8397)),c_Big__Operators_Olinorder__class_OMin(U_8396,U_8398))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398) = c_Orderings_Obot__class_Obot(tc_fun(U_8396,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8396),U_8398))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8396),U_8397))
| ~ class_Orderings_Olinorder(U_8396) ),
inference(clausify,[status(thm)],[f_2456_3]) ).
fof(f_2457_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint]) ).
fof(f_2457_2,plain,
! [U_8401,U_8400,U_8399] :
( c_Big__Operators_Olinorder__class_OMin(U_8399,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8399,tc_HOL_Obool)),U_8400),U_8401)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8399),c_Big__Operators_Olinorder__class_OMin(U_8399,U_8400)),c_Big__Operators_Olinorder__class_OMin(U_8399,U_8401))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8399,tc_HOL_Obool)),U_8400),U_8401) != c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| U_8401 = c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8399),U_8401))
| U_8400 = c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8399),U_8400))
| ~ class_Orderings_Olinorder(U_8399) ),
inference(variable_rename,[status(thm)],[f_2457_1]) ).
fof(f_2457_3,plain,
! [U_8399,U_8400,U_8401] :
( c_Big__Operators_Olinorder__class_OMin(U_8399,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8399,tc_HOL_Obool)),U_8400),U_8401)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8399),c_Big__Operators_Olinorder__class_OMin(U_8399,U_8400)),c_Big__Operators_Olinorder__class_OMin(U_8399,U_8401))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8399,tc_HOL_Obool)),U_8400),U_8401) != c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| U_8401 = c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8399),U_8401))
| U_8400 = c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8399),U_8400))
| ~ class_Orderings_Olinorder(U_8399) ),
inference(definitional_conversion,[status(esa)],[f_2457_2]) ).
cnf(f_2457_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8399,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8399,tc_HOL_Obool)),U_8400),U_8401)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8399),c_Big__Operators_Olinorder__class_OMin(U_8399,U_8400)),c_Big__Operators_Olinorder__class_OMin(U_8399,U_8401))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8399,tc_HOL_Obool)),U_8400),U_8401) != c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| U_8401 = c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8399),U_8401))
| U_8400 = c_Orderings_Obot__class_Obot(tc_fun(U_8399,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8399),U_8400))
| ~ class_Orderings_Olinorder(U_8399) ),
inference(clausify,[status(thm)],[f_2457_3]) ).
fof(f_2458_1,plain,
! [V_A_2,T_b] :
( 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))
| ? [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))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed]) ).
fof(f_2458_2,plain,
! [U_8405,U_8404] :
( hBOOL(hAPP(hAPP(c_member(U_8404),c_Big__Operators_Olattice_OInf__fin(U_8404,c_Orderings_Oord__class_Omin(U_8404),U_8405)),U_8405))
| ? [U_8403,U_8402] : ~ hBOOL(hAPP(hAPP(c_member(U_8404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8404),U_8403),U_8402)),hAPP(hAPP(c_Set_Oinsert(U_8404),U_8403),hAPP(hAPP(c_Set_Oinsert(U_8404),U_8402),c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))))))
| U_8405 = c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8404),U_8405))
| ~ class_Orderings_Olinorder(U_8404) ),
inference(variable_rename,[status(thm)],[f_2458_1]) ).
fof(f_2458_3,plain,
! [U_8405,U_8404] :
( hBOOL(hAPP(hAPP(c_member(U_8404),c_Big__Operators_Olattice_OInf__fin(U_8404,c_Orderings_Oord__class_Omin(U_8404),U_8405)),U_8405))
| ? [U_8402] : ~ hBOOL(hAPP(hAPP(c_member(U_8404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8404),sK225(U_8405,U_8404)),U_8402)),hAPP(hAPP(c_Set_Oinsert(U_8404),sK225(U_8405,U_8404)),hAPP(hAPP(c_Set_Oinsert(U_8404),U_8402),c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))))))
| U_8405 = c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8404),U_8405))
| ~ class_Orderings_Olinorder(U_8404) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_8403,sK225(U_8405,U_8404))],[f_2458_2]) ).
fof(f_2458_4,plain,
! [U_8405,U_8404] :
( hBOOL(hAPP(hAPP(c_member(U_8404),c_Big__Operators_Olattice_OInf__fin(U_8404,c_Orderings_Oord__class_Omin(U_8404),U_8405)),U_8405))
| ~ hBOOL(hAPP(hAPP(c_member(U_8404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8404),sK225(U_8405,U_8404)),sK226(U_8405,U_8404))),hAPP(hAPP(c_Set_Oinsert(U_8404),sK225(U_8405,U_8404)),hAPP(hAPP(c_Set_Oinsert(U_8404),sK226(U_8405,U_8404)),c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))))))
| U_8405 = c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8404),U_8405))
| ~ class_Orderings_Olinorder(U_8404) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_8402,sK226(U_8405,U_8404))],[f_2458_3]) ).
fof(f_2458_5,plain,
! [U_8404,U_8405] :
( hBOOL(hAPP(hAPP(c_member(U_8404),c_Big__Operators_Olattice_OInf__fin(U_8404,c_Orderings_Oord__class_Omin(U_8404),U_8405)),U_8405))
| ~ hBOOL(hAPP(hAPP(c_member(U_8404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8404),sK225(U_8405,U_8404)),sK226(U_8405,U_8404))),hAPP(hAPP(c_Set_Oinsert(U_8404),sK225(U_8405,U_8404)),hAPP(hAPP(c_Set_Oinsert(U_8404),sK226(U_8405,U_8404)),c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))))))
| U_8405 = c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8404),U_8405))
| ~ class_Orderings_Olinorder(U_8404) ),
inference(definitional_conversion,[status(esa)],[f_2458_4]) ).
cnf(f_2458_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8404),c_Big__Operators_Olattice_OInf__fin(U_8404,c_Orderings_Oord__class_Omin(U_8404),U_8405)),U_8405))
| ~ hBOOL(hAPP(hAPP(c_member(U_8404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8404),sK225(U_8405,U_8404)),sK226(U_8405,U_8404))),hAPP(hAPP(c_Set_Oinsert(U_8404),sK225(U_8405,U_8404)),hAPP(hAPP(c_Set_Oinsert(U_8404),sK226(U_8405,U_8404)),c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))))))
| U_8405 = c_Orderings_Obot__class_Obot(tc_fun(U_8404,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8404),U_8405))
| ~ class_Orderings_Olinorder(U_8404) ),
inference(clausify,[status(thm)],[f_2458_5]) ).
fof(f_2459_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))
| ? [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))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oclosed]) ).
fof(f_2459_2,plain,
! [U_8409,U_8408] :
( hBOOL(hAPP(hAPP(c_member(U_8408),c_Big__Operators_Olinorder__class_OMin(U_8408,U_8409)),U_8409))
| ? [U_8407,U_8406] : ~ hBOOL(hAPP(hAPP(c_member(U_8408),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8408),U_8407),U_8406)),hAPP(hAPP(c_Set_Oinsert(U_8408),U_8407),hAPP(hAPP(c_Set_Oinsert(U_8408),U_8406),c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))))))
| U_8409 = c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8408),U_8409))
| ~ class_Orderings_Olinorder(U_8408) ),
inference(variable_rename,[status(thm)],[f_2459_1]) ).
fof(f_2459_3,plain,
! [U_8409,U_8408] :
( hBOOL(hAPP(hAPP(c_member(U_8408),c_Big__Operators_Olinorder__class_OMin(U_8408,U_8409)),U_8409))
| ? [U_8406] : ~ hBOOL(hAPP(hAPP(c_member(U_8408),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8408),sK227(U_8409,U_8408)),U_8406)),hAPP(hAPP(c_Set_Oinsert(U_8408),sK227(U_8409,U_8408)),hAPP(hAPP(c_Set_Oinsert(U_8408),U_8406),c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))))))
| U_8409 = c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8408),U_8409))
| ~ class_Orderings_Olinorder(U_8408) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_8407,sK227(U_8409,U_8408))],[f_2459_2]) ).
fof(f_2459_4,plain,
! [U_8409,U_8408] :
( hBOOL(hAPP(hAPP(c_member(U_8408),c_Big__Operators_Olinorder__class_OMin(U_8408,U_8409)),U_8409))
| ~ hBOOL(hAPP(hAPP(c_member(U_8408),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8408),sK227(U_8409,U_8408)),sK228(U_8409,U_8408))),hAPP(hAPP(c_Set_Oinsert(U_8408),sK227(U_8409,U_8408)),hAPP(hAPP(c_Set_Oinsert(U_8408),sK228(U_8409,U_8408)),c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))))))
| U_8409 = c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8408),U_8409))
| ~ class_Orderings_Olinorder(U_8408) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_8406,sK228(U_8409,U_8408))],[f_2459_3]) ).
fof(f_2459_5,plain,
! [U_8408,U_8409] :
( hBOOL(hAPP(hAPP(c_member(U_8408),c_Big__Operators_Olinorder__class_OMin(U_8408,U_8409)),U_8409))
| ~ hBOOL(hAPP(hAPP(c_member(U_8408),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8408),sK227(U_8409,U_8408)),sK228(U_8409,U_8408))),hAPP(hAPP(c_Set_Oinsert(U_8408),sK227(U_8409,U_8408)),hAPP(hAPP(c_Set_Oinsert(U_8408),sK228(U_8409,U_8408)),c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))))))
| U_8409 = c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8408),U_8409))
| ~ class_Orderings_Olinorder(U_8408) ),
inference(definitional_conversion,[status(esa)],[f_2459_4]) ).
cnf(f_2459_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8408),c_Big__Operators_Olinorder__class_OMin(U_8408,U_8409)),U_8409))
| ~ hBOOL(hAPP(hAPP(c_member(U_8408),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8408),sK227(U_8409,U_8408)),sK228(U_8409,U_8408))),hAPP(hAPP(c_Set_Oinsert(U_8408),sK227(U_8409,U_8408)),hAPP(hAPP(c_Set_Oinsert(U_8408),sK228(U_8409,U_8408)),c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))))))
| U_8409 = c_Orderings_Obot__class_Obot(tc_fun(U_8408,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8408),U_8409))
| ~ class_Orderings_Olinorder(U_8408) ),
inference(clausify,[status(thm)],[f_2459_5]) ).
fof(f_2460_1,plain,
! [V_N_2,V_h_2,T_b] :
( 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))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [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))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute]) ).
fof(f_2460_2,plain,
! [U_8414,U_8413,U_8412] :
( hAPP(U_8413,c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),U_8414)) = c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),hAPP(c_Set_Oimage(U_8412,U_8412,U_8413),U_8414))
| U_8414 = c_Orderings_Obot__class_Obot(tc_fun(U_8412,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8412),U_8414))
| ? [U_8411,U_8410] : hAPP(U_8413,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),U_8411),U_8410)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),hAPP(U_8413,U_8411)),hAPP(U_8413,U_8410))
| ~ class_Orderings_Olinorder(U_8412) ),
inference(variable_rename,[status(thm)],[f_2460_1]) ).
fof(f_2460_3,plain,
! [U_8414,U_8413,U_8412] :
( hAPP(U_8413,c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),U_8414)) = c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),hAPP(c_Set_Oimage(U_8412,U_8412,U_8413),U_8414))
| U_8414 = c_Orderings_Obot__class_Obot(tc_fun(U_8412,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8412),U_8414))
| ? [U_8410] : hAPP(U_8413,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),sK229(U_8414,U_8413,U_8412)),U_8410)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),hAPP(U_8413,sK229(U_8414,U_8413,U_8412))),hAPP(U_8413,U_8410))
| ~ class_Orderings_Olinorder(U_8412) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_8411,sK229(U_8414,U_8413,U_8412))],[f_2460_2]) ).
fof(f_2460_4,plain,
! [U_8414,U_8413,U_8412] :
( hAPP(U_8413,c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),U_8414)) = c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),hAPP(c_Set_Oimage(U_8412,U_8412,U_8413),U_8414))
| U_8414 = c_Orderings_Obot__class_Obot(tc_fun(U_8412,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8412),U_8414))
| hAPP(U_8413,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),sK229(U_8414,U_8413,U_8412)),sK230(U_8414,U_8413,U_8412))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),hAPP(U_8413,sK229(U_8414,U_8413,U_8412))),hAPP(U_8413,sK230(U_8414,U_8413,U_8412)))
| ~ class_Orderings_Olinorder(U_8412) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_8410,sK230(U_8414,U_8413,U_8412))],[f_2460_3]) ).
fof(f_2460_5,plain,
! [U_8412,U_8413,U_8414] :
( hAPP(U_8413,c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),U_8414)) = c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),hAPP(c_Set_Oimage(U_8412,U_8412,U_8413),U_8414))
| U_8414 = c_Orderings_Obot__class_Obot(tc_fun(U_8412,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8412),U_8414))
| hAPP(U_8413,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),sK229(U_8414,U_8413,U_8412)),sK230(U_8414,U_8413,U_8412))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),hAPP(U_8413,sK229(U_8414,U_8413,U_8412))),hAPP(U_8413,sK230(U_8414,U_8413,U_8412)))
| ~ class_Orderings_Olinorder(U_8412) ),
inference(definitional_conversion,[status(esa)],[f_2460_4]) ).
cnf(f_2460_6,plain,
( hAPP(U_8413,c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),U_8414)) = c_Big__Operators_Olattice_OInf__fin(U_8412,c_Orderings_Oord__class_Omin(U_8412),hAPP(c_Set_Oimage(U_8412,U_8412,U_8413),U_8414))
| U_8414 = c_Orderings_Obot__class_Obot(tc_fun(U_8412,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8412),U_8414))
| hAPP(U_8413,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),sK229(U_8414,U_8413,U_8412)),sK230(U_8414,U_8413,U_8412))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8412),hAPP(U_8413,sK229(U_8414,U_8413,U_8412))),hAPP(U_8413,sK230(U_8414,U_8413,U_8412)))
| ~ class_Orderings_Olinorder(U_8412) ),
inference(clausify,[status(thm)],[f_2460_5]) ).
fof(f_2461_1,plain,
! [V_N_2,V_h_2,T_b] :
( 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))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [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))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute]) ).
fof(f_2461_2,plain,
! [U_8419,U_8418,U_8417] :
( hAPP(U_8418,c_Big__Operators_Olinorder__class_OMin(U_8417,U_8419)) = c_Big__Operators_Olinorder__class_OMin(U_8417,hAPP(c_Set_Oimage(U_8417,U_8417,U_8418),U_8419))
| U_8419 = c_Orderings_Obot__class_Obot(tc_fun(U_8417,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8417),U_8419))
| ? [U_8416,U_8415] : hAPP(U_8418,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),U_8416),U_8415)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),hAPP(U_8418,U_8416)),hAPP(U_8418,U_8415))
| ~ class_Orderings_Olinorder(U_8417) ),
inference(variable_rename,[status(thm)],[f_2461_1]) ).
fof(f_2461_3,plain,
! [U_8419,U_8418,U_8417] :
( hAPP(U_8418,c_Big__Operators_Olinorder__class_OMin(U_8417,U_8419)) = c_Big__Operators_Olinorder__class_OMin(U_8417,hAPP(c_Set_Oimage(U_8417,U_8417,U_8418),U_8419))
| U_8419 = c_Orderings_Obot__class_Obot(tc_fun(U_8417,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8417),U_8419))
| ? [U_8415] : hAPP(U_8418,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),sK231(U_8419,U_8418,U_8417)),U_8415)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),hAPP(U_8418,sK231(U_8419,U_8418,U_8417))),hAPP(U_8418,U_8415))
| ~ class_Orderings_Olinorder(U_8417) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_8416,sK231(U_8419,U_8418,U_8417))],[f_2461_2]) ).
fof(f_2461_4,plain,
! [U_8419,U_8418,U_8417] :
( hAPP(U_8418,c_Big__Operators_Olinorder__class_OMin(U_8417,U_8419)) = c_Big__Operators_Olinorder__class_OMin(U_8417,hAPP(c_Set_Oimage(U_8417,U_8417,U_8418),U_8419))
| U_8419 = c_Orderings_Obot__class_Obot(tc_fun(U_8417,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8417),U_8419))
| hAPP(U_8418,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),sK231(U_8419,U_8418,U_8417)),sK232(U_8419,U_8418,U_8417))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),hAPP(U_8418,sK231(U_8419,U_8418,U_8417))),hAPP(U_8418,sK232(U_8419,U_8418,U_8417)))
| ~ class_Orderings_Olinorder(U_8417) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_8415,sK232(U_8419,U_8418,U_8417))],[f_2461_3]) ).
fof(f_2461_5,plain,
! [U_8417,U_8418,U_8419] :
( hAPP(U_8418,c_Big__Operators_Olinorder__class_OMin(U_8417,U_8419)) = c_Big__Operators_Olinorder__class_OMin(U_8417,hAPP(c_Set_Oimage(U_8417,U_8417,U_8418),U_8419))
| U_8419 = c_Orderings_Obot__class_Obot(tc_fun(U_8417,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8417),U_8419))
| hAPP(U_8418,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),sK231(U_8419,U_8418,U_8417)),sK232(U_8419,U_8418,U_8417))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),hAPP(U_8418,sK231(U_8419,U_8418,U_8417))),hAPP(U_8418,sK232(U_8419,U_8418,U_8417)))
| ~ class_Orderings_Olinorder(U_8417) ),
inference(definitional_conversion,[status(esa)],[f_2461_4]) ).
cnf(f_2461_6,plain,
( hAPP(U_8418,c_Big__Operators_Olinorder__class_OMin(U_8417,U_8419)) = c_Big__Operators_Olinorder__class_OMin(U_8417,hAPP(c_Set_Oimage(U_8417,U_8417,U_8418),U_8419))
| U_8419 = c_Orderings_Obot__class_Obot(tc_fun(U_8417,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8417),U_8419))
| hAPP(U_8418,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),sK231(U_8419,U_8418,U_8417)),sK232(U_8419,U_8418,U_8417))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8417),hAPP(U_8418,sK231(U_8419,U_8418,U_8417))),hAPP(U_8418,sK232(U_8419,U_8418,U_8417)))
| ~ class_Orderings_Olinorder(U_8417) ),
inference(clausify,[status(thm)],[f_2461_5]) ).
fof(f_2462_1,plain,
! [V_S_2,T_b] :
( 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))
| V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min]) ).
fof(f_2462_2,plain,
! [U_8421,U_8420] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8420),c_Big__Operators_Olinorder__class_OMax(U_8420,U_8421)) = c_Big__Operators_Olinorder__class_OMin(U_8420,hAPP(c_Set_Oimage(U_8420,U_8420,c_Groups_Ouminus__class_Ouminus(U_8420)),U_8421))
| U_8421 = c_Orderings_Obot__class_Obot(tc_fun(U_8420,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8420),U_8421))
| ~ class_Groups_Olinordered__ab__group__add(U_8420) ),
inference(variable_rename,[status(thm)],[f_2462_1]) ).
fof(f_2462_3,plain,
! [U_8420,U_8421] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8420),c_Big__Operators_Olinorder__class_OMax(U_8420,U_8421)) = c_Big__Operators_Olinorder__class_OMin(U_8420,hAPP(c_Set_Oimage(U_8420,U_8420,c_Groups_Ouminus__class_Ouminus(U_8420)),U_8421))
| U_8421 = c_Orderings_Obot__class_Obot(tc_fun(U_8420,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8420),U_8421))
| ~ class_Groups_Olinordered__ab__group__add(U_8420) ),
inference(definitional_conversion,[status(esa)],[f_2462_2]) ).
cnf(f_2462_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8420),c_Big__Operators_Olinorder__class_OMax(U_8420,U_8421)) = c_Big__Operators_Olinorder__class_OMin(U_8420,hAPP(c_Set_Oimage(U_8420,U_8420,c_Groups_Ouminus__class_Ouminus(U_8420)),U_8421))
| U_8421 = c_Orderings_Obot__class_Obot(tc_fun(U_8420,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8420),U_8421))
| ~ class_Groups_Olinordered__ab__group__add(U_8420) ),
inference(clausify,[status(thm)],[f_2462_3]) ).
fof(f_2463_1,plain,
! [V_S_2,T_b] :
( 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))
| V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max]) ).
fof(f_2463_2,plain,
! [U_8423,U_8422] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8422),c_Big__Operators_Olinorder__class_OMin(U_8422,U_8423)) = c_Big__Operators_Olinorder__class_OMax(U_8422,hAPP(c_Set_Oimage(U_8422,U_8422,c_Groups_Ouminus__class_Ouminus(U_8422)),U_8423))
| U_8423 = c_Orderings_Obot__class_Obot(tc_fun(U_8422,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8422),U_8423))
| ~ class_Groups_Olinordered__ab__group__add(U_8422) ),
inference(variable_rename,[status(thm)],[f_2463_1]) ).
fof(f_2463_3,plain,
! [U_8422,U_8423] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8422),c_Big__Operators_Olinorder__class_OMin(U_8422,U_8423)) = c_Big__Operators_Olinorder__class_OMax(U_8422,hAPP(c_Set_Oimage(U_8422,U_8422,c_Groups_Ouminus__class_Ouminus(U_8422)),U_8423))
| U_8423 = c_Orderings_Obot__class_Obot(tc_fun(U_8422,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8422),U_8423))
| ~ class_Groups_Olinordered__ab__group__add(U_8422) ),
inference(definitional_conversion,[status(esa)],[f_2463_2]) ).
cnf(f_2463_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8422),c_Big__Operators_Olinorder__class_OMin(U_8422,U_8423)) = c_Big__Operators_Olinorder__class_OMax(U_8422,hAPP(c_Set_Oimage(U_8422,U_8422,c_Groups_Ouminus__class_Ouminus(U_8422)),U_8423))
| U_8423 = c_Orderings_Obot__class_Obot(tc_fun(U_8422,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8422),U_8423))
| ~ class_Groups_Olinordered__ab__group__add(U_8422) ),
inference(clausify,[status(thm)],[f_2463_3]) ).
fof(f_2464_1,plain,
! [V_ca_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf]) ).
fof(f_2464_2,plain,
! [U_8428,U_8427,U_8426,U_8425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8425),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8425),U_8427),U_8428)),hAPP(hAPP(c_Finite__Set_Ofold(U_8425,U_8425,c_Orderings_Oord__class_Omin(U_8425)),U_8428),U_8426)))
| ? [U_8424] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8425),U_8427),U_8424))
& hBOOL(hAPP(hAPP(c_member(U_8425),U_8424),U_8426)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8425),U_8426))
| ~ class_Orderings_Olinorder(U_8425) ),
inference(variable_rename,[status(thm)],[f_2464_1]) ).
fof(f_2464_3,plain,
! [U_8428,U_8427,U_8426,U_8425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8425),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8425),U_8427),U_8428)),hAPP(hAPP(c_Finite__Set_Ofold(U_8425,U_8425,c_Orderings_Oord__class_Omin(U_8425)),U_8428),U_8426)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8425),U_8427),sK233(U_8428,U_8427,U_8426,U_8425)))
& hBOOL(hAPP(hAPP(c_member(U_8425),sK233(U_8428,U_8427,U_8426,U_8425)),U_8426)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8425),U_8426))
| ~ class_Orderings_Olinorder(U_8425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_8424,sK233(U_8428,U_8427,U_8426,U_8425))],[f_2464_2]) ).
fof(f_2464_4,plain,
( ! [U_8425,U_8426,U_8427,U_8428] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8425),U_8427),sK233(U_8428,U_8427,U_8426,U_8425)))
| ~ sP757(U_8425,U_8426,U_8427,U_8428) )
& ! [U_8425,U_8426,U_8427,U_8428] :
( hBOOL(hAPP(hAPP(c_member(U_8425),sK233(U_8428,U_8427,U_8426,U_8425)),U_8426))
| ~ sP757(U_8425,U_8426,U_8427,U_8428) )
& ! [U_8425,U_8426,U_8427,U_8428] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8425),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8425),U_8427),U_8428)),hAPP(hAPP(c_Finite__Set_Ofold(U_8425,U_8425,c_Orderings_Oord__class_Omin(U_8425)),U_8428),U_8426)))
| sP757(U_8425,U_8426,U_8427,U_8428)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8425),U_8426))
| ~ class_Orderings_Olinorder(U_8425) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP757])],[f_2464_3]) ).
cnf(f_2464_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8425),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8425),U_8427),U_8428)),hAPP(hAPP(c_Finite__Set_Ofold(U_8425,U_8425,c_Orderings_Oord__class_Omin(U_8425)),U_8428),U_8426)))
| sP757(U_8425,U_8426,U_8427,U_8428)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8425),U_8426))
| ~ class_Orderings_Olinorder(U_8425) ),
inference(clausify,[status(thm)],[f_2464_4]) ).
cnf(f_2464_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8425),sK233(U_8428,U_8427,U_8426,U_8425)),U_8426))
| ~ sP757(U_8425,U_8426,U_8427,U_8428) ),
inference(clausify,[status(thm)],[f_2464_4]) ).
cnf(f_2464_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8425),U_8427),sK233(U_8428,U_8427,U_8426,U_8425)))
| ~ sP757(U_8425,U_8426,U_8427,U_8428) ),
inference(clausify,[status(thm)],[f_2464_4]) ).
fof(f_2465_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__eqI]) ).
fof(f_2465_2,plain,
! [U_8432,U_8431,U_8430] :
( c_Big__Operators_Olinorder__class_OMin(U_8430,U_8431) = U_8432
| ~ hBOOL(hAPP(hAPP(c_member(U_8430),U_8432),U_8431))
| ? [U_8429] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8430),U_8432),U_8429))
& hBOOL(hAPP(hAPP(c_member(U_8430),U_8429),U_8431)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8430),U_8431))
| ~ class_Orderings_Olinorder(U_8430) ),
inference(variable_rename,[status(thm)],[f_2465_1]) ).
fof(f_2465_3,plain,
! [U_8432,U_8431,U_8430] :
( c_Big__Operators_Olinorder__class_OMin(U_8430,U_8431) = U_8432
| ~ hBOOL(hAPP(hAPP(c_member(U_8430),U_8432),U_8431))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8430),U_8432),sK234(U_8432,U_8431,U_8430)))
& hBOOL(hAPP(hAPP(c_member(U_8430),sK234(U_8432,U_8431,U_8430)),U_8431)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8430),U_8431))
| ~ class_Orderings_Olinorder(U_8430) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_8429,sK234(U_8432,U_8431,U_8430))],[f_2465_2]) ).
fof(f_2465_4,plain,
( ! [U_8430,U_8431,U_8432] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8430),U_8432),sK234(U_8432,U_8431,U_8430)))
| ~ sP758(U_8430,U_8431,U_8432) )
& ! [U_8430,U_8431,U_8432] :
( hBOOL(hAPP(hAPP(c_member(U_8430),sK234(U_8432,U_8431,U_8430)),U_8431))
| ~ sP758(U_8430,U_8431,U_8432) )
& ! [U_8430,U_8431,U_8432] :
( c_Big__Operators_Olinorder__class_OMin(U_8430,U_8431) = U_8432
| ~ hBOOL(hAPP(hAPP(c_member(U_8430),U_8432),U_8431))
| sP758(U_8430,U_8431,U_8432)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8430),U_8431))
| ~ class_Orderings_Olinorder(U_8430) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP758])],[f_2465_3]) ).
cnf(f_2465_5,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8430,U_8431) = U_8432
| ~ hBOOL(hAPP(hAPP(c_member(U_8430),U_8432),U_8431))
| sP758(U_8430,U_8431,U_8432)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8430),U_8431))
| ~ class_Orderings_Olinorder(U_8430) ),
inference(clausify,[status(thm)],[f_2465_4]) ).
cnf(f_2465_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8430),sK234(U_8432,U_8431,U_8430)),U_8431))
| ~ sP758(U_8430,U_8431,U_8432) ),
inference(clausify,[status(thm)],[f_2465_4]) ).
cnf(f_2465_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8430),U_8432),sK234(U_8432,U_8431,U_8430)))
| ~ sP758(U_8430,U_8431,U_8432) ),
inference(clausify,[status(thm)],[f_2465_4]) ).
fof(f_2466_1,plain,
! [V_x_2,T_b] :
( 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
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Osingleton]) ).
fof(f_2466_2,plain,
! [U_8434,U_8433] :
( c_Big__Operators_Olinorder__class_OMax(U_8433,hAPP(hAPP(c_Set_Oinsert(U_8433),U_8434),c_Orderings_Obot__class_Obot(tc_fun(U_8433,tc_HOL_Obool)))) = U_8434
| ~ class_Orderings_Olinorder(U_8433) ),
inference(variable_rename,[status(thm)],[f_2466_1]) ).
fof(f_2466_3,plain,
! [U_8434,U_8433] :
( c_Big__Operators_Olinorder__class_OMax(U_8433,hAPP(hAPP(c_Set_Oinsert(U_8433),U_8434),c_Orderings_Obot__class_Obot(tc_fun(U_8433,tc_HOL_Obool)))) = U_8434
| ~ class_Orderings_Olinorder(U_8433) ),
inference(definitional_conversion,[status(esa)],[f_2466_2]) ).
cnf(f_2466_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8433,hAPP(hAPP(c_Set_Oinsert(U_8433),U_8434),c_Orderings_Obot__class_Obot(tc_fun(U_8433,tc_HOL_Obool)))) = U_8434
| ~ class_Orderings_Olinorder(U_8433) ),
inference(clausify,[status(thm)],[f_2466_3]) ).
fof(f_2467_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__ge]) ).
fof(f_2467_2,plain,
! [U_8437,U_8436,U_8435] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8435),U_8437),c_Big__Operators_Olinorder__class_OMax(U_8435,U_8436)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8435),U_8437),U_8436))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8435),U_8436))
| ~ class_Orderings_Olinorder(U_8435) ),
inference(variable_rename,[status(thm)],[f_2467_1]) ).
fof(f_2467_3,plain,
! [U_8436,U_8435,U_8437] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8435),U_8437),c_Big__Operators_Olinorder__class_OMax(U_8435,U_8436)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8435),U_8437),U_8436))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8435),U_8436))
| ~ class_Orderings_Olinorder(U_8435) ),
inference(definitional_conversion,[status(esa)],[f_2467_2]) ).
cnf(f_2467_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8435),U_8437),c_Big__Operators_Olinorder__class_OMax(U_8435,U_8436)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8435),U_8437),U_8436))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8435),U_8436))
| ~ class_Orderings_Olinorder(U_8435) ),
inference(clausify,[status(thm)],[f_2467_3]) ).
fof(f_2468_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__in]) ).
fof(f_2468_2,plain,
! [U_8439,U_8438] :
( hBOOL(hAPP(hAPP(c_member(U_8438),c_Big__Operators_Olinorder__class_OMax(U_8438,U_8439)),U_8439))
| U_8439 = c_Orderings_Obot__class_Obot(tc_fun(U_8438,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8438),U_8439))
| ~ class_Orderings_Olinorder(U_8438) ),
inference(variable_rename,[status(thm)],[f_2468_1]) ).
fof(f_2468_3,plain,
! [U_8438,U_8439] :
( hBOOL(hAPP(hAPP(c_member(U_8438),c_Big__Operators_Olinorder__class_OMax(U_8438,U_8439)),U_8439))
| U_8439 = c_Orderings_Obot__class_Obot(tc_fun(U_8438,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8438),U_8439))
| ~ class_Orderings_Olinorder(U_8438) ),
inference(definitional_conversion,[status(esa)],[f_2468_2]) ).
cnf(f_2468_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8438),c_Big__Operators_Olinorder__class_OMax(U_8438,U_8439)),U_8439))
| U_8439 = c_Orderings_Obot__class_Obot(tc_fun(U_8438,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8438),U_8439))
| ~ class_Orderings_Olinorder(U_8438) ),
inference(clausify,[status(thm)],[f_2468_3]) ).
fof(f_2469_1,plain,
! [V_N_2,V_M_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__mono]) ).
fof(f_2469_2,plain,
! [U_8442,U_8441,U_8440] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),c_Big__Operators_Olinorder__class_OMax(U_8440,U_8441)),c_Big__Operators_Olinorder__class_OMax(U_8440,U_8442)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8440),U_8442))
| U_8441 = c_Orderings_Obot__class_Obot(tc_fun(U_8440,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8440,tc_HOL_Obool)),U_8441),U_8442))
| ~ class_Orderings_Olinorder(U_8440) ),
inference(variable_rename,[status(thm)],[f_2469_1]) ).
fof(f_2469_3,plain,
! [U_8440,U_8441,U_8442] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),c_Big__Operators_Olinorder__class_OMax(U_8440,U_8441)),c_Big__Operators_Olinorder__class_OMax(U_8440,U_8442)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8440),U_8442))
| U_8441 = c_Orderings_Obot__class_Obot(tc_fun(U_8440,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8440,tc_HOL_Obool)),U_8441),U_8442))
| ~ class_Orderings_Olinorder(U_8440) ),
inference(definitional_conversion,[status(esa)],[f_2469_2]) ).
cnf(f_2469_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),c_Big__Operators_Olinorder__class_OMax(U_8440,U_8441)),c_Big__Operators_Olinorder__class_OMax(U_8440,U_8442)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8440),U_8442))
| U_8441 = c_Orderings_Obot__class_Obot(tc_fun(U_8440,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8440,tc_HOL_Obool)),U_8441),U_8442))
| ~ class_Orderings_Olinorder(U_8440) ),
inference(clausify,[status(thm)],[f_2469_3]) ).
fof(f_2470_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oremove]) ).
fof(f_2470_2,plain,
! [U_8445,U_8444,U_8443] :
( ( ( c_Big__Operators_Olinorder__class_OMax(U_8443,U_8444) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8443),U_8445),c_Big__Operators_Olinorder__class_OMax(U_8443,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(U_8443,U_8444) = U_8445
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8443),U_8445),U_8444))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8443),U_8444))
| ~ class_Orderings_Olinorder(U_8443) ),
inference(variable_rename,[status(thm)],[f_2470_1]) ).
fof(f_2470_3,plain,
( ! [U_8444,U_8445,U_8443] :
( c_Big__Operators_Olinorder__class_OMax(U_8443,U_8444) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8443),U_8445),c_Big__Operators_Olinorder__class_OMax(U_8443,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool))
| ~ sP759(U_8444,U_8445,U_8443) )
& ! [U_8444,U_8445,U_8443] :
( c_Big__Operators_Olinorder__class_OMax(U_8443,U_8444) = U_8445
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool))
| ~ sP759(U_8444,U_8445,U_8443) )
& ! [U_8444,U_8445,U_8443] :
( sP759(U_8444,U_8445,U_8443)
| ~ hBOOL(hAPP(hAPP(c_member(U_8443),U_8445),U_8444))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8443),U_8444))
| ~ class_Orderings_Olinorder(U_8443) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP759])],[f_2470_2]) ).
cnf(f_2470_4,plain,
( sP759(U_8444,U_8445,U_8443)
| ~ hBOOL(hAPP(hAPP(c_member(U_8443),U_8445),U_8444))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8443),U_8444))
| ~ class_Orderings_Olinorder(U_8443) ),
inference(clausify,[status(thm)],[f_2470_3]) ).
cnf(f_2470_5,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8443,U_8444) = U_8445
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool))
| ~ sP759(U_8444,U_8445,U_8443) ),
inference(clausify,[status(thm)],[f_2470_3]) ).
cnf(f_2470_6,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8443,U_8444) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8443),U_8445),c_Big__Operators_Olinorder__class_OMax(U_8443,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8443,tc_HOL_Obool)),U_8444),hAPP(hAPP(c_Set_Oinsert(U_8443),U_8445),c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8443,tc_HOL_Obool))
| ~ sP759(U_8444,U_8445,U_8443) ),
inference(clausify,[status(thm)],[f_2470_3]) ).
fof(f_2471_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__eqI]) ).
fof(f_2471_2,plain,
! [U_8449,U_8448,U_8447] :
( c_Big__Operators_Olinorder__class_OMax(U_8447,U_8448) = U_8449
| ~ hBOOL(hAPP(hAPP(c_member(U_8447),U_8449),U_8448))
| ? [U_8446] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8447),U_8446),U_8449))
& hBOOL(hAPP(hAPP(c_member(U_8447),U_8446),U_8448)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8447),U_8448))
| ~ class_Orderings_Olinorder(U_8447) ),
inference(variable_rename,[status(thm)],[f_2471_1]) ).
fof(f_2471_3,plain,
! [U_8449,U_8448,U_8447] :
( c_Big__Operators_Olinorder__class_OMax(U_8447,U_8448) = U_8449
| ~ hBOOL(hAPP(hAPP(c_member(U_8447),U_8449),U_8448))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8447),sK235(U_8449,U_8448,U_8447)),U_8449))
& hBOOL(hAPP(hAPP(c_member(U_8447),sK235(U_8449,U_8448,U_8447)),U_8448)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8447),U_8448))
| ~ class_Orderings_Olinorder(U_8447) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_8446,sK235(U_8449,U_8448,U_8447))],[f_2471_2]) ).
fof(f_2471_4,plain,
( ! [U_8447,U_8448,U_8449] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8447),sK235(U_8449,U_8448,U_8447)),U_8449))
| ~ sP760(U_8447,U_8448,U_8449) )
& ! [U_8447,U_8448,U_8449] :
( hBOOL(hAPP(hAPP(c_member(U_8447),sK235(U_8449,U_8448,U_8447)),U_8448))
| ~ sP760(U_8447,U_8448,U_8449) )
& ! [U_8447,U_8448,U_8449] :
( c_Big__Operators_Olinorder__class_OMax(U_8447,U_8448) = U_8449
| ~ hBOOL(hAPP(hAPP(c_member(U_8447),U_8449),U_8448))
| sP760(U_8447,U_8448,U_8449)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8447),U_8448))
| ~ class_Orderings_Olinorder(U_8447) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP760])],[f_2471_3]) ).
cnf(f_2471_5,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8447,U_8448) = U_8449
| ~ hBOOL(hAPP(hAPP(c_member(U_8447),U_8449),U_8448))
| sP760(U_8447,U_8448,U_8449)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8447),U_8448))
| ~ class_Orderings_Olinorder(U_8447) ),
inference(clausify,[status(thm)],[f_2471_4]) ).
cnf(f_2471_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8447),sK235(U_8449,U_8448,U_8447)),U_8448))
| ~ sP760(U_8447,U_8448,U_8449) ),
inference(clausify,[status(thm)],[f_2471_4]) ).
cnf(f_2471_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8447),sK235(U_8449,U_8448,U_8447)),U_8449))
| ~ sP760(U_8447,U_8448,U_8449) ),
inference(clausify,[status(thm)],[f_2471_4]) ).
fof(f_2472_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold_H]) ).
fof(f_2472_2,plain,
! [U_8452,U_8451,U_8450] :
( c_Big__Operators_Olinorder__class_OMax(U_8450,hAPP(hAPP(c_Set_Oinsert(U_8450),U_8452),U_8451)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8450,U_8450,c_Orderings_Oord__class_Omax(U_8450)),U_8452),U_8451)
| hBOOL(hAPP(hAPP(c_member(U_8450),U_8452),U_8451))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8450),U_8451))
| ~ class_Orderings_Olinorder(U_8450) ),
inference(variable_rename,[status(thm)],[f_2472_1]) ).
fof(f_2472_3,plain,
! [U_8452,U_8450,U_8451] :
( c_Big__Operators_Olinorder__class_OMax(U_8450,hAPP(hAPP(c_Set_Oinsert(U_8450),U_8452),U_8451)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8450,U_8450,c_Orderings_Oord__class_Omax(U_8450)),U_8452),U_8451)
| hBOOL(hAPP(hAPP(c_member(U_8450),U_8452),U_8451))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8450),U_8451))
| ~ class_Orderings_Olinorder(U_8450) ),
inference(definitional_conversion,[status(esa)],[f_2472_2]) ).
cnf(f_2472_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8450,hAPP(hAPP(c_Set_Oinsert(U_8450),U_8452),U_8451)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8450,U_8450,c_Orderings_Oord__class_Omax(U_8450)),U_8452),U_8451)
| hBOOL(hAPP(hAPP(c_member(U_8450),U_8452),U_8451))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8450),U_8451))
| ~ class_Orderings_Olinorder(U_8450) ),
inference(clausify,[status(thm)],[f_2472_3]) ).
fof(f_2473_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter]) ).
fof(f_2473_2,plain,
! [U_8455,U_8454,U_8453] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8453),c_Big__Operators_Olinorder__class_OMax(U_8453,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455))),c_Big__Operators_Olinorder__class_OMax(U_8453,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8453),c_Big__Operators_Olinorder__class_OMax(U_8453,U_8454)),c_Big__Operators_Olinorder__class_OMax(U_8453,U_8455))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455) = c_Orderings_Obot__class_Obot(tc_fun(U_8453,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8453),U_8455))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8453),U_8454))
| ~ class_Orderings_Olinorder(U_8453) ),
inference(variable_rename,[status(thm)],[f_2473_1]) ).
fof(f_2473_3,plain,
! [U_8453,U_8454,U_8455] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8453),c_Big__Operators_Olinorder__class_OMax(U_8453,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455))),c_Big__Operators_Olinorder__class_OMax(U_8453,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8453),c_Big__Operators_Olinorder__class_OMax(U_8453,U_8454)),c_Big__Operators_Olinorder__class_OMax(U_8453,U_8455))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455) = c_Orderings_Obot__class_Obot(tc_fun(U_8453,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8453),U_8455))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8453),U_8454))
| ~ class_Orderings_Olinorder(U_8453) ),
inference(definitional_conversion,[status(esa)],[f_2473_2]) ).
cnf(f_2473_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8453),c_Big__Operators_Olinorder__class_OMax(U_8453,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455))),c_Big__Operators_Olinorder__class_OMax(U_8453,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8453),c_Big__Operators_Olinorder__class_OMax(U_8453,U_8454)),c_Big__Operators_Olinorder__class_OMax(U_8453,U_8455))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8453,tc_HOL_Obool)),U_8454),U_8455) = c_Orderings_Obot__class_Obot(tc_fun(U_8453,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8453),U_8455))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8453),U_8454))
| ~ class_Orderings_Olinorder(U_8453) ),
inference(clausify,[status(thm)],[f_2473_3]) ).
fof(f_2474_1,plain,
! [V_y,V_x,T_a] :
( 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
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb]) ).
fof(f_2474_2,plain,
! [U_8458,U_8457,U_8456] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8456),U_8457),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8456),U_8457),U_8458)) = U_8457
| ~ class_Orderings_Olinorder(U_8456) ),
inference(variable_rename,[status(thm)],[f_2474_1]) ).
fof(f_2474_3,plain,
! [U_8457,U_8456,U_8458] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8456),U_8457),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8456),U_8457),U_8458)) = U_8457
| ~ class_Orderings_Olinorder(U_8456) ),
inference(definitional_conversion,[status(esa)],[f_2474_2]) ).
cnf(f_2474_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8456),U_8457),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8456),U_8457),U_8458)) = U_8457
| ~ class_Orderings_Olinorder(U_8456) ),
inference(clausify,[status(thm)],[f_2474_3]) ).
fof(f_2475_1,plain,
! [V_y,V_x,T_a] :
( 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
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb]) ).
fof(f_2475_2,plain,
! [U_8461,U_8460,U_8459] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8459),U_8460),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8459),U_8460),U_8461)) = U_8460
| ~ class_Orderings_Olinorder(U_8459) ),
inference(variable_rename,[status(thm)],[f_2475_1]) ).
fof(f_2475_3,plain,
! [U_8459,U_8460,U_8461] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8459),U_8460),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8459),U_8460),U_8461)) = U_8460
| ~ class_Orderings_Olinorder(U_8459) ),
inference(definitional_conversion,[status(esa)],[f_2475_2]) ).
cnf(f_2475_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8459),U_8460),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8459),U_8460),U_8461)) = U_8460
| ~ class_Orderings_Olinorder(U_8459) ),
inference(clausify,[status(thm)],[f_2475_3]) ).
fof(f_2476_1,plain,
! [V_z,V_y,V_x,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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1]) ).
fof(f_2476_2,plain,
! [U_8465,U_8464,U_8463,U_8462] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8462),U_8464),U_8465)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8462),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),U_8464)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),U_8465))
| ~ class_Orderings_Olinorder(U_8462) ),
inference(variable_rename,[status(thm)],[f_2476_1]) ).
fof(f_2476_3,plain,
! [U_8462,U_8463,U_8464,U_8465] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8462),U_8464),U_8465)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8462),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),U_8464)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),U_8465))
| ~ class_Orderings_Olinorder(U_8462) ),
inference(definitional_conversion,[status(esa)],[f_2476_2]) ).
cnf(f_2476_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8462),U_8464),U_8465)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8462),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),U_8464)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8462),U_8463),U_8465))
| ~ class_Orderings_Olinorder(U_8462) ),
inference(clausify,[status(thm)],[f_2476_3]) ).
fof(f_2477_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1]) ).
fof(f_2477_2,plain,
! [U_8469,U_8468,U_8467,U_8466] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8466),U_8468),U_8469)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8466),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),U_8468)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),U_8469))
| ~ class_Orderings_Olinorder(U_8466) ),
inference(variable_rename,[status(thm)],[f_2477_1]) ).
fof(f_2477_3,plain,
! [U_8466,U_8467,U_8468,U_8469] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8466),U_8468),U_8469)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8466),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),U_8468)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),U_8469))
| ~ class_Orderings_Olinorder(U_8466) ),
inference(definitional_conversion,[status(esa)],[f_2477_2]) ).
cnf(f_2477_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8466),U_8468),U_8469)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8466),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),U_8468)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8466),U_8467),U_8469))
| ~ class_Orderings_Olinorder(U_8466) ),
inference(clausify,[status(thm)],[f_2477_3]) ).
fof(f_2478_1,plain,
! [V_x,V_z,V_y,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2]) ).
fof(f_2478_2,plain,
! [U_8473,U_8472,U_8471,U_8470] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),U_8471),U_8472)),U_8473) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),U_8471),U_8473)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),U_8472),U_8473))
| ~ class_Orderings_Olinorder(U_8470) ),
inference(variable_rename,[status(thm)],[f_2478_1]) ).
fof(f_2478_3,plain,
! [U_8470,U_8471,U_8472,U_8473] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),U_8471),U_8472)),U_8473) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),U_8471),U_8473)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),U_8472),U_8473))
| ~ class_Orderings_Olinorder(U_8470) ),
inference(definitional_conversion,[status(esa)],[f_2478_2]) ).
cnf(f_2478_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),U_8471),U_8472)),U_8473) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),U_8471),U_8473)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8470),U_8472),U_8473))
| ~ class_Orderings_Olinorder(U_8470) ),
inference(clausify,[status(thm)],[f_2478_3]) ).
fof(f_2479_1,plain,
! [V_x,V_z,V_y,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2]) ).
fof(f_2479_2,plain,
! [U_8477,U_8476,U_8475,U_8474] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8474),U_8475),U_8476)),U_8477) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8474),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8475),U_8477)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8476),U_8477))
| ~ class_Orderings_Olinorder(U_8474) ),
inference(variable_rename,[status(thm)],[f_2479_1]) ).
fof(f_2479_3,plain,
! [U_8474,U_8475,U_8476,U_8477] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8474),U_8475),U_8476)),U_8477) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8474),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8475),U_8477)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8476),U_8477))
| ~ class_Orderings_Olinorder(U_8474) ),
inference(definitional_conversion,[status(esa)],[f_2479_2]) ).
cnf(f_2479_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8474),U_8475),U_8476)),U_8477) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8474),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8475),U_8477)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8476),U_8477))
| ~ class_Orderings_Olinorder(U_8474) ),
inference(clausify,[status(thm)],[f_2479_3]) ).
fof(f_2480_1,plain,
! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n,
inference(fof_nnf,[status(thm)],[fact_max__0R]) ).
fof(f_2480_2,plain,
! [U_8478] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8478),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8478,
inference(variable_rename,[status(thm)],[f_2480_1]) ).
fof(f_2480_3,plain,
! [U_8478] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8478),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8478,
inference(definitional_conversion,[status(esa)],[f_2480_2]) ).
cnf(f_2480_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8478),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8478,
inference(clausify,[status(thm)],[f_2480_3]) ).
fof(f_2481_1,plain,
! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_max__0L]) ).
fof(f_2481_2,plain,
! [U_8479] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8479) = U_8479,
inference(variable_rename,[status(thm)],[f_2481_1]) ).
fof(f_2481_3,plain,
! [U_8479] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8479) = U_8479,
inference(definitional_conversion,[status(esa)],[f_2481_2]) ).
cnf(f_2481_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8479) = U_8479,
inference(clausify,[status(thm)],[f_2481_3]) ).
fof(f_2482_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup]) ).
fof(f_2482_2,plain,
! [U_8480] :
( c_Finite__Set_Ofun__left__comm__idem(U_8480,U_8480,c_Orderings_Oord__class_Omax(U_8480))
| ~ class_Orderings_Olinorder(U_8480) ),
inference(variable_rename,[status(thm)],[f_2482_1]) ).
fof(f_2482_3,plain,
! [U_8480] :
( c_Finite__Set_Ofun__left__comm__idem(U_8480,U_8480,c_Orderings_Oord__class_Omax(U_8480))
| ~ class_Orderings_Olinorder(U_8480) ),
inference(definitional_conversion,[status(esa)],[f_2482_2]) ).
cnf(f_2482_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_8480,U_8480,c_Orderings_Oord__class_Omax(U_8480))
| ~ class_Orderings_Olinorder(U_8480) ),
inference(clausify,[status(thm)],[f_2482_3]) ).
fof(f_2483_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_max__Suc__Suc]) ).
fof(f_2483_2,plain,
! [U_8482,U_8481] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8481)),hAPP(c_Nat_OSuc,U_8482)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8481),U_8482)),
inference(variable_rename,[status(thm)],[f_2483_1]) ).
fof(f_2483_3,plain,
! [U_8481,U_8482] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8481)),hAPP(c_Nat_OSuc,U_8482)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8481),U_8482)),
inference(definitional_conversion,[status(esa)],[f_2483_2]) ).
cnf(f_2483_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8481)),hAPP(c_Nat_OSuc,U_8482)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8481),U_8482)),
inference(clausify,[status(thm)],[f_2483_3]) ).
fof(f_2484_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oidem]) ).
fof(f_2484_2,plain,
! [U_8484,U_8483] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),U_8484) = U_8484
| ~ class_Orderings_Olinorder(U_8483) ),
inference(variable_rename,[status(thm)],[f_2484_1]) ).
fof(f_2484_3,plain,
! [U_8483,U_8484] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),U_8484) = U_8484
| ~ class_Orderings_Olinorder(U_8483) ),
inference(definitional_conversion,[status(esa)],[f_2484_2]) ).
cnf(f_2484_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),U_8484) = U_8484
| ~ class_Orderings_Olinorder(U_8483) ),
inference(clausify,[status(thm)],[f_2484_3]) ).
fof(f_2485_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem]) ).
fof(f_2485_2,plain,
! [U_8486,U_8485] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8485),U_8486),U_8486) = U_8486
| ~ class_Orderings_Olinorder(U_8485) ),
inference(variable_rename,[status(thm)],[f_2485_1]) ).
fof(f_2485_3,plain,
! [U_8485,U_8486] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8485),U_8486),U_8486) = U_8486
| ~ class_Orderings_Olinorder(U_8485) ),
inference(definitional_conversion,[status(esa)],[f_2485_2]) ).
cnf(f_2485_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8485),U_8486),U_8486) = U_8486
| ~ class_Orderings_Olinorder(U_8485) ),
inference(clausify,[status(thm)],[f_2485_3]) ).
fof(f_2486_1,plain,
! [V_b,V_a,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_b),V_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute]) ).
fof(f_2486_2,plain,
! [U_8489,U_8488,U_8487] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8487),U_8488),U_8489) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8487),U_8489),U_8488)
| ~ class_Orderings_Olinorder(U_8487) ),
inference(variable_rename,[status(thm)],[f_2486_1]) ).
fof(f_2486_3,plain,
! [U_8487,U_8488,U_8489] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8487),U_8488),U_8489) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8487),U_8489),U_8488)
| ~ class_Orderings_Olinorder(U_8487) ),
inference(definitional_conversion,[status(esa)],[f_2486_2]) ).
cnf(f_2486_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8487),U_8488),U_8489) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8487),U_8489),U_8488)
| ~ class_Orderings_Olinorder(U_8487) ),
inference(clausify,[status(thm)],[f_2486_3]) ).
fof(f_2487_1,plain,
! [V_y,V_x,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_y),V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute]) ).
fof(f_2487_2,plain,
! [U_8492,U_8491,U_8490] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8490),U_8491),U_8492) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8490),U_8492),U_8491)
| ~ class_Orderings_Olinorder(U_8490) ),
inference(variable_rename,[status(thm)],[f_2487_1]) ).
fof(f_2487_3,plain,
! [U_8490,U_8491,U_8492] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8490),U_8491),U_8492) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8490),U_8492),U_8491)
| ~ class_Orderings_Olinorder(U_8490) ),
inference(definitional_conversion,[status(esa)],[f_2487_2]) ).
cnf(f_2487_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8490),U_8491),U_8492) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8490),U_8492),U_8491)
| ~ class_Orderings_Olinorder(U_8490) ),
inference(clausify,[status(thm)],[f_2487_3]) ).
fof(f_2488_1,plain,
! [V_b,V_a,T_a] :
( 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)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem]) ).
fof(f_2488_2,plain,
! [U_8495,U_8494,U_8493] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),U_8495)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),U_8495)
| ~ class_Orderings_Olinorder(U_8493) ),
inference(variable_rename,[status(thm)],[f_2488_1]) ).
fof(f_2488_3,plain,
! [U_8493,U_8494,U_8495] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),U_8495)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),U_8495)
| ~ class_Orderings_Olinorder(U_8493) ),
inference(definitional_conversion,[status(esa)],[f_2488_2]) ).
cnf(f_2488_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),U_8495)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8493),U_8494),U_8495)
| ~ class_Orderings_Olinorder(U_8493) ),
inference(clausify,[status(thm)],[f_2488_3]) ).
fof(f_2489_1,plain,
! [V_y,V_x,T_a] :
( 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)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem]) ).
fof(f_2489_2,plain,
! [U_8498,U_8497,U_8496] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),U_8498)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),U_8498)
| ~ class_Orderings_Olinorder(U_8496) ),
inference(variable_rename,[status(thm)],[f_2489_1]) ).
fof(f_2489_3,plain,
! [U_8496,U_8497,U_8498] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),U_8498)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),U_8498)
| ~ class_Orderings_Olinorder(U_8496) ),
inference(definitional_conversion,[status(esa)],[f_2489_2]) ).
cnf(f_2489_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),U_8498)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8496),U_8497),U_8498)
| ~ class_Orderings_Olinorder(U_8496) ),
inference(clausify,[status(thm)],[f_2489_3]) ).
fof(f_2490_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute]) ).
fof(f_2490_2,plain,
! [U_8502,U_8501,U_8500,U_8499] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),U_8502)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),U_8502))
| ~ class_Orderings_Olinorder(U_8499) ),
inference(variable_rename,[status(thm)],[f_2490_1]) ).
fof(f_2490_3,plain,
! [U_8499,U_8500,U_8501,U_8502] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),U_8502)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),U_8502))
| ~ class_Orderings_Olinorder(U_8499) ),
inference(definitional_conversion,[status(esa)],[f_2490_2]) ).
cnf(f_2490_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),U_8502)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),U_8502))
| ~ class_Orderings_Olinorder(U_8499) ),
inference(clausify,[status(thm)],[f_2490_3]) ).
fof(f_2491_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute]) ).
fof(f_2491_2,plain,
! [U_8506,U_8505,U_8504,U_8503] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8504),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8505),U_8506)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8505),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8504),U_8506))
| ~ class_Orderings_Olinorder(U_8503) ),
inference(variable_rename,[status(thm)],[f_2491_1]) ).
fof(f_2491_3,plain,
! [U_8503,U_8504,U_8505,U_8506] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8504),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8505),U_8506)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8505),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8504),U_8506))
| ~ class_Orderings_Olinorder(U_8503) ),
inference(definitional_conversion,[status(esa)],[f_2491_2]) ).
cnf(f_2491_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8504),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8505),U_8506)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8505),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8503),U_8504),U_8506))
| ~ class_Orderings_Olinorder(U_8503) ),
inference(clausify,[status(thm)],[f_2491_3]) ).
fof(f_2492_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc]) ).
fof(f_2492_2,plain,
! [U_8510,U_8509,U_8508,U_8507] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8508),U_8509)),U_8510) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8508),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8509),U_8510))
| ~ class_Orderings_Olinorder(U_8507) ),
inference(variable_rename,[status(thm)],[f_2492_1]) ).
fof(f_2492_3,plain,
! [U_8507,U_8508,U_8509,U_8510] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8508),U_8509)),U_8510) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8508),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8509),U_8510))
| ~ class_Orderings_Olinorder(U_8507) ),
inference(definitional_conversion,[status(esa)],[f_2492_2]) ).
cnf(f_2492_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8508),U_8509)),U_8510) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8508),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8507),U_8509),U_8510))
| ~ class_Orderings_Olinorder(U_8507) ),
inference(clausify,[status(thm)],[f_2492_3]) ).
fof(f_2493_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc]) ).
fof(f_2493_2,plain,
! [U_8514,U_8513,U_8512,U_8511] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),U_8513)),U_8514) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8513),U_8514))
| ~ class_Orderings_Olinorder(U_8511) ),
inference(variable_rename,[status(thm)],[f_2493_1]) ).
fof(f_2493_3,plain,
! [U_8511,U_8512,U_8513,U_8514] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),U_8513)),U_8514) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8513),U_8514))
| ~ class_Orderings_Olinorder(U_8511) ),
inference(definitional_conversion,[status(esa)],[f_2493_2]) ).
cnf(f_2493_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),U_8513)),U_8514) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8513),U_8514))
| ~ class_Orderings_Olinorder(U_8511) ),
inference(clausify,[status(thm)],[f_2493_3]) ).
fof(f_2494_1,plain,
! [T_b] :
( c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__max]) ).
fof(f_2494_2,plain,
! [U_8515] :
( c_Lattices_Osemilattice__sup__class_Osup(U_8515) = c_Orderings_Oord__class_Omax(U_8515)
| ~ class_Orderings_Olinorder(U_8515)
| ~ class_Lattices_Osemilattice__sup(U_8515) ),
inference(variable_rename,[status(thm)],[f_2494_1]) ).
fof(f_2494_3,plain,
! [U_8515] :
( c_Lattices_Osemilattice__sup__class_Osup(U_8515) = c_Orderings_Oord__class_Omax(U_8515)
| ~ class_Orderings_Olinorder(U_8515)
| ~ class_Lattices_Osemilattice__sup(U_8515) ),
inference(definitional_conversion,[status(esa)],[f_2494_2]) ).
cnf(f_2494_4,plain,
( c_Lattices_Osemilattice__sup__class_Osup(U_8515) = c_Orderings_Oord__class_Omax(U_8515)
| ~ class_Orderings_Olinorder(U_8515)
| ~ class_Lattices_Osemilattice__sup(U_8515) ),
inference(clausify,[status(thm)],[f_2494_3]) ).
fof(f_2495_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left]) ).
fof(f_2495_2,plain,
! [U_8519,U_8518,U_8517,U_8516] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8516),U_8517),U_8518)),U_8519) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8516),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),U_8517),U_8519)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),U_8518),U_8519))
| ~ class_Groups_Oordered__ab__group__add(U_8516) ),
inference(variable_rename,[status(thm)],[f_2495_1]) ).
fof(f_2495_3,plain,
! [U_8516,U_8517,U_8518,U_8519] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8516),U_8517),U_8518)),U_8519) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8516),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),U_8517),U_8519)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),U_8518),U_8519))
| ~ class_Groups_Oordered__ab__group__add(U_8516) ),
inference(definitional_conversion,[status(esa)],[f_2495_2]) ).
cnf(f_2495_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8516),U_8517),U_8518)),U_8519) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8516),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),U_8517),U_8519)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8516),U_8518),U_8519))
| ~ class_Groups_Oordered__ab__group__add(U_8516) ),
inference(clausify,[status(thm)],[f_2495_3]) ).
fof(f_2496_1,plain,
! [V_x,V_b,V_a,T_a] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) )
| ~ 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))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supE]) ).
fof(f_2496_2,plain,
! [U_8523,U_8522,U_8521,U_8520] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),U_8522),U_8523))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),U_8521),U_8523)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8520),U_8521),U_8522)),U_8523))
| ~ class_Orderings_Olinorder(U_8520) ),
inference(variable_rename,[status(thm)],[f_2496_1]) ).
fof(f_2496_3,plain,
( ! [U_8520,U_8521,U_8522,U_8523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),U_8522),U_8523))
| ~ sP761(U_8520,U_8521,U_8522,U_8523) )
& ! [U_8520,U_8521,U_8522,U_8523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),U_8521),U_8523))
| ~ sP761(U_8520,U_8521,U_8522,U_8523) )
& ! [U_8520,U_8521,U_8522,U_8523] :
( sP761(U_8520,U_8521,U_8522,U_8523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8520),U_8521),U_8522)),U_8523))
| ~ class_Orderings_Olinorder(U_8520) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP761])],[f_2496_2]) ).
cnf(f_2496_4,plain,
( sP761(U_8520,U_8521,U_8522,U_8523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8520),U_8521),U_8522)),U_8523))
| ~ class_Orderings_Olinorder(U_8520) ),
inference(clausify,[status(thm)],[f_2496_3]) ).
cnf(f_2496_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),U_8521),U_8523))
| ~ sP761(U_8520,U_8521,U_8522,U_8523) ),
inference(clausify,[status(thm)],[f_2496_3]) ).
cnf(f_2496_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8520),U_8522),U_8523))
| ~ sP761(U_8520,U_8521,U_8522,U_8523) ),
inference(clausify,[status(thm)],[f_2496_3]) ).
fof(f_2497_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono]) ).
fof(f_2497_2,plain,
! [U_8528,U_8527,U_8526,U_8525,U_8524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8525),U_8527)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8526),U_8528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),U_8527),U_8528))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),U_8525),U_8526))
| ~ class_Orderings_Olinorder(U_8524) ),
inference(variable_rename,[status(thm)],[f_2497_1]) ).
fof(f_2497_3,plain,
! [U_8524,U_8525,U_8526,U_8527,U_8528] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8525),U_8527)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8526),U_8528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),U_8527),U_8528))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),U_8525),U_8526))
| ~ class_Orderings_Olinorder(U_8524) ),
inference(definitional_conversion,[status(esa)],[f_2497_2]) ).
cnf(f_2497_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8525),U_8527)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8526),U_8528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),U_8527),U_8528))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8524),U_8525),U_8526))
| ~ class_Orderings_Olinorder(U_8524) ),
inference(clausify,[status(thm)],[f_2497_3]) ).
fof(f_2498_1,plain,
! [V_z,V_x,V_y,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least]) ).
fof(f_2498_2,plain,
! [U_8532,U_8531,U_8530,U_8529] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8529),U_8530),U_8532)),U_8531))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8531))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531))
| ~ class_Orderings_Olinorder(U_8529) ),
inference(variable_rename,[status(thm)],[f_2498_1]) ).
fof(f_2498_3,plain,
! [U_8529,U_8530,U_8531,U_8532] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8529),U_8530),U_8532)),U_8531))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8531))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531))
| ~ class_Orderings_Olinorder(U_8529) ),
inference(definitional_conversion,[status(esa)],[f_2498_2]) ).
cnf(f_2498_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8529),U_8530),U_8532)),U_8531))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8531))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531))
| ~ class_Orderings_Olinorder(U_8529) ),
inference(clausify,[status(thm)],[f_2498_3]) ).
fof(f_2499_1,plain,
! [V_b,V_x,V_a,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI]) ).
fof(f_2499_2,plain,
! [U_8536,U_8535,U_8534,U_8533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8533),U_8534),U_8536)),U_8535))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),U_8536),U_8535))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),U_8534),U_8535))
| ~ class_Orderings_Olinorder(U_8533) ),
inference(variable_rename,[status(thm)],[f_2499_1]) ).
fof(f_2499_3,plain,
! [U_8533,U_8534,U_8535,U_8536] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8533),U_8534),U_8536)),U_8535))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),U_8536),U_8535))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),U_8534),U_8535))
| ~ class_Orderings_Olinorder(U_8533) ),
inference(definitional_conversion,[status(esa)],[f_2499_2]) ).
cnf(f_2499_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8533),U_8534),U_8536)),U_8535))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),U_8536),U_8535))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8533),U_8534),U_8535))
| ~ class_Orderings_Olinorder(U_8533) ),
inference(clausify,[status(thm)],[f_2499_3]) ).
fof(f_2500_1,plain,
! [V_x,V_y,T_a] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1]) ).
fof(f_2500_2,plain,
! [U_8539,U_8538,U_8537] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8537),U_8539),U_8538) = U_8539
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8537),U_8538),U_8539))
| ~ class_Orderings_Olinorder(U_8537) ),
inference(variable_rename,[status(thm)],[f_2500_1]) ).
fof(f_2500_3,plain,
! [U_8537,U_8538,U_8539] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8537),U_8539),U_8538) = U_8539
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8537),U_8538),U_8539))
| ~ class_Orderings_Olinorder(U_8537) ),
inference(definitional_conversion,[status(esa)],[f_2500_2]) ).
cnf(f_2500_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8537),U_8539),U_8538) = U_8539
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8537),U_8538),U_8539))
| ~ class_Orderings_Olinorder(U_8537) ),
inference(clausify,[status(thm)],[f_2500_3]) ).
fof(f_2501_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2]) ).
fof(f_2501_2,plain,
! [U_8542,U_8541,U_8540] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8540),U_8541),U_8542) = U_8542
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8540),U_8541),U_8542))
| ~ class_Orderings_Olinorder(U_8540) ),
inference(variable_rename,[status(thm)],[f_2501_1]) ).
fof(f_2501_3,plain,
! [U_8540,U_8541,U_8542] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8540),U_8541),U_8542) = U_8542
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8540),U_8541),U_8542))
| ~ class_Orderings_Olinorder(U_8540) ),
inference(definitional_conversion,[status(esa)],[f_2501_2]) ).
cnf(f_2501_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8540),U_8541),U_8542) = U_8542
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8540),U_8541),U_8542))
| ~ class_Orderings_Olinorder(U_8540) ),
inference(clausify,[status(thm)],[f_2501_3]) ).
fof(f_2502_1,plain,
! [V_a,V_b,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2]) ).
fof(f_2502_2,plain,
! [U_8546,U_8545,U_8544,U_8543] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8543),U_8544),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8543),U_8546),U_8545)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8543),U_8544),U_8545))
| ~ class_Orderings_Olinorder(U_8543) ),
inference(variable_rename,[status(thm)],[f_2502_1]) ).
fof(f_2502_3,plain,
! [U_8543,U_8544,U_8545,U_8546] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8543),U_8544),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8543),U_8546),U_8545)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8543),U_8544),U_8545))
| ~ class_Orderings_Olinorder(U_8543) ),
inference(definitional_conversion,[status(esa)],[f_2502_2]) ).
cnf(f_2502_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8543),U_8544),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8543),U_8546),U_8545)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8543),U_8544),U_8545))
| ~ class_Orderings_Olinorder(U_8543) ),
inference(clausify,[status(thm)],[f_2502_3]) ).
fof(f_2503_1,plain,
! [V_b,V_a,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1]) ).
fof(f_2503_2,plain,
! [U_8550,U_8549,U_8548,U_8547] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),U_8548),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),U_8549),U_8550)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),U_8548),U_8549))
| ~ class_Orderings_Olinorder(U_8547) ),
inference(variable_rename,[status(thm)],[f_2503_1]) ).
fof(f_2503_3,plain,
! [U_8547,U_8548,U_8549,U_8550] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),U_8548),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),U_8549),U_8550)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),U_8548),U_8549))
| ~ class_Orderings_Olinorder(U_8547) ),
inference(definitional_conversion,[status(esa)],[f_2503_2]) ).
cnf(f_2503_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),U_8548),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),U_8549),U_8550)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),U_8548),U_8549))
| ~ class_Orderings_Olinorder(U_8547) ),
inference(clausify,[status(thm)],[f_2503_3]) ).
fof(f_2504_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
| ~ 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)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff]) ).
fof(f_2504_2,plain,
! [U_8554,U_8553,U_8552,U_8551] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),U_8552),U_8553)),U_8554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8553),U_8554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8552),U_8554)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8553),U_8554))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8552),U_8554)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),U_8552),U_8553)),U_8554)) ) )
| ~ class_Orderings_Olinorder(U_8551) ),
inference(variable_rename,[status(thm)],[f_2504_1]) ).
fof(f_2504_3,plain,
( ! [U_8551,U_8552,U_8553,U_8554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8553),U_8554))
| ~ sP762(U_8551,U_8552,U_8553,U_8554) )
& ! [U_8551,U_8552,U_8553,U_8554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8552),U_8554))
| ~ sP762(U_8551,U_8552,U_8553,U_8554) )
& ! [U_8551,U_8552,U_8553,U_8554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),U_8552),U_8553)),U_8554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8553),U_8554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8552),U_8554))
| ~ sP763(U_8551,U_8552,U_8553,U_8554) )
& ! [U_8551,U_8552,U_8553,U_8554] :
( sP762(U_8551,U_8552,U_8553,U_8554)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),U_8552),U_8553)),U_8554))
| ~ sP763(U_8551,U_8552,U_8553,U_8554) )
& ! [U_8551,U_8552,U_8553,U_8554] :
( sP763(U_8551,U_8552,U_8553,U_8554)
| ~ class_Orderings_Olinorder(U_8551) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP762,sP763])],[f_2504_2]) ).
cnf(f_2504_4,plain,
( sP763(U_8551,U_8552,U_8553,U_8554)
| ~ class_Orderings_Olinorder(U_8551) ),
inference(clausify,[status(thm)],[f_2504_3]) ).
cnf(f_2504_5,plain,
( sP762(U_8551,U_8552,U_8553,U_8554)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),U_8552),U_8553)),U_8554))
| ~ sP763(U_8551,U_8552,U_8553,U_8554) ),
inference(clausify,[status(thm)],[f_2504_3]) ).
cnf(f_2504_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),U_8552),U_8553)),U_8554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8553),U_8554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8552),U_8554))
| ~ sP763(U_8551,U_8552,U_8553,U_8554) ),
inference(clausify,[status(thm)],[f_2504_3]) ).
cnf(f_2504_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8552),U_8554))
| ~ sP762(U_8551,U_8552,U_8553,U_8554) ),
inference(clausify,[status(thm)],[f_2504_3]) ).
cnf(f_2504_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8551),U_8553),U_8554))
| ~ sP762(U_8551,U_8552,U_8553,U_8554) ),
inference(clausify,[status(thm)],[f_2504_3]) ).
fof(f_2505_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) != V_y_2 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup]) ).
fof(f_2505_2,plain,
! [U_8557,U_8556,U_8555] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8555),U_8556),U_8557))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8555),U_8556),U_8557) != U_8557 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8555),U_8556),U_8557) = U_8557
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8555),U_8556),U_8557)) ) )
| ~ class_Orderings_Olinorder(U_8555) ),
inference(variable_rename,[status(thm)],[f_2505_1]) ).
fof(f_2505_3,plain,
( ! [U_8557,U_8555,U_8556] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8555),U_8556),U_8557))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8555),U_8556),U_8557) != U_8557
| ~ sP764(U_8557,U_8555,U_8556) )
& ! [U_8557,U_8555,U_8556] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8555),U_8556),U_8557) = U_8557
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8555),U_8556),U_8557))
| ~ sP764(U_8557,U_8555,U_8556) )
& ! [U_8557,U_8555,U_8556] :
( sP764(U_8557,U_8555,U_8556)
| ~ class_Orderings_Olinorder(U_8555) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP764])],[f_2505_2]) ).
cnf(f_2505_4,plain,
( sP764(U_8557,U_8555,U_8556)
| ~ class_Orderings_Olinorder(U_8555) ),
inference(clausify,[status(thm)],[f_2505_3]) ).
cnf(f_2505_5,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8555),U_8556),U_8557) = U_8557
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8555),U_8556),U_8557))
| ~ sP764(U_8557,U_8555,U_8556) ),
inference(clausify,[status(thm)],[f_2505_3]) ).
cnf(f_2505_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8555),U_8556),U_8557))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8555),U_8556),U_8557) != U_8557
| ~ sP764(U_8557,U_8555,U_8556) ),
inference(clausify,[status(thm)],[f_2505_3]) ).
fof(f_2506_1,plain,
! [V_x,V_y,T_a] :
( 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)))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__maxI2]) ).
fof(f_2506_2,plain,
! [U_8560,U_8559,U_8558] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8558),U_8559),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8558),U_8560),U_8559)))
| ~ class_Orderings_Olinorder(U_8558) ),
inference(variable_rename,[status(thm)],[f_2506_1]) ).
fof(f_2506_3,plain,
! [U_8560,U_8559,U_8558] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8558),U_8559),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8558),U_8560),U_8559)))
| ~ class_Orderings_Olinorder(U_8558) ),
inference(definitional_conversion,[status(esa)],[f_2506_2]) ).
cnf(f_2506_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8558),U_8559),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8558),U_8560),U_8559)))
| ~ class_Orderings_Olinorder(U_8558) ),
inference(clausify,[status(thm)],[f_2506_3]) ).
fof(f_2507_1,plain,
! [V_y,V_x,T_a] :
( 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)))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__maxI1]) ).
fof(f_2507_2,plain,
! [U_8563,U_8562,U_8561] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8561),U_8562),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8561),U_8562),U_8563)))
| ~ class_Orderings_Olinorder(U_8561) ),
inference(variable_rename,[status(thm)],[f_2507_1]) ).
fof(f_2507_3,plain,
! [U_8561,U_8562,U_8563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8561),U_8562),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8561),U_8562),U_8563)))
| ~ class_Orderings_Olinorder(U_8561) ),
inference(definitional_conversion,[status(esa)],[f_2507_2]) ).
cnf(f_2507_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8561),U_8562),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8561),U_8562),U_8563)))
| ~ class_Orderings_Olinorder(U_8561) ),
inference(clausify,[status(thm)],[f_2507_3]) ).
fof(f_2508_1,plain,
! [V_y_2,V_x_2,V_z_2,T_b] :
( ( ( 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)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj]) ).
fof(f_2508_2,plain,
! [U_8567,U_8566,U_8565,U_8564] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8564),U_8566),U_8567)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8567))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8566)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8567))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8564),U_8566),U_8567))) ) )
| ~ class_Orderings_Olinorder(U_8564) ),
inference(variable_rename,[status(thm)],[f_2508_1]) ).
fof(f_2508_3,plain,
( ! [U_8564,U_8565,U_8566,U_8567] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8567))
| ~ sP765(U_8564,U_8565,U_8566,U_8567) )
& ! [U_8564,U_8565,U_8566,U_8567] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8566))
| ~ sP765(U_8564,U_8565,U_8566,U_8567) )
& ! [U_8564,U_8565,U_8566,U_8567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8564),U_8566),U_8567)))
| sP765(U_8564,U_8565,U_8566,U_8567)
| ~ sP766(U_8564,U_8565,U_8566,U_8567) )
& ! [U_8564,U_8565,U_8566,U_8567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8567))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8564),U_8566),U_8567)))
| ~ sP766(U_8564,U_8565,U_8566,U_8567) )
& ! [U_8564,U_8565,U_8566,U_8567] :
( sP766(U_8564,U_8565,U_8566,U_8567)
| ~ class_Orderings_Olinorder(U_8564) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP765,sP766])],[f_2508_2]) ).
cnf(f_2508_4,plain,
( sP766(U_8564,U_8565,U_8566,U_8567)
| ~ class_Orderings_Olinorder(U_8564) ),
inference(clausify,[status(thm)],[f_2508_3]) ).
cnf(f_2508_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8567))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8564),U_8566),U_8567)))
| ~ sP766(U_8564,U_8565,U_8566,U_8567) ),
inference(clausify,[status(thm)],[f_2508_3]) ).
cnf(f_2508_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8564),U_8566),U_8567)))
| sP765(U_8564,U_8565,U_8566,U_8567)
| ~ sP766(U_8564,U_8565,U_8566,U_8567) ),
inference(clausify,[status(thm)],[f_2508_3]) ).
cnf(f_2508_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8566))
| ~ sP765(U_8564,U_8565,U_8566,U_8567) ),
inference(clausify,[status(thm)],[f_2508_3]) ).
cnf(f_2508_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8564),U_8565),U_8567))
| ~ sP765(U_8564,U_8565,U_8566,U_8567) ),
inference(clausify,[status(thm)],[f_2508_3]) ).
fof(f_2509_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left]) ).
fof(f_2509_2,plain,
! [U_8571,U_8570,U_8569,U_8568] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8568),U_8569),U_8570)),U_8571) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),U_8569),U_8571)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),U_8570),U_8571))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8568) ),
inference(variable_rename,[status(thm)],[f_2509_1]) ).
fof(f_2509_3,plain,
! [U_8568,U_8569,U_8570,U_8571] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8568),U_8569),U_8570)),U_8571) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),U_8569),U_8571)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),U_8570),U_8571))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8568) ),
inference(definitional_conversion,[status(esa)],[f_2509_2]) ).
cnf(f_2509_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8568),U_8569),U_8570)),U_8571) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),U_8569),U_8571)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),U_8570),U_8571))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8568) ),
inference(clausify,[status(thm)],[f_2509_3]) ).
fof(f_2510_1,plain,
! [V_a,V_b,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2]) ).
fof(f_2510_2,plain,
! [U_8575,U_8574,U_8573,U_8572] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8572),U_8573),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8572),U_8575),U_8574)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8572),U_8573),U_8574))
| ~ class_Orderings_Olinorder(U_8572) ),
inference(variable_rename,[status(thm)],[f_2510_1]) ).
fof(f_2510_3,plain,
! [U_8572,U_8573,U_8574,U_8575] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8572),U_8573),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8572),U_8575),U_8574)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8572),U_8573),U_8574))
| ~ class_Orderings_Olinorder(U_8572) ),
inference(definitional_conversion,[status(esa)],[f_2510_2]) ).
cnf(f_2510_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8572),U_8573),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8572),U_8575),U_8574)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8572),U_8573),U_8574))
| ~ class_Orderings_Olinorder(U_8572) ),
inference(clausify,[status(thm)],[f_2510_3]) ).
fof(f_2511_1,plain,
! [V_b,V_a,V_x,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1]) ).
fof(f_2511_2,plain,
! [U_8579,U_8578,U_8577,U_8576] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8576),U_8577),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8576),U_8578),U_8579)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8576),U_8577),U_8578))
| ~ class_Orderings_Olinorder(U_8576) ),
inference(variable_rename,[status(thm)],[f_2511_1]) ).
fof(f_2511_3,plain,
! [U_8576,U_8577,U_8578,U_8579] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8576),U_8577),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8576),U_8578),U_8579)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8576),U_8577),U_8578))
| ~ class_Orderings_Olinorder(U_8576) ),
inference(definitional_conversion,[status(esa)],[f_2511_2]) ).
cnf(f_2511_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8576),U_8577),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8576),U_8578),U_8579)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8576),U_8577),U_8578))
| ~ class_Orderings_Olinorder(U_8576) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
fof(f_2512_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) )
| ~ 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)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj]) ).
fof(f_2512_2,plain,
! [U_8583,U_8582,U_8581,U_8580] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8580),U_8581),U_8582)),U_8583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8582),U_8583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8581),U_8583)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8582),U_8583))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8581),U_8583)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8580),U_8581),U_8582)),U_8583)) ) )
| ~ class_Orderings_Olinorder(U_8580) ),
inference(variable_rename,[status(thm)],[f_2512_1]) ).
fof(f_2512_3,plain,
( ! [U_8580,U_8581,U_8582,U_8583] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8582),U_8583))
| ~ sP767(U_8580,U_8581,U_8582,U_8583) )
& ! [U_8580,U_8581,U_8582,U_8583] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8581),U_8583))
| ~ sP767(U_8580,U_8581,U_8582,U_8583) )
& ! [U_8580,U_8581,U_8582,U_8583] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8580),U_8581),U_8582)),U_8583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8582),U_8583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8581),U_8583))
| ~ sP768(U_8580,U_8581,U_8582,U_8583) )
& ! [U_8580,U_8581,U_8582,U_8583] :
( sP767(U_8580,U_8581,U_8582,U_8583)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8580),U_8581),U_8582)),U_8583))
| ~ sP768(U_8580,U_8581,U_8582,U_8583) )
& ! [U_8580,U_8581,U_8582,U_8583] :
( sP768(U_8580,U_8581,U_8582,U_8583)
| ~ class_Orderings_Olinorder(U_8580) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP767,sP768])],[f_2512_2]) ).
cnf(f_2512_4,plain,
( sP768(U_8580,U_8581,U_8582,U_8583)
| ~ class_Orderings_Olinorder(U_8580) ),
inference(clausify,[status(thm)],[f_2512_3]) ).
cnf(f_2512_5,plain,
( sP767(U_8580,U_8581,U_8582,U_8583)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8580),U_8581),U_8582)),U_8583))
| ~ sP768(U_8580,U_8581,U_8582,U_8583) ),
inference(clausify,[status(thm)],[f_2512_3]) ).
cnf(f_2512_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8580),U_8581),U_8582)),U_8583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8582),U_8583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8581),U_8583))
| ~ sP768(U_8580,U_8581,U_8582,U_8583) ),
inference(clausify,[status(thm)],[f_2512_3]) ).
cnf(f_2512_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8581),U_8583))
| ~ sP767(U_8580,U_8581,U_8582,U_8583) ),
inference(clausify,[status(thm)],[f_2512_3]) ).
cnf(f_2512_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8580),U_8582),U_8583))
| ~ sP767(U_8580,U_8581,U_8582,U_8583) ),
inference(clausify,[status(thm)],[f_2512_3]) ).
fof(f_2513_1,plain,
! [V_y_2,V_x_2,V_z_2,T_b] :
( ( ( 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)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj]) ).
fof(f_2513_2,plain,
! [U_8587,U_8586,U_8585,U_8584] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8584),U_8586),U_8587)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8587))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8586)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8584),U_8586),U_8587))) ) )
| ~ class_Orderings_Olinorder(U_8584) ),
inference(variable_rename,[status(thm)],[f_2513_1]) ).
fof(f_2513_3,plain,
( ! [U_8585,U_8587,U_8584,U_8586] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8587))
| ~ sP769(U_8585,U_8587,U_8584,U_8586) )
& ! [U_8585,U_8587,U_8584,U_8586] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8586))
| ~ sP769(U_8585,U_8587,U_8584,U_8586) )
& ! [U_8585,U_8587,U_8584,U_8586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8584),U_8586),U_8587)))
| sP769(U_8585,U_8587,U_8584,U_8586)
| ~ sP770(U_8585,U_8587,U_8584,U_8586) )
& ! [U_8585,U_8587,U_8584,U_8586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8584),U_8586),U_8587)))
| ~ sP770(U_8585,U_8587,U_8584,U_8586) )
& ! [U_8585,U_8587,U_8584,U_8586] :
( sP770(U_8585,U_8587,U_8584,U_8586)
| ~ class_Orderings_Olinorder(U_8584) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP769,sP770])],[f_2513_2]) ).
cnf(f_2513_4,plain,
( sP770(U_8585,U_8587,U_8584,U_8586)
| ~ class_Orderings_Olinorder(U_8584) ),
inference(clausify,[status(thm)],[f_2513_3]) ).
cnf(f_2513_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8584),U_8586),U_8587)))
| ~ sP770(U_8585,U_8587,U_8584,U_8586) ),
inference(clausify,[status(thm)],[f_2513_3]) ).
cnf(f_2513_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8584),U_8586),U_8587)))
| sP769(U_8585,U_8587,U_8584,U_8586)
| ~ sP770(U_8585,U_8587,U_8584,U_8586) ),
inference(clausify,[status(thm)],[f_2513_3]) ).
cnf(f_2513_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8586))
| ~ sP769(U_8585,U_8587,U_8584,U_8586) ),
inference(clausify,[status(thm)],[f_2513_3]) ).
cnf(f_2513_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8584),U_8585),U_8587))
| ~ sP769(U_8585,U_8587,U_8584,U_8586) ),
inference(clausify,[status(thm)],[f_2513_3]) ).
fof(f_2514_1,plain,
! [V_v,V_u,T_b] :
( ( ( 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)
| 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))) )
& ( 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)
| ~ 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))) ) )
| ~ class_Orderings_Oord(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_max__number__of]) ).
fof(f_2514_2,plain,
! [U_8590,U_8589,U_8588] :
( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590))) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590))) ) )
| ~ class_Orderings_Oord(U_8588)
| ~ class_Int_Onumber(U_8588) ),
inference(variable_rename,[status(thm)],[f_2514_1]) ).
fof(f_2514_3,plain,
( ! [U_8590,U_8589,U_8588] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)))
| ~ sP771(U_8590,U_8589,U_8588) )
& ! [U_8590,U_8589,U_8588] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)))
| ~ sP771(U_8590,U_8589,U_8588) )
& ! [U_8590,U_8589,U_8588] :
( sP771(U_8590,U_8589,U_8588)
| ~ class_Orderings_Oord(U_8588)
| ~ class_Int_Onumber(U_8588) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP771])],[f_2514_2]) ).
cnf(f_2514_4,plain,
( sP771(U_8590,U_8589,U_8588)
| ~ class_Orderings_Oord(U_8588)
| ~ class_Int_Onumber(U_8588) ),
inference(clausify,[status(thm)],[f_2514_3]) ).
cnf(f_2514_5,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)))
| ~ sP771(U_8590,U_8589,U_8588) ),
inference(clausify,[status(thm)],[f_2514_3]) ).
cnf(f_2514_6,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8588),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8589)),hAPP(c_Int_Onumber__class_Onumber__of(U_8588),U_8590)))
| ~ sP771(U_8590,U_8589,U_8588) ),
inference(clausify,[status(thm)],[f_2514_3]) ).
fof(f_2515_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le]) ).
fof(f_2515_2,plain,
! [U_8594,U_8593,U_8592,U_8591] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8591),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8591),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),U_8593)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),U_8594))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8591),U_8593),U_8594))))
| ~ class_Orderings_Olinorder(U_8591) ),
inference(variable_rename,[status(thm)],[f_2515_1]) ).
fof(f_2515_3,plain,
! [U_8591,U_8592,U_8593,U_8594] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8591),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8591),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),U_8593)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),U_8594))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8591),U_8593),U_8594))))
| ~ class_Orderings_Olinorder(U_8591) ),
inference(definitional_conversion,[status(esa)],[f_2515_2]) ).
cnf(f_2515_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8591),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8591),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),U_8593)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),U_8594))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8591),U_8592),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8591),U_8593),U_8594))))
| ~ class_Orderings_Olinorder(U_8591) ),
inference(clausify,[status(thm)],[f_2515_3]) ).
fof(f_2516_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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))))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le]) ).
fof(f_2516_2,plain,
! [U_8598,U_8597,U_8596,U_8595] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8595),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8595),U_8597),U_8598))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8595),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),U_8597)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),U_8598))))
| ~ class_Orderings_Olinorder(U_8595) ),
inference(variable_rename,[status(thm)],[f_2516_1]) ).
fof(f_2516_3,plain,
! [U_8595,U_8596,U_8597,U_8598] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8595),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8595),U_8597),U_8598))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8595),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),U_8597)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),U_8598))))
| ~ class_Orderings_Olinorder(U_8595) ),
inference(definitional_conversion,[status(esa)],[f_2516_2]) ).
cnf(f_2516_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8595),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8595),U_8597),U_8598))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8595),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),U_8597)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8595),U_8596),U_8598))))
| ~ class_Orderings_Olinorder(U_8595) ),
inference(clausify,[status(thm)],[f_2516_3]) ).
fof(f_2517_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max]) ).
fof(f_2517_2,plain,
! [U_8601,U_8600,U_8599] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8599),U_8600),U_8601)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8599),hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),U_8600)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),U_8601))
| ~ class_Groups_Olinordered__ab__group__add(U_8599) ),
inference(variable_rename,[status(thm)],[f_2517_1]) ).
fof(f_2517_3,plain,
! [U_8599,U_8600,U_8601] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8599),U_8600),U_8601)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8599),hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),U_8600)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),U_8601))
| ~ class_Groups_Olinordered__ab__group__add(U_8599) ),
inference(definitional_conversion,[status(esa)],[f_2517_2]) ).
cnf(f_2517_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8599),U_8600),U_8601)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8599),hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),U_8600)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8599),U_8601))
| ~ class_Groups_Olinordered__ab__group__add(U_8599) ),
inference(clausify,[status(thm)],[f_2517_3]) ).
fof(f_2518_1,plain,
! [V_y,V_x,T_a] :
( 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))
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min]) ).
fof(f_2518_2,plain,
! [U_8604,U_8603,U_8602] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8602),U_8603),U_8604)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8602),hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),U_8603)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),U_8604))
| ~ class_Groups_Olinordered__ab__group__add(U_8602) ),
inference(variable_rename,[status(thm)],[f_2518_1]) ).
fof(f_2518_3,plain,
! [U_8602,U_8603,U_8604] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8602),U_8603),U_8604)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8602),hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),U_8603)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),U_8604))
| ~ class_Groups_Olinordered__ab__group__add(U_8602) ),
inference(definitional_conversion,[status(esa)],[f_2518_2]) ).
cnf(f_2518_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8602),U_8603),U_8604)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8602),hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),U_8603)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8602),U_8604))
| ~ class_Groups_Olinordered__ab__group__add(U_8602) ),
inference(clausify,[status(thm)],[f_2518_3]) ).
fof(f_2519_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__minus__add__max]) ).
fof(f_2519_2,plain,
! [U_8606,U_8605] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8605),U_8606)),U_8606) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8605),U_8606),
inference(variable_rename,[status(thm)],[f_2519_1]) ).
fof(f_2519_3,plain,
! [U_8605,U_8606] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8605),U_8606)),U_8606) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8605),U_8606),
inference(definitional_conversion,[status(esa)],[f_2519_2]) ).
cnf(f_2519_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8605),U_8606)),U_8606) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8605),U_8606),
inference(clausify,[status(thm)],[f_2519_3]) ).
fof(f_2520_1,plain,
! [V_a_2,V_b_2,V_A_2,T_b] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert]) ).
fof(f_2520_2,plain,
! [U_8610,U_8609,U_8608,U_8607] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_8607,U_8607,c_Orderings_Oord__class_Omax(U_8607)),U_8609),hAPP(hAPP(c_Set_Oinsert(U_8607),U_8610),U_8608)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8607),U_8610),hAPP(hAPP(c_Finite__Set_Ofold(U_8607,U_8607,c_Orderings_Oord__class_Omax(U_8607)),U_8609),U_8608))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8607),U_8608))
| ~ class_Orderings_Olinorder(U_8607) ),
inference(variable_rename,[status(thm)],[f_2520_1]) ).
fof(f_2520_3,plain,
! [U_8607,U_8608,U_8609,U_8610] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_8607,U_8607,c_Orderings_Oord__class_Omax(U_8607)),U_8609),hAPP(hAPP(c_Set_Oinsert(U_8607),U_8610),U_8608)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8607),U_8610),hAPP(hAPP(c_Finite__Set_Ofold(U_8607,U_8607,c_Orderings_Oord__class_Omax(U_8607)),U_8609),U_8608))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8607),U_8608))
| ~ class_Orderings_Olinorder(U_8607) ),
inference(definitional_conversion,[status(esa)],[f_2520_2]) ).
cnf(f_2520_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_8607,U_8607,c_Orderings_Oord__class_Omax(U_8607)),U_8609),hAPP(hAPP(c_Set_Oinsert(U_8607),U_8610),U_8608)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8607),U_8610),hAPP(hAPP(c_Finite__Set_Ofold(U_8607,U_8607,c_Orderings_Oord__class_Omax(U_8607)),U_8609),U_8608))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8607),U_8608))
| ~ class_Orderings_Olinorder(U_8607) ),
inference(clausify,[status(thm)],[f_2520_3]) ).
fof(f_2521_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem]) ).
fof(f_2521_2,plain,
! [U_8613,U_8612,U_8611] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8611),U_8613),c_Big__Operators_Olinorder__class_OMax(U_8611,U_8612)) = c_Big__Operators_Olinorder__class_OMax(U_8611,U_8612)
| ~ hBOOL(hAPP(hAPP(c_member(U_8611),U_8613),U_8612))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8611),U_8612))
| ~ class_Orderings_Olinorder(U_8611) ),
inference(variable_rename,[status(thm)],[f_2521_1]) ).
fof(f_2521_3,plain,
! [U_8611,U_8612,U_8613] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8611),U_8613),c_Big__Operators_Olinorder__class_OMax(U_8611,U_8612)) = c_Big__Operators_Olinorder__class_OMax(U_8611,U_8612)
| ~ hBOOL(hAPP(hAPP(c_member(U_8611),U_8613),U_8612))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8611),U_8612))
| ~ class_Orderings_Olinorder(U_8611) ),
inference(definitional_conversion,[status(esa)],[f_2521_2]) ).
cnf(f_2521_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8611),U_8613),c_Big__Operators_Olinorder__class_OMax(U_8611,U_8612)) = c_Big__Operators_Olinorder__class_OMax(U_8611,U_8612)
| ~ hBOOL(hAPP(hAPP(c_member(U_8611),U_8613),U_8612))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8611),U_8612))
| ~ class_Orderings_Olinorder(U_8611) ),
inference(clausify,[status(thm)],[f_2521_3]) ).
fof(f_2522_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost]) ).
fof(f_2522_2,plain,
! [U_8618,U_8617,U_8616,U_8615,U_8614] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8614,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8614,U_8615,U_8616)),c_SetInterval_Oord__class_OatLeastAtMost(U_8614,U_8617,U_8618)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8614,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8614),U_8615),U_8617),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8614),U_8616),U_8618))
| ~ class_Orderings_Olinorder(U_8614) ),
inference(variable_rename,[status(thm)],[f_2522_1]) ).
fof(f_2522_3,plain,
! [U_8614,U_8615,U_8616,U_8617,U_8618] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8614,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8614,U_8615,U_8616)),c_SetInterval_Oord__class_OatLeastAtMost(U_8614,U_8617,U_8618)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8614,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8614),U_8615),U_8617),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8614),U_8616),U_8618))
| ~ class_Orderings_Olinorder(U_8614) ),
inference(definitional_conversion,[status(esa)],[f_2522_2]) ).
cnf(f_2522_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8614,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8614,U_8615,U_8616)),c_SetInterval_Oord__class_OatLeastAtMost(U_8614,U_8617,U_8618)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8614,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8614),U_8615),U_8617),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8614),U_8616),U_8618))
| ~ class_Orderings_Olinorder(U_8614) ),
inference(clausify,[status(thm)],[f_2522_3]) ).
fof(f_2523_1,plain,
! [V_d_2,V_ca_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(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_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_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan]) ).
fof(f_2523_2,plain,
! [U_8623,U_8622,U_8621,U_8620,U_8619] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8619,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,U_8620),U_8621)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,U_8622),U_8623)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8619),U_8620),U_8622)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8619),U_8621),U_8623))
| ~ class_Orderings_Olinorder(U_8619) ),
inference(variable_rename,[status(thm)],[f_2523_1]) ).
fof(f_2523_3,plain,
! [U_8619,U_8620,U_8621,U_8622,U_8623] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8619,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,U_8620),U_8621)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,U_8622),U_8623)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8619),U_8620),U_8622)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8619),U_8621),U_8623))
| ~ class_Orderings_Olinorder(U_8619) ),
inference(definitional_conversion,[status(esa)],[f_2523_2]) ).
cnf(f_2523_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8619,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,U_8620),U_8621)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,U_8622),U_8623)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8619,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8619),U_8620),U_8622)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8619),U_8621),U_8623))
| ~ class_Orderings_Olinorder(U_8619) ),
inference(clausify,[status(thm)],[f_2523_3]) ).
fof(f_2524_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost]) ).
fof(f_2524_2,plain,
! [U_8628,U_8627,U_8626,U_8625,U_8624] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8624,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,U_8625,U_8626)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,U_8627,U_8628)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8624),U_8625),U_8627),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8624),U_8626),U_8628))
| ~ class_Orderings_Olinorder(U_8624) ),
inference(variable_rename,[status(thm)],[f_2524_1]) ).
fof(f_2524_3,plain,
! [U_8624,U_8625,U_8626,U_8627,U_8628] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8624,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,U_8625,U_8626)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,U_8627,U_8628)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8624),U_8625),U_8627),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8624),U_8626),U_8628))
| ~ class_Orderings_Olinorder(U_8624) ),
inference(definitional_conversion,[status(esa)],[f_2524_2]) ).
cnf(f_2524_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8624,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,U_8625,U_8626)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,U_8627,U_8628)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8624,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8624),U_8625),U_8627),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8624),U_8626),U_8628))
| ~ class_Orderings_Olinorder(U_8624) ),
inference(clausify,[status(thm)],[f_2524_3]) ).
fof(f_2525_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
( 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan]) ).
fof(f_2525_2,plain,
! [U_8633,U_8632,U_8631,U_8630,U_8629] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8629,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,U_8630,U_8631)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,U_8632,U_8633)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8629),U_8630),U_8632),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8629),U_8631),U_8633))
| ~ class_Orderings_Olinorder(U_8629) ),
inference(variable_rename,[status(thm)],[f_2525_1]) ).
fof(f_2525_3,plain,
! [U_8629,U_8630,U_8631,U_8632,U_8633] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8629,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,U_8630,U_8631)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,U_8632,U_8633)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8629),U_8630),U_8632),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8629),U_8631),U_8633))
| ~ class_Orderings_Olinorder(U_8629) ),
inference(definitional_conversion,[status(esa)],[f_2525_2]) ).
cnf(f_2525_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8629,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,U_8630,U_8631)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,U_8632,U_8633)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_8629,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8629),U_8630),U_8632),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8629),U_8631),U_8633))
| ~ class_Orderings_Olinorder(U_8629) ),
inference(clausify,[status(thm)],[f_2525_3]) ).
fof(f_2526_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_b] :
( 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_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2]) ).
fof(f_2526_2,plain,
! [U_8637,U_8636,U_8635,U_8634] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8634,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8634,U_8635,U_8636)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8634),U_8637)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8634,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8634),U_8635),U_8637),U_8636)
| ~ class_Orderings_Olinorder(U_8634) ),
inference(variable_rename,[status(thm)],[f_2526_1]) ).
fof(f_2526_3,plain,
! [U_8634,U_8635,U_8636,U_8637] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8634,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8634,U_8635,U_8636)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8634),U_8637)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8634,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8634),U_8635),U_8637),U_8636)
| ~ class_Orderings_Olinorder(U_8634) ),
inference(definitional_conversion,[status(esa)],[f_2526_2]) ).
cnf(f_2526_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8634,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8634,U_8635,U_8636)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8634),U_8637)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8634,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8634),U_8635),U_8637),U_8636)
| ~ class_Orderings_Olinorder(U_8634) ),
inference(clausify,[status(thm)],[f_2526_3]) ).
fof(f_2527_1,plain,
! [V_d_2,V_ca_2,V_a_2,T_b] :
( 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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2]) ).
fof(f_2527_2,plain,
! [U_8641,U_8640,U_8639,U_8638] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8638,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8638),U_8639)),c_SetInterval_Oord__class_OatLeastAtMost(U_8638,U_8640,U_8641)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8638,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8638),U_8639),U_8640),U_8641)
| ~ class_Orderings_Olinorder(U_8638) ),
inference(variable_rename,[status(thm)],[f_2527_1]) ).
fof(f_2527_3,plain,
! [U_8638,U_8639,U_8640,U_8641] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8638,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8638),U_8639)),c_SetInterval_Oord__class_OatLeastAtMost(U_8638,U_8640,U_8641)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8638,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8638),U_8639),U_8640),U_8641)
| ~ class_Orderings_Olinorder(U_8638) ),
inference(definitional_conversion,[status(esa)],[f_2527_2]) ).
cnf(f_2527_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8638,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8638),U_8639)),c_SetInterval_Oord__class_OatLeastAtMost(U_8638,U_8640,U_8641)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8638,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8638),U_8639),U_8640),U_8641)
| ~ class_Orderings_Olinorder(U_8638) ),
inference(clausify,[status(thm)],[f_2527_3]) ).
fof(f_2528_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_OF__eq]) ).
fof(f_2528_2,plain,
! [U_8643,U_8642] :
( c_Big__Operators_Olinorder__class_OMax(U_8642,U_8643) = hAPP(c_Finite__Set_Ofold1(U_8642,c_Orderings_Oord__class_Omax(U_8642)),U_8643)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8642),U_8643))
| ~ class_Orderings_Olinorder(U_8642) ),
inference(variable_rename,[status(thm)],[f_2528_1]) ).
fof(f_2528_3,plain,
! [U_8642,U_8643] :
( c_Big__Operators_Olinorder__class_OMax(U_8642,U_8643) = hAPP(c_Finite__Set_Ofold1(U_8642,c_Orderings_Oord__class_Omax(U_8642)),U_8643)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8642),U_8643))
| ~ class_Orderings_Olinorder(U_8642) ),
inference(definitional_conversion,[status(esa)],[f_2528_2]) ).
cnf(f_2528_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8642,U_8643) = hAPP(c_Finite__Set_Ofold1(U_8642,c_Orderings_Oord__class_Omax(U_8642)),U_8643)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8642),U_8643))
| ~ class_Orderings_Olinorder(U_8642) ),
inference(clausify,[status(thm)],[f_2528_3]) ).
fof(f_2529_1,plain,
! [V_b_2,V_a_2,V_A_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup]) ).
fof(f_2529_2,plain,
! [U_8647,U_8646,U_8645,U_8644] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8644),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8644),U_8646),U_8647)),hAPP(hAPP(c_Finite__Set_Ofold(U_8644,U_8644,c_Orderings_Oord__class_Omax(U_8644)),U_8647),U_8645)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8644),U_8646),U_8645))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8644),U_8645))
| ~ class_Orderings_Olinorder(U_8644) ),
inference(variable_rename,[status(thm)],[f_2529_1]) ).
fof(f_2529_3,plain,
! [U_8644,U_8645,U_8646,U_8647] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8644),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8644),U_8646),U_8647)),hAPP(hAPP(c_Finite__Set_Ofold(U_8644,U_8644,c_Orderings_Oord__class_Omax(U_8644)),U_8647),U_8645)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8644),U_8646),U_8645))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8644),U_8645))
| ~ class_Orderings_Olinorder(U_8644) ),
inference(definitional_conversion,[status(esa)],[f_2529_2]) ).
cnf(f_2529_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8644),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8644),U_8646),U_8647)),hAPP(hAPP(c_Finite__Set_Ofold(U_8644,U_8644,c_Orderings_Oord__class_Omax(U_8644)),U_8647),U_8645)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8644),U_8646),U_8645))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8644),U_8645))
| ~ class_Orderings_Olinorder(U_8644) ),
inference(clausify,[status(thm)],[f_2529_3]) ).
fof(f_2530_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__insert]) ).
fof(f_2530_2,plain,
! [U_8650,U_8649,U_8648] :
( c_Big__Operators_Olinorder__class_OMax(U_8648,hAPP(hAPP(c_Set_Oinsert(U_8648),U_8650),U_8649)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8648),U_8650),c_Big__Operators_Olinorder__class_OMax(U_8648,U_8649))
| U_8649 = c_Orderings_Obot__class_Obot(tc_fun(U_8648,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8648),U_8649))
| ~ class_Orderings_Olinorder(U_8648) ),
inference(variable_rename,[status(thm)],[f_2530_1]) ).
fof(f_2530_3,plain,
! [U_8648,U_8649,U_8650] :
( c_Big__Operators_Olinorder__class_OMax(U_8648,hAPP(hAPP(c_Set_Oinsert(U_8648),U_8650),U_8649)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8648),U_8650),c_Big__Operators_Olinorder__class_OMax(U_8648,U_8649))
| U_8649 = c_Orderings_Obot__class_Obot(tc_fun(U_8648,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8648),U_8649))
| ~ class_Orderings_Olinorder(U_8648) ),
inference(definitional_conversion,[status(esa)],[f_2530_2]) ).
cnf(f_2530_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8648,hAPP(hAPP(c_Set_Oinsert(U_8648),U_8650),U_8649)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8648),U_8650),c_Big__Operators_Olinorder__class_OMax(U_8648,U_8649))
| U_8649 = c_Orderings_Obot__class_Obot(tc_fun(U_8648,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8648),U_8649))
| ~ class_Orderings_Olinorder(U_8648) ),
inference(clausify,[status(thm)],[f_2530_3]) ).
fof(f_2531_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem]) ).
fof(f_2531_2,plain,
! [U_8653,U_8652,U_8651] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8651),c_Big__Operators_Olinorder__class_OMax(U_8651,U_8653)),c_Big__Operators_Olinorder__class_OMax(U_8651,U_8652)) = c_Big__Operators_Olinorder__class_OMax(U_8651,U_8652)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8651,tc_HOL_Obool)),U_8653),U_8652))
| U_8653 = c_Orderings_Obot__class_Obot(tc_fun(U_8651,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8651),U_8652))
| ~ class_Orderings_Olinorder(U_8651) ),
inference(variable_rename,[status(thm)],[f_2531_1]) ).
fof(f_2531_3,plain,
! [U_8651,U_8652,U_8653] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8651),c_Big__Operators_Olinorder__class_OMax(U_8651,U_8653)),c_Big__Operators_Olinorder__class_OMax(U_8651,U_8652)) = c_Big__Operators_Olinorder__class_OMax(U_8651,U_8652)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8651,tc_HOL_Obool)),U_8653),U_8652))
| U_8653 = c_Orderings_Obot__class_Obot(tc_fun(U_8651,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8651),U_8652))
| ~ class_Orderings_Olinorder(U_8651) ),
inference(definitional_conversion,[status(esa)],[f_2531_2]) ).
cnf(f_2531_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8651),c_Big__Operators_Olinorder__class_OMax(U_8651,U_8653)),c_Big__Operators_Olinorder__class_OMax(U_8651,U_8652)) = c_Big__Operators_Olinorder__class_OMax(U_8651,U_8652)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8651,tc_HOL_Obool)),U_8653),U_8652))
| U_8653 = c_Orderings_Obot__class_Obot(tc_fun(U_8651,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8651),U_8652))
| ~ class_Orderings_Olinorder(U_8651) ),
inference(clausify,[status(thm)],[f_2531_3]) ).
fof(f_2532_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb]) ).
fof(f_2532_2,plain,
! [U_8656,U_8655,U_8654] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8654),U_8656),c_Big__Operators_Olattice_OInf__fin(U_8654,c_Orderings_Oord__class_Omin(U_8654),U_8655)) = U_8656
| ~ hBOOL(hAPP(hAPP(c_member(U_8654),U_8656),U_8655))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8654),U_8655))
| ~ class_Orderings_Olinorder(U_8654) ),
inference(variable_rename,[status(thm)],[f_2532_1]) ).
fof(f_2532_3,plain,
! [U_8656,U_8655,U_8654] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8654),U_8656),c_Big__Operators_Olattice_OInf__fin(U_8654,c_Orderings_Oord__class_Omin(U_8654),U_8655)) = U_8656
| ~ hBOOL(hAPP(hAPP(c_member(U_8654),U_8656),U_8655))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8654),U_8655))
| ~ class_Orderings_Olinorder(U_8654) ),
inference(definitional_conversion,[status(esa)],[f_2532_2]) ).
cnf(f_2532_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8654),U_8656),c_Big__Operators_Olattice_OInf__fin(U_8654,c_Orderings_Oord__class_Omin(U_8654),U_8655)) = U_8656
| ~ hBOOL(hAPP(hAPP(c_member(U_8654),U_8656),U_8655))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8654),U_8655))
| ~ class_Orderings_Olinorder(U_8654) ),
inference(clausify,[status(thm)],[f_2532_3]) ).
fof(f_2533_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__Un]) ).
fof(f_2533_2,plain,
! [U_8659,U_8658,U_8657] :
( c_Big__Operators_Olinorder__class_OMax(U_8657,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),U_8659)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8657),c_Big__Operators_Olinorder__class_OMax(U_8657,U_8658)),c_Big__Operators_Olinorder__class_OMax(U_8657,U_8659))
| U_8659 = c_Orderings_Obot__class_Obot(tc_fun(U_8657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8657),U_8659))
| U_8658 = c_Orderings_Obot__class_Obot(tc_fun(U_8657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8657),U_8658))
| ~ class_Orderings_Olinorder(U_8657) ),
inference(variable_rename,[status(thm)],[f_2533_1]) ).
fof(f_2533_3,plain,
! [U_8657,U_8658,U_8659] :
( c_Big__Operators_Olinorder__class_OMax(U_8657,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),U_8659)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8657),c_Big__Operators_Olinorder__class_OMax(U_8657,U_8658)),c_Big__Operators_Olinorder__class_OMax(U_8657,U_8659))
| U_8659 = c_Orderings_Obot__class_Obot(tc_fun(U_8657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8657),U_8659))
| U_8658 = c_Orderings_Obot__class_Obot(tc_fun(U_8657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8657),U_8658))
| ~ class_Orderings_Olinorder(U_8657) ),
inference(definitional_conversion,[status(esa)],[f_2533_2]) ).
cnf(f_2533_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8657,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),U_8659)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8657),c_Big__Operators_Olinorder__class_OMax(U_8657,U_8658)),c_Big__Operators_Olinorder__class_OMax(U_8657,U_8659))
| U_8659 = c_Orderings_Obot__class_Obot(tc_fun(U_8657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8657),U_8659))
| U_8658 = c_Orderings_Obot__class_Obot(tc_fun(U_8657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8657),U_8658))
| ~ class_Orderings_Olinorder(U_8657) ),
inference(clausify,[status(thm)],[f_2533_3]) ).
fof(f_2534_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H]) ).
fof(f_2534_2,plain,
! [U_8662,U_8661,U_8660] :
( c_Big__Operators_Olinorder__class_OMax(U_8660,hAPP(hAPP(c_Set_Oinsert(U_8660),U_8662),U_8661)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8660,U_8660,c_Orderings_Oord__class_Omax(U_8660)),U_8662),U_8661)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8660),U_8661))
| ~ class_Orderings_Olinorder(U_8660) ),
inference(variable_rename,[status(thm)],[f_2534_1]) ).
fof(f_2534_3,plain,
! [U_8660,U_8661,U_8662] :
( c_Big__Operators_Olinorder__class_OMax(U_8660,hAPP(hAPP(c_Set_Oinsert(U_8660),U_8662),U_8661)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8660,U_8660,c_Orderings_Oord__class_Omax(U_8660)),U_8662),U_8661)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8660),U_8661))
| ~ class_Orderings_Olinorder(U_8660) ),
inference(definitional_conversion,[status(esa)],[f_2534_2]) ).
cnf(f_2534_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8660,hAPP(hAPP(c_Set_Oinsert(U_8660),U_8662),U_8661)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8660,U_8660,c_Orderings_Oord__class_Omax(U_8660)),U_8662),U_8661)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8660),U_8661))
| ~ class_Orderings_Olinorder(U_8660) ),
inference(clausify,[status(thm)],[f_2534_3]) ).
fof(f_2535_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oinsert]) ).
fof(f_2535_2,plain,
! [U_8665,U_8664,U_8663] :
( c_Big__Operators_Olinorder__class_OMax(U_8663,hAPP(hAPP(c_Set_Oinsert(U_8663),U_8665),U_8664)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8663),U_8665),c_Big__Operators_Olinorder__class_OMax(U_8663,U_8664))
| U_8664 = c_Orderings_Obot__class_Obot(tc_fun(U_8663,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8663),U_8665),U_8664))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8663),U_8664))
| ~ class_Orderings_Olinorder(U_8663) ),
inference(variable_rename,[status(thm)],[f_2535_1]) ).
fof(f_2535_3,plain,
! [U_8663,U_8664,U_8665] :
( c_Big__Operators_Olinorder__class_OMax(U_8663,hAPP(hAPP(c_Set_Oinsert(U_8663),U_8665),U_8664)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8663),U_8665),c_Big__Operators_Olinorder__class_OMax(U_8663,U_8664))
| U_8664 = c_Orderings_Obot__class_Obot(tc_fun(U_8663,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8663),U_8665),U_8664))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8663),U_8664))
| ~ class_Orderings_Olinorder(U_8663) ),
inference(definitional_conversion,[status(esa)],[f_2535_2]) ).
cnf(f_2535_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8663,hAPP(hAPP(c_Set_Oinsert(U_8663),U_8665),U_8664)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8663),U_8665),c_Big__Operators_Olinorder__class_OMax(U_8663,U_8664))
| U_8664 = c_Orderings_Obot__class_Obot(tc_fun(U_8663,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8663),U_8665),U_8664))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8663),U_8664))
| ~ class_Orderings_Olinorder(U_8663) ),
inference(clausify,[status(thm)],[f_2535_3]) ).
fof(f_2536_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove]) ).
fof(f_2536_2,plain,
! [U_8668,U_8667,U_8666] :
( ( ( c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),U_8667)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8666),U_8668),c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),U_8667)) = U_8668
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8666),U_8667))
| ~ class_Orderings_Olinorder(U_8666) ),
inference(variable_rename,[status(thm)],[f_2536_1]) ).
fof(f_2536_3,plain,
( ! [U_8666,U_8667,U_8668] :
( c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),U_8667)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8666),U_8668),c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool))
| ~ sP772(U_8666,U_8667,U_8668) )
& ! [U_8666,U_8667,U_8668] :
( c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),U_8667)) = U_8668
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool))
| ~ sP772(U_8666,U_8667,U_8668) )
& ! [U_8666,U_8667,U_8668] :
( sP772(U_8666,U_8667,U_8668)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8666),U_8667))
| ~ class_Orderings_Olinorder(U_8666) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP772])],[f_2536_2]) ).
cnf(f_2536_4,plain,
( sP772(U_8666,U_8667,U_8668)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8666),U_8667))
| ~ class_Orderings_Olinorder(U_8666) ),
inference(clausify,[status(thm)],[f_2536_3]) ).
cnf(f_2536_5,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),U_8667)) = U_8668
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool))
| ~ sP772(U_8666,U_8667,U_8668) ),
inference(clausify,[status(thm)],[f_2536_3]) ).
cnf(f_2536_6,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),U_8667)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8666),U_8668),c_Big__Operators_Olinorder__class_OMax(U_8666,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8666,tc_HOL_Obool)),U_8667),hAPP(hAPP(c_Set_Oinsert(U_8666),U_8668),c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8666,tc_HOL_Obool))
| ~ sP772(U_8666,U_8667,U_8668) ),
inference(clausify,[status(thm)],[f_2536_3]) ).
fof(f_2537_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint]) ).
fof(f_2537_2,plain,
! [U_8671,U_8670,U_8669] :
( c_Big__Operators_Olinorder__class_OMax(U_8669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8669,tc_HOL_Obool)),U_8670),U_8671)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8669),c_Big__Operators_Olinorder__class_OMax(U_8669,U_8670)),c_Big__Operators_Olinorder__class_OMax(U_8669,U_8671))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8669,tc_HOL_Obool)),U_8670),U_8671) != c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| U_8671 = c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8669),U_8671))
| U_8670 = c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8669),U_8670))
| ~ class_Orderings_Olinorder(U_8669) ),
inference(variable_rename,[status(thm)],[f_2537_1]) ).
fof(f_2537_3,plain,
! [U_8669,U_8670,U_8671] :
( c_Big__Operators_Olinorder__class_OMax(U_8669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8669,tc_HOL_Obool)),U_8670),U_8671)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8669),c_Big__Operators_Olinorder__class_OMax(U_8669,U_8670)),c_Big__Operators_Olinorder__class_OMax(U_8669,U_8671))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8669,tc_HOL_Obool)),U_8670),U_8671) != c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| U_8671 = c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8669),U_8671))
| U_8670 = c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8669),U_8670))
| ~ class_Orderings_Olinorder(U_8669) ),
inference(definitional_conversion,[status(esa)],[f_2537_2]) ).
cnf(f_2537_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8669,tc_HOL_Obool)),U_8670),U_8671)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8669),c_Big__Operators_Olinorder__class_OMax(U_8669,U_8670)),c_Big__Operators_Olinorder__class_OMax(U_8669,U_8671))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8669,tc_HOL_Obool)),U_8670),U_8671) != c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| U_8671 = c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8669),U_8671))
| U_8670 = c_Orderings_Obot__class_Obot(tc_fun(U_8669,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8669),U_8670))
| ~ class_Orderings_Olinorder(U_8669) ),
inference(clausify,[status(thm)],[f_2537_3]) ).
fof(f_2538_1,plain,
! [T_b] :
( c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b))
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_max__ord__max]) ).
fof(f_2538_2,plain,
! [U_8672] :
( c_Orderings_Oord__class_Omax(U_8672) = c_Orderings_Oord_Omax(U_8672,c_Orderings_Oord__class_Oless__eq(U_8672))
| ~ class_Orderings_Oord(U_8672) ),
inference(variable_rename,[status(thm)],[f_2538_1]) ).
fof(f_2538_3,plain,
! [U_8672] :
( c_Orderings_Oord__class_Omax(U_8672) = c_Orderings_Oord_Omax(U_8672,c_Orderings_Oord__class_Oless__eq(U_8672))
| ~ class_Orderings_Oord(U_8672) ),
inference(definitional_conversion,[status(esa)],[f_2538_2]) ).
cnf(f_2538_4,plain,
( c_Orderings_Oord__class_Omax(U_8672) = c_Orderings_Oord_Omax(U_8672,c_Orderings_Oord__class_Oless__eq(U_8672))
| ~ class_Orderings_Oord(U_8672) ),
inference(clausify,[status(thm)],[f_2538_3]) ).
fof(f_2539_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))
| ? [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))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oclosed]) ).
fof(f_2539_2,plain,
! [U_8676,U_8675] :
( hBOOL(hAPP(hAPP(c_member(U_8675),c_Big__Operators_Olinorder__class_OMax(U_8675,U_8676)),U_8676))
| ? [U_8674,U_8673] : ~ hBOOL(hAPP(hAPP(c_member(U_8675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8675),U_8674),U_8673)),hAPP(hAPP(c_Set_Oinsert(U_8675),U_8674),hAPP(hAPP(c_Set_Oinsert(U_8675),U_8673),c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))))))
| U_8676 = c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8675),U_8676))
| ~ class_Orderings_Olinorder(U_8675) ),
inference(variable_rename,[status(thm)],[f_2539_1]) ).
fof(f_2539_3,plain,
! [U_8676,U_8675] :
( hBOOL(hAPP(hAPP(c_member(U_8675),c_Big__Operators_Olinorder__class_OMax(U_8675,U_8676)),U_8676))
| ? [U_8673] : ~ hBOOL(hAPP(hAPP(c_member(U_8675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8675),sK236(U_8676,U_8675)),U_8673)),hAPP(hAPP(c_Set_Oinsert(U_8675),sK236(U_8676,U_8675)),hAPP(hAPP(c_Set_Oinsert(U_8675),U_8673),c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))))))
| U_8676 = c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8675),U_8676))
| ~ class_Orderings_Olinorder(U_8675) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_8674,sK236(U_8676,U_8675))],[f_2539_2]) ).
fof(f_2539_4,plain,
! [U_8676,U_8675] :
( hBOOL(hAPP(hAPP(c_member(U_8675),c_Big__Operators_Olinorder__class_OMax(U_8675,U_8676)),U_8676))
| ~ hBOOL(hAPP(hAPP(c_member(U_8675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8675),sK236(U_8676,U_8675)),sK237(U_8676,U_8675))),hAPP(hAPP(c_Set_Oinsert(U_8675),sK236(U_8676,U_8675)),hAPP(hAPP(c_Set_Oinsert(U_8675),sK237(U_8676,U_8675)),c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))))))
| U_8676 = c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8675),U_8676))
| ~ class_Orderings_Olinorder(U_8675) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_8673,sK237(U_8676,U_8675))],[f_2539_3]) ).
fof(f_2539_5,plain,
! [U_8675,U_8676] :
( hBOOL(hAPP(hAPP(c_member(U_8675),c_Big__Operators_Olinorder__class_OMax(U_8675,U_8676)),U_8676))
| ~ hBOOL(hAPP(hAPP(c_member(U_8675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8675),sK236(U_8676,U_8675)),sK237(U_8676,U_8675))),hAPP(hAPP(c_Set_Oinsert(U_8675),sK236(U_8676,U_8675)),hAPP(hAPP(c_Set_Oinsert(U_8675),sK237(U_8676,U_8675)),c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))))))
| U_8676 = c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8675),U_8676))
| ~ class_Orderings_Olinorder(U_8675) ),
inference(definitional_conversion,[status(esa)],[f_2539_4]) ).
cnf(f_2539_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8675),c_Big__Operators_Olinorder__class_OMax(U_8675,U_8676)),U_8676))
| ~ hBOOL(hAPP(hAPP(c_member(U_8675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8675),sK236(U_8676,U_8675)),sK237(U_8676,U_8675))),hAPP(hAPP(c_Set_Oinsert(U_8675),sK236(U_8676,U_8675)),hAPP(hAPP(c_Set_Oinsert(U_8675),sK237(U_8676,U_8675)),c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))))))
| U_8676 = c_Orderings_Obot__class_Obot(tc_fun(U_8675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8675),U_8676))
| ~ class_Orderings_Olinorder(U_8675) ),
inference(clausify,[status(thm)],[f_2539_5]) ).
fof(f_2540_1,plain,
! [V_A_2,T_b] :
( 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)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup]) ).
fof(f_2540_2,plain,
! [U_8678,U_8677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8677),c_Big__Operators_Olattice_OInf__fin(U_8677,c_Orderings_Oord__class_Omin(U_8677),U_8678)),c_Big__Operators_Olattice_OSup__fin(U_8677,c_Orderings_Oord__class_Omax(U_8677),U_8678)))
| U_8678 = c_Orderings_Obot__class_Obot(tc_fun(U_8677,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8677),U_8678))
| ~ class_Orderings_Olinorder(U_8677) ),
inference(variable_rename,[status(thm)],[f_2540_1]) ).
fof(f_2540_3,plain,
! [U_8678,U_8677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8677),c_Big__Operators_Olattice_OInf__fin(U_8677,c_Orderings_Oord__class_Omin(U_8677),U_8678)),c_Big__Operators_Olattice_OSup__fin(U_8677,c_Orderings_Oord__class_Omax(U_8677),U_8678)))
| U_8678 = c_Orderings_Obot__class_Obot(tc_fun(U_8677,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8677),U_8678))
| ~ class_Orderings_Olinorder(U_8677) ),
inference(definitional_conversion,[status(esa)],[f_2540_2]) ).
cnf(f_2540_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8677),c_Big__Operators_Olattice_OInf__fin(U_8677,c_Orderings_Oord__class_Omin(U_8677),U_8678)),c_Big__Operators_Olattice_OSup__fin(U_8677,c_Orderings_Oord__class_Omax(U_8677),U_8678)))
| U_8678 = c_Orderings_Obot__class_Obot(tc_fun(U_8677,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8677),U_8678))
| ~ class_Orderings_Olinorder(U_8677) ),
inference(clausify,[status(thm)],[f_2540_3]) ).
fof(f_2541_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove]) ).
fof(f_2541_2,plain,
! [U_8681,U_8680,U_8679] :
( ( ( c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),U_8680) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8679),U_8681),c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),U_8680) = U_8681
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8679),U_8681),U_8680))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8679),U_8680))
| ~ class_Orderings_Olinorder(U_8679) ),
inference(variable_rename,[status(thm)],[f_2541_1]) ).
fof(f_2541_3,plain,
( ! [U_8679,U_8680,U_8681] :
( c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),U_8680) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8679),U_8681),c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool))
| ~ sP773(U_8679,U_8680,U_8681) )
& ! [U_8679,U_8680,U_8681] :
( c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),U_8680) = U_8681
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool))
| ~ sP773(U_8679,U_8680,U_8681) )
& ! [U_8679,U_8680,U_8681] :
( sP773(U_8679,U_8680,U_8681)
| ~ hBOOL(hAPP(hAPP(c_member(U_8679),U_8681),U_8680))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8679),U_8680))
| ~ class_Orderings_Olinorder(U_8679) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP773])],[f_2541_2]) ).
cnf(f_2541_4,plain,
( sP773(U_8679,U_8680,U_8681)
| ~ hBOOL(hAPP(hAPP(c_member(U_8679),U_8681),U_8680))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8679),U_8680))
| ~ class_Orderings_Olinorder(U_8679) ),
inference(clausify,[status(thm)],[f_2541_3]) ).
cnf(f_2541_5,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),U_8680) = U_8681
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool))
| ~ sP773(U_8679,U_8680,U_8681) ),
inference(clausify,[status(thm)],[f_2541_3]) ).
cnf(f_2541_6,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),U_8680) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8679),U_8681),c_Big__Operators_Olattice_OSup__fin(U_8679,c_Orderings_Oord__class_Omax(U_8679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8679,tc_HOL_Obool)),U_8680),hAPP(hAPP(c_Set_Oinsert(U_8679),U_8681),c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8679,tc_HOL_Obool))
| ~ sP773(U_8679,U_8680,U_8681) ),
inference(clausify,[status(thm)],[f_2541_3]) ).
fof(f_2542_1,plain,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_sup__nat__def]) ).
fof(f_2542_2,plain,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_2542_1]) ).
cnf(f_2542_3,plain,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2542_2]) ).
fof(f_2543_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem]) ).
fof(f_2543_2,plain,
! [U_8684,U_8683,U_8682] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8682),U_8684),c_Big__Operators_Olattice_OSup__fin(U_8682,c_Orderings_Oord__class_Omax(U_8682),U_8683)) = c_Big__Operators_Olattice_OSup__fin(U_8682,c_Orderings_Oord__class_Omax(U_8682),U_8683)
| ~ hBOOL(hAPP(hAPP(c_member(U_8682),U_8684),U_8683))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8682),U_8683))
| ~ class_Orderings_Olinorder(U_8682) ),
inference(variable_rename,[status(thm)],[f_2543_1]) ).
fof(f_2543_3,plain,
! [U_8683,U_8684,U_8682] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8682),U_8684),c_Big__Operators_Olattice_OSup__fin(U_8682,c_Orderings_Oord__class_Omax(U_8682),U_8683)) = c_Big__Operators_Olattice_OSup__fin(U_8682,c_Orderings_Oord__class_Omax(U_8682),U_8683)
| ~ hBOOL(hAPP(hAPP(c_member(U_8682),U_8684),U_8683))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8682),U_8683))
| ~ class_Orderings_Olinorder(U_8682) ),
inference(definitional_conversion,[status(esa)],[f_2543_2]) ).
cnf(f_2543_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8682),U_8684),c_Big__Operators_Olattice_OSup__fin(U_8682,c_Orderings_Oord__class_Omax(U_8682),U_8683)) = c_Big__Operators_Olattice_OSup__fin(U_8682,c_Orderings_Oord__class_Omax(U_8682),U_8683)
| ~ hBOOL(hAPP(hAPP(c_member(U_8682),U_8684),U_8683))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8682),U_8683))
| ~ class_Orderings_Olinorder(U_8682) ),
inference(clausify,[status(thm)],[f_2543_3]) ).
fof(f_2544_1,plain,
! [V_x_2,T_b] :
( 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
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton]) ).
fof(f_2544_2,plain,
! [U_8686,U_8685] :
( c_Big__Operators_Olattice_OSup__fin(U_8685,c_Orderings_Oord__class_Omax(U_8685),hAPP(hAPP(c_Set_Oinsert(U_8685),U_8686),c_Orderings_Obot__class_Obot(tc_fun(U_8685,tc_HOL_Obool)))) = U_8686
| ~ class_Orderings_Olinorder(U_8685) ),
inference(variable_rename,[status(thm)],[f_2544_1]) ).
fof(f_2544_3,plain,
! [U_8686,U_8685] :
( c_Big__Operators_Olattice_OSup__fin(U_8685,c_Orderings_Oord__class_Omax(U_8685),hAPP(hAPP(c_Set_Oinsert(U_8685),U_8686),c_Orderings_Obot__class_Obot(tc_fun(U_8685,tc_HOL_Obool)))) = U_8686
| ~ class_Orderings_Olinorder(U_8685) ),
inference(definitional_conversion,[status(esa)],[f_2544_2]) ).
cnf(f_2544_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8685,c_Orderings_Oord__class_Omax(U_8685),hAPP(hAPP(c_Set_Oinsert(U_8685),U_8686),c_Orderings_Obot__class_Obot(tc_fun(U_8685,tc_HOL_Obool)))) = U_8686
| ~ class_Orderings_Olinorder(U_8685) ),
inference(clausify,[status(thm)],[f_2544_3]) ).
fof(f_2545_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq]) ).
fof(f_2545_2,plain,
! [U_8688,U_8687] :
( c_Big__Operators_Olattice_OSup__fin(U_8687,c_Orderings_Oord__class_Omax(U_8687),U_8688) = hAPP(c_Finite__Set_Ofold1(U_8687,c_Orderings_Oord__class_Omax(U_8687)),U_8688)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8687),U_8688))
| ~ class_Orderings_Olinorder(U_8687) ),
inference(variable_rename,[status(thm)],[f_2545_1]) ).
fof(f_2545_3,plain,
! [U_8687,U_8688] :
( c_Big__Operators_Olattice_OSup__fin(U_8687,c_Orderings_Oord__class_Omax(U_8687),U_8688) = hAPP(c_Finite__Set_Ofold1(U_8687,c_Orderings_Oord__class_Omax(U_8687)),U_8688)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8687),U_8688))
| ~ class_Orderings_Olinorder(U_8687) ),
inference(definitional_conversion,[status(esa)],[f_2545_2]) ).
cnf(f_2545_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8687,c_Orderings_Oord__class_Omax(U_8687),U_8688) = hAPP(c_Finite__Set_Ofold1(U_8687,c_Orderings_Oord__class_Omax(U_8687)),U_8688)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8687),U_8688))
| ~ class_Orderings_Olinorder(U_8687) ),
inference(clausify,[status(thm)],[f_2545_3]) ).
fof(f_2546_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem]) ).
fof(f_2546_2,plain,
! [U_8691,U_8690,U_8689] :
( c_Big__Operators_Olattice_OSup__fin(U_8689,c_Orderings_Oord__class_Omax(U_8689),hAPP(hAPP(c_Set_Oinsert(U_8689),U_8691),U_8690)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8689),U_8691),c_Big__Operators_Olattice_OSup__fin(U_8689,c_Orderings_Oord__class_Omax(U_8689),U_8690))
| U_8690 = c_Orderings_Obot__class_Obot(tc_fun(U_8689,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8689),U_8690))
| ~ class_Orderings_Olinorder(U_8689) ),
inference(variable_rename,[status(thm)],[f_2546_1]) ).
fof(f_2546_3,plain,
! [U_8689,U_8690,U_8691] :
( c_Big__Operators_Olattice_OSup__fin(U_8689,c_Orderings_Oord__class_Omax(U_8689),hAPP(hAPP(c_Set_Oinsert(U_8689),U_8691),U_8690)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8689),U_8691),c_Big__Operators_Olattice_OSup__fin(U_8689,c_Orderings_Oord__class_Omax(U_8689),U_8690))
| U_8690 = c_Orderings_Obot__class_Obot(tc_fun(U_8689,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8689),U_8690))
| ~ class_Orderings_Olinorder(U_8689) ),
inference(definitional_conversion,[status(esa)],[f_2546_2]) ).
cnf(f_2546_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8689,c_Orderings_Oord__class_Omax(U_8689),hAPP(hAPP(c_Set_Oinsert(U_8689),U_8691),U_8690)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8689),U_8691),c_Big__Operators_Olattice_OSup__fin(U_8689,c_Orderings_Oord__class_Omax(U_8689),U_8690))
| U_8690 = c_Orderings_Obot__class_Obot(tc_fun(U_8689,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8689),U_8690))
| ~ class_Orderings_Olinorder(U_8689) ),
inference(clausify,[status(thm)],[f_2546_3]) ).
fof(f_2547_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem]) ).
fof(f_2547_2,plain,
! [U_8694,U_8693,U_8692] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8692),c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8694)),c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8693)) = c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8693)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8692,tc_HOL_Obool)),U_8694),U_8693))
| U_8694 = c_Orderings_Obot__class_Obot(tc_fun(U_8692,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8692),U_8693))
| ~ class_Orderings_Olinorder(U_8692) ),
inference(variable_rename,[status(thm)],[f_2547_1]) ).
fof(f_2547_3,plain,
! [U_8692,U_8693,U_8694] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8692),c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8694)),c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8693)) = c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8693)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8692,tc_HOL_Obool)),U_8694),U_8693))
| U_8694 = c_Orderings_Obot__class_Obot(tc_fun(U_8692,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8692),U_8693))
| ~ class_Orderings_Olinorder(U_8692) ),
inference(definitional_conversion,[status(esa)],[f_2547_2]) ).
cnf(f_2547_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8692),c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8694)),c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8693)) = c_Big__Operators_Olattice_OSup__fin(U_8692,c_Orderings_Oord__class_Omax(U_8692),U_8693)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8692,tc_HOL_Obool)),U_8694),U_8693))
| U_8694 = c_Orderings_Obot__class_Obot(tc_fun(U_8692,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8692),U_8693))
| ~ class_Orderings_Olinorder(U_8692) ),
inference(clausify,[status(thm)],[f_2547_3]) ).
fof(f_2548_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb]) ).
fof(f_2548_2,plain,
! [U_8697,U_8696,U_8695] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8695),U_8697),c_Big__Operators_Olattice_OSup__fin(U_8695,c_Orderings_Oord__class_Omax(U_8695),U_8696)) = U_8697
| ~ hBOOL(hAPP(hAPP(c_member(U_8695),U_8697),U_8696))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8695),U_8696))
| ~ class_Orderings_Olinorder(U_8695) ),
inference(variable_rename,[status(thm)],[f_2548_1]) ).
fof(f_2548_3,plain,
! [U_8697,U_8696,U_8695] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8695),U_8697),c_Big__Operators_Olattice_OSup__fin(U_8695,c_Orderings_Oord__class_Omax(U_8695),U_8696)) = U_8697
| ~ hBOOL(hAPP(hAPP(c_member(U_8695),U_8697),U_8696))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8695),U_8696))
| ~ class_Orderings_Olinorder(U_8695) ),
inference(definitional_conversion,[status(esa)],[f_2548_2]) ).
cnf(f_2548_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8695),U_8697),c_Big__Operators_Olattice_OSup__fin(U_8695,c_Orderings_Oord__class_Omax(U_8695),U_8696)) = U_8697
| ~ hBOOL(hAPP(hAPP(c_member(U_8695),U_8697),U_8696))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8695),U_8696))
| ~ class_Orderings_Olinorder(U_8695) ),
inference(clausify,[status(thm)],[f_2548_3]) ).
fof(f_2549_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem]) ).
fof(f_2549_2,plain,
! [U_8700,U_8699,U_8698] :
( c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8698,tc_HOL_Obool)),U_8699),U_8700)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8698),c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),U_8699)),c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),U_8700))
| U_8700 = c_Orderings_Obot__class_Obot(tc_fun(U_8698,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8698),U_8700))
| U_8699 = c_Orderings_Obot__class_Obot(tc_fun(U_8698,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8698),U_8699))
| ~ class_Orderings_Olinorder(U_8698) ),
inference(variable_rename,[status(thm)],[f_2549_1]) ).
fof(f_2549_3,plain,
! [U_8698,U_8699,U_8700] :
( c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8698,tc_HOL_Obool)),U_8699),U_8700)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8698),c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),U_8699)),c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),U_8700))
| U_8700 = c_Orderings_Obot__class_Obot(tc_fun(U_8698,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8698),U_8700))
| U_8699 = c_Orderings_Obot__class_Obot(tc_fun(U_8698,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8698),U_8699))
| ~ class_Orderings_Olinorder(U_8698) ),
inference(definitional_conversion,[status(esa)],[f_2549_2]) ).
cnf(f_2549_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8698,tc_HOL_Obool)),U_8699),U_8700)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8698),c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),U_8699)),c_Big__Operators_Olattice_OSup__fin(U_8698,c_Orderings_Oord__class_Omax(U_8698),U_8700))
| U_8700 = c_Orderings_Obot__class_Obot(tc_fun(U_8698,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8698),U_8700))
| U_8699 = c_Orderings_Obot__class_Obot(tc_fun(U_8698,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8698),U_8699))
| ~ class_Orderings_Olinorder(U_8698) ),
inference(clausify,[status(thm)],[f_2549_3]) ).
fof(f_2550_1,plain,
! [V_a_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H]) ).
fof(f_2550_2,plain,
! [U_8703,U_8702,U_8701] :
( c_Big__Operators_Olattice_OSup__fin(U_8701,c_Orderings_Oord__class_Omax(U_8701),hAPP(hAPP(c_Set_Oinsert(U_8701),U_8703),U_8702)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8701,U_8701,c_Orderings_Oord__class_Omax(U_8701)),U_8703),U_8702)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8701),U_8702))
| ~ class_Orderings_Olinorder(U_8701) ),
inference(variable_rename,[status(thm)],[f_2550_1]) ).
fof(f_2550_3,plain,
! [U_8703,U_8702,U_8701] :
( c_Big__Operators_Olattice_OSup__fin(U_8701,c_Orderings_Oord__class_Omax(U_8701),hAPP(hAPP(c_Set_Oinsert(U_8701),U_8703),U_8702)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8701,U_8701,c_Orderings_Oord__class_Omax(U_8701)),U_8703),U_8702)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8701),U_8702))
| ~ class_Orderings_Olinorder(U_8701) ),
inference(definitional_conversion,[status(esa)],[f_2550_2]) ).
cnf(f_2550_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8701,c_Orderings_Oord__class_Omax(U_8701),hAPP(hAPP(c_Set_Oinsert(U_8701),U_8703),U_8702)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8701,U_8701,c_Orderings_Oord__class_Omax(U_8701)),U_8703),U_8702)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8701),U_8702))
| ~ class_Orderings_Olinorder(U_8701) ),
inference(clausify,[status(thm)],[f_2550_3]) ).
fof(f_2551_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).
fof(f_2551_2,plain,
! [U_8706,U_8705,U_8704] :
( c_Big__Operators_Olattice_OSup__fin(U_8704,c_Orderings_Oord__class_Omax(U_8704),hAPP(hAPP(c_Set_Oinsert(U_8704),U_8706),U_8705)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8704),U_8706),c_Big__Operators_Olattice_OSup__fin(U_8704,c_Orderings_Oord__class_Omax(U_8704),U_8705))
| U_8705 = c_Orderings_Obot__class_Obot(tc_fun(U_8704,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8704),U_8706),U_8705))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8704),U_8705))
| ~ class_Orderings_Olinorder(U_8704) ),
inference(variable_rename,[status(thm)],[f_2551_1]) ).
fof(f_2551_3,plain,
! [U_8704,U_8705,U_8706] :
( c_Big__Operators_Olattice_OSup__fin(U_8704,c_Orderings_Oord__class_Omax(U_8704),hAPP(hAPP(c_Set_Oinsert(U_8704),U_8706),U_8705)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8704),U_8706),c_Big__Operators_Olattice_OSup__fin(U_8704,c_Orderings_Oord__class_Omax(U_8704),U_8705))
| U_8705 = c_Orderings_Obot__class_Obot(tc_fun(U_8704,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8704),U_8706),U_8705))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8704),U_8705))
| ~ class_Orderings_Olinorder(U_8704) ),
inference(definitional_conversion,[status(esa)],[f_2551_2]) ).
cnf(f_2551_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8704,c_Orderings_Oord__class_Omax(U_8704),hAPP(hAPP(c_Set_Oinsert(U_8704),U_8706),U_8705)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8704),U_8706),c_Big__Operators_Olattice_OSup__fin(U_8704,c_Orderings_Oord__class_Omax(U_8704),U_8705))
| U_8705 = c_Orderings_Obot__class_Obot(tc_fun(U_8704,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8704),U_8706),U_8705))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8704),U_8705))
| ~ class_Orderings_Olinorder(U_8704) ),
inference(clausify,[status(thm)],[f_2551_3]) ).
fof(f_2552_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( 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))))))
| 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)) )
& ( 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
| 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)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove]) ).
fof(f_2552_2,plain,
! [U_8709,U_8708,U_8707] :
( ( ( c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),U_8708)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8707),U_8709),c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),U_8708)) = U_8709
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8707),U_8708))
| ~ class_Orderings_Olinorder(U_8707) ),
inference(variable_rename,[status(thm)],[f_2552_1]) ).
fof(f_2552_3,plain,
( ! [U_8708,U_8707,U_8709] :
( c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),U_8708)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8707),U_8709),c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool))
| ~ sP774(U_8708,U_8707,U_8709) )
& ! [U_8708,U_8707,U_8709] :
( c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),U_8708)) = U_8709
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool))
| ~ sP774(U_8708,U_8707,U_8709) )
& ! [U_8708,U_8707,U_8709] :
( sP774(U_8708,U_8707,U_8709)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8707),U_8708))
| ~ class_Orderings_Olinorder(U_8707) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP774])],[f_2552_2]) ).
cnf(f_2552_4,plain,
( sP774(U_8708,U_8707,U_8709)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8707),U_8708))
| ~ class_Orderings_Olinorder(U_8707) ),
inference(clausify,[status(thm)],[f_2552_3]) ).
cnf(f_2552_5,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),U_8708)) = U_8709
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool))
| ~ sP774(U_8708,U_8707,U_8709) ),
inference(clausify,[status(thm)],[f_2552_3]) ).
cnf(f_2552_6,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),U_8708)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8707),U_8709),c_Big__Operators_Olattice_OSup__fin(U_8707,c_Orderings_Oord__class_Omax(U_8707),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8707,tc_HOL_Obool)),U_8708),hAPP(hAPP(c_Set_Oinsert(U_8707),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8707,tc_HOL_Obool))
| ~ sP774(U_8708,U_8707,U_8709) ),
inference(clausify,[status(thm)],[f_2552_3]) ).
fof(f_2553_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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))
| 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter]) ).
fof(f_2553_2,plain,
! [U_8712,U_8711,U_8710] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8710),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712))),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8710),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),U_8711)),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),U_8712))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712) = c_Orderings_Obot__class_Obot(tc_fun(U_8710,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8710),U_8712))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8710),U_8711))
| ~ class_Orderings_Olinorder(U_8710) ),
inference(variable_rename,[status(thm)],[f_2553_1]) ).
fof(f_2553_3,plain,
! [U_8712,U_8711,U_8710] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8710),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712))),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8710),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),U_8711)),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),U_8712))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712) = c_Orderings_Obot__class_Obot(tc_fun(U_8710,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8710),U_8712))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8710),U_8711))
| ~ class_Orderings_Olinorder(U_8710) ),
inference(definitional_conversion,[status(esa)],[f_2553_2]) ).
cnf(f_2553_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8710),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712))),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8710),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),U_8711)),c_Big__Operators_Olattice_OSup__fin(U_8710,c_Orderings_Oord__class_Omax(U_8710),U_8712))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8710,tc_HOL_Obool)),U_8711),U_8712) = c_Orderings_Obot__class_Obot(tc_fun(U_8710,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8710),U_8712))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8710),U_8711))
| ~ class_Orderings_Olinorder(U_8710) ),
inference(clausify,[status(thm)],[f_2553_3]) ).
fof(f_2554_1,plain,
! [V_B_2,V_A_2,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)) = 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))
| 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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint]) ).
fof(f_2554_2,plain,
! [U_8715,U_8714,U_8713] :
( c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8713,tc_HOL_Obool)),U_8714),U_8715)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8713),c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),U_8714)),c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),U_8715))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8713,tc_HOL_Obool)),U_8714),U_8715) != c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| U_8715 = c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8713),U_8715))
| U_8714 = c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8713),U_8714))
| ~ class_Orderings_Olinorder(U_8713) ),
inference(variable_rename,[status(thm)],[f_2554_1]) ).
fof(f_2554_3,plain,
! [U_8714,U_8713,U_8715] :
( c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8713,tc_HOL_Obool)),U_8714),U_8715)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8713),c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),U_8714)),c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),U_8715))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8713,tc_HOL_Obool)),U_8714),U_8715) != c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| U_8715 = c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8713),U_8715))
| U_8714 = c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8713),U_8714))
| ~ class_Orderings_Olinorder(U_8713) ),
inference(definitional_conversion,[status(esa)],[f_2554_2]) ).
cnf(f_2554_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8713,tc_HOL_Obool)),U_8714),U_8715)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8713),c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),U_8714)),c_Big__Operators_Olattice_OSup__fin(U_8713,c_Orderings_Oord__class_Omax(U_8713),U_8715))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8713,tc_HOL_Obool)),U_8714),U_8715) != c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| U_8715 = c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8713),U_8715))
| U_8714 = c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8713),U_8714))
| ~ class_Orderings_Olinorder(U_8713) ),
inference(clausify,[status(thm)],[f_2554_3]) ).
fof(f_2555_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).
fof(f_2555_2,plain,
! [U_8718,U_8717,U_8716] :
( c_Big__Operators_Olattice_OSup__fin(U_8716,c_Orderings_Oord__class_Omax(U_8716),hAPP(hAPP(c_Set_Oinsert(U_8716),U_8718),U_8717)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8716,U_8716,c_Orderings_Oord__class_Omax(U_8716)),U_8718),U_8717)
| hBOOL(hAPP(hAPP(c_member(U_8716),U_8718),U_8717))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8716),U_8717))
| ~ class_Orderings_Olinorder(U_8716) ),
inference(variable_rename,[status(thm)],[f_2555_1]) ).
fof(f_2555_3,plain,
! [U_8717,U_8718,U_8716] :
( c_Big__Operators_Olattice_OSup__fin(U_8716,c_Orderings_Oord__class_Omax(U_8716),hAPP(hAPP(c_Set_Oinsert(U_8716),U_8718),U_8717)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8716,U_8716,c_Orderings_Oord__class_Omax(U_8716)),U_8718),U_8717)
| hBOOL(hAPP(hAPP(c_member(U_8716),U_8718),U_8717))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8716),U_8717))
| ~ class_Orderings_Olinorder(U_8716) ),
inference(definitional_conversion,[status(esa)],[f_2555_2]) ).
cnf(f_2555_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8716,c_Orderings_Oord__class_Omax(U_8716),hAPP(hAPP(c_Set_Oinsert(U_8716),U_8718),U_8717)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8716,U_8716,c_Orderings_Oord__class_Omax(U_8716)),U_8718),U_8717)
| hBOOL(hAPP(hAPP(c_member(U_8716),U_8718),U_8717))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8716),U_8717))
| ~ class_Orderings_Olinorder(U_8716) ),
inference(clausify,[status(thm)],[f_2555_3]) ).
fof(f_2556_1,plain,
! [V_A_2,T_b] :
( 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))
| ? [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))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed]) ).
fof(f_2556_2,plain,
! [U_8722,U_8721] :
( hBOOL(hAPP(hAPP(c_member(U_8721),c_Big__Operators_Olattice_OSup__fin(U_8721,c_Orderings_Oord__class_Omax(U_8721),U_8722)),U_8722))
| ? [U_8720,U_8719] : ~ hBOOL(hAPP(hAPP(c_member(U_8721),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8721),U_8720),U_8719)),hAPP(hAPP(c_Set_Oinsert(U_8721),U_8720),hAPP(hAPP(c_Set_Oinsert(U_8721),U_8719),c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))))))
| U_8722 = c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8721),U_8722))
| ~ class_Orderings_Olinorder(U_8721) ),
inference(variable_rename,[status(thm)],[f_2556_1]) ).
fof(f_2556_3,plain,
! [U_8722,U_8721] :
( hBOOL(hAPP(hAPP(c_member(U_8721),c_Big__Operators_Olattice_OSup__fin(U_8721,c_Orderings_Oord__class_Omax(U_8721),U_8722)),U_8722))
| ? [U_8719] : ~ hBOOL(hAPP(hAPP(c_member(U_8721),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8721),sK238(U_8722,U_8721)),U_8719)),hAPP(hAPP(c_Set_Oinsert(U_8721),sK238(U_8722,U_8721)),hAPP(hAPP(c_Set_Oinsert(U_8721),U_8719),c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))))))
| U_8722 = c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8721),U_8722))
| ~ class_Orderings_Olinorder(U_8721) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_8720,sK238(U_8722,U_8721))],[f_2556_2]) ).
fof(f_2556_4,plain,
! [U_8722,U_8721] :
( hBOOL(hAPP(hAPP(c_member(U_8721),c_Big__Operators_Olattice_OSup__fin(U_8721,c_Orderings_Oord__class_Omax(U_8721),U_8722)),U_8722))
| ~ hBOOL(hAPP(hAPP(c_member(U_8721),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8721),sK238(U_8722,U_8721)),sK239(U_8722,U_8721))),hAPP(hAPP(c_Set_Oinsert(U_8721),sK238(U_8722,U_8721)),hAPP(hAPP(c_Set_Oinsert(U_8721),sK239(U_8722,U_8721)),c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))))))
| U_8722 = c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8721),U_8722))
| ~ class_Orderings_Olinorder(U_8721) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_8719,sK239(U_8722,U_8721))],[f_2556_3]) ).
fof(f_2556_5,plain,
! [U_8721,U_8722] :
( hBOOL(hAPP(hAPP(c_member(U_8721),c_Big__Operators_Olattice_OSup__fin(U_8721,c_Orderings_Oord__class_Omax(U_8721),U_8722)),U_8722))
| ~ hBOOL(hAPP(hAPP(c_member(U_8721),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8721),sK238(U_8722,U_8721)),sK239(U_8722,U_8721))),hAPP(hAPP(c_Set_Oinsert(U_8721),sK238(U_8722,U_8721)),hAPP(hAPP(c_Set_Oinsert(U_8721),sK239(U_8722,U_8721)),c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))))))
| U_8722 = c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8721),U_8722))
| ~ class_Orderings_Olinorder(U_8721) ),
inference(definitional_conversion,[status(esa)],[f_2556_4]) ).
cnf(f_2556_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8721),c_Big__Operators_Olattice_OSup__fin(U_8721,c_Orderings_Oord__class_Omax(U_8721),U_8722)),U_8722))
| ~ hBOOL(hAPP(hAPP(c_member(U_8721),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8721),sK238(U_8722,U_8721)),sK239(U_8722,U_8721))),hAPP(hAPP(c_Set_Oinsert(U_8721),sK238(U_8722,U_8721)),hAPP(hAPP(c_Set_Oinsert(U_8721),sK239(U_8722,U_8721)),c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))))))
| U_8722 = c_Orderings_Obot__class_Obot(tc_fun(U_8721,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8721),U_8722))
| ~ class_Orderings_Olinorder(U_8721) ),
inference(clausify,[status(thm)],[f_2556_5]) ).
fof(f_2557_1,plain,
! [V_N_2,V_h_2,T_b] :
( 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))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [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))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute]) ).
fof(f_2557_2,plain,
! [U_8727,U_8726,U_8725] :
( hAPP(U_8726,c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),U_8727)) = c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),hAPP(c_Set_Oimage(U_8725,U_8725,U_8726),U_8727))
| U_8727 = c_Orderings_Obot__class_Obot(tc_fun(U_8725,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8725),U_8727))
| ? [U_8724,U_8723] : hAPP(U_8726,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),U_8724),U_8723)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),hAPP(U_8726,U_8724)),hAPP(U_8726,U_8723))
| ~ class_Orderings_Olinorder(U_8725) ),
inference(variable_rename,[status(thm)],[f_2557_1]) ).
fof(f_2557_3,plain,
! [U_8727,U_8726,U_8725] :
( hAPP(U_8726,c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),U_8727)) = c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),hAPP(c_Set_Oimage(U_8725,U_8725,U_8726),U_8727))
| U_8727 = c_Orderings_Obot__class_Obot(tc_fun(U_8725,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8725),U_8727))
| ? [U_8723] : hAPP(U_8726,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),sK240(U_8727,U_8726,U_8725)),U_8723)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),hAPP(U_8726,sK240(U_8727,U_8726,U_8725))),hAPP(U_8726,U_8723))
| ~ class_Orderings_Olinorder(U_8725) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_8724,sK240(U_8727,U_8726,U_8725))],[f_2557_2]) ).
fof(f_2557_4,plain,
! [U_8727,U_8726,U_8725] :
( hAPP(U_8726,c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),U_8727)) = c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),hAPP(c_Set_Oimage(U_8725,U_8725,U_8726),U_8727))
| U_8727 = c_Orderings_Obot__class_Obot(tc_fun(U_8725,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8725),U_8727))
| hAPP(U_8726,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),sK240(U_8727,U_8726,U_8725)),sK241(U_8727,U_8726,U_8725))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),hAPP(U_8726,sK240(U_8727,U_8726,U_8725))),hAPP(U_8726,sK241(U_8727,U_8726,U_8725)))
| ~ class_Orderings_Olinorder(U_8725) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_8723,sK241(U_8727,U_8726,U_8725))],[f_2557_3]) ).
fof(f_2557_5,plain,
! [U_8725,U_8726,U_8727] :
( hAPP(U_8726,c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),U_8727)) = c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),hAPP(c_Set_Oimage(U_8725,U_8725,U_8726),U_8727))
| U_8727 = c_Orderings_Obot__class_Obot(tc_fun(U_8725,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8725),U_8727))
| hAPP(U_8726,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),sK240(U_8727,U_8726,U_8725)),sK241(U_8727,U_8726,U_8725))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),hAPP(U_8726,sK240(U_8727,U_8726,U_8725))),hAPP(U_8726,sK241(U_8727,U_8726,U_8725)))
| ~ class_Orderings_Olinorder(U_8725) ),
inference(definitional_conversion,[status(esa)],[f_2557_4]) ).
cnf(f_2557_6,plain,
( hAPP(U_8726,c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),U_8727)) = c_Big__Operators_Olattice_OSup__fin(U_8725,c_Orderings_Oord__class_Omax(U_8725),hAPP(c_Set_Oimage(U_8725,U_8725,U_8726),U_8727))
| U_8727 = c_Orderings_Obot__class_Obot(tc_fun(U_8725,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8725),U_8727))
| hAPP(U_8726,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),sK240(U_8727,U_8726,U_8725)),sK241(U_8727,U_8726,U_8725))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8725),hAPP(U_8726,sK240(U_8727,U_8726,U_8725))),hAPP(U_8726,sK241(U_8727,U_8726,U_8725)))
| ~ class_Orderings_Olinorder(U_8725) ),
inference(clausify,[status(thm)],[f_2557_5]) ).
fof(f_2558_1,plain,
! [V_N_2,V_h_2,T_b] :
( 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))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [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))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute]) ).
fof(f_2558_2,plain,
! [U_8732,U_8731,U_8730] :
( hAPP(U_8731,c_Big__Operators_Olinorder__class_OMax(U_8730,U_8732)) = c_Big__Operators_Olinorder__class_OMax(U_8730,hAPP(c_Set_Oimage(U_8730,U_8730,U_8731),U_8732))
| U_8732 = c_Orderings_Obot__class_Obot(tc_fun(U_8730,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8730),U_8732))
| ? [U_8729,U_8728] : hAPP(U_8731,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),U_8729),U_8728)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),hAPP(U_8731,U_8729)),hAPP(U_8731,U_8728))
| ~ class_Orderings_Olinorder(U_8730) ),
inference(variable_rename,[status(thm)],[f_2558_1]) ).
fof(f_2558_3,plain,
! [U_8732,U_8731,U_8730] :
( hAPP(U_8731,c_Big__Operators_Olinorder__class_OMax(U_8730,U_8732)) = c_Big__Operators_Olinorder__class_OMax(U_8730,hAPP(c_Set_Oimage(U_8730,U_8730,U_8731),U_8732))
| U_8732 = c_Orderings_Obot__class_Obot(tc_fun(U_8730,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8730),U_8732))
| ? [U_8728] : hAPP(U_8731,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),sK242(U_8732,U_8731,U_8730)),U_8728)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),hAPP(U_8731,sK242(U_8732,U_8731,U_8730))),hAPP(U_8731,U_8728))
| ~ class_Orderings_Olinorder(U_8730) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_8729,sK242(U_8732,U_8731,U_8730))],[f_2558_2]) ).
fof(f_2558_4,plain,
! [U_8732,U_8731,U_8730] :
( hAPP(U_8731,c_Big__Operators_Olinorder__class_OMax(U_8730,U_8732)) = c_Big__Operators_Olinorder__class_OMax(U_8730,hAPP(c_Set_Oimage(U_8730,U_8730,U_8731),U_8732))
| U_8732 = c_Orderings_Obot__class_Obot(tc_fun(U_8730,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8730),U_8732))
| hAPP(U_8731,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),sK242(U_8732,U_8731,U_8730)),sK243(U_8732,U_8731,U_8730))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),hAPP(U_8731,sK242(U_8732,U_8731,U_8730))),hAPP(U_8731,sK243(U_8732,U_8731,U_8730)))
| ~ class_Orderings_Olinorder(U_8730) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_8728,sK243(U_8732,U_8731,U_8730))],[f_2558_3]) ).
fof(f_2558_5,plain,
! [U_8731,U_8730,U_8732] :
( hAPP(U_8731,c_Big__Operators_Olinorder__class_OMax(U_8730,U_8732)) = c_Big__Operators_Olinorder__class_OMax(U_8730,hAPP(c_Set_Oimage(U_8730,U_8730,U_8731),U_8732))
| U_8732 = c_Orderings_Obot__class_Obot(tc_fun(U_8730,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8730),U_8732))
| hAPP(U_8731,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),sK242(U_8732,U_8731,U_8730)),sK243(U_8732,U_8731,U_8730))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),hAPP(U_8731,sK242(U_8732,U_8731,U_8730))),hAPP(U_8731,sK243(U_8732,U_8731,U_8730)))
| ~ class_Orderings_Olinorder(U_8730) ),
inference(definitional_conversion,[status(esa)],[f_2558_4]) ).
cnf(f_2558_6,plain,
( hAPP(U_8731,c_Big__Operators_Olinorder__class_OMax(U_8730,U_8732)) = c_Big__Operators_Olinorder__class_OMax(U_8730,hAPP(c_Set_Oimage(U_8730,U_8730,U_8731),U_8732))
| U_8732 = c_Orderings_Obot__class_Obot(tc_fun(U_8730,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8730),U_8732))
| hAPP(U_8731,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),sK242(U_8732,U_8731,U_8730)),sK243(U_8732,U_8731,U_8730))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8730),hAPP(U_8731,sK242(U_8732,U_8731,U_8730))),hAPP(U_8731,sK243(U_8732,U_8731,U_8730)))
| ~ class_Orderings_Olinorder(U_8730) ),
inference(clausify,[status(thm)],[f_2558_5]) ).
fof(f_2559_1,plain,
! [V_ca_2,V_b_2,V_A_2,T_b] :
( 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_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup]) ).
fof(f_2559_2,plain,
! [U_8737,U_8736,U_8735,U_8734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8734),hAPP(hAPP(c_Finite__Set_Ofold(U_8734,U_8734,c_Orderings_Oord__class_Omax(U_8734)),U_8737),U_8735)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8734),U_8736),U_8737)))
| ? [U_8733] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8734),U_8733),U_8736))
& hBOOL(hAPP(hAPP(c_member(U_8734),U_8733),U_8735)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8734),U_8735))
| ~ class_Orderings_Olinorder(U_8734) ),
inference(variable_rename,[status(thm)],[f_2559_1]) ).
fof(f_2559_3,plain,
! [U_8737,U_8736,U_8735,U_8734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8734),hAPP(hAPP(c_Finite__Set_Ofold(U_8734,U_8734,c_Orderings_Oord__class_Omax(U_8734)),U_8737),U_8735)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8734),U_8736),U_8737)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8734),sK244(U_8737,U_8736,U_8735,U_8734)),U_8736))
& hBOOL(hAPP(hAPP(c_member(U_8734),sK244(U_8737,U_8736,U_8735,U_8734)),U_8735)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8734),U_8735))
| ~ class_Orderings_Olinorder(U_8734) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_8733,sK244(U_8737,U_8736,U_8735,U_8734))],[f_2559_2]) ).
fof(f_2559_4,plain,
( ! [U_8734,U_8735,U_8736,U_8737] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8734),sK244(U_8737,U_8736,U_8735,U_8734)),U_8736))
| ~ sP775(U_8734,U_8735,U_8736,U_8737) )
& ! [U_8734,U_8735,U_8736,U_8737] :
( hBOOL(hAPP(hAPP(c_member(U_8734),sK244(U_8737,U_8736,U_8735,U_8734)),U_8735))
| ~ sP775(U_8734,U_8735,U_8736,U_8737) )
& ! [U_8734,U_8735,U_8736,U_8737] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8734),hAPP(hAPP(c_Finite__Set_Ofold(U_8734,U_8734,c_Orderings_Oord__class_Omax(U_8734)),U_8737),U_8735)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8734),U_8736),U_8737)))
| sP775(U_8734,U_8735,U_8736,U_8737)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8734),U_8735))
| ~ class_Orderings_Olinorder(U_8734) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP775])],[f_2559_3]) ).
cnf(f_2559_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8734),hAPP(hAPP(c_Finite__Set_Ofold(U_8734,U_8734,c_Orderings_Oord__class_Omax(U_8734)),U_8737),U_8735)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8734),U_8736),U_8737)))
| sP775(U_8734,U_8735,U_8736,U_8737)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8734),U_8735))
| ~ class_Orderings_Olinorder(U_8734) ),
inference(clausify,[status(thm)],[f_2559_4]) ).
cnf(f_2559_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8734),sK244(U_8737,U_8736,U_8735,U_8734)),U_8735))
| ~ sP775(U_8734,U_8735,U_8736,U_8737) ),
inference(clausify,[status(thm)],[f_2559_4]) ).
cnf(f_2559_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8734),sK244(U_8737,U_8736,U_8735,U_8734)),U_8736))
| ~ sP775(U_8734,U_8735,U_8736,U_8737) ),
inference(clausify,[status(thm)],[f_2559_4]) ).
fof(f_2560_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_pair__box_Osize_I1_J]) ).
fof(f_2560_2,plain,
! [U_8743,U_8742,U_8741,U_8740,U_8739,U_8738] : c_Nitpick_Opair__box_Opair__box__size(U_8738,U_8739,U_8740,U_8741,c_Nitpick_Opair__box_OPairBox(U_8738,U_8739,U_8742,U_8743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_8740,U_8742)),hAPP(U_8741,U_8743))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2560_1]) ).
fof(f_2560_3,plain,
! [U_8739,U_8738,U_8740,U_8741,U_8742,U_8743] : c_Nitpick_Opair__box_Opair__box__size(U_8738,U_8739,U_8740,U_8741,c_Nitpick_Opair__box_OPairBox(U_8738,U_8739,U_8742,U_8743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_8740,U_8742)),hAPP(U_8741,U_8743))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2560_2]) ).
cnf(f_2560_4,plain,
c_Nitpick_Opair__box_Opair__box__size(U_8738,U_8739,U_8740,U_8741,c_Nitpick_Opair__box_OPairBox(U_8738,U_8739,U_8742,U_8743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_8740,U_8742)),hAPP(U_8741,U_8743))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2560_3]) ).
fof(f_2561_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_arith__series__int]) ).
fof(f_2561_2,plain,
! [U_8746,U_8745,U_8744] : 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),U_8744)),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))),U_8745))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8746))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8744),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8744),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),U_8746),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8745)))),
inference(variable_rename,[status(thm)],[f_2561_1]) ).
fof(f_2561_3,plain,
! [U_8744,U_8745,U_8746] : 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),U_8744)),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))),U_8745))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8746))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8744),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8744),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),U_8746),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8745)))),
inference(definitional_conversion,[status(esa)],[f_2561_2]) ).
cnf(f_2561_4,plain,
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),U_8744)),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))),U_8745))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8746))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8744),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8744),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),U_8746),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8745)))),
inference(clausify,[status(thm)],[f_2561_3]) ).
fof(f_2562_1,plain,
! [V_w] :
( ( ( 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))))
| 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)))) )
& ( 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)))
| ~ 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)))) ) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).
fof(f_2562_2,plain,
! [U_8747] :
( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)),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),U_8747))))
| 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),U_8747)))) )
& ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)) = 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),U_8747)))
| ~ 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),U_8747)))) ) )
| ~ 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),U_8747))) ),
inference(variable_rename,[status(thm)],[f_2562_1]) ).
fof(f_2562_3,plain,
( ! [U_8747] :
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)),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),U_8747))))
| 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),U_8747))))
| ~ sP776(U_8747) )
& ! [U_8747] :
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)) = 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),U_8747)))
| ~ 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),U_8747))))
| ~ sP776(U_8747) )
& ! [U_8747] :
( sP776(U_8747)
| ~ 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),U_8747))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP776])],[f_2562_2]) ).
cnf(f_2562_4,plain,
( sP776(U_8747)
| ~ 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),U_8747))) ),
inference(clausify,[status(thm)],[f_2562_3]) ).
cnf(f_2562_5,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)) = 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),U_8747)))
| ~ 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),U_8747))))
| ~ sP776(U_8747) ),
inference(clausify,[status(thm)],[f_2562_3]) ).
cnf(f_2562_6,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8747)),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),U_8747))))
| 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),U_8747))))
| ~ sP776(U_8747) ),
inference(clausify,[status(thm)],[f_2562_3]) ).
fof(f_2563_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_nat_Osize_I2_J]) ).
fof(f_2563_2,plain,
! [U_8748] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_8748)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_8748)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2563_1]) ).
fof(f_2563_3,plain,
! [U_8748] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_8748)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_8748)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2563_2]) ).
cnf(f_2563_4,plain,
c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_8748)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_8748)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2563_3]) ).
fof(f_2564_1,plain,
! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
| ~ 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_ca_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF2__E]) ).
fof(f_2564_2,plain,
! [U_8756,U_8755,U_8754,U_8753,U_8752,U_8751,U_8750,U_8749] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8749),U_8756),U_8752))
| hBOOL(hAPP(hAPP(hAPP(U_8753,U_8756),U_8754),U_8755))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8749,tc_fun(U_8750,tc_fun(U_8751,tc_HOL_Obool))),U_8752),U_8753),U_8754),U_8755)) ),
inference(variable_rename,[status(thm)],[f_2564_1]) ).
fof(f_2564_3,plain,
! [U_8749,U_8750,U_8751,U_8752,U_8753,U_8754,U_8755,U_8756] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8749),U_8756),U_8752))
| hBOOL(hAPP(hAPP(hAPP(U_8753,U_8756),U_8754),U_8755))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8749,tc_fun(U_8750,tc_fun(U_8751,tc_HOL_Obool))),U_8752),U_8753),U_8754),U_8755)) ),
inference(definitional_conversion,[status(esa)],[f_2564_2]) ).
cnf(f_2564_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8749),U_8756),U_8752))
| hBOOL(hAPP(hAPP(hAPP(U_8753,U_8756),U_8754),U_8755))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8749,tc_fun(U_8750,tc_fun(U_8751,tc_HOL_Obool))),U_8752),U_8753),U_8754),U_8755)) ),
inference(clausify,[status(thm)],[f_2564_3]) ).
fof(f_2565_1,plain,
! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ 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_ca_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF2__D]) ).
fof(f_2565_2,plain,
! [U_8764,U_8763,U_8762,U_8761,U_8760,U_8759,U_8758,U_8757] :
( hBOOL(hAPP(hAPP(hAPP(U_8761,U_8764),U_8762),U_8763))
| ~ hBOOL(hAPP(hAPP(c_member(U_8757),U_8764),U_8760))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8757,tc_fun(U_8758,tc_fun(U_8759,tc_HOL_Obool))),U_8760),U_8761),U_8762),U_8763)) ),
inference(variable_rename,[status(thm)],[f_2565_1]) ).
fof(f_2565_3,plain,
! [U_8757,U_8758,U_8759,U_8760,U_8761,U_8762,U_8763,U_8764] :
( hBOOL(hAPP(hAPP(hAPP(U_8761,U_8764),U_8762),U_8763))
| ~ hBOOL(hAPP(hAPP(c_member(U_8757),U_8764),U_8760))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8757,tc_fun(U_8758,tc_fun(U_8759,tc_HOL_Obool))),U_8760),U_8761),U_8762),U_8763)) ),
inference(definitional_conversion,[status(esa)],[f_2565_2]) ).
cnf(f_2565_4,plain,
( hBOOL(hAPP(hAPP(hAPP(U_8761,U_8764),U_8762),U_8763))
| ~ hBOOL(hAPP(hAPP(c_member(U_8757),U_8764),U_8760))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8757,tc_fun(U_8758,tc_fun(U_8759,tc_HOL_Obool))),U_8760),U_8761),U_8762),U_8763)) ),
inference(clausify,[status(thm)],[f_2565_3]) ).
fof(f_2566_1,plain,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_INF1__E]) ).
fof(f_2566_2,plain,
! [U_8770,U_8769,U_8768,U_8767,U_8766,U_8765] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8765),U_8770),U_8767))
| hBOOL(hAPP(hAPP(U_8768,U_8770),U_8769))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8765,tc_fun(U_8766,tc_HOL_Obool)),U_8767),U_8768),U_8769)) ),
inference(variable_rename,[status(thm)],[f_2566_1]) ).
fof(f_2566_3,plain,
! [U_8766,U_8765,U_8767,U_8768,U_8769,U_8770] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8765),U_8770),U_8767))
| hBOOL(hAPP(hAPP(U_8768,U_8770),U_8769))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8765,tc_fun(U_8766,tc_HOL_Obool)),U_8767),U_8768),U_8769)) ),
inference(definitional_conversion,[status(esa)],[f_2566_2]) ).
cnf(f_2566_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8765),U_8770),U_8767))
| hBOOL(hAPP(hAPP(U_8768,U_8770),U_8769))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8765,tc_fun(U_8766,tc_HOL_Obool)),U_8767),U_8768),U_8769)) ),
inference(clausify,[status(thm)],[f_2566_3]) ).
fof(f_2567_1,plain,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_INF1__D]) ).
fof(f_2567_2,plain,
! [U_8776,U_8775,U_8774,U_8773,U_8772,U_8771] :
( hBOOL(hAPP(hAPP(U_8774,U_8776),U_8775))
| ~ hBOOL(hAPP(hAPP(c_member(U_8771),U_8776),U_8773))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8771,tc_fun(U_8772,tc_HOL_Obool)),U_8773),U_8774),U_8775)) ),
inference(variable_rename,[status(thm)],[f_2567_1]) ).
fof(f_2567_3,plain,
! [U_8771,U_8772,U_8773,U_8774,U_8775,U_8776] :
( hBOOL(hAPP(hAPP(U_8774,U_8776),U_8775))
| ~ hBOOL(hAPP(hAPP(c_member(U_8771),U_8776),U_8773))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8771,tc_fun(U_8772,tc_HOL_Obool)),U_8773),U_8774),U_8775)) ),
inference(definitional_conversion,[status(esa)],[f_2567_2]) ).
cnf(f_2567_4,plain,
( hBOOL(hAPP(hAPP(U_8774,U_8776),U_8775))
| ~ hBOOL(hAPP(hAPP(c_member(U_8771),U_8776),U_8773))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8771,tc_fun(U_8772,tc_HOL_Obool)),U_8773),U_8774),U_8775)) ),
inference(clausify,[status(thm)],[f_2567_3]) ).
fof(f_2568_1,plain,
! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_INT__D]) ).
fof(f_2568_2,plain,
! [U_8782,U_8781,U_8780,U_8779,U_8778,U_8777] :
( hBOOL(hAPP(hAPP(c_member(U_8777),U_8778),hAPP(U_8781,U_8782)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8779),U_8782),U_8780))
| ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8778),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8779,tc_fun(U_8777,tc_HOL_Obool)),U_8780),U_8781))) ),
inference(variable_rename,[status(thm)],[f_2568_1]) ).
fof(f_2568_3,plain,
! [U_8777,U_8778,U_8779,U_8780,U_8781,U_8782] :
( hBOOL(hAPP(hAPP(c_member(U_8777),U_8778),hAPP(U_8781,U_8782)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8779),U_8782),U_8780))
| ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8778),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8779,tc_fun(U_8777,tc_HOL_Obool)),U_8780),U_8781))) ),
inference(definitional_conversion,[status(esa)],[f_2568_2]) ).
cnf(f_2568_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8777),U_8778),hAPP(U_8781,U_8782)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8779),U_8782),U_8780))
| ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8778),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8779,tc_fun(U_8777,tc_HOL_Obool)),U_8780),U_8781))) ),
inference(clausify,[status(thm)],[f_2568_3]) ).
fof(f_2569_1,plain,
! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_INT__E]) ).
fof(f_2569_2,plain,
! [U_8788,U_8787,U_8786,U_8785,U_8784,U_8783] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8785),U_8788),U_8786))
| hBOOL(hAPP(hAPP(c_member(U_8783),U_8784),hAPP(U_8787,U_8788)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8783),U_8784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8785,tc_fun(U_8783,tc_HOL_Obool)),U_8786),U_8787))) ),
inference(variable_rename,[status(thm)],[f_2569_1]) ).
fof(f_2569_3,plain,
! [U_8783,U_8784,U_8785,U_8786,U_8787,U_8788] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8785),U_8788),U_8786))
| hBOOL(hAPP(hAPP(c_member(U_8783),U_8784),hAPP(U_8787,U_8788)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8783),U_8784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8785,tc_fun(U_8783,tc_HOL_Obool)),U_8786),U_8787))) ),
inference(definitional_conversion,[status(esa)],[f_2569_2]) ).
cnf(f_2569_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8785),U_8788),U_8786))
| hBOOL(hAPP(hAPP(c_member(U_8783),U_8784),hAPP(U_8787,U_8788)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8783),U_8784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8785,tc_fun(U_8783,tc_HOL_Obool)),U_8786),U_8787))) ),
inference(clausify,[status(thm)],[f_2569_3]) ).
fof(f_2570_1,plain,
! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( 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_ca_2))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_SUP2__I]) ).
fof(f_2570_2,plain,
! [U_8796,U_8795,U_8794,U_8793,U_8792,U_8791,U_8790,U_8789] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8789,tc_fun(U_8795,tc_fun(U_8796,tc_HOL_Obool))),U_8791),U_8792),U_8793),U_8794))
| ~ hBOOL(hAPP(hAPP(hAPP(U_8792,U_8790),U_8793),U_8794))
| ~ hBOOL(hAPP(hAPP(c_member(U_8789),U_8790),U_8791)) ),
inference(variable_rename,[status(thm)],[f_2570_1]) ).
fof(f_2570_3,plain,
! [U_8789,U_8790,U_8791,U_8792,U_8793,U_8794,U_8795,U_8796] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8789,tc_fun(U_8795,tc_fun(U_8796,tc_HOL_Obool))),U_8791),U_8792),U_8793),U_8794))
| ~ hBOOL(hAPP(hAPP(hAPP(U_8792,U_8790),U_8793),U_8794))
| ~ hBOOL(hAPP(hAPP(c_member(U_8789),U_8790),U_8791)) ),
inference(definitional_conversion,[status(esa)],[f_2570_2]) ).
cnf(f_2570_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8789,tc_fun(U_8795,tc_fun(U_8796,tc_HOL_Obool))),U_8791),U_8792),U_8793),U_8794))
| ~ hBOOL(hAPP(hAPP(hAPP(U_8792,U_8790),U_8793),U_8794))
| ~ hBOOL(hAPP(hAPP(c_member(U_8789),U_8790),U_8791)) ),
inference(clausify,[status(thm)],[f_2570_3]) ).
fof(f_2571_1,plain,
! [V_A_2,T_c,V_I_2,T_b] :
( 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)))
| ! [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__INT]) ).
fof(f_2571_2,plain,
! [U_8801,U_8800,U_8799,U_8798] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8798,tc_fun(U_8800,tc_HOL_Obool)),U_8799),U_8801)))
| ! [U_8797] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),hAPP(U_8801,U_8797)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8798),U_8797),U_8799)) ) ),
inference(variable_rename,[status(thm)],[f_2571_1]) ).
fof(f_2571_3,plain,
! [U_8797,U_8798,U_8799,U_8800,U_8801] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8798,tc_fun(U_8800,tc_HOL_Obool)),U_8799),U_8801)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),hAPP(U_8801,U_8797)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8798),U_8797),U_8799)) ),
inference(definitional_conversion,[status(esa)],[f_2571_2]) ).
cnf(f_2571_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8798,tc_fun(U_8800,tc_HOL_Obool)),U_8799),U_8801)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),hAPP(U_8801,U_8797)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8798),U_8797),U_8799)) ),
inference(clausify,[status(thm)],[f_2571_3]) ).
fof(f_2572_1,plain,
! [T_b,V_a_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
| ~ hBOOL(hAPP(V_Pa_2,V_a_2)) ),
inference(fof_nnf,[status(thm)],[fact_CollectI]) ).
fof(f_2572_2,plain,
! [U_8804,U_8803,U_8802] :
( hBOOL(hAPP(hAPP(c_member(U_8804),U_8803),hAPP(c_Set_OCollect(U_8804),U_8802)))
| ~ hBOOL(hAPP(U_8802,U_8803)) ),
inference(variable_rename,[status(thm)],[f_2572_1]) ).
fof(f_2572_3,plain,
! [U_8803,U_8802,U_8804] :
( hBOOL(hAPP(hAPP(c_member(U_8804),U_8803),hAPP(c_Set_OCollect(U_8804),U_8802)))
| ~ hBOOL(hAPP(U_8802,U_8803)) ),
inference(definitional_conversion,[status(esa)],[f_2572_2]) ).
cnf(f_2572_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8804),U_8803),hAPP(c_Set_OCollect(U_8804),U_8802)))
| ~ hBOOL(hAPP(U_8802,U_8803)) ),
inference(clausify,[status(thm)],[f_2572_3]) ).
fof(f_2573_1,plain,
! [V_Qa_2,V_Pa_2,T_b] :
( 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))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).
fof(f_2573_2,plain,
! [U_8807,U_8806,U_8805] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),hAPP(hAPP(c_COMBS(U_8805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8805),c_fconj),U_8806)),U_8807))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),U_8807)))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),U_8806))) ) ),
inference(variable_rename,[status(thm)],[f_2573_1]) ).
fof(f_2573_3,plain,
( ! [U_8805,U_8806,U_8807] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),U_8807)))
| ~ sP777(U_8805,U_8806,U_8807) )
& ! [U_8805,U_8806,U_8807] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),U_8806)))
| ~ sP777(U_8805,U_8806,U_8807) )
& ! [U_8805,U_8806,U_8807] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),hAPP(hAPP(c_COMBS(U_8805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8805),c_fconj),U_8806)),U_8807))))
| sP777(U_8805,U_8806,U_8807) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP777])],[f_2573_2]) ).
cnf(f_2573_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),hAPP(hAPP(c_COMBS(U_8805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8805),c_fconj),U_8806)),U_8807))))
| sP777(U_8805,U_8806,U_8807) ),
inference(clausify,[status(thm)],[f_2573_3]) ).
cnf(f_2573_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),U_8806)))
| ~ sP777(U_8805,U_8806,U_8807) ),
inference(clausify,[status(thm)],[f_2573_3]) ).
cnf(f_2573_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8805),hAPP(c_Set_OCollect(U_8805),U_8807)))
| ~ sP777(U_8805,U_8806,U_8807) ),
inference(clausify,[status(thm)],[f_2573_3]) ).
fof(f_2574_1,plain,
! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__I]) ).
fof(f_2574_2,plain,
! [U_8813,U_8812,U_8811,U_8810,U_8809,U_8808] :
( hBOOL(hAPP(hAPP(c_member(U_8811),U_8812),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8808,tc_fun(U_8811,tc_HOL_Obool)),U_8810),U_8813)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8811),U_8812),hAPP(U_8813,U_8809)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8808),U_8809),U_8810)) ),
inference(variable_rename,[status(thm)],[f_2574_1]) ).
fof(f_2574_3,plain,
! [U_8810,U_8808,U_8809,U_8811,U_8812,U_8813] :
( hBOOL(hAPP(hAPP(c_member(U_8811),U_8812),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8808,tc_fun(U_8811,tc_HOL_Obool)),U_8810),U_8813)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8811),U_8812),hAPP(U_8813,U_8809)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8808),U_8809),U_8810)) ),
inference(definitional_conversion,[status(esa)],[f_2574_2]) ).
cnf(f_2574_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8811),U_8812),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8808,tc_fun(U_8811,tc_HOL_Obool)),U_8810),U_8813)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8811),U_8812),hAPP(U_8813,U_8809)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8808),U_8809),U_8810)) ),
inference(clausify,[status(thm)],[f_2574_3]) ).
fof(f_2575_1,plain,
! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_SUP1__I]) ).
fof(f_2575_2,plain,
! [U_8819,U_8818,U_8817,U_8816,U_8815,U_8814] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8814,tc_fun(U_8819,tc_HOL_Obool)),U_8816),U_8817),U_8818))
| ~ hBOOL(hAPP(hAPP(U_8817,U_8815),U_8818))
| ~ hBOOL(hAPP(hAPP(c_member(U_8814),U_8815),U_8816)) ),
inference(variable_rename,[status(thm)],[f_2575_1]) ).
fof(f_2575_3,plain,
! [U_8815,U_8814,U_8816,U_8817,U_8818,U_8819] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8814,tc_fun(U_8819,tc_HOL_Obool)),U_8816),U_8817),U_8818))
| ~ hBOOL(hAPP(hAPP(U_8817,U_8815),U_8818))
| ~ hBOOL(hAPP(hAPP(c_member(U_8814),U_8815),U_8816)) ),
inference(definitional_conversion,[status(esa)],[f_2575_2]) ).
cnf(f_2575_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8814,tc_fun(U_8819,tc_HOL_Obool)),U_8816),U_8817),U_8818))
| ~ hBOOL(hAPP(hAPP(U_8817,U_8815),U_8818))
| ~ hBOOL(hAPP(hAPP(c_member(U_8814),U_8815),U_8816)) ),
inference(clausify,[status(thm)],[f_2575_3]) ).
fof(f_2576_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__less__nat]) ).
fof(f_2576_2,plain,
! [U_8820] : 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)),U_8820)))),
inference(variable_rename,[status(thm)],[f_2576_1]) ).
fof(f_2576_3,plain,
! [U_8820] : 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)),U_8820)))),
inference(definitional_conversion,[status(esa)],[f_2576_2]) ).
cnf(f_2576_4,plain,
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)),U_8820)))),
inference(clausify,[status(thm)],[f_2576_3]) ).
fof(f_2577_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__le__nat]) ).
fof(f_2577_2,plain,
! [U_8821] : 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)),U_8821)))),
inference(variable_rename,[status(thm)],[f_2577_1]) ).
fof(f_2577_3,plain,
! [U_8821] : 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)),U_8821)))),
inference(definitional_conversion,[status(esa)],[f_2577_2]) ).
cnf(f_2577_4,plain,
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)),U_8821)))),
inference(clausify,[status(thm)],[f_2577_3]) ).
fof(f_2578_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__abs]) ).
fof(f_2578_2,plain,
! [U_8825,U_8824,U_8823,U_8822] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8822),hAPP(c_Groups_Oabs__class_Oabs(U_8822),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8823,U_8822),U_8824),U_8825))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8823,U_8822),hAPP(hAPP(c_COMBB(U_8822,U_8822,U_8823),c_Groups_Oabs__class_Oabs(U_8822)),U_8824)),U_8825)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_8822) ),
inference(variable_rename,[status(thm)],[f_2578_1]) ).
fof(f_2578_3,plain,
! [U_8822,U_8823,U_8824,U_8825] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8822),hAPP(c_Groups_Oabs__class_Oabs(U_8822),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8823,U_8822),U_8824),U_8825))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8823,U_8822),hAPP(hAPP(c_COMBB(U_8822,U_8822,U_8823),c_Groups_Oabs__class_Oabs(U_8822)),U_8824)),U_8825)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_8822) ),
inference(definitional_conversion,[status(esa)],[f_2578_2]) ).
cnf(f_2578_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8822),hAPP(c_Groups_Oabs__class_Oabs(U_8822),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8823,U_8822),U_8824),U_8825))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8823,U_8822),hAPP(hAPP(c_COMBB(U_8822,U_8822,U_8823),c_Groups_Oabs__class_Oabs(U_8822)),U_8824)),U_8825)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_8822) ),
inference(clausify,[status(thm)],[f_2578_3]) ).
fof(f_2579_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero]) ).
fof(f_2579_2,plain,
! [U_8829,U_8828,U_8827,U_8826] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8826),c_Groups_Ozero__class_Ozero(U_8826)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8827,U_8826),hAPP(hAPP(c_COMBB(U_8826,U_8826,U_8827),c_Groups_Oabs__class_Oabs(U_8826)),U_8828)),U_8829)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_8826) ),
inference(variable_rename,[status(thm)],[f_2579_1]) ).
fof(f_2579_3,plain,
! [U_8826,U_8827,U_8828,U_8829] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8826),c_Groups_Ozero__class_Ozero(U_8826)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8827,U_8826),hAPP(hAPP(c_COMBB(U_8826,U_8826,U_8827),c_Groups_Oabs__class_Oabs(U_8826)),U_8828)),U_8829)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_8826) ),
inference(definitional_conversion,[status(esa)],[f_2579_2]) ).
cnf(f_2579_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8826),c_Groups_Ozero__class_Ozero(U_8826)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8827,U_8826),hAPP(hAPP(c_COMBB(U_8826,U_8826,U_8827),c_Groups_Oabs__class_Oabs(U_8826)),U_8828)),U_8829)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_8826) ),
inference(clausify,[status(thm)],[f_2579_3]) ).
fof(f_2580_1,plain,
! [V_A_2,T_b] :
( 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))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets]) ).
fof(f_2580_2,plain,
! [U_8831,U_8830] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8830,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_8830,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_8830,tc_HOL_Obool),tc_fun(U_8830,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_8830,tc_HOL_Obool))),U_8831))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8830),U_8831)) ),
inference(variable_rename,[status(thm)],[f_2580_1]) ).
fof(f_2580_3,plain,
! [U_8830,U_8831] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8830,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_8830,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_8830,tc_HOL_Obool),tc_fun(U_8830,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_8830,tc_HOL_Obool))),U_8831))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8830),U_8831)) ),
inference(definitional_conversion,[status(esa)],[f_2580_2]) ).
cnf(f_2580_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8830,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_8830,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_8830,tc_HOL_Obool),tc_fun(U_8830,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_8830,tc_HOL_Obool))),U_8831))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8830),U_8831)) ),
inference(clausify,[status(thm)],[f_2580_3]) ).
fof(f_2581_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_insert__def]) ).
fof(f_2581_2,plain,
! [U_8834,U_8833,U_8832] : hAPP(hAPP(c_Set_Oinsert(U_8832),U_8833),U_8834) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8832,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8832),hAPP(hAPP(c_COMBC(U_8832,U_8832,tc_HOL_Obool),c_fequal),U_8833))),U_8834),
inference(variable_rename,[status(thm)],[f_2581_1]) ).
fof(f_2581_3,plain,
! [U_8832,U_8833,U_8834] : hAPP(hAPP(c_Set_Oinsert(U_8832),U_8833),U_8834) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8832,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8832),hAPP(hAPP(c_COMBC(U_8832,U_8832,tc_HOL_Obool),c_fequal),U_8833))),U_8834),
inference(definitional_conversion,[status(esa)],[f_2581_2]) ).
cnf(f_2581_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_8832),U_8833),U_8834) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8832,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8832),hAPP(hAPP(c_COMBC(U_8832,U_8832,tc_HOL_Obool),c_fequal),U_8833))),U_8834),
inference(clausify,[status(thm)],[f_2581_3]) ).
fof(f_2582_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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) = 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))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J]) ).
fof(f_2582_2,plain,
! [U_8839,U_8838,U_8837,U_8836,U_8835] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8836,tc_fun(U_8837,tc_HOL_Obool)),U_8835),U_8838)),U_8839) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8836,tc_fun(U_8837,tc_HOL_Obool)),U_8835),hAPP(hAPP(c_COMBC(U_8836,tc_fun(U_8837,tc_HOL_Obool),tc_fun(U_8837,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8837,tc_HOL_Obool),tc_fun(tc_fun(U_8837,tc_HOL_Obool),tc_fun(U_8837,tc_HOL_Obool)),U_8836),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8837,tc_HOL_Obool))),U_8838)),U_8839))
| U_8835 = c_Orderings_Obot__class_Obot(tc_fun(U_8836,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8836,tc_fun(U_8837,tc_HOL_Obool)),U_8835),U_8838)),U_8839) = U_8839
| U_8835 != c_Orderings_Obot__class_Obot(tc_fun(U_8836,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2582_1]) ).
fof(f_2582_3,plain,
( ! [U_8849,U_8847,U_8845,U_8843,U_8841] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8845,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8843,tc_fun(U_8845,tc_HOL_Obool)),U_8841),U_8847)),U_8849) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8843,tc_fun(U_8845,tc_HOL_Obool)),U_8841),hAPP(hAPP(c_COMBC(U_8843,tc_fun(U_8845,tc_HOL_Obool),tc_fun(U_8845,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8845,tc_HOL_Obool),tc_fun(tc_fun(U_8845,tc_HOL_Obool),tc_fun(U_8845,tc_HOL_Obool)),U_8843),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8845,tc_HOL_Obool))),U_8847)),U_8849))
| U_8841 = c_Orderings_Obot__class_Obot(tc_fun(U_8843,tc_HOL_Obool)) )
& ! [U_8848,U_8846,U_8844,U_8842,U_8840] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8844,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8842,tc_fun(U_8844,tc_HOL_Obool)),U_8840),U_8846)),U_8848) = U_8848
| U_8840 != c_Orderings_Obot__class_Obot(tc_fun(U_8842,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2582_2]) ).
fof(f_2582_4,plain,
( ! [U_8849,U_8841,U_8843,U_8845,U_8847] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8845,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8843,tc_fun(U_8845,tc_HOL_Obool)),U_8841),U_8847)),U_8849) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8843,tc_fun(U_8845,tc_HOL_Obool)),U_8841),hAPP(hAPP(c_COMBC(U_8843,tc_fun(U_8845,tc_HOL_Obool),tc_fun(U_8845,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8845,tc_HOL_Obool),tc_fun(tc_fun(U_8845,tc_HOL_Obool),tc_fun(U_8845,tc_HOL_Obool)),U_8843),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8845,tc_HOL_Obool))),U_8847)),U_8849))
| U_8841 = c_Orderings_Obot__class_Obot(tc_fun(U_8843,tc_HOL_Obool)) )
& ! [U_8844,U_8842,U_8846,U_8840,U_8848] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8844,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8842,tc_fun(U_8844,tc_HOL_Obool)),U_8840),U_8846)),U_8848) = U_8848
| U_8840 != c_Orderings_Obot__class_Obot(tc_fun(U_8842,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2582_3]) ).
cnf(f_2582_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8844,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8842,tc_fun(U_8844,tc_HOL_Obool)),U_8840),U_8846)),U_8848) = U_8848
| U_8840 != c_Orderings_Obot__class_Obot(tc_fun(U_8842,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2582_4]) ).
cnf(f_2582_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8845,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8843,tc_fun(U_8845,tc_HOL_Obool)),U_8841),U_8847)),U_8849) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8843,tc_fun(U_8845,tc_HOL_Obool)),U_8841),hAPP(hAPP(c_COMBC(U_8843,tc_fun(U_8845,tc_HOL_Obool),tc_fun(U_8845,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8845,tc_HOL_Obool),tc_fun(tc_fun(U_8845,tc_HOL_Obool),tc_fun(U_8845,tc_HOL_Obool)),U_8843),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8845,tc_HOL_Obool))),U_8847)),U_8849))
| U_8841 = c_Orderings_Obot__class_Obot(tc_fun(U_8843,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2582_4]) ).
fof(f_2583_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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))
| V_C_2 = c_Orderings_Obot__class_Obot(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),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
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J]) ).
fof(f_2583_2,plain,
! [U_8854,U_8853,U_8852,U_8851,U_8850] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8852,tc_HOL_Obool)),U_8853),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8851,tc_fun(U_8852,tc_HOL_Obool)),U_8850),U_8854)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8851,tc_fun(U_8852,tc_HOL_Obool)),U_8850),hAPP(hAPP(c_COMBB(tc_fun(U_8852,tc_HOL_Obool),tc_fun(U_8852,tc_HOL_Obool),U_8851),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8852,tc_HOL_Obool)),U_8853)),U_8854))
| U_8850 = c_Orderings_Obot__class_Obot(tc_fun(U_8851,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8852,tc_HOL_Obool)),U_8853),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8851,tc_fun(U_8852,tc_HOL_Obool)),U_8850),U_8854)) = U_8853
| U_8850 != c_Orderings_Obot__class_Obot(tc_fun(U_8851,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2583_1]) ).
fof(f_2583_3,plain,
( ! [U_8864,U_8862,U_8860,U_8858,U_8856] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8860,tc_HOL_Obool)),U_8862),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8858,tc_fun(U_8860,tc_HOL_Obool)),U_8856),U_8864)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8858,tc_fun(U_8860,tc_HOL_Obool)),U_8856),hAPP(hAPP(c_COMBB(tc_fun(U_8860,tc_HOL_Obool),tc_fun(U_8860,tc_HOL_Obool),U_8858),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8860,tc_HOL_Obool)),U_8862)),U_8864))
| U_8856 = c_Orderings_Obot__class_Obot(tc_fun(U_8858,tc_HOL_Obool)) )
& ! [U_8863,U_8861,U_8859,U_8857,U_8855] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8859,tc_HOL_Obool)),U_8861),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8857,tc_fun(U_8859,tc_HOL_Obool)),U_8855),U_8863)) = U_8861
| U_8855 != c_Orderings_Obot__class_Obot(tc_fun(U_8857,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2583_2]) ).
fof(f_2583_4,plain,
( ! [U_8856,U_8858,U_8860,U_8862,U_8864] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8860,tc_HOL_Obool)),U_8862),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8858,tc_fun(U_8860,tc_HOL_Obool)),U_8856),U_8864)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8858,tc_fun(U_8860,tc_HOL_Obool)),U_8856),hAPP(hAPP(c_COMBB(tc_fun(U_8860,tc_HOL_Obool),tc_fun(U_8860,tc_HOL_Obool),U_8858),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8860,tc_HOL_Obool)),U_8862)),U_8864))
| U_8856 = c_Orderings_Obot__class_Obot(tc_fun(U_8858,tc_HOL_Obool)) )
& ! [U_8859,U_8861,U_8857,U_8855,U_8863] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8859,tc_HOL_Obool)),U_8861),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8857,tc_fun(U_8859,tc_HOL_Obool)),U_8855),U_8863)) = U_8861
| U_8855 != c_Orderings_Obot__class_Obot(tc_fun(U_8857,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2583_3]) ).
cnf(f_2583_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8859,tc_HOL_Obool)),U_8861),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8857,tc_fun(U_8859,tc_HOL_Obool)),U_8855),U_8863)) = U_8861
| U_8855 != c_Orderings_Obot__class_Obot(tc_fun(U_8857,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2583_4]) ).
cnf(f_2583_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8860,tc_HOL_Obool)),U_8862),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8858,tc_fun(U_8860,tc_HOL_Obool)),U_8856),U_8864)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8858,tc_fun(U_8860,tc_HOL_Obool)),U_8856),hAPP(hAPP(c_COMBB(tc_fun(U_8860,tc_HOL_Obool),tc_fun(U_8860,tc_HOL_Obool),U_8858),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8860,tc_HOL_Obool)),U_8862)),U_8864))
| U_8856 = c_Orderings_Obot__class_Obot(tc_fun(U_8858,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2583_4]) ).
fof(f_2584_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J]) ).
fof(f_2584_2,plain,
! [U_8869,U_8868,U_8867,U_8866,U_8865] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8866,tc_fun(U_8867,tc_HOL_Obool)),U_8865),hAPP(hAPP(c_COMBC(U_8866,tc_fun(U_8867,tc_HOL_Obool),tc_fun(U_8867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8867,tc_HOL_Obool),tc_fun(tc_fun(U_8867,tc_HOL_Obool),tc_fun(U_8867,tc_HOL_Obool)),U_8866),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8867,tc_HOL_Obool))),U_8868)),U_8869)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8867,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8866,tc_fun(U_8867,tc_HOL_Obool)),U_8865),U_8868)),U_8869)
| U_8865 = c_Orderings_Obot__class_Obot(tc_fun(U_8866,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8866,tc_fun(U_8867,tc_HOL_Obool)),U_8865),hAPP(hAPP(c_COMBC(U_8866,tc_fun(U_8867,tc_HOL_Obool),tc_fun(U_8867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8867,tc_HOL_Obool),tc_fun(tc_fun(U_8867,tc_HOL_Obool),tc_fun(U_8867,tc_HOL_Obool)),U_8866),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8867,tc_HOL_Obool))),U_8868)),U_8869)) = c_Orderings_Obot__class_Obot(tc_fun(U_8867,tc_HOL_Obool))
| U_8865 != c_Orderings_Obot__class_Obot(tc_fun(U_8866,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2584_1]) ).
fof(f_2584_3,plain,
( ! [U_8879,U_8877,U_8875,U_8873,U_8871] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8873,tc_fun(U_8875,tc_HOL_Obool)),U_8871),hAPP(hAPP(c_COMBC(U_8873,tc_fun(U_8875,tc_HOL_Obool),tc_fun(U_8875,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8875,tc_HOL_Obool),tc_fun(tc_fun(U_8875,tc_HOL_Obool),tc_fun(U_8875,tc_HOL_Obool)),U_8873),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8875,tc_HOL_Obool))),U_8877)),U_8879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8875,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8873,tc_fun(U_8875,tc_HOL_Obool)),U_8871),U_8877)),U_8879)
| U_8871 = c_Orderings_Obot__class_Obot(tc_fun(U_8873,tc_HOL_Obool)) )
& ! [U_8878,U_8876,U_8874,U_8872,U_8870] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8872,tc_fun(U_8874,tc_HOL_Obool)),U_8870),hAPP(hAPP(c_COMBC(U_8872,tc_fun(U_8874,tc_HOL_Obool),tc_fun(U_8874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8874,tc_HOL_Obool),tc_fun(tc_fun(U_8874,tc_HOL_Obool),tc_fun(U_8874,tc_HOL_Obool)),U_8872),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8874,tc_HOL_Obool))),U_8876)),U_8878)) = c_Orderings_Obot__class_Obot(tc_fun(U_8874,tc_HOL_Obool))
| U_8870 != c_Orderings_Obot__class_Obot(tc_fun(U_8872,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2584_2]) ).
fof(f_2584_4,plain,
( ! [U_8871,U_8873,U_8875,U_8877,U_8879] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8873,tc_fun(U_8875,tc_HOL_Obool)),U_8871),hAPP(hAPP(c_COMBC(U_8873,tc_fun(U_8875,tc_HOL_Obool),tc_fun(U_8875,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8875,tc_HOL_Obool),tc_fun(tc_fun(U_8875,tc_HOL_Obool),tc_fun(U_8875,tc_HOL_Obool)),U_8873),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8875,tc_HOL_Obool))),U_8877)),U_8879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8875,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8873,tc_fun(U_8875,tc_HOL_Obool)),U_8871),U_8877)),U_8879)
| U_8871 = c_Orderings_Obot__class_Obot(tc_fun(U_8873,tc_HOL_Obool)) )
& ! [U_8876,U_8870,U_8874,U_8878,U_8872] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8872,tc_fun(U_8874,tc_HOL_Obool)),U_8870),hAPP(hAPP(c_COMBC(U_8872,tc_fun(U_8874,tc_HOL_Obool),tc_fun(U_8874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8874,tc_HOL_Obool),tc_fun(tc_fun(U_8874,tc_HOL_Obool),tc_fun(U_8874,tc_HOL_Obool)),U_8872),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8874,tc_HOL_Obool))),U_8876)),U_8878)) = c_Orderings_Obot__class_Obot(tc_fun(U_8874,tc_HOL_Obool))
| U_8870 != c_Orderings_Obot__class_Obot(tc_fun(U_8872,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2584_3]) ).
cnf(f_2584_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8872,tc_fun(U_8874,tc_HOL_Obool)),U_8870),hAPP(hAPP(c_COMBC(U_8872,tc_fun(U_8874,tc_HOL_Obool),tc_fun(U_8874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8874,tc_HOL_Obool),tc_fun(tc_fun(U_8874,tc_HOL_Obool),tc_fun(U_8874,tc_HOL_Obool)),U_8872),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8874,tc_HOL_Obool))),U_8876)),U_8878)) = c_Orderings_Obot__class_Obot(tc_fun(U_8874,tc_HOL_Obool))
| U_8870 != c_Orderings_Obot__class_Obot(tc_fun(U_8872,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2584_4]) ).
cnf(f_2584_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8873,tc_fun(U_8875,tc_HOL_Obool)),U_8871),hAPP(hAPP(c_COMBC(U_8873,tc_fun(U_8875,tc_HOL_Obool),tc_fun(U_8875,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8875,tc_HOL_Obool),tc_fun(tc_fun(U_8875,tc_HOL_Obool),tc_fun(U_8875,tc_HOL_Obool)),U_8873),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8875,tc_HOL_Obool))),U_8877)),U_8879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8875,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8873,tc_fun(U_8875,tc_HOL_Obool)),U_8871),U_8877)),U_8879)
| U_8871 = c_Orderings_Obot__class_Obot(tc_fun(U_8873,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2584_4]) ).
fof(f_2585_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J]) ).
fof(f_2585_2,plain,
! [U_8884,U_8883,U_8882,U_8881,U_8880] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(U_8882,tc_HOL_Obool)),U_8880),hAPP(hAPP(c_COMBB(tc_fun(U_8882,tc_HOL_Obool),tc_fun(U_8882,tc_HOL_Obool),U_8881),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8882,tc_HOL_Obool)),U_8883)),U_8884)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8882,tc_HOL_Obool)),U_8883),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(U_8882,tc_HOL_Obool)),U_8880),U_8884))
| U_8880 = c_Orderings_Obot__class_Obot(tc_fun(U_8881,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(U_8882,tc_HOL_Obool)),U_8880),hAPP(hAPP(c_COMBB(tc_fun(U_8882,tc_HOL_Obool),tc_fun(U_8882,tc_HOL_Obool),U_8881),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8882,tc_HOL_Obool)),U_8883)),U_8884)) = c_Orderings_Obot__class_Obot(tc_fun(U_8882,tc_HOL_Obool))
| U_8880 != c_Orderings_Obot__class_Obot(tc_fun(U_8881,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2585_1]) ).
fof(f_2585_3,plain,
( ! [U_8894,U_8892,U_8890,U_8888,U_8886] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8888,tc_fun(U_8890,tc_HOL_Obool)),U_8886),hAPP(hAPP(c_COMBB(tc_fun(U_8890,tc_HOL_Obool),tc_fun(U_8890,tc_HOL_Obool),U_8888),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8890,tc_HOL_Obool)),U_8892)),U_8894)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8890,tc_HOL_Obool)),U_8892),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8888,tc_fun(U_8890,tc_HOL_Obool)),U_8886),U_8894))
| U_8886 = c_Orderings_Obot__class_Obot(tc_fun(U_8888,tc_HOL_Obool)) )
& ! [U_8893,U_8891,U_8889,U_8887,U_8885] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8887,tc_fun(U_8889,tc_HOL_Obool)),U_8885),hAPP(hAPP(c_COMBB(tc_fun(U_8889,tc_HOL_Obool),tc_fun(U_8889,tc_HOL_Obool),U_8887),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8889,tc_HOL_Obool)),U_8891)),U_8893)) = c_Orderings_Obot__class_Obot(tc_fun(U_8889,tc_HOL_Obool))
| U_8885 != c_Orderings_Obot__class_Obot(tc_fun(U_8887,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2585_2]) ).
fof(f_2585_4,plain,
( ! [U_8886,U_8888,U_8890,U_8892,U_8894] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8888,tc_fun(U_8890,tc_HOL_Obool)),U_8886),hAPP(hAPP(c_COMBB(tc_fun(U_8890,tc_HOL_Obool),tc_fun(U_8890,tc_HOL_Obool),U_8888),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8890,tc_HOL_Obool)),U_8892)),U_8894)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8890,tc_HOL_Obool)),U_8892),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8888,tc_fun(U_8890,tc_HOL_Obool)),U_8886),U_8894))
| U_8886 = c_Orderings_Obot__class_Obot(tc_fun(U_8888,tc_HOL_Obool)) )
& ! [U_8893,U_8887,U_8889,U_8891,U_8885] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8887,tc_fun(U_8889,tc_HOL_Obool)),U_8885),hAPP(hAPP(c_COMBB(tc_fun(U_8889,tc_HOL_Obool),tc_fun(U_8889,tc_HOL_Obool),U_8887),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8889,tc_HOL_Obool)),U_8891)),U_8893)) = c_Orderings_Obot__class_Obot(tc_fun(U_8889,tc_HOL_Obool))
| U_8885 != c_Orderings_Obot__class_Obot(tc_fun(U_8887,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2585_3]) ).
cnf(f_2585_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8887,tc_fun(U_8889,tc_HOL_Obool)),U_8885),hAPP(hAPP(c_COMBB(tc_fun(U_8889,tc_HOL_Obool),tc_fun(U_8889,tc_HOL_Obool),U_8887),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8889,tc_HOL_Obool)),U_8891)),U_8893)) = c_Orderings_Obot__class_Obot(tc_fun(U_8889,tc_HOL_Obool))
| U_8885 != c_Orderings_Obot__class_Obot(tc_fun(U_8887,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2585_4]) ).
cnf(f_2585_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8888,tc_fun(U_8890,tc_HOL_Obool)),U_8886),hAPP(hAPP(c_COMBB(tc_fun(U_8890,tc_HOL_Obool),tc_fun(U_8890,tc_HOL_Obool),U_8888),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8890,tc_HOL_Obool)),U_8892)),U_8894)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8890,tc_HOL_Obool)),U_8892),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8888,tc_fun(U_8890,tc_HOL_Obool)),U_8886),U_8894))
| U_8886 = c_Orderings_Obot__class_Obot(tc_fun(U_8888,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2585_4]) ).
fof(f_2586_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__insert]) ).
fof(f_2586_2,plain,
! [U_8899,U_8898,U_8897,U_8896,U_8895] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8895,tc_fun(U_8896,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8895),U_8897),U_8898)),U_8899) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8896,tc_HOL_Obool)),hAPP(U_8899,U_8897)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8895,tc_fun(U_8896,tc_HOL_Obool)),U_8898),U_8899)),
inference(variable_rename,[status(thm)],[f_2586_1]) ).
fof(f_2586_3,plain,
! [U_8895,U_8897,U_8896,U_8898,U_8899] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8895,tc_fun(U_8896,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8895),U_8897),U_8898)),U_8899) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8896,tc_HOL_Obool)),hAPP(U_8899,U_8897)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8895,tc_fun(U_8896,tc_HOL_Obool)),U_8898),U_8899)),
inference(definitional_conversion,[status(esa)],[f_2586_2]) ).
cnf(f_2586_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8895,tc_fun(U_8896,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8895),U_8897),U_8898)),U_8899) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8896,tc_HOL_Obool)),hAPP(U_8899,U_8897)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8895,tc_fun(U_8896,tc_HOL_Obool)),U_8898),U_8899)),
inference(clausify,[status(thm)],[f_2586_3]) ).
fof(f_2587_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).
fof(f_2587_2,plain,
! [U_8902,U_8901,U_8900] : hAPP(c_Set_OCollect(U_8900),hAPP(hAPP(c_COMBS(U_8900,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8900),c_fimplies),U_8901)),U_8902)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8900,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8900,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8900),U_8901))),hAPP(c_Set_OCollect(U_8900),U_8902)),
inference(variable_rename,[status(thm)],[f_2587_1]) ).
fof(f_2587_3,plain,
! [U_8900,U_8901,U_8902] : hAPP(c_Set_OCollect(U_8900),hAPP(hAPP(c_COMBS(U_8900,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8900),c_fimplies),U_8901)),U_8902)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8900,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8900,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8900),U_8901))),hAPP(c_Set_OCollect(U_8900),U_8902)),
inference(definitional_conversion,[status(esa)],[f_2587_2]) ).
cnf(f_2587_4,plain,
hAPP(c_Set_OCollect(U_8900),hAPP(hAPP(c_COMBS(U_8900,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8900),c_fimplies),U_8901)),U_8902)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8900,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8900,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8900),U_8901))),hAPP(c_Set_OCollect(U_8900),U_8902)),
inference(clausify,[status(thm)],[f_2587_3]) ).
fof(f_2588_1,plain,
! [V_x_2,V_S_2,V_R_2,T_b] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup__Un__eq]) ).
fof(f_2588_2,plain,
! [U_8906,U_8905,U_8904,U_8903] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8903,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8903,tc_fun(U_8903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8903)),U_8904)),hAPP(hAPP(c_COMBC(U_8903,tc_fun(U_8903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8903)),U_8905)),U_8906))
| ~ hBOOL(hAPP(hAPP(c_member(U_8903),U_8906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8903,tc_HOL_Obool)),U_8904),U_8905))) )
& ( hBOOL(hAPP(hAPP(c_member(U_8903),U_8906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8903,tc_HOL_Obool)),U_8904),U_8905)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8903,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8903,tc_fun(U_8903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8903)),U_8904)),hAPP(hAPP(c_COMBC(U_8903,tc_fun(U_8903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8903)),U_8905)),U_8906)) ) ),
inference(variable_rename,[status(thm)],[f_2588_1]) ).
fof(f_2588_3,plain,
( ! [U_8914,U_8912,U_8910,U_8908] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8908,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8908,tc_fun(U_8908,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8908)),U_8910)),hAPP(hAPP(c_COMBC(U_8908,tc_fun(U_8908,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8908)),U_8912)),U_8914))
| ~ hBOOL(hAPP(hAPP(c_member(U_8908),U_8914),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8908,tc_HOL_Obool)),U_8910),U_8912))) )
& ! [U_8913,U_8911,U_8909,U_8907] :
( hBOOL(hAPP(hAPP(c_member(U_8907),U_8913),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8907,tc_HOL_Obool)),U_8909),U_8911)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8907,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8907,tc_fun(U_8907,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8907)),U_8909)),hAPP(hAPP(c_COMBC(U_8907,tc_fun(U_8907,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8907)),U_8911)),U_8913)) ) ),
inference(miniscope,[status(thm)],[f_2588_2]) ).
fof(f_2588_4,plain,
( ! [U_8908,U_8910,U_8912,U_8914] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8908,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8908,tc_fun(U_8908,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8908)),U_8910)),hAPP(hAPP(c_COMBC(U_8908,tc_fun(U_8908,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8908)),U_8912)),U_8914))
| ~ hBOOL(hAPP(hAPP(c_member(U_8908),U_8914),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8908,tc_HOL_Obool)),U_8910),U_8912))) )
& ! [U_8909,U_8913,U_8907,U_8911] :
( hBOOL(hAPP(hAPP(c_member(U_8907),U_8913),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8907,tc_HOL_Obool)),U_8909),U_8911)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8907,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8907,tc_fun(U_8907,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8907)),U_8909)),hAPP(hAPP(c_COMBC(U_8907,tc_fun(U_8907,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8907)),U_8911)),U_8913)) ) ),
inference(definitional_conversion,[status(esa)],[f_2588_3]) ).
cnf(f_2588_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8907),U_8913),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8907,tc_HOL_Obool)),U_8909),U_8911)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8907,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8907,tc_fun(U_8907,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8907)),U_8909)),hAPP(hAPP(c_COMBC(U_8907,tc_fun(U_8907,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8907)),U_8911)),U_8913)) ),
inference(clausify,[status(thm)],[f_2588_4]) ).
cnf(f_2588_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8908,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8908,tc_fun(U_8908,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8908)),U_8910)),hAPP(hAPP(c_COMBC(U_8908,tc_fun(U_8908,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8908)),U_8912)),U_8914))
| ~ hBOOL(hAPP(hAPP(c_member(U_8908),U_8914),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8908,tc_HOL_Obool)),U_8910),U_8912))) ),
inference(clausify,[status(thm)],[f_2588_4]) ).
fof(f_2589_1,plain,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2]) ).
fof(f_2589_2,plain,
! [U_8920,U_8919,U_8918,U_8917,U_8916,U_8915] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8915,tc_fun(U_8916,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8915,tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_fun(U_8916,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8916,tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_fun(U_8916,tc_HOL_Obool)),U_8915),c_COMBC(U_8916,tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8916,tc_prod(U_8915,U_8916)),tc_fun(U_8916,tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),U_8915),hAPP(c_COMBB(tc_prod(U_8915,U_8916),tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool),U_8916),c_member(tc_prod(U_8915,U_8916)))),c_Product__Type_OPair(U_8915,U_8916)))),U_8917)),hAPP(hAPP(c_COMBC(U_8915,tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_fun(U_8916,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8916,tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_fun(U_8916,tc_HOL_Obool)),U_8915),c_COMBC(U_8916,tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8916,tc_prod(U_8915,U_8916)),tc_fun(U_8916,tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),U_8915),hAPP(c_COMBB(tc_prod(U_8915,U_8916),tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool),U_8916),c_member(tc_prod(U_8915,U_8916)))),c_Product__Type_OPair(U_8915,U_8916)))),U_8918)),U_8919),U_8920))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8915,U_8916)),hAPP(hAPP(c_Product__Type_OPair(U_8915,U_8916),U_8919),U_8920)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool)),U_8917),U_8918))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8915,U_8916)),hAPP(hAPP(c_Product__Type_OPair(U_8915,U_8916),U_8919),U_8920)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool)),U_8917),U_8918)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8915,tc_fun(U_8916,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8915,tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_fun(U_8916,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8916,tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_fun(U_8916,tc_HOL_Obool)),U_8915),c_COMBC(U_8916,tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8916,tc_prod(U_8915,U_8916)),tc_fun(U_8916,tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),U_8915),hAPP(c_COMBB(tc_prod(U_8915,U_8916),tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool),U_8916),c_member(tc_prod(U_8915,U_8916)))),c_Product__Type_OPair(U_8915,U_8916)))),U_8917)),hAPP(hAPP(c_COMBC(U_8915,tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_fun(U_8916,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8916,tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_fun(U_8916,tc_HOL_Obool)),U_8915),c_COMBC(U_8916,tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8916,tc_prod(U_8915,U_8916)),tc_fun(U_8916,tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool)),U_8915),hAPP(c_COMBB(tc_prod(U_8915,U_8916),tc_fun(tc_fun(tc_prod(U_8915,U_8916),tc_HOL_Obool),tc_HOL_Obool),U_8916),c_member(tc_prod(U_8915,U_8916)))),c_Product__Type_OPair(U_8915,U_8916)))),U_8918)),U_8919),U_8920)) ) ),
inference(variable_rename,[status(thm)],[f_2589_1]) ).
fof(f_2589_3,plain,
( ! [U_8932,U_8930,U_8928,U_8926,U_8924,U_8922] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_fun(U_8924,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8922,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),U_8922),c_COMBC(U_8924,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_prod(U_8922,U_8924)),tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),U_8922),hAPP(c_COMBB(tc_prod(U_8922,U_8924),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool),U_8924),c_member(tc_prod(U_8922,U_8924)))),c_Product__Type_OPair(U_8922,U_8924)))),U_8926)),hAPP(hAPP(c_COMBC(U_8922,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),U_8922),c_COMBC(U_8924,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_prod(U_8922,U_8924)),tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),U_8922),hAPP(c_COMBB(tc_prod(U_8922,U_8924),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool),U_8924),c_member(tc_prod(U_8922,U_8924)))),c_Product__Type_OPair(U_8922,U_8924)))),U_8928)),U_8930),U_8932))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8922,U_8924)),hAPP(hAPP(c_Product__Type_OPair(U_8922,U_8924),U_8930),U_8932)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool)),U_8926),U_8928))) )
& ! [U_8931,U_8929,U_8927,U_8925,U_8923,U_8921] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8921,U_8923)),hAPP(hAPP(c_Product__Type_OPair(U_8921,U_8923),U_8929),U_8931)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool)),U_8925),U_8927)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8921,tc_fun(U_8923,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8921,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),U_8921),c_COMBC(U_8923,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_prod(U_8921,U_8923)),tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),U_8921),hAPP(c_COMBB(tc_prod(U_8921,U_8923),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool),U_8923),c_member(tc_prod(U_8921,U_8923)))),c_Product__Type_OPair(U_8921,U_8923)))),U_8925)),hAPP(hAPP(c_COMBC(U_8921,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),U_8921),c_COMBC(U_8923,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_prod(U_8921,U_8923)),tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),U_8921),hAPP(c_COMBB(tc_prod(U_8921,U_8923),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool),U_8923),c_member(tc_prod(U_8921,U_8923)))),c_Product__Type_OPair(U_8921,U_8923)))),U_8927)),U_8929),U_8931)) ) ),
inference(miniscope,[status(thm)],[f_2589_2]) ).
fof(f_2589_4,plain,
( ! [U_8922,U_8924,U_8926,U_8928,U_8930,U_8932] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_fun(U_8924,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8922,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),U_8922),c_COMBC(U_8924,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_prod(U_8922,U_8924)),tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),U_8922),hAPP(c_COMBB(tc_prod(U_8922,U_8924),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool),U_8924),c_member(tc_prod(U_8922,U_8924)))),c_Product__Type_OPair(U_8922,U_8924)))),U_8926)),hAPP(hAPP(c_COMBC(U_8922,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),U_8922),c_COMBC(U_8924,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_prod(U_8922,U_8924)),tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),U_8922),hAPP(c_COMBB(tc_prod(U_8922,U_8924),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool),U_8924),c_member(tc_prod(U_8922,U_8924)))),c_Product__Type_OPair(U_8922,U_8924)))),U_8928)),U_8930),U_8932))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8922,U_8924)),hAPP(hAPP(c_Product__Type_OPair(U_8922,U_8924),U_8930),U_8932)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool)),U_8926),U_8928))) )
& ! [U_8923,U_8927,U_8925,U_8921,U_8929,U_8931] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8921,U_8923)),hAPP(hAPP(c_Product__Type_OPair(U_8921,U_8923),U_8929),U_8931)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool)),U_8925),U_8927)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8921,tc_fun(U_8923,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8921,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),U_8921),c_COMBC(U_8923,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_prod(U_8921,U_8923)),tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),U_8921),hAPP(c_COMBB(tc_prod(U_8921,U_8923),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool),U_8923),c_member(tc_prod(U_8921,U_8923)))),c_Product__Type_OPair(U_8921,U_8923)))),U_8925)),hAPP(hAPP(c_COMBC(U_8921,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),U_8921),c_COMBC(U_8923,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_prod(U_8921,U_8923)),tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),U_8921),hAPP(c_COMBB(tc_prod(U_8921,U_8923),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool),U_8923),c_member(tc_prod(U_8921,U_8923)))),c_Product__Type_OPair(U_8921,U_8923)))),U_8927)),U_8929),U_8931)) ) ),
inference(definitional_conversion,[status(esa)],[f_2589_3]) ).
cnf(f_2589_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8921,U_8923)),hAPP(hAPP(c_Product__Type_OPair(U_8921,U_8923),U_8929),U_8931)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool)),U_8925),U_8927)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8921,tc_fun(U_8923,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8921,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),U_8921),c_COMBC(U_8923,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_prod(U_8921,U_8923)),tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),U_8921),hAPP(c_COMBB(tc_prod(U_8921,U_8923),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool),U_8923),c_member(tc_prod(U_8921,U_8923)))),c_Product__Type_OPair(U_8921,U_8923)))),U_8925)),hAPP(hAPP(c_COMBC(U_8921,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_fun(U_8923,tc_HOL_Obool)),U_8921),c_COMBC(U_8923,tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8923,tc_prod(U_8921,U_8923)),tc_fun(U_8923,tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool)),U_8921),hAPP(c_COMBB(tc_prod(U_8921,U_8923),tc_fun(tc_fun(tc_prod(U_8921,U_8923),tc_HOL_Obool),tc_HOL_Obool),U_8923),c_member(tc_prod(U_8921,U_8923)))),c_Product__Type_OPair(U_8921,U_8923)))),U_8927)),U_8929),U_8931)) ),
inference(clausify,[status(thm)],[f_2589_4]) ).
cnf(f_2589_6,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_fun(U_8924,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8922,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),U_8922),c_COMBC(U_8924,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_prod(U_8922,U_8924)),tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),U_8922),hAPP(c_COMBB(tc_prod(U_8922,U_8924),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool),U_8924),c_member(tc_prod(U_8922,U_8924)))),c_Product__Type_OPair(U_8922,U_8924)))),U_8926)),hAPP(hAPP(c_COMBC(U_8922,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_fun(U_8924,tc_HOL_Obool)),U_8922),c_COMBC(U_8924,tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8924,tc_prod(U_8922,U_8924)),tc_fun(U_8924,tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool)),U_8922),hAPP(c_COMBB(tc_prod(U_8922,U_8924),tc_fun(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool),tc_HOL_Obool),U_8924),c_member(tc_prod(U_8922,U_8924)))),c_Product__Type_OPair(U_8922,U_8924)))),U_8928)),U_8930),U_8932))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8922,U_8924)),hAPP(hAPP(c_Product__Type_OPair(U_8922,U_8924),U_8930),U_8932)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8922,U_8924),tc_HOL_Obool)),U_8926),U_8928))) ),
inference(clausify,[status(thm)],[f_2589_4]) ).
fof(f_2590_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__Un__distrib]) ).
fof(f_2590_2,plain,
! [U_8937,U_8936,U_8935,U_8934,U_8933] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),hAPP(hAPP(c_COMBS(U_8933,tc_fun(U_8934,tc_HOL_Obool),tc_fun(U_8934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8934,tc_HOL_Obool),tc_fun(tc_fun(U_8934,tc_HOL_Obool),tc_fun(U_8934,tc_HOL_Obool)),U_8933),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8934,tc_HOL_Obool))),U_8936)),U_8937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8934,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),U_8936)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),U_8937)),
inference(variable_rename,[status(thm)],[f_2590_1]) ).
fof(f_2590_3,plain,
! [U_8933,U_8934,U_8935,U_8936,U_8937] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),hAPP(hAPP(c_COMBS(U_8933,tc_fun(U_8934,tc_HOL_Obool),tc_fun(U_8934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8934,tc_HOL_Obool),tc_fun(tc_fun(U_8934,tc_HOL_Obool),tc_fun(U_8934,tc_HOL_Obool)),U_8933),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8934,tc_HOL_Obool))),U_8936)),U_8937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8934,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),U_8936)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),U_8937)),
inference(definitional_conversion,[status(esa)],[f_2590_2]) ).
cnf(f_2590_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),hAPP(hAPP(c_COMBS(U_8933,tc_fun(U_8934,tc_HOL_Obool),tc_fun(U_8934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8934,tc_HOL_Obool),tc_fun(tc_fun(U_8934,tc_HOL_Obool),tc_fun(U_8934,tc_HOL_Obool)),U_8933),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8934,tc_HOL_Obool))),U_8936)),U_8937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8934,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),U_8936)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8933,tc_fun(U_8934,tc_HOL_Obool)),U_8935),U_8937)),
inference(clausify,[status(thm)],[f_2590_3]) ).
fof(f_2591_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__Un]) ).
fof(f_2591_2,plain,
! [U_8942,U_8941,U_8940,U_8939,U_8938] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8938,tc_HOL_Obool)),U_8940),U_8941)),U_8942) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),U_8940),U_8942)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),U_8941),U_8942)),
inference(variable_rename,[status(thm)],[f_2591_1]) ).
fof(f_2591_3,plain,
! [U_8938,U_8939,U_8940,U_8941,U_8942] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8938,tc_HOL_Obool)),U_8940),U_8941)),U_8942) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),U_8940),U_8942)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),U_8941),U_8942)),
inference(definitional_conversion,[status(esa)],[f_2591_2]) ).
cnf(f_2591_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8938,tc_HOL_Obool)),U_8940),U_8941)),U_8942) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),U_8940),U_8942)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8938,tc_fun(U_8939,tc_HOL_Obool)),U_8941),U_8942)),
inference(clausify,[status(thm)],[f_2591_3]) ).
fof(f_2592_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I7_J]) ).
fof(f_2592_2,plain,
! [U_8947,U_8946,U_8945,U_8944,U_8943] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8943,tc_fun(U_8944,tc_HOL_Obool)),U_8945),hAPP(hAPP(c_COMBB(tc_fun(U_8944,tc_HOL_Obool),tc_fun(U_8944,tc_HOL_Obool),U_8943),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8944,tc_HOL_Obool)),U_8946)),U_8947)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8944,tc_HOL_Obool)),U_8946),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8943,tc_fun(U_8944,tc_HOL_Obool)),U_8945),U_8947)),
inference(variable_rename,[status(thm)],[f_2592_1]) ).
fof(f_2592_3,plain,
! [U_8943,U_8944,U_8945,U_8946,U_8947] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8943,tc_fun(U_8944,tc_HOL_Obool)),U_8945),hAPP(hAPP(c_COMBB(tc_fun(U_8944,tc_HOL_Obool),tc_fun(U_8944,tc_HOL_Obool),U_8943),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8944,tc_HOL_Obool)),U_8946)),U_8947)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8944,tc_HOL_Obool)),U_8946),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8943,tc_fun(U_8944,tc_HOL_Obool)),U_8945),U_8947)),
inference(definitional_conversion,[status(esa)],[f_2592_2]) ).
cnf(f_2592_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8943,tc_fun(U_8944,tc_HOL_Obool)),U_8945),hAPP(hAPP(c_COMBB(tc_fun(U_8944,tc_HOL_Obool),tc_fun(U_8944,tc_HOL_Obool),U_8943),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8944,tc_HOL_Obool)),U_8946)),U_8947)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8944,tc_HOL_Obool)),U_8946),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8943,tc_fun(U_8944,tc_HOL_Obool)),U_8945),U_8947)),
inference(clausify,[status(thm)],[f_2592_3]) ).
fof(f_2593_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I6_J]) ).
fof(f_2593_2,plain,
! [U_8952,U_8951,U_8950,U_8949,U_8948] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8948,tc_fun(U_8949,tc_HOL_Obool)),U_8950),hAPP(hAPP(c_COMBC(U_8948,tc_fun(U_8949,tc_HOL_Obool),tc_fun(U_8949,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8949,tc_HOL_Obool),tc_fun(tc_fun(U_8949,tc_HOL_Obool),tc_fun(U_8949,tc_HOL_Obool)),U_8948),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8949,tc_HOL_Obool))),U_8951)),U_8952)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8949,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8948,tc_fun(U_8949,tc_HOL_Obool)),U_8950),U_8951)),U_8952),
inference(variable_rename,[status(thm)],[f_2593_1]) ).
fof(f_2593_3,plain,
! [U_8948,U_8949,U_8950,U_8951,U_8952] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8948,tc_fun(U_8949,tc_HOL_Obool)),U_8950),hAPP(hAPP(c_COMBC(U_8948,tc_fun(U_8949,tc_HOL_Obool),tc_fun(U_8949,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8949,tc_HOL_Obool),tc_fun(tc_fun(U_8949,tc_HOL_Obool),tc_fun(U_8949,tc_HOL_Obool)),U_8948),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8949,tc_HOL_Obool))),U_8951)),U_8952)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8949,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8948,tc_fun(U_8949,tc_HOL_Obool)),U_8950),U_8951)),U_8952),
inference(definitional_conversion,[status(esa)],[f_2593_2]) ).
cnf(f_2593_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8948,tc_fun(U_8949,tc_HOL_Obool)),U_8950),hAPP(hAPP(c_COMBC(U_8948,tc_fun(U_8949,tc_HOL_Obool),tc_fun(U_8949,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8949,tc_HOL_Obool),tc_fun(tc_fun(U_8949,tc_HOL_Obool),tc_fun(U_8949,tc_HOL_Obool)),U_8948),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8949,tc_HOL_Obool))),U_8951)),U_8952)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8949,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8948,tc_fun(U_8949,tc_HOL_Obool)),U_8950),U_8951)),U_8952),
inference(clausify,[status(thm)],[f_2593_3]) ).
fof(f_2594_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I7_J]) ).
fof(f_2594_2,plain,
! [U_8957,U_8956,U_8955,U_8954,U_8953] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8953,tc_HOL_Obool)),U_8954),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8955,tc_fun(U_8953,tc_HOL_Obool)),U_8956),U_8957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8955,tc_fun(U_8953,tc_HOL_Obool)),U_8956),hAPP(hAPP(c_COMBB(tc_fun(U_8953,tc_HOL_Obool),tc_fun(U_8953,tc_HOL_Obool),U_8955),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8953,tc_HOL_Obool)),U_8954)),U_8957)),
inference(variable_rename,[status(thm)],[f_2594_1]) ).
fof(f_2594_3,plain,
! [U_8953,U_8954,U_8955,U_8956,U_8957] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8953,tc_HOL_Obool)),U_8954),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8955,tc_fun(U_8953,tc_HOL_Obool)),U_8956),U_8957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8955,tc_fun(U_8953,tc_HOL_Obool)),U_8956),hAPP(hAPP(c_COMBB(tc_fun(U_8953,tc_HOL_Obool),tc_fun(U_8953,tc_HOL_Obool),U_8955),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8953,tc_HOL_Obool)),U_8954)),U_8957)),
inference(definitional_conversion,[status(esa)],[f_2594_2]) ).
cnf(f_2594_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8953,tc_HOL_Obool)),U_8954),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8955,tc_fun(U_8953,tc_HOL_Obool)),U_8956),U_8957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8955,tc_fun(U_8953,tc_HOL_Obool)),U_8956),hAPP(hAPP(c_COMBB(tc_fun(U_8953,tc_HOL_Obool),tc_fun(U_8953,tc_HOL_Obool),U_8955),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8953,tc_HOL_Obool)),U_8954)),U_8957)),
inference(clausify,[status(thm)],[f_2594_3]) ).
fof(f_2595_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib]) ).
fof(f_2595_2,plain,
! [U_8962,U_8961,U_8960,U_8959,U_8958] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8958,tc_HOL_Obool)),U_8959),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8960,tc_fun(U_8958,tc_HOL_Obool)),U_8961),U_8962)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8960,tc_fun(U_8958,tc_HOL_Obool)),U_8961),hAPP(hAPP(c_COMBB(tc_fun(U_8958,tc_HOL_Obool),tc_fun(U_8958,tc_HOL_Obool),U_8960),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8958,tc_HOL_Obool)),U_8959)),U_8962)),
inference(variable_rename,[status(thm)],[f_2595_1]) ).
fof(f_2595_3,plain,
! [U_8958,U_8959,U_8960,U_8961,U_8962] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8958,tc_HOL_Obool)),U_8959),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8960,tc_fun(U_8958,tc_HOL_Obool)),U_8961),U_8962)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8960,tc_fun(U_8958,tc_HOL_Obool)),U_8961),hAPP(hAPP(c_COMBB(tc_fun(U_8958,tc_HOL_Obool),tc_fun(U_8958,tc_HOL_Obool),U_8960),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8958,tc_HOL_Obool)),U_8959)),U_8962)),
inference(definitional_conversion,[status(esa)],[f_2595_2]) ).
cnf(f_2595_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8958,tc_HOL_Obool)),U_8959),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8960,tc_fun(U_8958,tc_HOL_Obool)),U_8961),U_8962)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8960,tc_fun(U_8958,tc_HOL_Obool)),U_8961),hAPP(hAPP(c_COMBB(tc_fun(U_8958,tc_HOL_Obool),tc_fun(U_8958,tc_HOL_Obool),U_8960),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8958,tc_HOL_Obool)),U_8959)),U_8962)),
inference(clausify,[status(thm)],[f_2595_3]) ).
fof(f_2596_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I6_J]) ).
fof(f_2596_2,plain,
! [U_8967,U_8966,U_8965,U_8964,U_8963] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8963,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8964,tc_fun(U_8963,tc_HOL_Obool)),U_8965),U_8966)),U_8967) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8964,tc_fun(U_8963,tc_HOL_Obool)),U_8965),hAPP(hAPP(c_COMBC(U_8964,tc_fun(U_8963,tc_HOL_Obool),tc_fun(U_8963,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8963,tc_HOL_Obool),tc_fun(tc_fun(U_8963,tc_HOL_Obool),tc_fun(U_8963,tc_HOL_Obool)),U_8964),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8963,tc_HOL_Obool))),U_8966)),U_8967)),
inference(variable_rename,[status(thm)],[f_2596_1]) ).
fof(f_2596_3,plain,
! [U_8963,U_8964,U_8965,U_8966,U_8967] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8963,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8964,tc_fun(U_8963,tc_HOL_Obool)),U_8965),U_8966)),U_8967) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8964,tc_fun(U_8963,tc_HOL_Obool)),U_8965),hAPP(hAPP(c_COMBC(U_8964,tc_fun(U_8963,tc_HOL_Obool),tc_fun(U_8963,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8963,tc_HOL_Obool),tc_fun(tc_fun(U_8963,tc_HOL_Obool),tc_fun(U_8963,tc_HOL_Obool)),U_8964),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8963,tc_HOL_Obool))),U_8966)),U_8967)),
inference(definitional_conversion,[status(esa)],[f_2596_2]) ).
cnf(f_2596_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8963,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8964,tc_fun(U_8963,tc_HOL_Obool)),U_8965),U_8966)),U_8967) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8964,tc_fun(U_8963,tc_HOL_Obool)),U_8965),hAPP(hAPP(c_COMBC(U_8964,tc_fun(U_8963,tc_HOL_Obool),tc_fun(U_8963,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8963,tc_HOL_Obool),tc_fun(tc_fun(U_8963,tc_HOL_Obool),tc_fun(U_8963,tc_HOL_Obool)),U_8964),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8963,tc_HOL_Obool))),U_8966)),U_8967)),
inference(clausify,[status(thm)],[f_2596_3]) ).
fof(f_2597_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib2]) ).
fof(f_2597_2,plain,
! [U_8974,U_8973,U_8972,U_8971,U_8970,U_8969,U_8968] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8968,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8969,tc_fun(U_8968,tc_HOL_Obool)),U_8970),U_8971)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8972,tc_fun(U_8968,tc_HOL_Obool)),U_8973),U_8974)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8969,tc_fun(U_8968,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_COMBB(tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8968,tc_HOL_Obool),U_8969),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8972,tc_fun(U_8968,tc_HOL_Obool)),U_8973)),hAPP(hAPP(c_COMBC(U_8969,tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool)),tc_fun(tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool))),U_8969),c_COMBB(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool),U_8972)),hAPP(hAPP(c_COMBB(tc_fun(U_8968,tc_HOL_Obool),tc_fun(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool)),U_8969),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8968,tc_HOL_Obool))),U_8971))),U_8974))),
inference(variable_rename,[status(thm)],[f_2597_1]) ).
fof(f_2597_3,plain,
! [U_8968,U_8969,U_8970,U_8971,U_8972,U_8973,U_8974] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8968,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8969,tc_fun(U_8968,tc_HOL_Obool)),U_8970),U_8971)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8972,tc_fun(U_8968,tc_HOL_Obool)),U_8973),U_8974)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8969,tc_fun(U_8968,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_COMBB(tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8968,tc_HOL_Obool),U_8969),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8972,tc_fun(U_8968,tc_HOL_Obool)),U_8973)),hAPP(hAPP(c_COMBC(U_8969,tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool)),tc_fun(tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool))),U_8969),c_COMBB(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool),U_8972)),hAPP(hAPP(c_COMBB(tc_fun(U_8968,tc_HOL_Obool),tc_fun(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool)),U_8969),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8968,tc_HOL_Obool))),U_8971))),U_8974))),
inference(definitional_conversion,[status(esa)],[f_2597_2]) ).
cnf(f_2597_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8968,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8969,tc_fun(U_8968,tc_HOL_Obool)),U_8970),U_8971)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8972,tc_fun(U_8968,tc_HOL_Obool)),U_8973),U_8974)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8969,tc_fun(U_8968,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_COMBB(tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8968,tc_HOL_Obool),U_8969),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8972,tc_fun(U_8968,tc_HOL_Obool)),U_8973)),hAPP(hAPP(c_COMBC(U_8969,tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool)),tc_fun(tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool)),tc_fun(U_8972,tc_fun(U_8968,tc_HOL_Obool))),U_8969),c_COMBB(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool),U_8972)),hAPP(hAPP(c_COMBB(tc_fun(U_8968,tc_HOL_Obool),tc_fun(tc_fun(U_8968,tc_HOL_Obool),tc_fun(U_8968,tc_HOL_Obool)),U_8969),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8968,tc_HOL_Obool))),U_8971))),U_8974))),
inference(clausify,[status(thm)],[f_2597_3]) ).
fof(f_2598_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).
fof(f_2598_2,plain,
! [U_8977,U_8976,U_8975] : hAPP(c_Set_OCollect(U_8975),hAPP(hAPP(c_COMBS(U_8975,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8975),c_fdisj),U_8976)),U_8977)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8975,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8975),U_8976)),hAPP(c_Set_OCollect(U_8975),U_8977)),
inference(variable_rename,[status(thm)],[f_2598_1]) ).
fof(f_2598_3,plain,
! [U_8975,U_8976,U_8977] : hAPP(c_Set_OCollect(U_8975),hAPP(hAPP(c_COMBS(U_8975,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8975),c_fdisj),U_8976)),U_8977)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8975,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8975),U_8976)),hAPP(c_Set_OCollect(U_8975),U_8977)),
inference(definitional_conversion,[status(esa)],[f_2598_2]) ).
cnf(f_2598_4,plain,
hAPP(c_Set_OCollect(U_8975),hAPP(hAPP(c_COMBS(U_8975,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8975),c_fdisj),U_8976)),U_8977)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8975,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8975),U_8976)),hAPP(c_Set_OCollect(U_8975),U_8977)),
inference(clausify,[status(thm)],[f_2598_3]) ).
fof(f_2599_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( 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))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__fun__def]) ).
fof(f_2599_2,plain,
! [U_8982,U_8981,U_8980,U_8979,U_8978] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8979,U_8978)),U_8980),U_8981),U_8982) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8978),hAPP(U_8980,U_8982)),hAPP(U_8981,U_8982))
| ~ class_Lattices_Olattice(U_8978) ),
inference(variable_rename,[status(thm)],[f_2599_1]) ).
fof(f_2599_3,plain,
! [U_8978,U_8979,U_8980,U_8981,U_8982] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8979,U_8978)),U_8980),U_8981),U_8982) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8978),hAPP(U_8980,U_8982)),hAPP(U_8981,U_8982))
| ~ class_Lattices_Olattice(U_8978) ),
inference(definitional_conversion,[status(esa)],[f_2599_2]) ).
cnf(f_2599_4,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8979,U_8978)),U_8980),U_8981),U_8982) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8978),hAPP(U_8980,U_8982)),hAPP(U_8981,U_8982))
| ~ class_Lattices_Olattice(U_8978) ),
inference(clausify,[status(thm)],[f_2599_3]) ).
fof(f_2600_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__Inter]) ).
fof(f_2600_2,plain,
! [U_8985,U_8984,U_8983] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8983,tc_HOL_Obool)),U_8984),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8983,tc_HOL_Obool),U_8985)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_8983,tc_HOL_Obool),tc_fun(U_8983,tc_HOL_Obool)),U_8985),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8983,tc_HOL_Obool)),U_8984)),
inference(variable_rename,[status(thm)],[f_2600_1]) ).
fof(f_2600_3,plain,
! [U_8983,U_8984,U_8985] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8983,tc_HOL_Obool)),U_8984),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8983,tc_HOL_Obool),U_8985)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_8983,tc_HOL_Obool),tc_fun(U_8983,tc_HOL_Obool)),U_8985),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8983,tc_HOL_Obool)),U_8984)),
inference(definitional_conversion,[status(esa)],[f_2600_2]) ).
cnf(f_2600_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8983,tc_HOL_Obool)),U_8984),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8983,tc_HOL_Obool),U_8985)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_8983,tc_HOL_Obool),tc_fun(U_8983,tc_HOL_Obool)),U_8985),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8983,tc_HOL_Obool)),U_8984)),
inference(clausify,[status(thm)],[f_2600_3]) ).
fof(f_2601_1,plain,
! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__absorb]) ).
fof(f_2601_2,plain,
! [U_8990,U_8989,U_8988,U_8987,U_8986] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8989,tc_HOL_Obool)),hAPP(U_8990,U_8987)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8986,tc_fun(U_8989,tc_HOL_Obool)),U_8988),U_8990)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8986,tc_fun(U_8989,tc_HOL_Obool)),U_8988),U_8990)
| ~ hBOOL(hAPP(hAPP(c_member(U_8986),U_8987),U_8988)) ),
inference(variable_rename,[status(thm)],[f_2601_1]) ).
fof(f_2601_3,plain,
! [U_8986,U_8987,U_8988,U_8989,U_8990] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8989,tc_HOL_Obool)),hAPP(U_8990,U_8987)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8986,tc_fun(U_8989,tc_HOL_Obool)),U_8988),U_8990)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8986,tc_fun(U_8989,tc_HOL_Obool)),U_8988),U_8990)
| ~ hBOOL(hAPP(hAPP(c_member(U_8986),U_8987),U_8988)) ),
inference(definitional_conversion,[status(esa)],[f_2601_2]) ).
cnf(f_2601_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8989,tc_HOL_Obool)),hAPP(U_8990,U_8987)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8986,tc_fun(U_8989,tc_HOL_Obool)),U_8988),U_8990)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8986,tc_fun(U_8989,tc_HOL_Obool)),U_8988),U_8990)
| ~ hBOOL(hAPP(hAPP(c_member(U_8986),U_8987),U_8988)) ),
inference(clausify,[status(thm)],[f_2601_3]) ).
fof(f_2602_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Un__def]) ).
fof(f_2602_2,plain,
! [U_8993,U_8992,U_8991] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8991,tc_HOL_Obool)),U_8992),U_8993) = hAPP(c_Set_OCollect(U_8991),hAPP(hAPP(c_COMBS(U_8991,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8991),c_fdisj),hAPP(hAPP(c_COMBC(U_8991,tc_fun(U_8991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8991)),U_8992))),hAPP(hAPP(c_COMBC(U_8991,tc_fun(U_8991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8991)),U_8993))),
inference(variable_rename,[status(thm)],[f_2602_1]) ).
fof(f_2602_3,plain,
! [U_8991,U_8992,U_8993] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8991,tc_HOL_Obool)),U_8992),U_8993) = hAPP(c_Set_OCollect(U_8991),hAPP(hAPP(c_COMBS(U_8991,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8991),c_fdisj),hAPP(hAPP(c_COMBC(U_8991,tc_fun(U_8991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8991)),U_8992))),hAPP(hAPP(c_COMBC(U_8991,tc_fun(U_8991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8991)),U_8993))),
inference(definitional_conversion,[status(esa)],[f_2602_2]) ).
cnf(f_2602_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8991,tc_HOL_Obool)),U_8992),U_8993) = hAPP(c_Set_OCollect(U_8991),hAPP(hAPP(c_COMBS(U_8991,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8991),c_fdisj),hAPP(hAPP(c_COMBC(U_8991,tc_fun(U_8991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8991)),U_8992))),hAPP(hAPP(c_COMBC(U_8991,tc_fun(U_8991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8991)),U_8993))),
inference(clausify,[status(thm)],[f_2602_3]) ).
fof(f_2603_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__Un]) ).
fof(f_2603_2,plain,
! [U_8998,U_8997,U_8996,U_8995,U_8994] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8994,tc_HOL_Obool)),U_8996),U_8997)),U_8998) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8995,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),U_8996),U_8998)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),U_8997),U_8998)),
inference(variable_rename,[status(thm)],[f_2603_1]) ).
fof(f_2603_3,plain,
! [U_8994,U_8995,U_8996,U_8997,U_8998] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8994,tc_HOL_Obool)),U_8996),U_8997)),U_8998) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8995,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),U_8996),U_8998)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),U_8997),U_8998)),
inference(definitional_conversion,[status(esa)],[f_2603_2]) ).
cnf(f_2603_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8994,tc_HOL_Obool)),U_8996),U_8997)),U_8998) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8995,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),U_8996),U_8998)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8994,tc_fun(U_8995,tc_HOL_Obool)),U_8997),U_8998)),
inference(clausify,[status(thm)],[f_2603_3]) ).
fof(f_2604_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Union__image__eq]) ).
fof(f_2604_2,plain,
! [U_9002,U_9001,U_9000,U_8999] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8999,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9000,tc_fun(U_8999,tc_HOL_Obool),U_9001),U_9002)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9000,tc_fun(U_8999,tc_HOL_Obool)),U_9002),U_9001),
inference(variable_rename,[status(thm)],[f_2604_1]) ).
fof(f_2604_3,plain,
! [U_8999,U_9000,U_9001,U_9002] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8999,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9000,tc_fun(U_8999,tc_HOL_Obool),U_9001),U_9002)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9000,tc_fun(U_8999,tc_HOL_Obool)),U_9002),U_9001),
inference(definitional_conversion,[status(esa)],[f_2604_2]) ).
cnf(f_2604_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8999,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9000,tc_fun(U_8999,tc_HOL_Obool),U_9001),U_9002)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9000,tc_fun(U_8999,tc_HOL_Obool)),U_9002),U_9001),
inference(clausify,[status(thm)],[f_2604_3]) ).
fof(f_2605_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UNION__eq__Union__image]) ).
fof(f_2605_2,plain,
! [U_9006,U_9005,U_9004,U_9003] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9003,tc_fun(U_9004,tc_HOL_Obool)),U_9005),U_9006) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9004,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9003,tc_fun(U_9004,tc_HOL_Obool),U_9006),U_9005)),
inference(variable_rename,[status(thm)],[f_2605_1]) ).
fof(f_2605_3,plain,
! [U_9003,U_9004,U_9005,U_9006] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9003,tc_fun(U_9004,tc_HOL_Obool)),U_9005),U_9006) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9004,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9003,tc_fun(U_9004,tc_HOL_Obool),U_9006),U_9005)),
inference(definitional_conversion,[status(esa)],[f_2605_2]) ).
cnf(f_2605_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9003,tc_fun(U_9004,tc_HOL_Obool)),U_9005),U_9006) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9004,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9003,tc_fun(U_9004,tc_HOL_Obool),U_9006),U_9005)),
inference(clausify,[status(thm)],[f_2605_3]) ).
fof(f_2606_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J]) ).
fof(f_2606_2,plain,
! [U_9011,U_9010,U_9009,U_9008,U_9007] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9008,tc_fun(U_9009,tc_HOL_Obool)),U_9007),hAPP(hAPP(c_COMBC(U_9008,tc_fun(U_9009,tc_HOL_Obool),tc_fun(U_9009,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9009,tc_HOL_Obool),tc_fun(tc_fun(U_9009,tc_HOL_Obool),tc_fun(U_9009,tc_HOL_Obool)),U_9008),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9009,tc_HOL_Obool))),U_9010)),U_9011)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9009,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9008,tc_fun(U_9009,tc_HOL_Obool)),U_9007),U_9010)),U_9011)
| U_9007 = c_Orderings_Obot__class_Obot(tc_fun(U_9008,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9008,tc_fun(U_9009,tc_HOL_Obool)),U_9007),hAPP(hAPP(c_COMBC(U_9008,tc_fun(U_9009,tc_HOL_Obool),tc_fun(U_9009,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9009,tc_HOL_Obool),tc_fun(tc_fun(U_9009,tc_HOL_Obool),tc_fun(U_9009,tc_HOL_Obool)),U_9008),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9009,tc_HOL_Obool))),U_9010)),U_9011)) = c_Orderings_Otop__class_Otop(tc_fun(U_9009,tc_HOL_Obool))
| U_9007 != c_Orderings_Obot__class_Obot(tc_fun(U_9008,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2606_1]) ).
fof(f_2606_3,plain,
( ! [U_9021,U_9019,U_9017,U_9015,U_9013] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9015,tc_fun(U_9017,tc_HOL_Obool)),U_9013),hAPP(hAPP(c_COMBC(U_9015,tc_fun(U_9017,tc_HOL_Obool),tc_fun(U_9017,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9017,tc_HOL_Obool),tc_fun(tc_fun(U_9017,tc_HOL_Obool),tc_fun(U_9017,tc_HOL_Obool)),U_9015),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9017,tc_HOL_Obool))),U_9019)),U_9021)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9017,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9015,tc_fun(U_9017,tc_HOL_Obool)),U_9013),U_9019)),U_9021)
| U_9013 = c_Orderings_Obot__class_Obot(tc_fun(U_9015,tc_HOL_Obool)) )
& ! [U_9020,U_9018,U_9016,U_9014,U_9012] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9014,tc_fun(U_9016,tc_HOL_Obool)),U_9012),hAPP(hAPP(c_COMBC(U_9014,tc_fun(U_9016,tc_HOL_Obool),tc_fun(U_9016,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9016,tc_HOL_Obool),tc_fun(tc_fun(U_9016,tc_HOL_Obool),tc_fun(U_9016,tc_HOL_Obool)),U_9014),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9016,tc_HOL_Obool))),U_9018)),U_9020)) = c_Orderings_Otop__class_Otop(tc_fun(U_9016,tc_HOL_Obool))
| U_9012 != c_Orderings_Obot__class_Obot(tc_fun(U_9014,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2606_2]) ).
fof(f_2606_4,plain,
( ! [U_9013,U_9015,U_9017,U_9019,U_9021] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9015,tc_fun(U_9017,tc_HOL_Obool)),U_9013),hAPP(hAPP(c_COMBC(U_9015,tc_fun(U_9017,tc_HOL_Obool),tc_fun(U_9017,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9017,tc_HOL_Obool),tc_fun(tc_fun(U_9017,tc_HOL_Obool),tc_fun(U_9017,tc_HOL_Obool)),U_9015),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9017,tc_HOL_Obool))),U_9019)),U_9021)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9017,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9015,tc_fun(U_9017,tc_HOL_Obool)),U_9013),U_9019)),U_9021)
| U_9013 = c_Orderings_Obot__class_Obot(tc_fun(U_9015,tc_HOL_Obool)) )
& ! [U_9018,U_9014,U_9012,U_9016,U_9020] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9014,tc_fun(U_9016,tc_HOL_Obool)),U_9012),hAPP(hAPP(c_COMBC(U_9014,tc_fun(U_9016,tc_HOL_Obool),tc_fun(U_9016,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9016,tc_HOL_Obool),tc_fun(tc_fun(U_9016,tc_HOL_Obool),tc_fun(U_9016,tc_HOL_Obool)),U_9014),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9016,tc_HOL_Obool))),U_9018)),U_9020)) = c_Orderings_Otop__class_Otop(tc_fun(U_9016,tc_HOL_Obool))
| U_9012 != c_Orderings_Obot__class_Obot(tc_fun(U_9014,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2606_3]) ).
cnf(f_2606_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9014,tc_fun(U_9016,tc_HOL_Obool)),U_9012),hAPP(hAPP(c_COMBC(U_9014,tc_fun(U_9016,tc_HOL_Obool),tc_fun(U_9016,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9016,tc_HOL_Obool),tc_fun(tc_fun(U_9016,tc_HOL_Obool),tc_fun(U_9016,tc_HOL_Obool)),U_9014),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9016,tc_HOL_Obool))),U_9018)),U_9020)) = c_Orderings_Otop__class_Otop(tc_fun(U_9016,tc_HOL_Obool))
| U_9012 != c_Orderings_Obot__class_Obot(tc_fun(U_9014,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2606_4]) ).
cnf(f_2606_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9015,tc_fun(U_9017,tc_HOL_Obool)),U_9013),hAPP(hAPP(c_COMBC(U_9015,tc_fun(U_9017,tc_HOL_Obool),tc_fun(U_9017,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9017,tc_HOL_Obool),tc_fun(tc_fun(U_9017,tc_HOL_Obool),tc_fun(U_9017,tc_HOL_Obool)),U_9015),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9017,tc_HOL_Obool))),U_9019)),U_9021)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9017,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9015,tc_fun(U_9017,tc_HOL_Obool)),U_9013),U_9019)),U_9021)
| U_9013 = c_Orderings_Obot__class_Obot(tc_fun(U_9015,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2606_4]) ).
fof(f_2607_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J]) ).
fof(f_2607_2,plain,
! [U_9026,U_9025,U_9024,U_9023,U_9022] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9023,tc_fun(U_9024,tc_HOL_Obool)),U_9022),hAPP(hAPP(c_COMBB(tc_fun(U_9024,tc_HOL_Obool),tc_fun(U_9024,tc_HOL_Obool),U_9023),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9024,tc_HOL_Obool)),U_9025)),U_9026)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9024,tc_HOL_Obool)),U_9025),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9023,tc_fun(U_9024,tc_HOL_Obool)),U_9022),U_9026))
| U_9022 = c_Orderings_Obot__class_Obot(tc_fun(U_9023,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9023,tc_fun(U_9024,tc_HOL_Obool)),U_9022),hAPP(hAPP(c_COMBB(tc_fun(U_9024,tc_HOL_Obool),tc_fun(U_9024,tc_HOL_Obool),U_9023),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9024,tc_HOL_Obool)),U_9025)),U_9026)) = c_Orderings_Otop__class_Otop(tc_fun(U_9024,tc_HOL_Obool))
| U_9022 != c_Orderings_Obot__class_Obot(tc_fun(U_9023,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2607_1]) ).
fof(f_2607_3,plain,
( ! [U_9036,U_9034,U_9032,U_9030,U_9028] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9030,tc_fun(U_9032,tc_HOL_Obool)),U_9028),hAPP(hAPP(c_COMBB(tc_fun(U_9032,tc_HOL_Obool),tc_fun(U_9032,tc_HOL_Obool),U_9030),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9032,tc_HOL_Obool)),U_9034)),U_9036)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9032,tc_HOL_Obool)),U_9034),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9030,tc_fun(U_9032,tc_HOL_Obool)),U_9028),U_9036))
| U_9028 = c_Orderings_Obot__class_Obot(tc_fun(U_9030,tc_HOL_Obool)) )
& ! [U_9035,U_9033,U_9031,U_9029,U_9027] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9029,tc_fun(U_9031,tc_HOL_Obool)),U_9027),hAPP(hAPP(c_COMBB(tc_fun(U_9031,tc_HOL_Obool),tc_fun(U_9031,tc_HOL_Obool),U_9029),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9031,tc_HOL_Obool)),U_9033)),U_9035)) = c_Orderings_Otop__class_Otop(tc_fun(U_9031,tc_HOL_Obool))
| U_9027 != c_Orderings_Obot__class_Obot(tc_fun(U_9029,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2607_2]) ).
fof(f_2607_4,plain,
( ! [U_9028,U_9030,U_9032,U_9034,U_9036] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9030,tc_fun(U_9032,tc_HOL_Obool)),U_9028),hAPP(hAPP(c_COMBB(tc_fun(U_9032,tc_HOL_Obool),tc_fun(U_9032,tc_HOL_Obool),U_9030),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9032,tc_HOL_Obool)),U_9034)),U_9036)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9032,tc_HOL_Obool)),U_9034),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9030,tc_fun(U_9032,tc_HOL_Obool)),U_9028),U_9036))
| U_9028 = c_Orderings_Obot__class_Obot(tc_fun(U_9030,tc_HOL_Obool)) )
& ! [U_9033,U_9027,U_9031,U_9029,U_9035] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9029,tc_fun(U_9031,tc_HOL_Obool)),U_9027),hAPP(hAPP(c_COMBB(tc_fun(U_9031,tc_HOL_Obool),tc_fun(U_9031,tc_HOL_Obool),U_9029),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9031,tc_HOL_Obool)),U_9033)),U_9035)) = c_Orderings_Otop__class_Otop(tc_fun(U_9031,tc_HOL_Obool))
| U_9027 != c_Orderings_Obot__class_Obot(tc_fun(U_9029,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2607_3]) ).
cnf(f_2607_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9029,tc_fun(U_9031,tc_HOL_Obool)),U_9027),hAPP(hAPP(c_COMBB(tc_fun(U_9031,tc_HOL_Obool),tc_fun(U_9031,tc_HOL_Obool),U_9029),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9031,tc_HOL_Obool)),U_9033)),U_9035)) = c_Orderings_Otop__class_Otop(tc_fun(U_9031,tc_HOL_Obool))
| U_9027 != c_Orderings_Obot__class_Obot(tc_fun(U_9029,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2607_4]) ).
cnf(f_2607_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9030,tc_fun(U_9032,tc_HOL_Obool)),U_9028),hAPP(hAPP(c_COMBB(tc_fun(U_9032,tc_HOL_Obool),tc_fun(U_9032,tc_HOL_Obool),U_9030),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9032,tc_HOL_Obool)),U_9034)),U_9036)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9032,tc_HOL_Obool)),U_9034),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9030,tc_fun(U_9032,tc_HOL_Obool)),U_9028),U_9036))
| U_9028 = c_Orderings_Obot__class_Obot(tc_fun(U_9030,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2607_4]) ).
fof(f_2608_1,plain,
! [V_x_2,V_S_2,V_R_2,T_b] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_inf__Int__eq]) ).
fof(f_2608_2,plain,
! [U_9040,U_9039,U_9038,U_9037] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9037,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9037,tc_fun(U_9037,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9037)),U_9038)),hAPP(hAPP(c_COMBC(U_9037,tc_fun(U_9037,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9037)),U_9039)),U_9040))
| ~ hBOOL(hAPP(hAPP(c_member(U_9037),U_9040),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9037,tc_HOL_Obool)),U_9038),U_9039))) )
& ( hBOOL(hAPP(hAPP(c_member(U_9037),U_9040),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9037,tc_HOL_Obool)),U_9038),U_9039)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9037,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9037,tc_fun(U_9037,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9037)),U_9038)),hAPP(hAPP(c_COMBC(U_9037,tc_fun(U_9037,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9037)),U_9039)),U_9040)) ) ),
inference(variable_rename,[status(thm)],[f_2608_1]) ).
fof(f_2608_3,plain,
( ! [U_9048,U_9046,U_9044,U_9042] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9042,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9042,tc_fun(U_9042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9042)),U_9044)),hAPP(hAPP(c_COMBC(U_9042,tc_fun(U_9042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9042)),U_9046)),U_9048))
| ~ hBOOL(hAPP(hAPP(c_member(U_9042),U_9048),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9042,tc_HOL_Obool)),U_9044),U_9046))) )
& ! [U_9047,U_9045,U_9043,U_9041] :
( hBOOL(hAPP(hAPP(c_member(U_9041),U_9047),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9041,tc_HOL_Obool)),U_9043),U_9045)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9041,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9041,tc_fun(U_9041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9041)),U_9043)),hAPP(hAPP(c_COMBC(U_9041,tc_fun(U_9041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9041)),U_9045)),U_9047)) ) ),
inference(miniscope,[status(thm)],[f_2608_2]) ).
fof(f_2608_4,plain,
( ! [U_9042,U_9044,U_9046,U_9048] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9042,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9042,tc_fun(U_9042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9042)),U_9044)),hAPP(hAPP(c_COMBC(U_9042,tc_fun(U_9042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9042)),U_9046)),U_9048))
| ~ hBOOL(hAPP(hAPP(c_member(U_9042),U_9048),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9042,tc_HOL_Obool)),U_9044),U_9046))) )
& ! [U_9043,U_9047,U_9045,U_9041] :
( hBOOL(hAPP(hAPP(c_member(U_9041),U_9047),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9041,tc_HOL_Obool)),U_9043),U_9045)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9041,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9041,tc_fun(U_9041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9041)),U_9043)),hAPP(hAPP(c_COMBC(U_9041,tc_fun(U_9041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9041)),U_9045)),U_9047)) ) ),
inference(definitional_conversion,[status(esa)],[f_2608_3]) ).
cnf(f_2608_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9041),U_9047),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9041,tc_HOL_Obool)),U_9043),U_9045)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9041,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9041,tc_fun(U_9041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9041)),U_9043)),hAPP(hAPP(c_COMBC(U_9041,tc_fun(U_9041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9041)),U_9045)),U_9047)) ),
inference(clausify,[status(thm)],[f_2608_4]) ).
cnf(f_2608_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9042,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9042,tc_fun(U_9042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9042)),U_9044)),hAPP(hAPP(c_COMBC(U_9042,tc_fun(U_9042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9042)),U_9046)),U_9048))
| ~ hBOOL(hAPP(hAPP(c_member(U_9042),U_9048),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9042,tc_HOL_Obool)),U_9044),U_9046))) ),
inference(clausify,[status(thm)],[f_2608_4]) ).
fof(f_2609_1,plain,
! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__absorb]) ).
fof(f_2609_2,plain,
! [U_9053,U_9052,U_9051,U_9050,U_9049] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9052,tc_HOL_Obool)),hAPP(U_9053,U_9050)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9049,tc_fun(U_9052,tc_HOL_Obool)),U_9051),U_9053)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9049,tc_fun(U_9052,tc_HOL_Obool)),U_9051),U_9053)
| ~ hBOOL(hAPP(hAPP(c_member(U_9049),U_9050),U_9051)) ),
inference(variable_rename,[status(thm)],[f_2609_1]) ).
fof(f_2609_3,plain,
! [U_9050,U_9049,U_9051,U_9052,U_9053] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9052,tc_HOL_Obool)),hAPP(U_9053,U_9050)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9049,tc_fun(U_9052,tc_HOL_Obool)),U_9051),U_9053)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9049,tc_fun(U_9052,tc_HOL_Obool)),U_9051),U_9053)
| ~ hBOOL(hAPP(hAPP(c_member(U_9049),U_9050),U_9051)) ),
inference(definitional_conversion,[status(esa)],[f_2609_2]) ).
cnf(f_2609_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9052,tc_HOL_Obool)),hAPP(U_9053,U_9050)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9049,tc_fun(U_9052,tc_HOL_Obool)),U_9051),U_9053)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9049,tc_fun(U_9052,tc_HOL_Obool)),U_9051),U_9053)
| ~ hBOOL(hAPP(hAPP(c_member(U_9049),U_9050),U_9051)) ),
inference(clausify,[status(thm)],[f_2609_3]) ).
fof(f_2610_1,plain,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2]) ).
fof(f_2610_2,plain,
! [U_9059,U_9058,U_9057,U_9056,U_9055,U_9054] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9054,tc_fun(U_9055,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9054,tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_fun(U_9055,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9055,tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_fun(U_9055,tc_HOL_Obool)),U_9054),c_COMBC(U_9055,tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9055,tc_prod(U_9054,U_9055)),tc_fun(U_9055,tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),U_9054),hAPP(c_COMBB(tc_prod(U_9054,U_9055),tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool),U_9055),c_member(tc_prod(U_9054,U_9055)))),c_Product__Type_OPair(U_9054,U_9055)))),U_9056)),hAPP(hAPP(c_COMBC(U_9054,tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_fun(U_9055,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9055,tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_fun(U_9055,tc_HOL_Obool)),U_9054),c_COMBC(U_9055,tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9055,tc_prod(U_9054,U_9055)),tc_fun(U_9055,tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),U_9054),hAPP(c_COMBB(tc_prod(U_9054,U_9055),tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool),U_9055),c_member(tc_prod(U_9054,U_9055)))),c_Product__Type_OPair(U_9054,U_9055)))),U_9057)),U_9058),U_9059))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9054,U_9055)),hAPP(hAPP(c_Product__Type_OPair(U_9054,U_9055),U_9058),U_9059)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool)),U_9056),U_9057))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9054,U_9055)),hAPP(hAPP(c_Product__Type_OPair(U_9054,U_9055),U_9058),U_9059)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool)),U_9056),U_9057)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9054,tc_fun(U_9055,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9054,tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_fun(U_9055,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9055,tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_fun(U_9055,tc_HOL_Obool)),U_9054),c_COMBC(U_9055,tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9055,tc_prod(U_9054,U_9055)),tc_fun(U_9055,tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),U_9054),hAPP(c_COMBB(tc_prod(U_9054,U_9055),tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool),U_9055),c_member(tc_prod(U_9054,U_9055)))),c_Product__Type_OPair(U_9054,U_9055)))),U_9056)),hAPP(hAPP(c_COMBC(U_9054,tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_fun(U_9055,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9055,tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_fun(U_9055,tc_HOL_Obool)),U_9054),c_COMBC(U_9055,tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9055,tc_prod(U_9054,U_9055)),tc_fun(U_9055,tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool)),U_9054),hAPP(c_COMBB(tc_prod(U_9054,U_9055),tc_fun(tc_fun(tc_prod(U_9054,U_9055),tc_HOL_Obool),tc_HOL_Obool),U_9055),c_member(tc_prod(U_9054,U_9055)))),c_Product__Type_OPair(U_9054,U_9055)))),U_9057)),U_9058),U_9059)) ) ),
inference(variable_rename,[status(thm)],[f_2610_1]) ).
fof(f_2610_3,plain,
( ! [U_9071,U_9069,U_9067,U_9065,U_9063,U_9061] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9061,tc_fun(U_9063,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9061,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),U_9061),c_COMBC(U_9063,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_prod(U_9061,U_9063)),tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),U_9061),hAPP(c_COMBB(tc_prod(U_9061,U_9063),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool),U_9063),c_member(tc_prod(U_9061,U_9063)))),c_Product__Type_OPair(U_9061,U_9063)))),U_9065)),hAPP(hAPP(c_COMBC(U_9061,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),U_9061),c_COMBC(U_9063,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_prod(U_9061,U_9063)),tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),U_9061),hAPP(c_COMBB(tc_prod(U_9061,U_9063),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool),U_9063),c_member(tc_prod(U_9061,U_9063)))),c_Product__Type_OPair(U_9061,U_9063)))),U_9067)),U_9069),U_9071))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9061,U_9063)),hAPP(hAPP(c_Product__Type_OPair(U_9061,U_9063),U_9069),U_9071)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool)),U_9065),U_9067))) )
& ! [U_9070,U_9068,U_9066,U_9064,U_9062,U_9060] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9060,U_9062)),hAPP(hAPP(c_Product__Type_OPair(U_9060,U_9062),U_9068),U_9070)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool)),U_9064),U_9066)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9060,tc_fun(U_9062,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9060,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),U_9060),c_COMBC(U_9062,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_prod(U_9060,U_9062)),tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),U_9060),hAPP(c_COMBB(tc_prod(U_9060,U_9062),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool),U_9062),c_member(tc_prod(U_9060,U_9062)))),c_Product__Type_OPair(U_9060,U_9062)))),U_9064)),hAPP(hAPP(c_COMBC(U_9060,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),U_9060),c_COMBC(U_9062,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_prod(U_9060,U_9062)),tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),U_9060),hAPP(c_COMBB(tc_prod(U_9060,U_9062),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool),U_9062),c_member(tc_prod(U_9060,U_9062)))),c_Product__Type_OPair(U_9060,U_9062)))),U_9066)),U_9068),U_9070)) ) ),
inference(miniscope,[status(thm)],[f_2610_2]) ).
fof(f_2610_4,plain,
( ! [U_9061,U_9063,U_9065,U_9067,U_9069,U_9071] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9061,tc_fun(U_9063,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9061,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),U_9061),c_COMBC(U_9063,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_prod(U_9061,U_9063)),tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),U_9061),hAPP(c_COMBB(tc_prod(U_9061,U_9063),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool),U_9063),c_member(tc_prod(U_9061,U_9063)))),c_Product__Type_OPair(U_9061,U_9063)))),U_9065)),hAPP(hAPP(c_COMBC(U_9061,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),U_9061),c_COMBC(U_9063,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_prod(U_9061,U_9063)),tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),U_9061),hAPP(c_COMBB(tc_prod(U_9061,U_9063),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool),U_9063),c_member(tc_prod(U_9061,U_9063)))),c_Product__Type_OPair(U_9061,U_9063)))),U_9067)),U_9069),U_9071))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9061,U_9063)),hAPP(hAPP(c_Product__Type_OPair(U_9061,U_9063),U_9069),U_9071)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool)),U_9065),U_9067))) )
& ! [U_9066,U_9062,U_9060,U_9064,U_9068,U_9070] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9060,U_9062)),hAPP(hAPP(c_Product__Type_OPair(U_9060,U_9062),U_9068),U_9070)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool)),U_9064),U_9066)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9060,tc_fun(U_9062,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9060,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),U_9060),c_COMBC(U_9062,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_prod(U_9060,U_9062)),tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),U_9060),hAPP(c_COMBB(tc_prod(U_9060,U_9062),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool),U_9062),c_member(tc_prod(U_9060,U_9062)))),c_Product__Type_OPair(U_9060,U_9062)))),U_9064)),hAPP(hAPP(c_COMBC(U_9060,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),U_9060),c_COMBC(U_9062,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_prod(U_9060,U_9062)),tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),U_9060),hAPP(c_COMBB(tc_prod(U_9060,U_9062),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool),U_9062),c_member(tc_prod(U_9060,U_9062)))),c_Product__Type_OPair(U_9060,U_9062)))),U_9066)),U_9068),U_9070)) ) ),
inference(definitional_conversion,[status(esa)],[f_2610_3]) ).
cnf(f_2610_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9060,U_9062)),hAPP(hAPP(c_Product__Type_OPair(U_9060,U_9062),U_9068),U_9070)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool)),U_9064),U_9066)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9060,tc_fun(U_9062,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9060,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),U_9060),c_COMBC(U_9062,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_prod(U_9060,U_9062)),tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),U_9060),hAPP(c_COMBB(tc_prod(U_9060,U_9062),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool),U_9062),c_member(tc_prod(U_9060,U_9062)))),c_Product__Type_OPair(U_9060,U_9062)))),U_9064)),hAPP(hAPP(c_COMBC(U_9060,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_fun(U_9062,tc_HOL_Obool)),U_9060),c_COMBC(U_9062,tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9062,tc_prod(U_9060,U_9062)),tc_fun(U_9062,tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool)),U_9060),hAPP(c_COMBB(tc_prod(U_9060,U_9062),tc_fun(tc_fun(tc_prod(U_9060,U_9062),tc_HOL_Obool),tc_HOL_Obool),U_9062),c_member(tc_prod(U_9060,U_9062)))),c_Product__Type_OPair(U_9060,U_9062)))),U_9066)),U_9068),U_9070)) ),
inference(clausify,[status(thm)],[f_2610_4]) ).
cnf(f_2610_6,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9061,tc_fun(U_9063,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9061,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),U_9061),c_COMBC(U_9063,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_prod(U_9061,U_9063)),tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),U_9061),hAPP(c_COMBB(tc_prod(U_9061,U_9063),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool),U_9063),c_member(tc_prod(U_9061,U_9063)))),c_Product__Type_OPair(U_9061,U_9063)))),U_9065)),hAPP(hAPP(c_COMBC(U_9061,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_fun(U_9063,tc_HOL_Obool)),U_9061),c_COMBC(U_9063,tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9063,tc_prod(U_9061,U_9063)),tc_fun(U_9063,tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool)),U_9061),hAPP(c_COMBB(tc_prod(U_9061,U_9063),tc_fun(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool),tc_HOL_Obool),U_9063),c_member(tc_prod(U_9061,U_9063)))),c_Product__Type_OPair(U_9061,U_9063)))),U_9067)),U_9069),U_9071))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9061,U_9063)),hAPP(hAPP(c_Product__Type_OPair(U_9061,U_9063),U_9069),U_9071)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9061,U_9063),tc_HOL_Obool)),U_9065),U_9067))) ),
inference(clausify,[status(thm)],[f_2610_4]) ).
fof(f_2611_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__insert]) ).
fof(f_2611_2,plain,
! [U_9076,U_9075,U_9074,U_9073,U_9072] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9072,tc_fun(U_9073,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9072),U_9074),U_9075)),U_9076) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9073,tc_HOL_Obool)),hAPP(U_9076,U_9074)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9072,tc_fun(U_9073,tc_HOL_Obool)),U_9075),U_9076)),
inference(variable_rename,[status(thm)],[f_2611_1]) ).
fof(f_2611_3,plain,
! [U_9072,U_9073,U_9074,U_9075,U_9076] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9072,tc_fun(U_9073,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9072),U_9074),U_9075)),U_9076) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9073,tc_HOL_Obool)),hAPP(U_9076,U_9074)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9072,tc_fun(U_9073,tc_HOL_Obool)),U_9075),U_9076)),
inference(definitional_conversion,[status(esa)],[f_2611_2]) ).
cnf(f_2611_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9072,tc_fun(U_9073,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9072),U_9074),U_9075)),U_9076) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9073,tc_HOL_Obool)),hAPP(U_9076,U_9074)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9072,tc_fun(U_9073,tc_HOL_Obool)),U_9075),U_9076)),
inference(clausify,[status(thm)],[f_2611_3]) ).
fof(f_2612_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J]) ).
fof(f_2612_2,plain,
! [U_9081,U_9080,U_9079,U_9078,U_9077] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9079,tc_HOL_Obool)),U_9080),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9078,tc_fun(U_9079,tc_HOL_Obool)),U_9077),U_9081)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9078,tc_fun(U_9079,tc_HOL_Obool)),U_9077),hAPP(hAPP(c_COMBB(tc_fun(U_9079,tc_HOL_Obool),tc_fun(U_9079,tc_HOL_Obool),U_9078),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9079,tc_HOL_Obool)),U_9080)),U_9081))
| U_9077 = c_Orderings_Obot__class_Obot(tc_fun(U_9078,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9079,tc_HOL_Obool)),U_9080),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9078,tc_fun(U_9079,tc_HOL_Obool)),U_9077),U_9081)) = U_9080
| U_9077 != c_Orderings_Obot__class_Obot(tc_fun(U_9078,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2612_1]) ).
fof(f_2612_3,plain,
( ! [U_9091,U_9089,U_9087,U_9085,U_9083] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9087,tc_HOL_Obool)),U_9089),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9085,tc_fun(U_9087,tc_HOL_Obool)),U_9083),U_9091)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9085,tc_fun(U_9087,tc_HOL_Obool)),U_9083),hAPP(hAPP(c_COMBB(tc_fun(U_9087,tc_HOL_Obool),tc_fun(U_9087,tc_HOL_Obool),U_9085),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9087,tc_HOL_Obool)),U_9089)),U_9091))
| U_9083 = c_Orderings_Obot__class_Obot(tc_fun(U_9085,tc_HOL_Obool)) )
& ! [U_9090,U_9088,U_9086,U_9084,U_9082] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9086,tc_HOL_Obool)),U_9088),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9084,tc_fun(U_9086,tc_HOL_Obool)),U_9082),U_9090)) = U_9088
| U_9082 != c_Orderings_Obot__class_Obot(tc_fun(U_9084,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2612_2]) ).
fof(f_2612_4,plain,
( ! [U_9083,U_9085,U_9087,U_9089,U_9091] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9087,tc_HOL_Obool)),U_9089),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9085,tc_fun(U_9087,tc_HOL_Obool)),U_9083),U_9091)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9085,tc_fun(U_9087,tc_HOL_Obool)),U_9083),hAPP(hAPP(c_COMBB(tc_fun(U_9087,tc_HOL_Obool),tc_fun(U_9087,tc_HOL_Obool),U_9085),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9087,tc_HOL_Obool)),U_9089)),U_9091))
| U_9083 = c_Orderings_Obot__class_Obot(tc_fun(U_9085,tc_HOL_Obool)) )
& ! [U_9084,U_9082,U_9086,U_9088,U_9090] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9086,tc_HOL_Obool)),U_9088),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9084,tc_fun(U_9086,tc_HOL_Obool)),U_9082),U_9090)) = U_9088
| U_9082 != c_Orderings_Obot__class_Obot(tc_fun(U_9084,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2612_3]) ).
cnf(f_2612_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9086,tc_HOL_Obool)),U_9088),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9084,tc_fun(U_9086,tc_HOL_Obool)),U_9082),U_9090)) = U_9088
| U_9082 != c_Orderings_Obot__class_Obot(tc_fun(U_9084,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2612_4]) ).
cnf(f_2612_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9087,tc_HOL_Obool)),U_9089),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9085,tc_fun(U_9087,tc_HOL_Obool)),U_9083),U_9091)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9085,tc_fun(U_9087,tc_HOL_Obool)),U_9083),hAPP(hAPP(c_COMBB(tc_fun(U_9087,tc_HOL_Obool),tc_fun(U_9087,tc_HOL_Obool),U_9085),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9087,tc_HOL_Obool)),U_9089)),U_9091))
| U_9083 = c_Orderings_Obot__class_Obot(tc_fun(U_9085,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2612_4]) ).
fof(f_2613_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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) = 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))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J]) ).
fof(f_2613_2,plain,
! [U_9096,U_9095,U_9094,U_9093,U_9092] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9094,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9093,tc_fun(U_9094,tc_HOL_Obool)),U_9092),U_9095)),U_9096) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9093,tc_fun(U_9094,tc_HOL_Obool)),U_9092),hAPP(hAPP(c_COMBC(U_9093,tc_fun(U_9094,tc_HOL_Obool),tc_fun(U_9094,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9094,tc_HOL_Obool),tc_fun(tc_fun(U_9094,tc_HOL_Obool),tc_fun(U_9094,tc_HOL_Obool)),U_9093),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9094,tc_HOL_Obool))),U_9095)),U_9096))
| U_9092 = c_Orderings_Obot__class_Obot(tc_fun(U_9093,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9094,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9093,tc_fun(U_9094,tc_HOL_Obool)),U_9092),U_9095)),U_9096) = U_9096
| U_9092 != c_Orderings_Obot__class_Obot(tc_fun(U_9093,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2613_1]) ).
fof(f_2613_3,plain,
( ! [U_9106,U_9104,U_9102,U_9100,U_9098] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9102,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9100,tc_fun(U_9102,tc_HOL_Obool)),U_9098),U_9104)),U_9106) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9100,tc_fun(U_9102,tc_HOL_Obool)),U_9098),hAPP(hAPP(c_COMBC(U_9100,tc_fun(U_9102,tc_HOL_Obool),tc_fun(U_9102,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9102,tc_HOL_Obool),tc_fun(tc_fun(U_9102,tc_HOL_Obool),tc_fun(U_9102,tc_HOL_Obool)),U_9100),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9102,tc_HOL_Obool))),U_9104)),U_9106))
| U_9098 = c_Orderings_Obot__class_Obot(tc_fun(U_9100,tc_HOL_Obool)) )
& ! [U_9105,U_9103,U_9101,U_9099,U_9097] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9101,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9099,tc_fun(U_9101,tc_HOL_Obool)),U_9097),U_9103)),U_9105) = U_9105
| U_9097 != c_Orderings_Obot__class_Obot(tc_fun(U_9099,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2613_2]) ).
fof(f_2613_4,plain,
( ! [U_9098,U_9106,U_9100,U_9102,U_9104] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9102,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9100,tc_fun(U_9102,tc_HOL_Obool)),U_9098),U_9104)),U_9106) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9100,tc_fun(U_9102,tc_HOL_Obool)),U_9098),hAPP(hAPP(c_COMBC(U_9100,tc_fun(U_9102,tc_HOL_Obool),tc_fun(U_9102,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9102,tc_HOL_Obool),tc_fun(tc_fun(U_9102,tc_HOL_Obool),tc_fun(U_9102,tc_HOL_Obool)),U_9100),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9102,tc_HOL_Obool))),U_9104)),U_9106))
| U_9098 = c_Orderings_Obot__class_Obot(tc_fun(U_9100,tc_HOL_Obool)) )
& ! [U_9101,U_9103,U_9099,U_9105,U_9097] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9101,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9099,tc_fun(U_9101,tc_HOL_Obool)),U_9097),U_9103)),U_9105) = U_9105
| U_9097 != c_Orderings_Obot__class_Obot(tc_fun(U_9099,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2613_3]) ).
cnf(f_2613_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9101,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9099,tc_fun(U_9101,tc_HOL_Obool)),U_9097),U_9103)),U_9105) = U_9105
| U_9097 != c_Orderings_Obot__class_Obot(tc_fun(U_9099,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2613_4]) ).
cnf(f_2613_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9102,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9100,tc_fun(U_9102,tc_HOL_Obool)),U_9098),U_9104)),U_9106) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9100,tc_fun(U_9102,tc_HOL_Obool)),U_9098),hAPP(hAPP(c_COMBC(U_9100,tc_fun(U_9102,tc_HOL_Obool),tc_fun(U_9102,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9102,tc_HOL_Obool),tc_fun(tc_fun(U_9102,tc_HOL_Obool),tc_fun(U_9102,tc_HOL_Obool)),U_9100),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9102,tc_HOL_Obool))),U_9104)),U_9106))
| U_9098 = c_Orderings_Obot__class_Obot(tc_fun(U_9100,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2613_4]) ).
fof(f_2614_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__Union]) ).
fof(f_2614_2,plain,
! [U_9109,U_9108,U_9107] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9107,tc_HOL_Obool)),U_9108),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9107,tc_HOL_Obool),U_9109)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9107,tc_HOL_Obool),tc_fun(U_9107,tc_HOL_Obool)),U_9109),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9107,tc_HOL_Obool)),U_9108)),
inference(variable_rename,[status(thm)],[f_2614_1]) ).
fof(f_2614_3,plain,
! [U_9109,U_9108,U_9107] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9107,tc_HOL_Obool)),U_9108),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9107,tc_HOL_Obool),U_9109)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9107,tc_HOL_Obool),tc_fun(U_9107,tc_HOL_Obool)),U_9109),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9107,tc_HOL_Obool)),U_9108)),
inference(definitional_conversion,[status(esa)],[f_2614_2]) ).
cnf(f_2614_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9107,tc_HOL_Obool)),U_9108),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9107,tc_HOL_Obool),U_9109)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9107,tc_HOL_Obool),tc_fun(U_9107,tc_HOL_Obool)),U_9109),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9107,tc_HOL_Obool)),U_9108)),
inference(clausify,[status(thm)],[f_2614_3]) ).
fof(f_2615_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__Union2]) ).
fof(f_2615_2,plain,
! [U_9112,U_9111,U_9110] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9110,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9110,tc_HOL_Obool),U_9111)),U_9112) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool)),U_9111),hAPP(hAPP(c_COMBC(tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9110,tc_HOL_Obool))),U_9112)),
inference(variable_rename,[status(thm)],[f_2615_1]) ).
fof(f_2615_3,plain,
! [U_9110,U_9111,U_9112] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9110,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9110,tc_HOL_Obool),U_9111)),U_9112) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool)),U_9111),hAPP(hAPP(c_COMBC(tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9110,tc_HOL_Obool))),U_9112)),
inference(definitional_conversion,[status(esa)],[f_2615_2]) ).
cnf(f_2615_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9110,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9110,tc_HOL_Obool),U_9111)),U_9112) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool)),U_9111),hAPP(hAPP(c_COMBC(tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool),tc_fun(U_9110,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9110,tc_HOL_Obool))),U_9112)),
inference(clausify,[status(thm)],[f_2615_3]) ).
fof(f_2616_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I5_J]) ).
fof(f_2616_2,plain,
! [U_9117,U_9116,U_9115,U_9114,U_9113] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9113,tc_fun(U_9114,tc_HOL_Obool)),U_9115),hAPP(hAPP(c_COMBB(tc_fun(U_9114,tc_HOL_Obool),tc_fun(U_9114,tc_HOL_Obool),U_9113),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9114,tc_HOL_Obool)),U_9116)),U_9117)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9114,tc_HOL_Obool)),U_9116),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9113,tc_fun(U_9114,tc_HOL_Obool)),U_9115),U_9117)),
inference(variable_rename,[status(thm)],[f_2616_1]) ).
fof(f_2616_3,plain,
! [U_9113,U_9114,U_9115,U_9116,U_9117] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9113,tc_fun(U_9114,tc_HOL_Obool)),U_9115),hAPP(hAPP(c_COMBB(tc_fun(U_9114,tc_HOL_Obool),tc_fun(U_9114,tc_HOL_Obool),U_9113),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9114,tc_HOL_Obool)),U_9116)),U_9117)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9114,tc_HOL_Obool)),U_9116),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9113,tc_fun(U_9114,tc_HOL_Obool)),U_9115),U_9117)),
inference(definitional_conversion,[status(esa)],[f_2616_2]) ).
cnf(f_2616_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9113,tc_fun(U_9114,tc_HOL_Obool)),U_9115),hAPP(hAPP(c_COMBB(tc_fun(U_9114,tc_HOL_Obool),tc_fun(U_9114,tc_HOL_Obool),U_9113),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9114,tc_HOL_Obool)),U_9116)),U_9117)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9114,tc_HOL_Obool)),U_9116),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9113,tc_fun(U_9114,tc_HOL_Obool)),U_9115),U_9117)),
inference(clausify,[status(thm)],[f_2616_3]) ).
fof(f_2617_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I4_J]) ).
fof(f_2617_2,plain,
! [U_9122,U_9121,U_9120,U_9119,U_9118] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9118,tc_fun(U_9119,tc_HOL_Obool)),U_9120),hAPP(hAPP(c_COMBC(U_9118,tc_fun(U_9119,tc_HOL_Obool),tc_fun(U_9119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9119,tc_HOL_Obool),tc_fun(tc_fun(U_9119,tc_HOL_Obool),tc_fun(U_9119,tc_HOL_Obool)),U_9118),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9119,tc_HOL_Obool))),U_9121)),U_9122)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9119,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9118,tc_fun(U_9119,tc_HOL_Obool)),U_9120),U_9121)),U_9122),
inference(variable_rename,[status(thm)],[f_2617_1]) ).
fof(f_2617_3,plain,
! [U_9118,U_9119,U_9120,U_9121,U_9122] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9118,tc_fun(U_9119,tc_HOL_Obool)),U_9120),hAPP(hAPP(c_COMBC(U_9118,tc_fun(U_9119,tc_HOL_Obool),tc_fun(U_9119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9119,tc_HOL_Obool),tc_fun(tc_fun(U_9119,tc_HOL_Obool),tc_fun(U_9119,tc_HOL_Obool)),U_9118),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9119,tc_HOL_Obool))),U_9121)),U_9122)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9119,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9118,tc_fun(U_9119,tc_HOL_Obool)),U_9120),U_9121)),U_9122),
inference(definitional_conversion,[status(esa)],[f_2617_2]) ).
cnf(f_2617_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9118,tc_fun(U_9119,tc_HOL_Obool)),U_9120),hAPP(hAPP(c_COMBC(U_9118,tc_fun(U_9119,tc_HOL_Obool),tc_fun(U_9119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9119,tc_HOL_Obool),tc_fun(tc_fun(U_9119,tc_HOL_Obool),tc_fun(U_9119,tc_HOL_Obool)),U_9118),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9119,tc_HOL_Obool))),U_9121)),U_9122)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9119,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9118,tc_fun(U_9119,tc_HOL_Obool)),U_9120),U_9121)),U_9122),
inference(clausify,[status(thm)],[f_2617_3]) ).
fof(f_2618_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I5_J]) ).
fof(f_2618_2,plain,
! [U_9127,U_9126,U_9125,U_9124,U_9123] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9123,tc_HOL_Obool)),U_9124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9125,tc_fun(U_9123,tc_HOL_Obool)),U_9126),U_9127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9125,tc_fun(U_9123,tc_HOL_Obool)),U_9126),hAPP(hAPP(c_COMBB(tc_fun(U_9123,tc_HOL_Obool),tc_fun(U_9123,tc_HOL_Obool),U_9125),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9123,tc_HOL_Obool)),U_9124)),U_9127)),
inference(variable_rename,[status(thm)],[f_2618_1]) ).
fof(f_2618_3,plain,
! [U_9123,U_9124,U_9125,U_9126,U_9127] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9123,tc_HOL_Obool)),U_9124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9125,tc_fun(U_9123,tc_HOL_Obool)),U_9126),U_9127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9125,tc_fun(U_9123,tc_HOL_Obool)),U_9126),hAPP(hAPP(c_COMBB(tc_fun(U_9123,tc_HOL_Obool),tc_fun(U_9123,tc_HOL_Obool),U_9125),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9123,tc_HOL_Obool)),U_9124)),U_9127)),
inference(definitional_conversion,[status(esa)],[f_2618_2]) ).
cnf(f_2618_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9123,tc_HOL_Obool)),U_9124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9125,tc_fun(U_9123,tc_HOL_Obool)),U_9126),U_9127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9125,tc_fun(U_9123,tc_HOL_Obool)),U_9126),hAPP(hAPP(c_COMBB(tc_fun(U_9123,tc_HOL_Obool),tc_fun(U_9123,tc_HOL_Obool),U_9125),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9123,tc_HOL_Obool)),U_9124)),U_9127)),
inference(clausify,[status(thm)],[f_2618_3]) ).
fof(f_2619_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib]) ).
fof(f_2619_2,plain,
! [U_9132,U_9131,U_9130,U_9129,U_9128] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9128,tc_HOL_Obool)),U_9129),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9130,tc_fun(U_9128,tc_HOL_Obool)),U_9131),U_9132)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9130,tc_fun(U_9128,tc_HOL_Obool)),U_9131),hAPP(hAPP(c_COMBB(tc_fun(U_9128,tc_HOL_Obool),tc_fun(U_9128,tc_HOL_Obool),U_9130),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9128,tc_HOL_Obool)),U_9129)),U_9132)),
inference(variable_rename,[status(thm)],[f_2619_1]) ).
fof(f_2619_3,plain,
! [U_9128,U_9129,U_9130,U_9131,U_9132] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9128,tc_HOL_Obool)),U_9129),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9130,tc_fun(U_9128,tc_HOL_Obool)),U_9131),U_9132)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9130,tc_fun(U_9128,tc_HOL_Obool)),U_9131),hAPP(hAPP(c_COMBB(tc_fun(U_9128,tc_HOL_Obool),tc_fun(U_9128,tc_HOL_Obool),U_9130),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9128,tc_HOL_Obool)),U_9129)),U_9132)),
inference(definitional_conversion,[status(esa)],[f_2619_2]) ).
cnf(f_2619_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9128,tc_HOL_Obool)),U_9129),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9130,tc_fun(U_9128,tc_HOL_Obool)),U_9131),U_9132)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9130,tc_fun(U_9128,tc_HOL_Obool)),U_9131),hAPP(hAPP(c_COMBB(tc_fun(U_9128,tc_HOL_Obool),tc_fun(U_9128,tc_HOL_Obool),U_9130),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9128,tc_HOL_Obool)),U_9129)),U_9132)),
inference(clausify,[status(thm)],[f_2619_3]) ).
fof(f_2620_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I4_J]) ).
fof(f_2620_2,plain,
! [U_9137,U_9136,U_9135,U_9134,U_9133] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9133,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9134,tc_fun(U_9133,tc_HOL_Obool)),U_9135),U_9136)),U_9137) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9134,tc_fun(U_9133,tc_HOL_Obool)),U_9135),hAPP(hAPP(c_COMBC(U_9134,tc_fun(U_9133,tc_HOL_Obool),tc_fun(U_9133,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9133,tc_HOL_Obool),tc_fun(tc_fun(U_9133,tc_HOL_Obool),tc_fun(U_9133,tc_HOL_Obool)),U_9134),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9133,tc_HOL_Obool))),U_9136)),U_9137)),
inference(variable_rename,[status(thm)],[f_2620_1]) ).
fof(f_2620_3,plain,
! [U_9133,U_9134,U_9135,U_9136,U_9137] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9133,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9134,tc_fun(U_9133,tc_HOL_Obool)),U_9135),U_9136)),U_9137) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9134,tc_fun(U_9133,tc_HOL_Obool)),U_9135),hAPP(hAPP(c_COMBC(U_9134,tc_fun(U_9133,tc_HOL_Obool),tc_fun(U_9133,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9133,tc_HOL_Obool),tc_fun(tc_fun(U_9133,tc_HOL_Obool),tc_fun(U_9133,tc_HOL_Obool)),U_9134),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9133,tc_HOL_Obool))),U_9136)),U_9137)),
inference(definitional_conversion,[status(esa)],[f_2620_2]) ).
cnf(f_2620_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9133,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9134,tc_fun(U_9133,tc_HOL_Obool)),U_9135),U_9136)),U_9137) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9134,tc_fun(U_9133,tc_HOL_Obool)),U_9135),hAPP(hAPP(c_COMBC(U_9134,tc_fun(U_9133,tc_HOL_Obool),tc_fun(U_9133,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9133,tc_HOL_Obool),tc_fun(tc_fun(U_9133,tc_HOL_Obool),tc_fun(U_9133,tc_HOL_Obool)),U_9134),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9133,tc_HOL_Obool))),U_9136)),U_9137)),
inference(clausify,[status(thm)],[f_2620_3]) ).
fof(f_2621_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib2]) ).
fof(f_2621_2,plain,
! [U_9144,U_9143,U_9142,U_9141,U_9140,U_9139,U_9138] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9138,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9139,tc_fun(U_9138,tc_HOL_Obool)),U_9140),U_9141)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9142,tc_fun(U_9138,tc_HOL_Obool)),U_9143),U_9144)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9139,tc_fun(U_9138,tc_HOL_Obool)),U_9140),hAPP(hAPP(c_COMBB(tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9138,tc_HOL_Obool),U_9139),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9142,tc_fun(U_9138,tc_HOL_Obool)),U_9143)),hAPP(hAPP(c_COMBC(U_9139,tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool)),tc_fun(tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool))),U_9139),c_COMBB(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool),U_9142)),hAPP(hAPP(c_COMBB(tc_fun(U_9138,tc_HOL_Obool),tc_fun(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool)),U_9139),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9138,tc_HOL_Obool))),U_9141))),U_9144))),
inference(variable_rename,[status(thm)],[f_2621_1]) ).
fof(f_2621_3,plain,
! [U_9138,U_9139,U_9140,U_9141,U_9142,U_9143,U_9144] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9138,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9139,tc_fun(U_9138,tc_HOL_Obool)),U_9140),U_9141)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9142,tc_fun(U_9138,tc_HOL_Obool)),U_9143),U_9144)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9139,tc_fun(U_9138,tc_HOL_Obool)),U_9140),hAPP(hAPP(c_COMBB(tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9138,tc_HOL_Obool),U_9139),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9142,tc_fun(U_9138,tc_HOL_Obool)),U_9143)),hAPP(hAPP(c_COMBC(U_9139,tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool)),tc_fun(tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool))),U_9139),c_COMBB(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool),U_9142)),hAPP(hAPP(c_COMBB(tc_fun(U_9138,tc_HOL_Obool),tc_fun(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool)),U_9139),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9138,tc_HOL_Obool))),U_9141))),U_9144))),
inference(definitional_conversion,[status(esa)],[f_2621_2]) ).
cnf(f_2621_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9138,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9139,tc_fun(U_9138,tc_HOL_Obool)),U_9140),U_9141)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9142,tc_fun(U_9138,tc_HOL_Obool)),U_9143),U_9144)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9139,tc_fun(U_9138,tc_HOL_Obool)),U_9140),hAPP(hAPP(c_COMBB(tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9138,tc_HOL_Obool),U_9139),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9142,tc_fun(U_9138,tc_HOL_Obool)),U_9143)),hAPP(hAPP(c_COMBC(U_9139,tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool)),tc_fun(tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool)),tc_fun(U_9142,tc_fun(U_9138,tc_HOL_Obool))),U_9139),c_COMBB(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool),U_9142)),hAPP(hAPP(c_COMBB(tc_fun(U_9138,tc_HOL_Obool),tc_fun(tc_fun(U_9138,tc_HOL_Obool),tc_fun(U_9138,tc_HOL_Obool)),U_9139),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9138,tc_HOL_Obool))),U_9141))),U_9144))),
inference(clausify,[status(thm)],[f_2621_3]) ).
fof(f_2622_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__Int__distrib]) ).
fof(f_2622_2,plain,
! [U_9149,U_9148,U_9147,U_9146,U_9145] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),hAPP(hAPP(c_COMBS(U_9145,tc_fun(U_9146,tc_HOL_Obool),tc_fun(U_9146,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9146,tc_HOL_Obool),tc_fun(tc_fun(U_9146,tc_HOL_Obool),tc_fun(U_9146,tc_HOL_Obool)),U_9145),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9146,tc_HOL_Obool))),U_9148)),U_9149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9146,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),U_9148)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),U_9149)),
inference(variable_rename,[status(thm)],[f_2622_1]) ).
fof(f_2622_3,plain,
! [U_9145,U_9146,U_9147,U_9148,U_9149] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),hAPP(hAPP(c_COMBS(U_9145,tc_fun(U_9146,tc_HOL_Obool),tc_fun(U_9146,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9146,tc_HOL_Obool),tc_fun(tc_fun(U_9146,tc_HOL_Obool),tc_fun(U_9146,tc_HOL_Obool)),U_9145),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9146,tc_HOL_Obool))),U_9148)),U_9149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9146,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),U_9148)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),U_9149)),
inference(definitional_conversion,[status(esa)],[f_2622_2]) ).
cnf(f_2622_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),hAPP(hAPP(c_COMBS(U_9145,tc_fun(U_9146,tc_HOL_Obool),tc_fun(U_9146,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9146,tc_HOL_Obool),tc_fun(tc_fun(U_9146,tc_HOL_Obool),tc_fun(U_9146,tc_HOL_Obool)),U_9145),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9146,tc_HOL_Obool))),U_9148)),U_9149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9146,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),U_9148)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9145,tc_fun(U_9146,tc_HOL_Obool)),U_9147),U_9149)),
inference(clausify,[status(thm)],[f_2622_3]) ).
fof(f_2623_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).
fof(f_2623_2,plain,
! [U_9152,U_9151,U_9150] : hAPP(c_Set_OCollect(U_9150),hAPP(hAPP(c_COMBS(U_9150,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9150),c_fconj),U_9151)),U_9152)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9150,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9150),U_9151)),hAPP(c_Set_OCollect(U_9150),U_9152)),
inference(variable_rename,[status(thm)],[f_2623_1]) ).
fof(f_2623_3,plain,
! [U_9150,U_9151,U_9152] : hAPP(c_Set_OCollect(U_9150),hAPP(hAPP(c_COMBS(U_9150,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9150),c_fconj),U_9151)),U_9152)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9150,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9150),U_9151)),hAPP(c_Set_OCollect(U_9150),U_9152)),
inference(definitional_conversion,[status(esa)],[f_2623_2]) ).
cnf(f_2623_4,plain,
hAPP(c_Set_OCollect(U_9150),hAPP(hAPP(c_COMBS(U_9150,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9150),c_fconj),U_9151)),U_9152)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9150,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9150),U_9151)),hAPP(c_Set_OCollect(U_9150),U_9152)),
inference(clausify,[status(thm)],[f_2623_3]) ).
fof(f_2624_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( 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))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__fun__def]) ).
fof(f_2624_2,plain,
! [U_9157,U_9156,U_9155,U_9154,U_9153] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9154,U_9153)),U_9155),U_9156),U_9157) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9153),hAPP(U_9155,U_9157)),hAPP(U_9156,U_9157))
| ~ class_Lattices_Olattice(U_9153) ),
inference(variable_rename,[status(thm)],[f_2624_1]) ).
fof(f_2624_3,plain,
! [U_9153,U_9154,U_9155,U_9156,U_9157] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9154,U_9153)),U_9155),U_9156),U_9157) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9153),hAPP(U_9155,U_9157)),hAPP(U_9156,U_9157))
| ~ class_Lattices_Olattice(U_9153) ),
inference(definitional_conversion,[status(esa)],[f_2624_2]) ).
cnf(f_2624_4,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9154,U_9153)),U_9155),U_9156),U_9157) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9153),hAPP(U_9155,U_9157)),hAPP(U_9156,U_9157))
| ~ class_Lattices_Olattice(U_9153) ),
inference(clausify,[status(thm)],[f_2624_3]) ).
fof(f_2625_1,plain,
! [V_Pa_2,V_A_2,V_x_2,T_b] :
( ( 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))))
| ~ hBOOL(hAPP(V_Pa_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).
fof(f_2625_2,plain,
! [U_9161,U_9160,U_9159,U_9158] :
( ( hBOOL(hAPP(hAPP(c_member(U_9158),U_9159),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9158,tc_HOL_Obool)),U_9160),hAPP(c_Set_OCollect(U_9158),U_9161))))
| ~ hBOOL(hAPP(U_9161,U_9159))
| ~ hBOOL(hAPP(hAPP(c_member(U_9158),U_9159),U_9160)) )
& ( ( hBOOL(hAPP(U_9161,U_9159))
& hBOOL(hAPP(hAPP(c_member(U_9158),U_9159),U_9160)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9158),U_9159),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9158,tc_HOL_Obool)),U_9160),hAPP(c_Set_OCollect(U_9158),U_9161)))) ) ),
inference(variable_rename,[status(thm)],[f_2625_1]) ).
fof(f_2625_3,plain,
( ! [U_9169,U_9167,U_9165,U_9163] :
( hBOOL(hAPP(hAPP(c_member(U_9163),U_9165),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9163,tc_HOL_Obool)),U_9167),hAPP(c_Set_OCollect(U_9163),U_9169))))
| ~ hBOOL(hAPP(U_9169,U_9165))
| ~ hBOOL(hAPP(hAPP(c_member(U_9163),U_9165),U_9167)) )
& ! [U_9168,U_9166,U_9164,U_9162] :
( ( hBOOL(hAPP(U_9168,U_9164))
& hBOOL(hAPP(hAPP(c_member(U_9162),U_9164),U_9166)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9162),U_9164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9162,tc_HOL_Obool)),U_9166),hAPP(c_Set_OCollect(U_9162),U_9168)))) ) ),
inference(miniscope,[status(thm)],[f_2625_2]) ).
fof(f_2625_4,plain,
( ! [U_9168,U_9164,U_9162,U_9166] :
( hBOOL(hAPP(U_9168,U_9164))
| ~ sP778(U_9168,U_9164,U_9162,U_9166) )
& ! [U_9168,U_9164,U_9162,U_9166] :
( hBOOL(hAPP(hAPP(c_member(U_9162),U_9164),U_9166))
| ~ sP778(U_9168,U_9164,U_9162,U_9166) )
& ! [U_9165,U_9163,U_9169,U_9167] :
( hBOOL(hAPP(hAPP(c_member(U_9163),U_9165),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9163,tc_HOL_Obool)),U_9167),hAPP(c_Set_OCollect(U_9163),U_9169))))
| ~ hBOOL(hAPP(U_9169,U_9165))
| ~ hBOOL(hAPP(hAPP(c_member(U_9163),U_9165),U_9167)) )
& ! [U_9168,U_9164,U_9162,U_9166] :
( sP778(U_9168,U_9164,U_9162,U_9166)
| ~ hBOOL(hAPP(hAPP(c_member(U_9162),U_9164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9162,tc_HOL_Obool)),U_9166),hAPP(c_Set_OCollect(U_9162),U_9168)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP778])],[f_2625_3]) ).
cnf(f_2625_5,plain,
( sP778(U_9168,U_9164,U_9162,U_9166)
| ~ hBOOL(hAPP(hAPP(c_member(U_9162),U_9164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9162,tc_HOL_Obool)),U_9166),hAPP(c_Set_OCollect(U_9162),U_9168)))) ),
inference(clausify,[status(thm)],[f_2625_4]) ).
cnf(f_2625_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9163),U_9165),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9163,tc_HOL_Obool)),U_9167),hAPP(c_Set_OCollect(U_9163),U_9169))))
| ~ hBOOL(hAPP(U_9169,U_9165))
| ~ hBOOL(hAPP(hAPP(c_member(U_9163),U_9165),U_9167)) ),
inference(clausify,[status(thm)],[f_2625_4]) ).
cnf(f_2625_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_9162),U_9164),U_9166))
| ~ sP778(U_9168,U_9164,U_9162,U_9166) ),
inference(clausify,[status(thm)],[f_2625_4]) ).
cnf(f_2625_8,plain,
( hBOOL(hAPP(U_9168,U_9164))
| ~ sP778(U_9168,U_9164,U_9162,U_9166) ),
inference(clausify,[status(thm)],[f_2625_4]) ).
fof(f_2626_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Int__def]) ).
fof(f_2626_2,plain,
! [U_9172,U_9171,U_9170] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9170,tc_HOL_Obool)),U_9171),U_9172) = hAPP(c_Set_OCollect(U_9170),hAPP(hAPP(c_COMBS(U_9170,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9170),c_fconj),hAPP(hAPP(c_COMBC(U_9170,tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9170)),U_9171))),hAPP(hAPP(c_COMBC(U_9170,tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9170)),U_9172))),
inference(variable_rename,[status(thm)],[f_2626_1]) ).
fof(f_2626_3,plain,
! [U_9170,U_9172,U_9171] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9170,tc_HOL_Obool)),U_9171),U_9172) = hAPP(c_Set_OCollect(U_9170),hAPP(hAPP(c_COMBS(U_9170,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9170),c_fconj),hAPP(hAPP(c_COMBC(U_9170,tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9170)),U_9171))),hAPP(hAPP(c_COMBC(U_9170,tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9170)),U_9172))),
inference(definitional_conversion,[status(esa)],[f_2626_2]) ).
cnf(f_2626_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9170,tc_HOL_Obool)),U_9171),U_9172) = hAPP(c_Set_OCollect(U_9170),hAPP(hAPP(c_COMBS(U_9170,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9170),c_fconj),hAPP(hAPP(c_COMBC(U_9170,tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9170)),U_9171))),hAPP(hAPP(c_COMBC(U_9170,tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9170)),U_9172))),
inference(clausify,[status(thm)],[f_2626_3]) ).
fof(f_2627_1,plain,
! [V_n_2,V_k_2,V_m_2,V_f_2,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,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))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl]) ).
fof(f_2627_2,plain,
! [U_9177,U_9176,U_9175,U_9174,U_9173] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9173),U_9174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9175),U_9176)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9177),U_9176))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9173),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9173,tc_Nat_Onat),U_9174),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9176))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_9175),U_9177))
| ~ class_Groups_Ocomm__monoid__add(U_9173) ),
inference(variable_rename,[status(thm)],[f_2627_1]) ).
fof(f_2627_3,plain,
! [U_9173,U_9174,U_9175,U_9176,U_9177] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9173),U_9174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9175),U_9176)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9177),U_9176))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9173),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9173,tc_Nat_Onat),U_9174),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9176))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_9175),U_9177))
| ~ class_Groups_Ocomm__monoid__add(U_9173) ),
inference(definitional_conversion,[status(esa)],[f_2627_2]) ).
cnf(f_2627_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9173),U_9174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9175),U_9176)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9177),U_9176))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9173),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9173,tc_Nat_Onat),U_9174),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9176))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_9175),U_9177))
| ~ class_Groups_Ocomm__monoid__add(U_9173) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
fof(f_2628_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_card__eq__setsum]) ).
fof(f_2628_2,plain,
! [U_9179,U_9178] : hAPP(c_Finite__Set_Ocard(U_9178),U_9179) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9178,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_9178),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_9179),
inference(variable_rename,[status(thm)],[f_2628_1]) ).
fof(f_2628_3,plain,
! [U_9178,U_9179] : hAPP(c_Finite__Set_Ocard(U_9178),U_9179) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9178,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_9178),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_9179),
inference(definitional_conversion,[status(esa)],[f_2628_2]) ).
cnf(f_2628_4,plain,
hAPP(c_Finite__Set_Ocard(U_9178),U_9179) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9178,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_9178),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_9179),
inference(clausify,[status(thm)],[f_2628_3]) ).
fof(f_2629_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_UN__UN__finite__eq]) ).
fof(f_2629_2,plain,
! [U_9181,U_9180] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,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(U_9180,tc_HOL_Obool)),tc_fun(U_9180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool)),tc_fun(U_9180,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_9181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_9181),
inference(variable_rename,[status(thm)],[f_2629_1]) ).
fof(f_2629_3,plain,
! [U_9180,U_9181] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,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(U_9180,tc_HOL_Obool)),tc_fun(U_9180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool)),tc_fun(U_9180,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_9181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_9181),
inference(definitional_conversion,[status(esa)],[f_2629_2]) ).
cnf(f_2629_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,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(U_9180,tc_HOL_Obool)),tc_fun(U_9180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool)),tc_fun(U_9180,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_9181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9180,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_9181),
inference(clausify,[status(thm)],[f_2629_3]) ).
fof(f_2630_1,plain,
! [V_n_2,V_m_2,V_f_2,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,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))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl]) ).
fof(f_2630_2,plain,
! [U_9185,U_9184,U_9183,U_9182] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9182),U_9183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9184),hAPP(c_Nat_OSuc,U_9185))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9182),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9182,tc_Nat_Onat),U_9183),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9184,U_9185))
| ~ class_Groups_Ocomm__monoid__add(U_9182) ),
inference(variable_rename,[status(thm)],[f_2630_1]) ).
fof(f_2630_3,plain,
! [U_9182,U_9183,U_9184,U_9185] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9182),U_9183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9184),hAPP(c_Nat_OSuc,U_9185))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9182),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9182,tc_Nat_Onat),U_9183),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9184,U_9185))
| ~ class_Groups_Ocomm__monoid__add(U_9182) ),
inference(definitional_conversion,[status(esa)],[f_2630_2]) ).
cnf(f_2630_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9182),U_9183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9184),hAPP(c_Nat_OSuc,U_9185))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9182),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9182,tc_Nat_Onat),U_9183),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9184,U_9185))
| ~ class_Groups_Ocomm__monoid__add(U_9182) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
fof(f_2631_1,plain,
! [V_A_2,V_f_2,T_b] :
( 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))
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J]) ).
fof(f_2631_2,plain,
! [U_9188,U_9187,U_9186] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9186),U_9187),U_9188) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9186),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9186,tc_Int_Oint),U_9187),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9188))
| ~ class_Groups_Ocomm__monoid__mult(U_9186)
| ~ class_Groups_Ocomm__monoid__add(U_9186) ),
inference(variable_rename,[status(thm)],[f_2631_1]) ).
fof(f_2631_3,plain,
! [U_9186,U_9187,U_9188] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9186),U_9187),U_9188) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9186),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9186,tc_Int_Oint),U_9187),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9188))
| ~ class_Groups_Ocomm__monoid__mult(U_9186)
| ~ class_Groups_Ocomm__monoid__add(U_9186) ),
inference(definitional_conversion,[status(esa)],[f_2631_2]) ).
cnf(f_2631_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9186),U_9187),U_9188) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9186),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9186,tc_Int_Oint),U_9187),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9188))
| ~ class_Groups_Ocomm__monoid__mult(U_9186)
| ~ class_Groups_Ocomm__monoid__add(U_9186) ),
inference(clausify,[status(thm)],[f_2631_3]) ).
fof(f_2632_1,plain,
! [V_n_2,V_k_2,V_m_2,V_f_2,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,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))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl]) ).
fof(f_2632_2,plain,
! [U_9193,U_9192,U_9191,U_9190,U_9189] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9189),U_9190),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9191),U_9192),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9193),U_9192))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9189),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9189,tc_Nat_Onat),U_9190),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9192))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9191,U_9193))
| ~ class_Groups_Ocomm__monoid__add(U_9189) ),
inference(variable_rename,[status(thm)],[f_2632_1]) ).
fof(f_2632_3,plain,
! [U_9189,U_9190,U_9191,U_9192,U_9193] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9189),U_9190),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9191),U_9192),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9193),U_9192))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9189),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9189,tc_Nat_Onat),U_9190),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9192))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9191,U_9193))
| ~ class_Groups_Ocomm__monoid__add(U_9189) ),
inference(definitional_conversion,[status(esa)],[f_2632_2]) ).
cnf(f_2632_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9189),U_9190),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9191),U_9192),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9193),U_9192))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9189),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9189,tc_Nat_Onat),U_9190),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9192))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9191,U_9193))
| ~ class_Groups_Ocomm__monoid__add(U_9189) ),
inference(clausify,[status(thm)],[f_2632_3]) ).
fof(f_2633_1,plain,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat_Osize_I1_J]) ).
fof(f_2633_2,plain,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_2633_1]) ).
cnf(f_2633_3,plain,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2633_2]) ).
fof(f_2634_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(f_2634_2,plain,
! [U_9194] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9194) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9194)),
inference(variable_rename,[status(thm)],[f_2634_1]) ).
fof(f_2634_3,plain,
! [U_9194] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9194) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9194)),
inference(definitional_conversion,[status(esa)],[f_2634_2]) ).
cnf(f_2634_4,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9194) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9194)),
inference(clausify,[status(thm)],[f_2634_3]) ).
fof(f_2635_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__Bit0]) ).
fof(f_2635_2,plain,
! [U_9195] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_9195)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_9195)),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))),
inference(variable_rename,[status(thm)],[f_2635_1]) ).
fof(f_2635_3,plain,
! [U_9195] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_9195)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_9195)),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))),
inference(definitional_conversion,[status(esa)],[f_2635_2]) ).
cnf(f_2635_4,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_9195)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_9195)),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))),
inference(clausify,[status(thm)],[f_2635_3]) ).
fof(f_2636_1,plain,
! [V_n_2,V_f_2,T_b,V_A_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| 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))) ),
inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite]) ).
fof(f_2636_2,plain,
! [U_9199,U_9198,U_9197,U_9196] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9197),U_9196))
| U_9196 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9197,U_9198),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)),U_9199))) ),
inference(variable_rename,[status(thm)],[f_2636_1]) ).
fof(f_2636_3,plain,
! [U_9196,U_9197,U_9198,U_9199] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9197),U_9196))
| U_9196 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9197,U_9198),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)),U_9199))) ),
inference(definitional_conversion,[status(esa)],[f_2636_2]) ).
cnf(f_2636_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9197),U_9196))
| U_9196 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9197,U_9198),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)),U_9199))) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
fof(f_2637_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_finite__M__bounded__by__nat]) ).
fof(f_2637_2,plain,
! [U_9201,U_9200] : 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),U_9200)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9201))))),
inference(variable_rename,[status(thm)],[f_2637_1]) ).
fof(f_2637_3,plain,
! [U_9200,U_9201] : 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),U_9200)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9201))))),
inference(definitional_conversion,[status(esa)],[f_2637_2]) ).
cnf(f_2637_4,plain,
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),U_9200)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9201))))),
inference(clausify,[status(thm)],[f_2637_3]) ).
fof(f_2638_1,plain,
! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
( ( ( 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))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ 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)) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_INF__less__iff]) ).
fof(f_2638_2,plain,
! [U_9208,U_9207,U_9206,U_9205,U_9204] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9205,U_9204),U_9206),U_9207)),U_9208))
| ! [U_9203] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(U_9207,U_9203)),U_9208))
| ~ hBOOL(hAPP(hAPP(c_member(U_9205),U_9203),U_9206)) ) )
& ( ? [U_9202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(U_9207,U_9202)),U_9208))
& hBOOL(hAPP(hAPP(c_member(U_9205),U_9202),U_9206)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9205,U_9204),U_9206),U_9207)),U_9208)) ) )
| ~ class_Orderings_Olinorder(U_9204)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9204) ),
inference(variable_rename,[status(thm)],[f_2638_1]) ).
fof(f_2638_3,plain,
! [U_9208,U_9207,U_9206,U_9205,U_9204] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9205,U_9204),U_9206),U_9207)),U_9208))
| ! [U_9203] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(U_9207,U_9203)),U_9208))
| ~ hBOOL(hAPP(hAPP(c_member(U_9205),U_9203),U_9206)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(U_9207,sK245(U_9208,U_9207,U_9206,U_9205,U_9204))),U_9208))
& hBOOL(hAPP(hAPP(c_member(U_9205),sK245(U_9208,U_9207,U_9206,U_9205,U_9204)),U_9206)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9205,U_9204),U_9206),U_9207)),U_9208)) ) )
| ~ class_Orderings_Olinorder(U_9204)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9204) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_9202,sK245(U_9208,U_9207,U_9206,U_9205,U_9204))],[f_2638_2]) ).
fof(f_2638_4,plain,
( ! [U_9204,U_9205,U_9206,U_9207,U_9208] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(U_9207,sK245(U_9208,U_9207,U_9206,U_9205,U_9204))),U_9208))
| ~ sP779(U_9204,U_9205,U_9206,U_9207,U_9208) )
& ! [U_9204,U_9205,U_9206,U_9207,U_9208] :
( hBOOL(hAPP(hAPP(c_member(U_9205),sK245(U_9208,U_9207,U_9206,U_9205,U_9204)),U_9206))
| ~ sP779(U_9204,U_9205,U_9206,U_9207,U_9208) )
& ! [U_9203,U_9204,U_9205,U_9206,U_9207,U_9208] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9205,U_9204),U_9206),U_9207)),U_9208))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(U_9207,U_9203)),U_9208))
| ~ hBOOL(hAPP(hAPP(c_member(U_9205),U_9203),U_9206))
| ~ sP780(U_9203,U_9204,U_9205,U_9206,U_9207,U_9208) )
& ! [U_9203,U_9204,U_9205,U_9206,U_9207,U_9208] :
( sP779(U_9204,U_9205,U_9206,U_9207,U_9208)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9205,U_9204),U_9206),U_9207)),U_9208))
| ~ sP780(U_9203,U_9204,U_9205,U_9206,U_9207,U_9208) )
& ! [U_9203,U_9204,U_9205,U_9206,U_9207,U_9208] :
( sP780(U_9203,U_9204,U_9205,U_9206,U_9207,U_9208)
| ~ class_Orderings_Olinorder(U_9204)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9204) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP779,sP780])],[f_2638_3]) ).
cnf(f_2638_5,plain,
( sP780(U_9203,U_9204,U_9205,U_9206,U_9207,U_9208)
| ~ class_Orderings_Olinorder(U_9204)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9204) ),
inference(clausify,[status(thm)],[f_2638_4]) ).
cnf(f_2638_6,plain,
( sP779(U_9204,U_9205,U_9206,U_9207,U_9208)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9205,U_9204),U_9206),U_9207)),U_9208))
| ~ sP780(U_9203,U_9204,U_9205,U_9206,U_9207,U_9208) ),
inference(clausify,[status(thm)],[f_2638_4]) ).
cnf(f_2638_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9205,U_9204),U_9206),U_9207)),U_9208))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(U_9207,U_9203)),U_9208))
| ~ hBOOL(hAPP(hAPP(c_member(U_9205),U_9203),U_9206))
| ~ sP780(U_9203,U_9204,U_9205,U_9206,U_9207,U_9208) ),
inference(clausify,[status(thm)],[f_2638_4]) ).
cnf(f_2638_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9205),sK245(U_9208,U_9207,U_9206,U_9205,U_9204)),U_9206))
| ~ sP779(U_9204,U_9205,U_9206,U_9207,U_9208) ),
inference(clausify,[status(thm)],[f_2638_4]) ).
cnf(f_2638_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9204),hAPP(U_9207,sK245(U_9208,U_9207,U_9206,U_9205,U_9204))),U_9208))
| ~ sP779(U_9204,U_9205,U_9206,U_9207,U_9208) ),
inference(clausify,[status(thm)],[f_2638_4]) ).
fof(f_2639_1,plain,
! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
( ( ( 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)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ 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))) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__SUP__iff]) ).
fof(f_2639_2,plain,
! [U_9215,U_9214,U_9213,U_9212,U_9211] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,U_9211),U_9214),U_9215)))
| ! [U_9210] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(U_9215,U_9210)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9213),U_9210),U_9214)) ) )
& ( ? [U_9209] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(U_9215,U_9209)))
& hBOOL(hAPP(hAPP(c_member(U_9213),U_9209),U_9214)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,U_9211),U_9214),U_9215))) ) )
| ~ class_Orderings_Olinorder(U_9211)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9211) ),
inference(variable_rename,[status(thm)],[f_2639_1]) ).
fof(f_2639_3,plain,
! [U_9215,U_9214,U_9213,U_9212,U_9211] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,U_9211),U_9214),U_9215)))
| ! [U_9210] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(U_9215,U_9210)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9213),U_9210),U_9214)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(U_9215,sK246(U_9215,U_9214,U_9213,U_9212,U_9211))))
& hBOOL(hAPP(hAPP(c_member(U_9213),sK246(U_9215,U_9214,U_9213,U_9212,U_9211)),U_9214)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,U_9211),U_9214),U_9215))) ) )
| ~ class_Orderings_Olinorder(U_9211)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9211) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_9209,sK246(U_9215,U_9214,U_9213,U_9212,U_9211))],[f_2639_2]) ).
fof(f_2639_4,plain,
( ! [U_9213,U_9212,U_9214,U_9211,U_9215] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(U_9215,sK246(U_9215,U_9214,U_9213,U_9212,U_9211))))
| ~ sP781(U_9213,U_9212,U_9214,U_9211,U_9215) )
& ! [U_9213,U_9212,U_9214,U_9211,U_9215] :
( hBOOL(hAPP(hAPP(c_member(U_9213),sK246(U_9215,U_9214,U_9213,U_9212,U_9211)),U_9214))
| ~ sP781(U_9213,U_9212,U_9214,U_9211,U_9215) )
& ! [U_9213,U_9210,U_9212,U_9214,U_9211,U_9215] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,U_9211),U_9214),U_9215)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(U_9215,U_9210)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9213),U_9210),U_9214))
| ~ sP782(U_9213,U_9210,U_9212,U_9214,U_9211,U_9215) )
& ! [U_9213,U_9210,U_9212,U_9214,U_9211,U_9215] :
( sP781(U_9213,U_9212,U_9214,U_9211,U_9215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,U_9211),U_9214),U_9215)))
| ~ sP782(U_9213,U_9210,U_9212,U_9214,U_9211,U_9215) )
& ! [U_9213,U_9210,U_9212,U_9214,U_9211,U_9215] :
( sP782(U_9213,U_9210,U_9212,U_9214,U_9211,U_9215)
| ~ class_Orderings_Olinorder(U_9211)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9211) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP781,sP782])],[f_2639_3]) ).
cnf(f_2639_5,plain,
( sP782(U_9213,U_9210,U_9212,U_9214,U_9211,U_9215)
| ~ class_Orderings_Olinorder(U_9211)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9211) ),
inference(clausify,[status(thm)],[f_2639_4]) ).
cnf(f_2639_6,plain,
( sP781(U_9213,U_9212,U_9214,U_9211,U_9215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,U_9211),U_9214),U_9215)))
| ~ sP782(U_9213,U_9210,U_9212,U_9214,U_9211,U_9215) ),
inference(clausify,[status(thm)],[f_2639_4]) ).
cnf(f_2639_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,U_9211),U_9214),U_9215)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(U_9215,U_9210)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9213),U_9210),U_9214))
| ~ sP782(U_9213,U_9210,U_9212,U_9214,U_9211,U_9215) ),
inference(clausify,[status(thm)],[f_2639_4]) ).
cnf(f_2639_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9213),sK246(U_9215,U_9214,U_9213,U_9212,U_9211)),U_9214))
| ~ sP781(U_9213,U_9212,U_9214,U_9211,U_9215) ),
inference(clausify,[status(thm)],[f_2639_4]) ).
cnf(f_2639_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9211),U_9212),hAPP(U_9215,sK246(U_9215,U_9214,U_9213,U_9212,U_9211))))
| ~ sP781(U_9213,U_9212,U_9214,U_9211,U_9215) ),
inference(clausify,[status(thm)],[f_2639_4]) ).
fof(f_2640_1,plain,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( 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))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__addf]) ).
fof(f_2640_2,plain,
! [U_9220,U_9219,U_9218,U_9217,U_9216] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),hAPP(hAPP(c_COMBS(U_9217,U_9216,U_9216),hAPP(hAPP(c_COMBB(U_9216,tc_fun(U_9216,U_9216),U_9217),c_Groups_Oplus__class_Oplus(U_9216)),U_9218)),U_9219)),U_9220) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9216),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),U_9218),U_9220)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),U_9219),U_9220))
| ~ class_Groups_Ocomm__monoid__add(U_9216) ),
inference(variable_rename,[status(thm)],[f_2640_1]) ).
fof(f_2640_3,plain,
! [U_9217,U_9218,U_9219,U_9216,U_9220] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),hAPP(hAPP(c_COMBS(U_9217,U_9216,U_9216),hAPP(hAPP(c_COMBB(U_9216,tc_fun(U_9216,U_9216),U_9217),c_Groups_Oplus__class_Oplus(U_9216)),U_9218)),U_9219)),U_9220) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9216),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),U_9218),U_9220)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),U_9219),U_9220))
| ~ class_Groups_Ocomm__monoid__add(U_9216) ),
inference(definitional_conversion,[status(esa)],[f_2640_2]) ).
cnf(f_2640_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),hAPP(hAPP(c_COMBS(U_9217,U_9216,U_9216),hAPP(hAPP(c_COMBB(U_9216,tc_fun(U_9216,U_9216),U_9217),c_Groups_Oplus__class_Oplus(U_9216)),U_9218)),U_9219)),U_9220) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9216),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),U_9218),U_9220)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9217,U_9216),U_9219),U_9220))
| ~ class_Groups_Ocomm__monoid__add(U_9216) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
fof(f_2641_1,plain,
! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
( ( ( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ 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))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__INF__iff]) ).
fof(f_2641_2,plain,
! [U_9227,U_9226,U_9225,U_9224,U_9223] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9225,U_9223),U_9226),U_9227)))
| ? [U_9222] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(U_9227,U_9222)))
& hBOOL(hAPP(hAPP(c_member(U_9225),U_9222),U_9226)) ) )
& ( ! [U_9221] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(U_9227,U_9221)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9225),U_9221),U_9226)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9225,U_9223),U_9226),U_9227))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9223) ),
inference(variable_rename,[status(thm)],[f_2641_1]) ).
fof(f_2641_3,plain,
! [U_9227,U_9226,U_9225,U_9224,U_9223] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9225,U_9223),U_9226),U_9227)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(U_9227,sK247(U_9227,U_9226,U_9225,U_9224,U_9223))))
& hBOOL(hAPP(hAPP(c_member(U_9225),sK247(U_9227,U_9226,U_9225,U_9224,U_9223)),U_9226)) ) )
& ( ! [U_9221] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(U_9227,U_9221)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9225),U_9221),U_9226)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9225,U_9223),U_9226),U_9227))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9223) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_9222,sK247(U_9227,U_9226,U_9225,U_9224,U_9223))],[f_2641_2]) ).
fof(f_2641_4,plain,
( ! [U_9223,U_9224,U_9225,U_9226,U_9227] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(U_9227,sK247(U_9227,U_9226,U_9225,U_9224,U_9223))))
| ~ sP783(U_9223,U_9224,U_9225,U_9226,U_9227) )
& ! [U_9223,U_9224,U_9225,U_9226,U_9227] :
( hBOOL(hAPP(hAPP(c_member(U_9225),sK247(U_9227,U_9226,U_9225,U_9224,U_9223)),U_9226))
| ~ sP783(U_9223,U_9224,U_9225,U_9226,U_9227) )
& ! [U_9221,U_9223,U_9224,U_9225,U_9226,U_9227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9225,U_9223),U_9226),U_9227)))
| sP783(U_9223,U_9224,U_9225,U_9226,U_9227)
| ~ sP784(U_9221,U_9223,U_9224,U_9225,U_9226,U_9227) )
& ! [U_9221,U_9223,U_9224,U_9225,U_9226,U_9227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(U_9227,U_9221)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9225),U_9221),U_9226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9225,U_9223),U_9226),U_9227)))
| ~ sP784(U_9221,U_9223,U_9224,U_9225,U_9226,U_9227) )
& ! [U_9221,U_9223,U_9224,U_9225,U_9226,U_9227] :
( sP784(U_9221,U_9223,U_9224,U_9225,U_9226,U_9227)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9223) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP783,sP784])],[f_2641_3]) ).
cnf(f_2641_5,plain,
( sP784(U_9221,U_9223,U_9224,U_9225,U_9226,U_9227)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9223) ),
inference(clausify,[status(thm)],[f_2641_4]) ).
cnf(f_2641_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(U_9227,U_9221)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9225),U_9221),U_9226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9225,U_9223),U_9226),U_9227)))
| ~ sP784(U_9221,U_9223,U_9224,U_9225,U_9226,U_9227) ),
inference(clausify,[status(thm)],[f_2641_4]) ).
cnf(f_2641_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9225,U_9223),U_9226),U_9227)))
| sP783(U_9223,U_9224,U_9225,U_9226,U_9227)
| ~ sP784(U_9221,U_9223,U_9224,U_9225,U_9226,U_9227) ),
inference(clausify,[status(thm)],[f_2641_4]) ).
cnf(f_2641_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9225),sK247(U_9227,U_9226,U_9225,U_9224,U_9223)),U_9226))
| ~ sP783(U_9223,U_9224,U_9225,U_9226,U_9227) ),
inference(clausify,[status(thm)],[f_2641_4]) ).
cnf(f_2641_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9223),U_9224),hAPP(U_9227,sK247(U_9227,U_9226,U_9225,U_9224,U_9223))))
| ~ sP783(U_9223,U_9224,U_9225,U_9226,U_9227) ),
inference(clausify,[status(thm)],[f_2641_4]) ).
fof(f_2642_1,plain,
! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
( ( ( 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))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ 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)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_SUP__le__iff]) ).
fof(f_2642_2,plain,
! [U_9234,U_9233,U_9232,U_9231,U_9230] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9231,U_9230),U_9232),U_9233)),U_9234))
| ? [U_9229] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(U_9233,U_9229)),U_9234))
& hBOOL(hAPP(hAPP(c_member(U_9231),U_9229),U_9232)) ) )
& ( ! [U_9228] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(U_9233,U_9228)),U_9234))
| ~ hBOOL(hAPP(hAPP(c_member(U_9231),U_9228),U_9232)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9231,U_9230),U_9232),U_9233)),U_9234)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9230) ),
inference(variable_rename,[status(thm)],[f_2642_1]) ).
fof(f_2642_3,plain,
! [U_9234,U_9233,U_9232,U_9231,U_9230] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9231,U_9230),U_9232),U_9233)),U_9234))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(U_9233,sK248(U_9234,U_9233,U_9232,U_9231,U_9230))),U_9234))
& hBOOL(hAPP(hAPP(c_member(U_9231),sK248(U_9234,U_9233,U_9232,U_9231,U_9230)),U_9232)) ) )
& ( ! [U_9228] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(U_9233,U_9228)),U_9234))
| ~ hBOOL(hAPP(hAPP(c_member(U_9231),U_9228),U_9232)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9231,U_9230),U_9232),U_9233)),U_9234)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9230) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_9229,sK248(U_9234,U_9233,U_9232,U_9231,U_9230))],[f_2642_2]) ).
fof(f_2642_4,plain,
( ! [U_9230,U_9231,U_9232,U_9233,U_9234] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(U_9233,sK248(U_9234,U_9233,U_9232,U_9231,U_9230))),U_9234))
| ~ sP785(U_9230,U_9231,U_9232,U_9233,U_9234) )
& ! [U_9230,U_9231,U_9232,U_9233,U_9234] :
( hBOOL(hAPP(hAPP(c_member(U_9231),sK248(U_9234,U_9233,U_9232,U_9231,U_9230)),U_9232))
| ~ sP785(U_9230,U_9231,U_9232,U_9233,U_9234) )
& ! [U_9230,U_9231,U_9232,U_9228,U_9233,U_9234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9231,U_9230),U_9232),U_9233)),U_9234))
| sP785(U_9230,U_9231,U_9232,U_9233,U_9234)
| ~ sP786(U_9230,U_9231,U_9232,U_9228,U_9233,U_9234) )
& ! [U_9230,U_9231,U_9232,U_9228,U_9233,U_9234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(U_9233,U_9228)),U_9234))
| ~ hBOOL(hAPP(hAPP(c_member(U_9231),U_9228),U_9232))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9231,U_9230),U_9232),U_9233)),U_9234))
| ~ sP786(U_9230,U_9231,U_9232,U_9228,U_9233,U_9234) )
& ! [U_9230,U_9231,U_9232,U_9228,U_9233,U_9234] :
( sP786(U_9230,U_9231,U_9232,U_9228,U_9233,U_9234)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9230) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP785,sP786])],[f_2642_3]) ).
cnf(f_2642_5,plain,
( sP786(U_9230,U_9231,U_9232,U_9228,U_9233,U_9234)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9230) ),
inference(clausify,[status(thm)],[f_2642_4]) ).
cnf(f_2642_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(U_9233,U_9228)),U_9234))
| ~ hBOOL(hAPP(hAPP(c_member(U_9231),U_9228),U_9232))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9231,U_9230),U_9232),U_9233)),U_9234))
| ~ sP786(U_9230,U_9231,U_9232,U_9228,U_9233,U_9234) ),
inference(clausify,[status(thm)],[f_2642_4]) ).
cnf(f_2642_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9231,U_9230),U_9232),U_9233)),U_9234))
| sP785(U_9230,U_9231,U_9232,U_9233,U_9234)
| ~ sP786(U_9230,U_9231,U_9232,U_9228,U_9233,U_9234) ),
inference(clausify,[status(thm)],[f_2642_4]) ).
cnf(f_2642_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9231),sK248(U_9234,U_9233,U_9232,U_9231,U_9230)),U_9232))
| ~ sP785(U_9230,U_9231,U_9232,U_9233,U_9234) ),
inference(clausify,[status(thm)],[f_2642_4]) ).
cnf(f_2642_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9230),hAPP(U_9233,sK248(U_9234,U_9233,U_9232,U_9231,U_9230))),U_9234))
| ~ sP785(U_9230,U_9231,U_9232,U_9233,U_9234) ),
inference(clausify,[status(thm)],[f_2642_4]) ).
fof(f_2643_1,plain,
! [V_A_2,V_I_2,T_c,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_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
| ? [B_x] :
( ~ 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)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) )
& ( ! [B_x] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__subset__iff]) ).
fof(f_2643_2,plain,
! [U_9241,U_9240,U_9239,U_9238,U_9237] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9237,tc_HOL_Obool)),U_9238),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9239,tc_fun(U_9237,tc_HOL_Obool)),U_9240),U_9241)))
| ? [U_9236] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9237,tc_HOL_Obool)),U_9238),hAPP(U_9241,U_9236)))
& hBOOL(hAPP(hAPP(c_member(U_9239),U_9236),U_9240)) ) )
& ( ! [U_9235] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9237,tc_HOL_Obool)),U_9238),hAPP(U_9241,U_9235)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9239),U_9235),U_9240)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9237,tc_HOL_Obool)),U_9238),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9239,tc_fun(U_9237,tc_HOL_Obool)),U_9240),U_9241))) ) ),
inference(variable_rename,[status(thm)],[f_2643_1]) ).
fof(f_2643_3,plain,
( ! [U_9251,U_9249,U_9247,U_9245,U_9243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9243,tc_HOL_Obool)),U_9245),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9247,tc_fun(U_9243,tc_HOL_Obool)),U_9249),U_9251)))
| ? [U_9236] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9243,tc_HOL_Obool)),U_9245),hAPP(U_9251,U_9236)))
& hBOOL(hAPP(hAPP(c_member(U_9247),U_9236),U_9249)) ) )
& ! [U_9250,U_9248,U_9246,U_9244,U_9242] :
( ! [U_9235] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9242,tc_HOL_Obool)),U_9244),hAPP(U_9250,U_9235)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9246),U_9235),U_9248)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9242,tc_HOL_Obool)),U_9244),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9246,tc_fun(U_9242,tc_HOL_Obool)),U_9248),U_9250))) ) ),
inference(miniscope,[status(thm)],[f_2643_2]) ).
fof(f_2643_4,plain,
( ! [U_9251,U_9249,U_9247,U_9245,U_9243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9243,tc_HOL_Obool)),U_9245),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9247,tc_fun(U_9243,tc_HOL_Obool)),U_9249),U_9251)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9243,tc_HOL_Obool)),U_9245),hAPP(U_9251,sK249(U_9251,U_9249,U_9247,U_9245,U_9243))))
& hBOOL(hAPP(hAPP(c_member(U_9247),sK249(U_9251,U_9249,U_9247,U_9245,U_9243)),U_9249)) ) )
& ! [U_9250,U_9248,U_9246,U_9244,U_9242] :
( ! [U_9235] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9242,tc_HOL_Obool)),U_9244),hAPP(U_9250,U_9235)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9246),U_9235),U_9248)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9242,tc_HOL_Obool)),U_9244),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9246,tc_fun(U_9242,tc_HOL_Obool)),U_9248),U_9250))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_9236,sK249(U_9251,U_9249,U_9247,U_9245,U_9243))],[f_2643_3]) ).
fof(f_2643_5,plain,
( ! [U_9247,U_9245,U_9243,U_9249,U_9251] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9243,tc_HOL_Obool)),U_9245),hAPP(U_9251,sK249(U_9251,U_9249,U_9247,U_9245,U_9243))))
| ~ sP787(U_9247,U_9245,U_9243,U_9249,U_9251) )
& ! [U_9247,U_9245,U_9243,U_9249,U_9251] :
( hBOOL(hAPP(hAPP(c_member(U_9247),sK249(U_9251,U_9249,U_9247,U_9245,U_9243)),U_9249))
| ~ sP787(U_9247,U_9245,U_9243,U_9249,U_9251) )
& ! [U_9247,U_9245,U_9243,U_9249,U_9251] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9243,tc_HOL_Obool)),U_9245),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9247,tc_fun(U_9243,tc_HOL_Obool)),U_9249),U_9251)))
| sP787(U_9247,U_9245,U_9243,U_9249,U_9251) )
& ! [U_9246,U_9244,U_9248,U_9242,U_9235,U_9250] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9242,tc_HOL_Obool)),U_9244),hAPP(U_9250,U_9235)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9246),U_9235),U_9248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9242,tc_HOL_Obool)),U_9244),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9246,tc_fun(U_9242,tc_HOL_Obool)),U_9248),U_9250))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP787])],[f_2643_4]) ).
cnf(f_2643_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9242,tc_HOL_Obool)),U_9244),hAPP(U_9250,U_9235)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9246),U_9235),U_9248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9242,tc_HOL_Obool)),U_9244),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9246,tc_fun(U_9242,tc_HOL_Obool)),U_9248),U_9250))) ),
inference(clausify,[status(thm)],[f_2643_5]) ).
cnf(f_2643_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9243,tc_HOL_Obool)),U_9245),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9247,tc_fun(U_9243,tc_HOL_Obool)),U_9249),U_9251)))
| sP787(U_9247,U_9245,U_9243,U_9249,U_9251) ),
inference(clausify,[status(thm)],[f_2643_5]) ).
cnf(f_2643_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9247),sK249(U_9251,U_9249,U_9247,U_9245,U_9243)),U_9249))
| ~ sP787(U_9247,U_9245,U_9243,U_9249,U_9251) ),
inference(clausify,[status(thm)],[f_2643_5]) ).
cnf(f_2643_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9243,tc_HOL_Obool)),U_9245),hAPP(U_9251,sK249(U_9251,U_9249,U_9247,U_9245,U_9243))))
| ~ sP787(U_9247,U_9245,U_9243,U_9249,U_9251) ),
inference(clausify,[status(thm)],[f_2643_5]) ).
fof(f_2644_1,plain,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
( ( 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))
| ? [B_x] :
( ~ 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))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) )
& ( ! [B_x] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__subset__iff]) ).
fof(f_2644_2,plain,
! [U_9258,U_9257,U_9256,U_9255,U_9254] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9254,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9255,tc_fun(U_9254,tc_HOL_Obool)),U_9256),U_9257)),U_9258))
| ? [U_9253] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9254,tc_HOL_Obool)),hAPP(U_9257,U_9253)),U_9258))
& hBOOL(hAPP(hAPP(c_member(U_9255),U_9253),U_9256)) ) )
& ( ! [U_9252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9254,tc_HOL_Obool)),hAPP(U_9257,U_9252)),U_9258))
| ~ hBOOL(hAPP(hAPP(c_member(U_9255),U_9252),U_9256)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9254,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9255,tc_fun(U_9254,tc_HOL_Obool)),U_9256),U_9257)),U_9258)) ) ),
inference(variable_rename,[status(thm)],[f_2644_1]) ).
fof(f_2644_3,plain,
( ! [U_9268,U_9266,U_9264,U_9262,U_9260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9260,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9262,tc_fun(U_9260,tc_HOL_Obool)),U_9264),U_9266)),U_9268))
| ? [U_9253] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9260,tc_HOL_Obool)),hAPP(U_9266,U_9253)),U_9268))
& hBOOL(hAPP(hAPP(c_member(U_9262),U_9253),U_9264)) ) )
& ! [U_9267,U_9265,U_9263,U_9261,U_9259] :
( ! [U_9252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9259,tc_HOL_Obool)),hAPP(U_9265,U_9252)),U_9267))
| ~ hBOOL(hAPP(hAPP(c_member(U_9261),U_9252),U_9263)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9259,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9261,tc_fun(U_9259,tc_HOL_Obool)),U_9263),U_9265)),U_9267)) ) ),
inference(miniscope,[status(thm)],[f_2644_2]) ).
fof(f_2644_4,plain,
( ! [U_9268,U_9266,U_9264,U_9262,U_9260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9260,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9262,tc_fun(U_9260,tc_HOL_Obool)),U_9264),U_9266)),U_9268))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9260,tc_HOL_Obool)),hAPP(U_9266,sK250(U_9268,U_9266,U_9264,U_9262,U_9260))),U_9268))
& hBOOL(hAPP(hAPP(c_member(U_9262),sK250(U_9268,U_9266,U_9264,U_9262,U_9260)),U_9264)) ) )
& ! [U_9267,U_9265,U_9263,U_9261,U_9259] :
( ! [U_9252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9259,tc_HOL_Obool)),hAPP(U_9265,U_9252)),U_9267))
| ~ hBOOL(hAPP(hAPP(c_member(U_9261),U_9252),U_9263)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9259,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9261,tc_fun(U_9259,tc_HOL_Obool)),U_9263),U_9265)),U_9267)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_9253,sK250(U_9268,U_9266,U_9264,U_9262,U_9260))],[f_2644_3]) ).
fof(f_2644_5,plain,
( ! [U_9260,U_9262,U_9264,U_9266,U_9268] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9260,tc_HOL_Obool)),hAPP(U_9266,sK250(U_9268,U_9266,U_9264,U_9262,U_9260))),U_9268))
| ~ sP788(U_9260,U_9262,U_9264,U_9266,U_9268) )
& ! [U_9260,U_9262,U_9264,U_9266,U_9268] :
( hBOOL(hAPP(hAPP(c_member(U_9262),sK250(U_9268,U_9266,U_9264,U_9262,U_9260)),U_9264))
| ~ sP788(U_9260,U_9262,U_9264,U_9266,U_9268) )
& ! [U_9260,U_9262,U_9264,U_9266,U_9268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9260,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9262,tc_fun(U_9260,tc_HOL_Obool)),U_9264),U_9266)),U_9268))
| sP788(U_9260,U_9262,U_9264,U_9266,U_9268) )
& ! [U_9252,U_9265,U_9261,U_9259,U_9267,U_9263] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9259,tc_HOL_Obool)),hAPP(U_9265,U_9252)),U_9267))
| ~ hBOOL(hAPP(hAPP(c_member(U_9261),U_9252),U_9263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9259,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9261,tc_fun(U_9259,tc_HOL_Obool)),U_9263),U_9265)),U_9267)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP788])],[f_2644_4]) ).
cnf(f_2644_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9259,tc_HOL_Obool)),hAPP(U_9265,U_9252)),U_9267))
| ~ hBOOL(hAPP(hAPP(c_member(U_9261),U_9252),U_9263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9259,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9261,tc_fun(U_9259,tc_HOL_Obool)),U_9263),U_9265)),U_9267)) ),
inference(clausify,[status(thm)],[f_2644_5]) ).
cnf(f_2644_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9260,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9262,tc_fun(U_9260,tc_HOL_Obool)),U_9264),U_9266)),U_9268))
| sP788(U_9260,U_9262,U_9264,U_9266,U_9268) ),
inference(clausify,[status(thm)],[f_2644_5]) ).
cnf(f_2644_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9262),sK250(U_9268,U_9266,U_9264,U_9262,U_9260)),U_9264))
| ~ sP788(U_9260,U_9262,U_9264,U_9266,U_9268) ),
inference(clausify,[status(thm)],[f_2644_5]) ).
cnf(f_2644_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9260,tc_HOL_Obool)),hAPP(U_9266,sK250(U_9268,U_9266,U_9264,U_9262,U_9260))),U_9268))
| ~ sP788(U_9260,U_9262,U_9264,U_9266,U_9268) ),
inference(clausify,[status(thm)],[f_2644_5]) ).
fof(f_2645_1,plain,
! [V_S_2,V_R_2,T_c,T_b] :
( ( 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)))
| ~ 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)) )
& ( 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))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2]) ).
fof(f_2645_2,plain,
! [U_9272,U_9271,U_9270,U_9269] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9269,tc_fun(U_9270,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9269,tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_fun(U_9270,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9270,tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_fun(U_9270,tc_HOL_Obool)),U_9269),c_COMBC(U_9270,tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9270,tc_prod(U_9269,U_9270)),tc_fun(U_9270,tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),U_9269),hAPP(c_COMBB(tc_prod(U_9269,U_9270),tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool),U_9270),c_member(tc_prod(U_9269,U_9270)))),c_Product__Type_OPair(U_9269,U_9270)))),U_9271)),hAPP(hAPP(c_COMBC(U_9269,tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_fun(U_9270,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9270,tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_fun(U_9270,tc_HOL_Obool)),U_9269),c_COMBC(U_9270,tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9270,tc_prod(U_9269,U_9270)),tc_fun(U_9270,tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),U_9269),hAPP(c_COMBB(tc_prod(U_9269,U_9270),tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool),U_9270),c_member(tc_prod(U_9269,U_9270)))),c_Product__Type_OPair(U_9269,U_9270)))),U_9272)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool)),U_9271),U_9272)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool)),U_9271),U_9272))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9269,tc_fun(U_9270,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9269,tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_fun(U_9270,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9270,tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_fun(U_9270,tc_HOL_Obool)),U_9269),c_COMBC(U_9270,tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9270,tc_prod(U_9269,U_9270)),tc_fun(U_9270,tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),U_9269),hAPP(c_COMBB(tc_prod(U_9269,U_9270),tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool),U_9270),c_member(tc_prod(U_9269,U_9270)))),c_Product__Type_OPair(U_9269,U_9270)))),U_9271)),hAPP(hAPP(c_COMBC(U_9269,tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_fun(U_9270,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9270,tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_fun(U_9270,tc_HOL_Obool)),U_9269),c_COMBC(U_9270,tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9270,tc_prod(U_9269,U_9270)),tc_fun(U_9270,tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool)),U_9269),hAPP(c_COMBB(tc_prod(U_9269,U_9270),tc_fun(tc_fun(tc_prod(U_9269,U_9270),tc_HOL_Obool),tc_HOL_Obool),U_9270),c_member(tc_prod(U_9269,U_9270)))),c_Product__Type_OPair(U_9269,U_9270)))),U_9272))) ) ),
inference(variable_rename,[status(thm)],[f_2645_1]) ).
fof(f_2645_3,plain,
( ! [U_9280,U_9278,U_9276,U_9274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9274,tc_fun(U_9276,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9274,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),U_9274),c_COMBC(U_9276,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_prod(U_9274,U_9276)),tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),U_9274),hAPP(c_COMBB(tc_prod(U_9274,U_9276),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool),U_9276),c_member(tc_prod(U_9274,U_9276)))),c_Product__Type_OPair(U_9274,U_9276)))),U_9278)),hAPP(hAPP(c_COMBC(U_9274,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),U_9274),c_COMBC(U_9276,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_prod(U_9274,U_9276)),tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),U_9274),hAPP(c_COMBB(tc_prod(U_9274,U_9276),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool),U_9276),c_member(tc_prod(U_9274,U_9276)))),c_Product__Type_OPair(U_9274,U_9276)))),U_9280)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool)),U_9278),U_9280)) )
& ! [U_9279,U_9277,U_9275,U_9273] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool)),U_9277),U_9279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9273,tc_fun(U_9275,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9273,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),U_9273),c_COMBC(U_9275,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_prod(U_9273,U_9275)),tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),U_9273),hAPP(c_COMBB(tc_prod(U_9273,U_9275),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool),U_9275),c_member(tc_prod(U_9273,U_9275)))),c_Product__Type_OPair(U_9273,U_9275)))),U_9277)),hAPP(hAPP(c_COMBC(U_9273,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),U_9273),c_COMBC(U_9275,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_prod(U_9273,U_9275)),tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),U_9273),hAPP(c_COMBB(tc_prod(U_9273,U_9275),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool),U_9275),c_member(tc_prod(U_9273,U_9275)))),c_Product__Type_OPair(U_9273,U_9275)))),U_9279))) ) ),
inference(miniscope,[status(thm)],[f_2645_2]) ).
fof(f_2645_4,plain,
( ! [U_9274,U_9276,U_9278,U_9280] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9274,tc_fun(U_9276,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9274,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),U_9274),c_COMBC(U_9276,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_prod(U_9274,U_9276)),tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),U_9274),hAPP(c_COMBB(tc_prod(U_9274,U_9276),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool),U_9276),c_member(tc_prod(U_9274,U_9276)))),c_Product__Type_OPair(U_9274,U_9276)))),U_9278)),hAPP(hAPP(c_COMBC(U_9274,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),U_9274),c_COMBC(U_9276,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_prod(U_9274,U_9276)),tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),U_9274),hAPP(c_COMBB(tc_prod(U_9274,U_9276),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool),U_9276),c_member(tc_prod(U_9274,U_9276)))),c_Product__Type_OPair(U_9274,U_9276)))),U_9280)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool)),U_9278),U_9280)) )
& ! [U_9277,U_9279,U_9275,U_9273] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool)),U_9277),U_9279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9273,tc_fun(U_9275,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9273,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),U_9273),c_COMBC(U_9275,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_prod(U_9273,U_9275)),tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),U_9273),hAPP(c_COMBB(tc_prod(U_9273,U_9275),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool),U_9275),c_member(tc_prod(U_9273,U_9275)))),c_Product__Type_OPair(U_9273,U_9275)))),U_9277)),hAPP(hAPP(c_COMBC(U_9273,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),U_9273),c_COMBC(U_9275,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_prod(U_9273,U_9275)),tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),U_9273),hAPP(c_COMBB(tc_prod(U_9273,U_9275),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool),U_9275),c_member(tc_prod(U_9273,U_9275)))),c_Product__Type_OPair(U_9273,U_9275)))),U_9279))) ) ),
inference(definitional_conversion,[status(esa)],[f_2645_3]) ).
cnf(f_2645_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool)),U_9277),U_9279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9273,tc_fun(U_9275,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9273,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),U_9273),c_COMBC(U_9275,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_prod(U_9273,U_9275)),tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),U_9273),hAPP(c_COMBB(tc_prod(U_9273,U_9275),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool),U_9275),c_member(tc_prod(U_9273,U_9275)))),c_Product__Type_OPair(U_9273,U_9275)))),U_9277)),hAPP(hAPP(c_COMBC(U_9273,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool)),U_9273),c_COMBC(U_9275,tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_prod(U_9273,U_9275)),tc_fun(U_9275,tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool)),U_9273),hAPP(c_COMBB(tc_prod(U_9273,U_9275),tc_fun(tc_fun(tc_prod(U_9273,U_9275),tc_HOL_Obool),tc_HOL_Obool),U_9275),c_member(tc_prod(U_9273,U_9275)))),c_Product__Type_OPair(U_9273,U_9275)))),U_9279))) ),
inference(clausify,[status(thm)],[f_2645_4]) ).
cnf(f_2645_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9274,tc_fun(U_9276,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9274,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),U_9274),c_COMBC(U_9276,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_prod(U_9274,U_9276)),tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),U_9274),hAPP(c_COMBB(tc_prod(U_9274,U_9276),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool),U_9276),c_member(tc_prod(U_9274,U_9276)))),c_Product__Type_OPair(U_9274,U_9276)))),U_9278)),hAPP(hAPP(c_COMBC(U_9274,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),U_9274),c_COMBC(U_9276,tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9276,tc_prod(U_9274,U_9276)),tc_fun(U_9276,tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool)),U_9274),hAPP(c_COMBB(tc_prod(U_9274,U_9276),tc_fun(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool),tc_HOL_Obool),U_9276),c_member(tc_prod(U_9274,U_9276)))),c_Product__Type_OPair(U_9274,U_9276)))),U_9280)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9274,U_9276),tc_HOL_Obool)),U_9278),U_9280)) ),
inference(clausify,[status(thm)],[f_2645_4]) ).
fof(f_2646_1,plain,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__lower]) ).
fof(f_2646_2,plain,
! [U_9285,U_9284,U_9283,U_9282,U_9281] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9281,tc_fun(U_9284,tc_HOL_Obool)),U_9283),U_9285)),hAPP(U_9285,U_9282)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9281),U_9282),U_9283)) ),
inference(variable_rename,[status(thm)],[f_2646_1]) ).
fof(f_2646_3,plain,
! [U_9281,U_9282,U_9283,U_9284,U_9285] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9281,tc_fun(U_9284,tc_HOL_Obool)),U_9283),U_9285)),hAPP(U_9285,U_9282)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9281),U_9282),U_9283)) ),
inference(definitional_conversion,[status(esa)],[f_2646_2]) ).
cnf(f_2646_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9281,tc_fun(U_9284,tc_HOL_Obool)),U_9283),U_9285)),hAPP(U_9285,U_9282)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9281),U_9282),U_9283)) ),
inference(clausify,[status(thm)],[f_2646_3]) ).
fof(f_2647_1,plain,
! [V_S_2,V_R_2,T_b] :
( ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__subset__eq]) ).
fof(f_2647_2,plain,
! [U_9288,U_9287,U_9286] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9286,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9286,tc_fun(U_9286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9286)),U_9287)),hAPP(hAPP(c_COMBC(U_9286,tc_fun(U_9286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9286)),U_9288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9286,tc_HOL_Obool)),U_9287),U_9288)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9286,tc_HOL_Obool)),U_9287),U_9288))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9286,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9286,tc_fun(U_9286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9286)),U_9287)),hAPP(hAPP(c_COMBC(U_9286,tc_fun(U_9286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9286)),U_9288))) ) ),
inference(variable_rename,[status(thm)],[f_2647_1]) ).
fof(f_2647_3,plain,
( ! [U_9294,U_9292,U_9290] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9290,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9290,tc_fun(U_9290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9290)),U_9292)),hAPP(hAPP(c_COMBC(U_9290,tc_fun(U_9290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9290)),U_9294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9290,tc_HOL_Obool)),U_9292),U_9294)) )
& ! [U_9293,U_9291,U_9289] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9289,tc_HOL_Obool)),U_9291),U_9293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9289,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9289,tc_fun(U_9289,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9289)),U_9291)),hAPP(hAPP(c_COMBC(U_9289,tc_fun(U_9289,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9289)),U_9293))) ) ),
inference(miniscope,[status(thm)],[f_2647_2]) ).
fof(f_2647_4,plain,
( ! [U_9290,U_9292,U_9294] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9290,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9290,tc_fun(U_9290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9290)),U_9292)),hAPP(hAPP(c_COMBC(U_9290,tc_fun(U_9290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9290)),U_9294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9290,tc_HOL_Obool)),U_9292),U_9294)) )
& ! [U_9291,U_9289,U_9293] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9289,tc_HOL_Obool)),U_9291),U_9293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9289,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9289,tc_fun(U_9289,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9289)),U_9291)),hAPP(hAPP(c_COMBC(U_9289,tc_fun(U_9289,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9289)),U_9293))) ) ),
inference(definitional_conversion,[status(esa)],[f_2647_3]) ).
cnf(f_2647_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9289,tc_HOL_Obool)),U_9291),U_9293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9289,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9289,tc_fun(U_9289,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9289)),U_9291)),hAPP(hAPP(c_COMBC(U_9289,tc_fun(U_9289,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9289)),U_9293))) ),
inference(clausify,[status(thm)],[f_2647_4]) ).
cnf(f_2647_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9290,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9290,tc_fun(U_9290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9290)),U_9292)),hAPP(hAPP(c_COMBC(U_9290,tc_fun(U_9290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9290)),U_9294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9290,tc_HOL_Obool)),U_9292),U_9294)) ),
inference(clausify,[status(thm)],[f_2647_4]) ).
fof(f_2648_1,plain,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__upper]) ).
fof(f_2648_2,plain,
! [U_9299,U_9298,U_9297,U_9296,U_9295] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9298,tc_HOL_Obool)),hAPP(U_9299,U_9296)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9295,tc_fun(U_9298,tc_HOL_Obool)),U_9297),U_9299)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9295),U_9296),U_9297)) ),
inference(variable_rename,[status(thm)],[f_2648_1]) ).
fof(f_2648_3,plain,
! [U_9295,U_9296,U_9297,U_9298,U_9299] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9298,tc_HOL_Obool)),hAPP(U_9299,U_9296)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9295,tc_fun(U_9298,tc_HOL_Obool)),U_9297),U_9299)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9295),U_9296),U_9297)) ),
inference(definitional_conversion,[status(esa)],[f_2648_2]) ).
cnf(f_2648_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9298,tc_HOL_Obool)),hAPP(U_9299,U_9296)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9295,tc_fun(U_9298,tc_HOL_Obool)),U_9297),U_9299)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9295),U_9296),U_9297)) ),
inference(clausify,[status(thm)],[f_2648_3]) ).
fof(f_2649_1,plain,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib]) ).
fof(f_2649_2,plain,
! [U_9304,U_9303,U_9302,U_9301,U_9300] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),hAPP(hAPP(c_COMBS(U_9301,U_9300,U_9300),hAPP(hAPP(c_COMBB(U_9300,tc_fun(U_9300,U_9300),U_9301),c_Groups_Oplus__class_Oplus(U_9300)),U_9303)),U_9304)),U_9302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),U_9303),U_9302)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),U_9304),U_9302))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9301),U_9302))
| ~ class_Groups_Ocomm__monoid__add(U_9300) ),
inference(variable_rename,[status(thm)],[f_2649_1]) ).
fof(f_2649_3,plain,
! [U_9300,U_9301,U_9302,U_9303,U_9304] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),hAPP(hAPP(c_COMBS(U_9301,U_9300,U_9300),hAPP(hAPP(c_COMBB(U_9300,tc_fun(U_9300,U_9300),U_9301),c_Groups_Oplus__class_Oplus(U_9300)),U_9303)),U_9304)),U_9302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),U_9303),U_9302)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),U_9304),U_9302))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9301),U_9302))
| ~ class_Groups_Ocomm__monoid__add(U_9300) ),
inference(definitional_conversion,[status(esa)],[f_2649_2]) ).
cnf(f_2649_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),hAPP(hAPP(c_COMBS(U_9301,U_9300,U_9300),hAPP(hAPP(c_COMBB(U_9300,tc_fun(U_9300,U_9300),U_9301),c_Groups_Oplus__class_Oplus(U_9300)),U_9303)),U_9304)),U_9302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),U_9303),U_9302)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9301,U_9300),U_9304),U_9302))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9301),U_9302))
| ~ class_Groups_Ocomm__monoid__add(U_9300) ),
inference(clausify,[status(thm)],[f_2649_3]) ).
fof(f_2650_1,plain,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INF__leI]) ).
fof(f_2650_2,plain,
! [U_9309,U_9308,U_9307,U_9306,U_9305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9305),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9306,U_9305),U_9308),U_9309)),hAPP(U_9309,U_9307)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9306),U_9307),U_9308))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9305) ),
inference(variable_rename,[status(thm)],[f_2650_1]) ).
fof(f_2650_3,plain,
! [U_9306,U_9305,U_9307,U_9308,U_9309] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9305),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9306,U_9305),U_9308),U_9309)),hAPP(U_9309,U_9307)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9306),U_9307),U_9308))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9305) ),
inference(definitional_conversion,[status(esa)],[f_2650_2]) ).
cnf(f_2650_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9305),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9306,U_9305),U_9308),U_9309)),hAPP(U_9309,U_9307)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9306),U_9307),U_9308))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9305) ),
inference(clausify,[status(thm)],[f_2650_3]) ).
fof(f_2651_1,plain,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__SUPI]) ).
fof(f_2651_2,plain,
! [U_9314,U_9313,U_9312,U_9311,U_9310] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9310),hAPP(U_9314,U_9312)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9311,U_9310),U_9313),U_9314)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9311),U_9312),U_9313))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9310) ),
inference(variable_rename,[status(thm)],[f_2651_1]) ).
fof(f_2651_3,plain,
! [U_9310,U_9311,U_9312,U_9313,U_9314] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9310),hAPP(U_9314,U_9312)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9311,U_9310),U_9313),U_9314)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9311),U_9312),U_9313))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9310) ),
inference(definitional_conversion,[status(esa)],[f_2651_2]) ).
cnf(f_2651_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9310),hAPP(U_9314,U_9312)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9311,U_9310),U_9313),U_9314)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9311),U_9312),U_9313))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9310) ),
inference(clausify,[status(thm)],[f_2651_3]) ).
fof(f_2652_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).
fof(f_2652_2,plain,
! [U_9315] : 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)))),U_9315))),
inference(variable_rename,[status(thm)],[f_2652_1]) ).
fof(f_2652_3,plain,
! [U_9315] : 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)))),U_9315))),
inference(definitional_conversion,[status(esa)],[f_2652_2]) ).
cnf(f_2652_4,plain,
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)))),U_9315))),
inference(clausify,[status(thm)],[f_2652_3]) ).
fof(f_2653_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Pow__def]) ).
fof(f_2653_2,plain,
! [U_9317,U_9316] : hAPP(c_Set_OPow(U_9316),U_9317) = hAPP(c_Set_OCollect(tc_fun(U_9316,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9316,tc_HOL_Obool),tc_fun(U_9316,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9316,tc_HOL_Obool))),U_9317)),
inference(variable_rename,[status(thm)],[f_2653_1]) ).
fof(f_2653_3,plain,
! [U_9316,U_9317] : hAPP(c_Set_OPow(U_9316),U_9317) = hAPP(c_Set_OCollect(tc_fun(U_9316,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9316,tc_HOL_Obool),tc_fun(U_9316,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9316,tc_HOL_Obool))),U_9317)),
inference(definitional_conversion,[status(esa)],[f_2653_2]) ).
cnf(f_2653_4,plain,
hAPP(c_Set_OPow(U_9316),U_9317) = hAPP(c_Set_OCollect(tc_fun(U_9316,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9316,tc_HOL_Obool),tc_fun(U_9316,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9316,tc_HOL_Obool))),U_9317)),
inference(clausify,[status(thm)],[f_2653_3]) ).
fof(f_2654_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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)
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J]) ).
fof(f_2654_2,plain,
! [U_9322,U_9321,U_9320,U_9319,U_9318] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9319,tc_fun(U_9320,tc_HOL_Obool)),U_9318),hAPP(hAPP(c_COMBC(U_9319,tc_fun(U_9320,tc_HOL_Obool),tc_fun(U_9320,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9320,tc_HOL_Obool),tc_fun(tc_fun(U_9320,tc_HOL_Obool),tc_fun(U_9320,tc_HOL_Obool)),U_9319),c_Groups_Ominus__class_Ominus(tc_fun(U_9320,tc_HOL_Obool))),U_9321)),U_9322)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9320,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9319,tc_fun(U_9320,tc_HOL_Obool)),U_9318),U_9321)),U_9322)
| U_9318 = c_Orderings_Obot__class_Obot(tc_fun(U_9319,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9319,tc_fun(U_9320,tc_HOL_Obool)),U_9318),hAPP(hAPP(c_COMBC(U_9319,tc_fun(U_9320,tc_HOL_Obool),tc_fun(U_9320,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9320,tc_HOL_Obool),tc_fun(tc_fun(U_9320,tc_HOL_Obool),tc_fun(U_9320,tc_HOL_Obool)),U_9319),c_Groups_Ominus__class_Ominus(tc_fun(U_9320,tc_HOL_Obool))),U_9321)),U_9322)) = c_Orderings_Otop__class_Otop(tc_fun(U_9320,tc_HOL_Obool))
| U_9318 != c_Orderings_Obot__class_Obot(tc_fun(U_9319,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2654_1]) ).
fof(f_2654_3,plain,
( ! [U_9332,U_9330,U_9328,U_9326,U_9324] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9326,tc_fun(U_9328,tc_HOL_Obool)),U_9324),hAPP(hAPP(c_COMBC(U_9326,tc_fun(U_9328,tc_HOL_Obool),tc_fun(U_9328,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9328,tc_HOL_Obool),tc_fun(tc_fun(U_9328,tc_HOL_Obool),tc_fun(U_9328,tc_HOL_Obool)),U_9326),c_Groups_Ominus__class_Ominus(tc_fun(U_9328,tc_HOL_Obool))),U_9330)),U_9332)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9328,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9326,tc_fun(U_9328,tc_HOL_Obool)),U_9324),U_9330)),U_9332)
| U_9324 = c_Orderings_Obot__class_Obot(tc_fun(U_9326,tc_HOL_Obool)) )
& ! [U_9331,U_9329,U_9327,U_9325,U_9323] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9325,tc_fun(U_9327,tc_HOL_Obool)),U_9323),hAPP(hAPP(c_COMBC(U_9325,tc_fun(U_9327,tc_HOL_Obool),tc_fun(U_9327,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9327,tc_HOL_Obool),tc_fun(tc_fun(U_9327,tc_HOL_Obool),tc_fun(U_9327,tc_HOL_Obool)),U_9325),c_Groups_Ominus__class_Ominus(tc_fun(U_9327,tc_HOL_Obool))),U_9329)),U_9331)) = c_Orderings_Otop__class_Otop(tc_fun(U_9327,tc_HOL_Obool))
| U_9323 != c_Orderings_Obot__class_Obot(tc_fun(U_9325,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2654_2]) ).
fof(f_2654_4,plain,
( ! [U_9324,U_9326,U_9328,U_9330,U_9332] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9326,tc_fun(U_9328,tc_HOL_Obool)),U_9324),hAPP(hAPP(c_COMBC(U_9326,tc_fun(U_9328,tc_HOL_Obool),tc_fun(U_9328,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9328,tc_HOL_Obool),tc_fun(tc_fun(U_9328,tc_HOL_Obool),tc_fun(U_9328,tc_HOL_Obool)),U_9326),c_Groups_Ominus__class_Ominus(tc_fun(U_9328,tc_HOL_Obool))),U_9330)),U_9332)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9328,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9326,tc_fun(U_9328,tc_HOL_Obool)),U_9324),U_9330)),U_9332)
| U_9324 = c_Orderings_Obot__class_Obot(tc_fun(U_9326,tc_HOL_Obool)) )
& ! [U_9325,U_9327,U_9329,U_9323,U_9331] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9325,tc_fun(U_9327,tc_HOL_Obool)),U_9323),hAPP(hAPP(c_COMBC(U_9325,tc_fun(U_9327,tc_HOL_Obool),tc_fun(U_9327,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9327,tc_HOL_Obool),tc_fun(tc_fun(U_9327,tc_HOL_Obool),tc_fun(U_9327,tc_HOL_Obool)),U_9325),c_Groups_Ominus__class_Ominus(tc_fun(U_9327,tc_HOL_Obool))),U_9329)),U_9331)) = c_Orderings_Otop__class_Otop(tc_fun(U_9327,tc_HOL_Obool))
| U_9323 != c_Orderings_Obot__class_Obot(tc_fun(U_9325,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2654_3]) ).
cnf(f_2654_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9325,tc_fun(U_9327,tc_HOL_Obool)),U_9323),hAPP(hAPP(c_COMBC(U_9325,tc_fun(U_9327,tc_HOL_Obool),tc_fun(U_9327,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9327,tc_HOL_Obool),tc_fun(tc_fun(U_9327,tc_HOL_Obool),tc_fun(U_9327,tc_HOL_Obool)),U_9325),c_Groups_Ominus__class_Ominus(tc_fun(U_9327,tc_HOL_Obool))),U_9329)),U_9331)) = c_Orderings_Otop__class_Otop(tc_fun(U_9327,tc_HOL_Obool))
| U_9323 != c_Orderings_Obot__class_Obot(tc_fun(U_9325,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2654_4]) ).
cnf(f_2654_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9326,tc_fun(U_9328,tc_HOL_Obool)),U_9324),hAPP(hAPP(c_COMBC(U_9326,tc_fun(U_9328,tc_HOL_Obool),tc_fun(U_9328,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9328,tc_HOL_Obool),tc_fun(tc_fun(U_9328,tc_HOL_Obool),tc_fun(U_9328,tc_HOL_Obool)),U_9326),c_Groups_Ominus__class_Ominus(tc_fun(U_9328,tc_HOL_Obool))),U_9330)),U_9332)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9328,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9326,tc_fun(U_9328,tc_HOL_Obool)),U_9324),U_9330)),U_9332)
| U_9324 = c_Orderings_Obot__class_Obot(tc_fun(U_9326,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2654_4]) ).
fof(f_2655_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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) = 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))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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)
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J]) ).
fof(f_2655_2,plain,
! [U_9337,U_9336,U_9335,U_9334,U_9333] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9335,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9334,tc_fun(U_9335,tc_HOL_Obool)),U_9333),U_9336)),U_9337) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9334,tc_fun(U_9335,tc_HOL_Obool)),U_9333),hAPP(hAPP(c_COMBC(U_9334,tc_fun(U_9335,tc_HOL_Obool),tc_fun(U_9335,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9335,tc_HOL_Obool),tc_fun(tc_fun(U_9335,tc_HOL_Obool),tc_fun(U_9335,tc_HOL_Obool)),U_9334),c_Groups_Ominus__class_Ominus(tc_fun(U_9335,tc_HOL_Obool))),U_9336)),U_9337))
| U_9333 = c_Orderings_Obot__class_Obot(tc_fun(U_9334,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9335,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9334,tc_fun(U_9335,tc_HOL_Obool)),U_9333),U_9336)),U_9337) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9335,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9335,tc_HOL_Obool))),U_9337)
| U_9333 != c_Orderings_Obot__class_Obot(tc_fun(U_9334,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2655_1]) ).
fof(f_2655_3,plain,
( ! [U_9347,U_9345,U_9343,U_9341,U_9339] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9341,tc_fun(U_9343,tc_HOL_Obool)),U_9339),U_9345)),U_9347) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9341,tc_fun(U_9343,tc_HOL_Obool)),U_9339),hAPP(hAPP(c_COMBC(U_9341,tc_fun(U_9343,tc_HOL_Obool),tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9343,tc_HOL_Obool),tc_fun(tc_fun(U_9343,tc_HOL_Obool),tc_fun(U_9343,tc_HOL_Obool)),U_9341),c_Groups_Ominus__class_Ominus(tc_fun(U_9343,tc_HOL_Obool))),U_9345)),U_9347))
| U_9339 = c_Orderings_Obot__class_Obot(tc_fun(U_9341,tc_HOL_Obool)) )
& ! [U_9346,U_9344,U_9342,U_9340,U_9338] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9342,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9340,tc_fun(U_9342,tc_HOL_Obool)),U_9338),U_9344)),U_9346) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9342,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9342,tc_HOL_Obool))),U_9346)
| U_9338 != c_Orderings_Obot__class_Obot(tc_fun(U_9340,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2655_2]) ).
fof(f_2655_4,plain,
( ! [U_9339,U_9341,U_9343,U_9345,U_9347] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9341,tc_fun(U_9343,tc_HOL_Obool)),U_9339),U_9345)),U_9347) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9341,tc_fun(U_9343,tc_HOL_Obool)),U_9339),hAPP(hAPP(c_COMBC(U_9341,tc_fun(U_9343,tc_HOL_Obool),tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9343,tc_HOL_Obool),tc_fun(tc_fun(U_9343,tc_HOL_Obool),tc_fun(U_9343,tc_HOL_Obool)),U_9341),c_Groups_Ominus__class_Ominus(tc_fun(U_9343,tc_HOL_Obool))),U_9345)),U_9347))
| U_9339 = c_Orderings_Obot__class_Obot(tc_fun(U_9341,tc_HOL_Obool)) )
& ! [U_9342,U_9344,U_9340,U_9338,U_9346] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9342,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9340,tc_fun(U_9342,tc_HOL_Obool)),U_9338),U_9344)),U_9346) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9342,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9342,tc_HOL_Obool))),U_9346)
| U_9338 != c_Orderings_Obot__class_Obot(tc_fun(U_9340,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2655_3]) ).
cnf(f_2655_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9342,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9340,tc_fun(U_9342,tc_HOL_Obool)),U_9338),U_9344)),U_9346) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9342,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9342,tc_HOL_Obool))),U_9346)
| U_9338 != c_Orderings_Obot__class_Obot(tc_fun(U_9340,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2655_4]) ).
cnf(f_2655_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9341,tc_fun(U_9343,tc_HOL_Obool)),U_9339),U_9345)),U_9347) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9341,tc_fun(U_9343,tc_HOL_Obool)),U_9339),hAPP(hAPP(c_COMBC(U_9341,tc_fun(U_9343,tc_HOL_Obool),tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9343,tc_HOL_Obool),tc_fun(tc_fun(U_9343,tc_HOL_Obool),tc_fun(U_9343,tc_HOL_Obool)),U_9341),c_Groups_Ominus__class_Ominus(tc_fun(U_9343,tc_HOL_Obool))),U_9345)),U_9347))
| U_9339 = c_Orderings_Obot__class_Obot(tc_fun(U_9341,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2655_4]) ).
fof(f_2656_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J]) ).
fof(f_2656_2,plain,
! [U_9352,U_9351,U_9350,U_9349,U_9348] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9350,tc_HOL_Obool)),U_9351),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9349,tc_fun(U_9350,tc_HOL_Obool)),U_9348),U_9352)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9349,tc_fun(U_9350,tc_HOL_Obool)),U_9348),hAPP(hAPP(c_COMBB(tc_fun(U_9350,tc_HOL_Obool),tc_fun(U_9350,tc_HOL_Obool),U_9349),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9350,tc_HOL_Obool)),U_9351)),U_9352))
| U_9348 = c_Orderings_Obot__class_Obot(tc_fun(U_9349,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9350,tc_HOL_Obool)),U_9351),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9349,tc_fun(U_9350,tc_HOL_Obool)),U_9348),U_9352)) = U_9351
| U_9348 != c_Orderings_Obot__class_Obot(tc_fun(U_9349,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2656_1]) ).
fof(f_2656_3,plain,
( ! [U_9362,U_9360,U_9358,U_9356,U_9354] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9358,tc_HOL_Obool)),U_9360),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9356,tc_fun(U_9358,tc_HOL_Obool)),U_9354),U_9362)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9356,tc_fun(U_9358,tc_HOL_Obool)),U_9354),hAPP(hAPP(c_COMBB(tc_fun(U_9358,tc_HOL_Obool),tc_fun(U_9358,tc_HOL_Obool),U_9356),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9358,tc_HOL_Obool)),U_9360)),U_9362))
| U_9354 = c_Orderings_Obot__class_Obot(tc_fun(U_9356,tc_HOL_Obool)) )
& ! [U_9361,U_9359,U_9357,U_9355,U_9353] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9357,tc_HOL_Obool)),U_9359),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9355,tc_fun(U_9357,tc_HOL_Obool)),U_9353),U_9361)) = U_9359
| U_9353 != c_Orderings_Obot__class_Obot(tc_fun(U_9355,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2656_2]) ).
fof(f_2656_4,plain,
( ! [U_9354,U_9356,U_9358,U_9360,U_9362] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9358,tc_HOL_Obool)),U_9360),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9356,tc_fun(U_9358,tc_HOL_Obool)),U_9354),U_9362)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9356,tc_fun(U_9358,tc_HOL_Obool)),U_9354),hAPP(hAPP(c_COMBB(tc_fun(U_9358,tc_HOL_Obool),tc_fun(U_9358,tc_HOL_Obool),U_9356),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9358,tc_HOL_Obool)),U_9360)),U_9362))
| U_9354 = c_Orderings_Obot__class_Obot(tc_fun(U_9356,tc_HOL_Obool)) )
& ! [U_9355,U_9359,U_9357,U_9353,U_9361] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9357,tc_HOL_Obool)),U_9359),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9355,tc_fun(U_9357,tc_HOL_Obool)),U_9353),U_9361)) = U_9359
| U_9353 != c_Orderings_Obot__class_Obot(tc_fun(U_9355,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2656_3]) ).
cnf(f_2656_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9357,tc_HOL_Obool)),U_9359),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9355,tc_fun(U_9357,tc_HOL_Obool)),U_9353),U_9361)) = U_9359
| U_9353 != c_Orderings_Obot__class_Obot(tc_fun(U_9355,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2656_4]) ).
cnf(f_2656_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9358,tc_HOL_Obool)),U_9360),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9356,tc_fun(U_9358,tc_HOL_Obool)),U_9354),U_9362)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9356,tc_fun(U_9358,tc_HOL_Obool)),U_9354),hAPP(hAPP(c_COMBB(tc_fun(U_9358,tc_HOL_Obool),tc_fun(U_9358,tc_HOL_Obool),U_9356),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9358,tc_HOL_Obool)),U_9360)),U_9362))
| U_9354 = c_Orderings_Obot__class_Obot(tc_fun(U_9356,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2656_4]) ).
fof(f_2657_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I7_J]) ).
fof(f_2657_2,plain,
! [U_9367,U_9366,U_9365,U_9364,U_9363] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9363,tc_fun(U_9364,tc_HOL_Obool)),U_9365),hAPP(hAPP(c_COMBB(tc_fun(U_9364,tc_HOL_Obool),tc_fun(U_9364,tc_HOL_Obool),U_9363),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9364,tc_HOL_Obool)),U_9366)),U_9367)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9364,tc_HOL_Obool)),U_9366),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9363,tc_fun(U_9364,tc_HOL_Obool)),U_9365),U_9367)),
inference(variable_rename,[status(thm)],[f_2657_1]) ).
fof(f_2657_3,plain,
! [U_9363,U_9364,U_9365,U_9366,U_9367] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9363,tc_fun(U_9364,tc_HOL_Obool)),U_9365),hAPP(hAPP(c_COMBB(tc_fun(U_9364,tc_HOL_Obool),tc_fun(U_9364,tc_HOL_Obool),U_9363),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9364,tc_HOL_Obool)),U_9366)),U_9367)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9364,tc_HOL_Obool)),U_9366),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9363,tc_fun(U_9364,tc_HOL_Obool)),U_9365),U_9367)),
inference(definitional_conversion,[status(esa)],[f_2657_2]) ).
cnf(f_2657_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9363,tc_fun(U_9364,tc_HOL_Obool)),U_9365),hAPP(hAPP(c_COMBB(tc_fun(U_9364,tc_HOL_Obool),tc_fun(U_9364,tc_HOL_Obool),U_9363),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9364,tc_HOL_Obool)),U_9366)),U_9367)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9364,tc_HOL_Obool)),U_9366),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9363,tc_fun(U_9364,tc_HOL_Obool)),U_9365),U_9367)),
inference(clausify,[status(thm)],[f_2657_3]) ).
fof(f_2658_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I6_J]) ).
fof(f_2658_2,plain,
! [U_9372,U_9371,U_9370,U_9369,U_9368] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9368,tc_fun(U_9369,tc_HOL_Obool)),U_9370),hAPP(hAPP(c_COMBC(U_9368,tc_fun(U_9369,tc_HOL_Obool),tc_fun(U_9369,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9369,tc_HOL_Obool),tc_fun(tc_fun(U_9369,tc_HOL_Obool),tc_fun(U_9369,tc_HOL_Obool)),U_9368),c_Groups_Ominus__class_Ominus(tc_fun(U_9369,tc_HOL_Obool))),U_9371)),U_9372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9369,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9368,tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9371)),U_9372),
inference(variable_rename,[status(thm)],[f_2658_1]) ).
fof(f_2658_3,plain,
! [U_9368,U_9369,U_9370,U_9371,U_9372] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9368,tc_fun(U_9369,tc_HOL_Obool)),U_9370),hAPP(hAPP(c_COMBC(U_9368,tc_fun(U_9369,tc_HOL_Obool),tc_fun(U_9369,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9369,tc_HOL_Obool),tc_fun(tc_fun(U_9369,tc_HOL_Obool),tc_fun(U_9369,tc_HOL_Obool)),U_9368),c_Groups_Ominus__class_Ominus(tc_fun(U_9369,tc_HOL_Obool))),U_9371)),U_9372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9369,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9368,tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9371)),U_9372),
inference(definitional_conversion,[status(esa)],[f_2658_2]) ).
cnf(f_2658_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9368,tc_fun(U_9369,tc_HOL_Obool)),U_9370),hAPP(hAPP(c_COMBC(U_9368,tc_fun(U_9369,tc_HOL_Obool),tc_fun(U_9369,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9369,tc_HOL_Obool),tc_fun(tc_fun(U_9369,tc_HOL_Obool),tc_fun(U_9369,tc_HOL_Obool)),U_9368),c_Groups_Ominus__class_Ominus(tc_fun(U_9369,tc_HOL_Obool))),U_9371)),U_9372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9369,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9368,tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9371)),U_9372),
inference(clausify,[status(thm)],[f_2658_3]) ).
fof(f_2659_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I7_J]) ).
fof(f_2659_2,plain,
! [U_9377,U_9376,U_9375,U_9374,U_9373] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9374),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9375,tc_fun(U_9373,tc_HOL_Obool)),U_9376),U_9377)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9375,tc_fun(U_9373,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_COMBB(tc_fun(U_9373,tc_HOL_Obool),tc_fun(U_9373,tc_HOL_Obool),U_9375),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9374)),U_9377)),
inference(variable_rename,[status(thm)],[f_2659_1]) ).
fof(f_2659_3,plain,
! [U_9373,U_9374,U_9375,U_9376,U_9377] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9374),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9375,tc_fun(U_9373,tc_HOL_Obool)),U_9376),U_9377)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9375,tc_fun(U_9373,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_COMBB(tc_fun(U_9373,tc_HOL_Obool),tc_fun(U_9373,tc_HOL_Obool),U_9375),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9374)),U_9377)),
inference(definitional_conversion,[status(esa)],[f_2659_2]) ).
cnf(f_2659_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9374),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9375,tc_fun(U_9373,tc_HOL_Obool)),U_9376),U_9377)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9375,tc_fun(U_9373,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_COMBB(tc_fun(U_9373,tc_HOL_Obool),tc_fun(U_9373,tc_HOL_Obool),U_9375),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9374)),U_9377)),
inference(clausify,[status(thm)],[f_2659_3]) ).
fof(f_2660_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I6_J]) ).
fof(f_2660_2,plain,
! [U_9382,U_9381,U_9380,U_9379,U_9378] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9378,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9378,tc_HOL_Obool)),U_9380),U_9381)),U_9382) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9378,tc_HOL_Obool)),U_9380),hAPP(hAPP(c_COMBC(U_9379,tc_fun(U_9378,tc_HOL_Obool),tc_fun(U_9378,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9378,tc_HOL_Obool),tc_fun(tc_fun(U_9378,tc_HOL_Obool),tc_fun(U_9378,tc_HOL_Obool)),U_9379),c_Groups_Ominus__class_Ominus(tc_fun(U_9378,tc_HOL_Obool))),U_9381)),U_9382)),
inference(variable_rename,[status(thm)],[f_2660_1]) ).
fof(f_2660_3,plain,
! [U_9378,U_9379,U_9380,U_9381,U_9382] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9378,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9378,tc_HOL_Obool)),U_9380),U_9381)),U_9382) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9378,tc_HOL_Obool)),U_9380),hAPP(hAPP(c_COMBC(U_9379,tc_fun(U_9378,tc_HOL_Obool),tc_fun(U_9378,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9378,tc_HOL_Obool),tc_fun(tc_fun(U_9378,tc_HOL_Obool),tc_fun(U_9378,tc_HOL_Obool)),U_9379),c_Groups_Ominus__class_Ominus(tc_fun(U_9378,tc_HOL_Obool))),U_9381)),U_9382)),
inference(definitional_conversion,[status(esa)],[f_2660_2]) ).
cnf(f_2660_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9378,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9378,tc_HOL_Obool)),U_9380),U_9381)),U_9382) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9378,tc_HOL_Obool)),U_9380),hAPP(hAPP(c_COMBC(U_9379,tc_fun(U_9378,tc_HOL_Obool),tc_fun(U_9378,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9378,tc_HOL_Obool),tc_fun(tc_fun(U_9378,tc_HOL_Obool),tc_fun(U_9378,tc_HOL_Obool)),U_9379),c_Groups_Ominus__class_Ominus(tc_fun(U_9378,tc_HOL_Obool))),U_9381)),U_9382)),
inference(clausify,[status(thm)],[f_2660_3]) ).
fof(f_2661_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( 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))
| ~ class_Groups_Ominus(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__diff__def]) ).
fof(f_2661_2,plain,
! [U_9387,U_9386,U_9385,U_9384,U_9383] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9384,U_9383)),U_9385),U_9386),U_9387) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9383),hAPP(U_9385,U_9387)),hAPP(U_9386,U_9387))
| ~ class_Groups_Ominus(U_9383) ),
inference(variable_rename,[status(thm)],[f_2661_1]) ).
fof(f_2661_3,plain,
! [U_9383,U_9384,U_9385,U_9386,U_9387] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9384,U_9383)),U_9385),U_9386),U_9387) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9383),hAPP(U_9385,U_9387)),hAPP(U_9386,U_9387))
| ~ class_Groups_Ominus(U_9383) ),
inference(definitional_conversion,[status(esa)],[f_2661_2]) ).
cnf(f_2661_4,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9384,U_9383)),U_9385),U_9386),U_9387) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9383),hAPP(U_9385,U_9387)),hAPP(U_9386,U_9387))
| ~ class_Groups_Ominus(U_9383) ),
inference(clausify,[status(thm)],[f_2661_3]) ).
fof(f_2662_1,plain,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( 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))
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__subtractf]) ).
fof(f_2662_2,plain,
! [U_9392,U_9391,U_9390,U_9389,U_9388] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),hAPP(hAPP(c_COMBS(U_9389,U_9388,U_9388),hAPP(hAPP(c_COMBB(U_9388,tc_fun(U_9388,U_9388),U_9389),c_Groups_Ominus__class_Ominus(U_9388)),U_9390)),U_9391)),U_9392) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9388),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),U_9390),U_9392)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),U_9391),U_9392))
| ~ class_Groups_Oab__group__add(U_9388) ),
inference(variable_rename,[status(thm)],[f_2662_1]) ).
fof(f_2662_3,plain,
! [U_9388,U_9389,U_9390,U_9391,U_9392] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),hAPP(hAPP(c_COMBS(U_9389,U_9388,U_9388),hAPP(hAPP(c_COMBB(U_9388,tc_fun(U_9388,U_9388),U_9389),c_Groups_Ominus__class_Ominus(U_9388)),U_9390)),U_9391)),U_9392) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9388),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),U_9390),U_9392)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),U_9391),U_9392))
| ~ class_Groups_Oab__group__add(U_9388) ),
inference(definitional_conversion,[status(esa)],[f_2662_2]) ).
cnf(f_2662_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),hAPP(hAPP(c_COMBS(U_9389,U_9388,U_9388),hAPP(hAPP(c_COMBB(U_9388,tc_fun(U_9388,U_9388),U_9389),c_Groups_Ominus__class_Ominus(U_9388)),U_9390)),U_9391)),U_9392) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9388),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),U_9390),U_9392)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9389,U_9388),U_9391),U_9392))
| ~ class_Groups_Oab__group__add(U_9388) ),
inference(clausify,[status(thm)],[f_2662_3]) ).
fof(f_2663_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_set__diff__eq]) ).
fof(f_2663_2,plain,
! [U_9395,U_9394,U_9393] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),U_9394),U_9395) = hAPP(c_Set_OCollect(U_9393),hAPP(hAPP(c_COMBS(U_9393,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9393),c_fconj),hAPP(hAPP(c_COMBC(U_9393,tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9393)),U_9394))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9393),c_fNot),hAPP(hAPP(c_COMBC(U_9393,tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9393)),U_9395)))),
inference(variable_rename,[status(thm)],[f_2663_1]) ).
fof(f_2663_3,plain,
! [U_9393,U_9394,U_9395] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),U_9394),U_9395) = hAPP(c_Set_OCollect(U_9393),hAPP(hAPP(c_COMBS(U_9393,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9393),c_fconj),hAPP(hAPP(c_COMBC(U_9393,tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9393)),U_9394))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9393),c_fNot),hAPP(hAPP(c_COMBC(U_9393,tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9393)),U_9395)))),
inference(definitional_conversion,[status(esa)],[f_2663_2]) ).
cnf(f_2663_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),U_9394),U_9395) = hAPP(c_Set_OCollect(U_9393),hAPP(hAPP(c_COMBS(U_9393,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9393),c_fconj),hAPP(hAPP(c_COMBC(U_9393,tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9393)),U_9394))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9393),c_fNot),hAPP(hAPP(c_COMBC(U_9393,tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9393)),U_9395)))),
inference(clausify,[status(thm)],[f_2663_3]) ).
fof(f_2664_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_insert__compr]) ).
fof(f_2664_2,plain,
! [U_9398,U_9397,U_9396] : hAPP(hAPP(c_Set_Oinsert(U_9396),U_9397),U_9398) = hAPP(c_Set_OCollect(U_9396),hAPP(hAPP(c_COMBS(U_9396,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9396),c_fdisj),hAPP(hAPP(c_COMBC(U_9396,U_9396,tc_HOL_Obool),c_fequal),U_9397))),hAPP(hAPP(c_COMBC(U_9396,tc_fun(U_9396,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9396)),U_9398))),
inference(variable_rename,[status(thm)],[f_2664_1]) ).
fof(f_2664_3,plain,
! [U_9396,U_9397,U_9398] : hAPP(hAPP(c_Set_Oinsert(U_9396),U_9397),U_9398) = hAPP(c_Set_OCollect(U_9396),hAPP(hAPP(c_COMBS(U_9396,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9396),c_fdisj),hAPP(hAPP(c_COMBC(U_9396,U_9396,tc_HOL_Obool),c_fequal),U_9397))),hAPP(hAPP(c_COMBC(U_9396,tc_fun(U_9396,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9396)),U_9398))),
inference(definitional_conversion,[status(esa)],[f_2664_2]) ).
cnf(f_2664_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_9396),U_9397),U_9398) = hAPP(c_Set_OCollect(U_9396),hAPP(hAPP(c_COMBS(U_9396,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9396),c_fdisj),hAPP(hAPP(c_COMBC(U_9396,U_9396,tc_HOL_Obool),c_fequal),U_9397))),hAPP(hAPP(c_COMBC(U_9396,tc_fun(U_9396,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9396)),U_9398))),
inference(clausify,[status(thm)],[f_2664_3]) ).
fof(f_2665_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_insert__compr__raw]) ).
fof(f_2665_2,plain,
! [U_9401,U_9400,U_9399] : hAPP(hAPP(c_Set_Oinsert(U_9399),U_9400),U_9401) = hAPP(c_Set_OCollect(U_9399),hAPP(hAPP(c_COMBS(U_9399,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9399),c_fdisj),hAPP(hAPP(c_COMBC(U_9399,U_9399,tc_HOL_Obool),c_fequal),U_9400))),hAPP(hAPP(c_COMBC(U_9399,tc_fun(U_9399,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9399)),U_9401))),
inference(variable_rename,[status(thm)],[f_2665_1]) ).
fof(f_2665_3,plain,
! [U_9399,U_9400,U_9401] : hAPP(hAPP(c_Set_Oinsert(U_9399),U_9400),U_9401) = hAPP(c_Set_OCollect(U_9399),hAPP(hAPP(c_COMBS(U_9399,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9399),c_fdisj),hAPP(hAPP(c_COMBC(U_9399,U_9399,tc_HOL_Obool),c_fequal),U_9400))),hAPP(hAPP(c_COMBC(U_9399,tc_fun(U_9399,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9399)),U_9401))),
inference(definitional_conversion,[status(esa)],[f_2665_2]) ).
cnf(f_2665_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_9399),U_9400),U_9401) = hAPP(c_Set_OCollect(U_9399),hAPP(hAPP(c_COMBS(U_9399,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9399),c_fdisj),hAPP(hAPP(c_COMBC(U_9399,U_9399,tc_HOL_Obool),c_fequal),U_9400))),hAPP(hAPP(c_COMBC(U_9399,tc_fun(U_9399,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9399)),U_9401))),
inference(clausify,[status(thm)],[f_2665_3]) ).
fof(f_2666_1,plain,
! [T_b,V_a_2,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_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))
| hBOOL(hAPP(V_Pa_2,V_a_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,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)))
| ~ hBOOL(hAPP(V_Pa_2,V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).
fof(f_2666_2,plain,
! [U_9404,U_9403,U_9402] :
( ( hAPP(c_Set_OCollect(U_9404),hAPP(hAPP(c_COMBS(U_9404,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9404),c_fconj),hAPP(hAPP(c_COMBC(U_9404,U_9404,tc_HOL_Obool),c_fequal),U_9403))),U_9402)) = c_Orderings_Obot__class_Obot(tc_fun(U_9404,tc_HOL_Obool))
| hBOOL(hAPP(U_9402,U_9403)) )
& ( hAPP(c_Set_OCollect(U_9404),hAPP(hAPP(c_COMBS(U_9404,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9404),c_fconj),hAPP(hAPP(c_COMBC(U_9404,U_9404,tc_HOL_Obool),c_fequal),U_9403))),U_9402)) = hAPP(hAPP(c_Set_Oinsert(U_9404),U_9403),c_Orderings_Obot__class_Obot(tc_fun(U_9404,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9402,U_9403)) ) ),
inference(variable_rename,[status(thm)],[f_2666_1]) ).
fof(f_2666_3,plain,
( ! [U_9410,U_9408,U_9406] :
( hAPP(c_Set_OCollect(U_9410),hAPP(hAPP(c_COMBS(U_9410,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9410),c_fconj),hAPP(hAPP(c_COMBC(U_9410,U_9410,tc_HOL_Obool),c_fequal),U_9408))),U_9406)) = c_Orderings_Obot__class_Obot(tc_fun(U_9410,tc_HOL_Obool))
| hBOOL(hAPP(U_9406,U_9408)) )
& ! [U_9409,U_9407,U_9405] :
( hAPP(c_Set_OCollect(U_9409),hAPP(hAPP(c_COMBS(U_9409,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9409),c_fconj),hAPP(hAPP(c_COMBC(U_9409,U_9409,tc_HOL_Obool),c_fequal),U_9407))),U_9405)) = hAPP(hAPP(c_Set_Oinsert(U_9409),U_9407),c_Orderings_Obot__class_Obot(tc_fun(U_9409,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9405,U_9407)) ) ),
inference(miniscope,[status(thm)],[f_2666_2]) ).
fof(f_2666_4,plain,
( ! [U_9406,U_9408,U_9410] :
( hAPP(c_Set_OCollect(U_9410),hAPP(hAPP(c_COMBS(U_9410,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9410),c_fconj),hAPP(hAPP(c_COMBC(U_9410,U_9410,tc_HOL_Obool),c_fequal),U_9408))),U_9406)) = c_Orderings_Obot__class_Obot(tc_fun(U_9410,tc_HOL_Obool))
| hBOOL(hAPP(U_9406,U_9408)) )
& ! [U_9407,U_9405,U_9409] :
( hAPP(c_Set_OCollect(U_9409),hAPP(hAPP(c_COMBS(U_9409,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9409),c_fconj),hAPP(hAPP(c_COMBC(U_9409,U_9409,tc_HOL_Obool),c_fequal),U_9407))),U_9405)) = hAPP(hAPP(c_Set_Oinsert(U_9409),U_9407),c_Orderings_Obot__class_Obot(tc_fun(U_9409,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9405,U_9407)) ) ),
inference(definitional_conversion,[status(esa)],[f_2666_3]) ).
cnf(f_2666_5,plain,
( hAPP(c_Set_OCollect(U_9409),hAPP(hAPP(c_COMBS(U_9409,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9409),c_fconj),hAPP(hAPP(c_COMBC(U_9409,U_9409,tc_HOL_Obool),c_fequal),U_9407))),U_9405)) = hAPP(hAPP(c_Set_Oinsert(U_9409),U_9407),c_Orderings_Obot__class_Obot(tc_fun(U_9409,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9405,U_9407)) ),
inference(clausify,[status(thm)],[f_2666_4]) ).
cnf(f_2666_6,plain,
( hAPP(c_Set_OCollect(U_9410),hAPP(hAPP(c_COMBS(U_9410,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9410),c_fconj),hAPP(hAPP(c_COMBC(U_9410,U_9410,tc_HOL_Obool),c_fequal),U_9408))),U_9406)) = c_Orderings_Obot__class_Obot(tc_fun(U_9410,tc_HOL_Obool))
| hBOOL(hAPP(U_9406,U_9408)) ),
inference(clausify,[status(thm)],[f_2666_4]) ).
fof(f_2667_1,plain,
! [T_b,V_a_2,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_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(V_Pa_2,V_a_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(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)))
| ~ hBOOL(hAPP(V_Pa_2,V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).
fof(f_2667_2,plain,
! [U_9413,U_9412,U_9411] :
( ( hAPP(c_Set_OCollect(U_9413),hAPP(hAPP(c_COMBS(U_9413,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9413),c_fconj),hAPP(c_fequal,U_9412))),U_9411)) = c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool))
| hBOOL(hAPP(U_9411,U_9412)) )
& ( hAPP(c_Set_OCollect(U_9413),hAPP(hAPP(c_COMBS(U_9413,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9413),c_fconj),hAPP(c_fequal,U_9412))),U_9411)) = hAPP(hAPP(c_Set_Oinsert(U_9413),U_9412),c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9411,U_9412)) ) ),
inference(variable_rename,[status(thm)],[f_2667_1]) ).
fof(f_2667_3,plain,
( ! [U_9419,U_9417,U_9415] :
( hAPP(c_Set_OCollect(U_9419),hAPP(hAPP(c_COMBS(U_9419,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9419),c_fconj),hAPP(c_fequal,U_9417))),U_9415)) = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool))
| hBOOL(hAPP(U_9415,U_9417)) )
& ! [U_9418,U_9416,U_9414] :
( hAPP(c_Set_OCollect(U_9418),hAPP(hAPP(c_COMBS(U_9418,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9418),c_fconj),hAPP(c_fequal,U_9416))),U_9414)) = hAPP(hAPP(c_Set_Oinsert(U_9418),U_9416),c_Orderings_Obot__class_Obot(tc_fun(U_9418,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9414,U_9416)) ) ),
inference(miniscope,[status(thm)],[f_2667_2]) ).
fof(f_2667_4,plain,
( ! [U_9415,U_9417,U_9419] :
( hAPP(c_Set_OCollect(U_9419),hAPP(hAPP(c_COMBS(U_9419,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9419),c_fconj),hAPP(c_fequal,U_9417))),U_9415)) = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool))
| hBOOL(hAPP(U_9415,U_9417)) )
& ! [U_9418,U_9416,U_9414] :
( hAPP(c_Set_OCollect(U_9418),hAPP(hAPP(c_COMBS(U_9418,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9418),c_fconj),hAPP(c_fequal,U_9416))),U_9414)) = hAPP(hAPP(c_Set_Oinsert(U_9418),U_9416),c_Orderings_Obot__class_Obot(tc_fun(U_9418,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9414,U_9416)) ) ),
inference(definitional_conversion,[status(esa)],[f_2667_3]) ).
cnf(f_2667_5,plain,
( hAPP(c_Set_OCollect(U_9418),hAPP(hAPP(c_COMBS(U_9418,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9418),c_fconj),hAPP(c_fequal,U_9416))),U_9414)) = hAPP(hAPP(c_Set_Oinsert(U_9418),U_9416),c_Orderings_Obot__class_Obot(tc_fun(U_9418,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9414,U_9416)) ),
inference(clausify,[status(thm)],[f_2667_4]) ).
cnf(f_2667_6,plain,
( hAPP(c_Set_OCollect(U_9419),hAPP(hAPP(c_COMBS(U_9419,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9419),c_fconj),hAPP(c_fequal,U_9417))),U_9415)) = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool))
| hBOOL(hAPP(U_9415,U_9417)) ),
inference(clausify,[status(thm)],[f_2667_4]) ).
fof(f_2668_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_singleton__conv]) ).
fof(f_2668_2,plain,
! [U_9421,U_9420] : hAPP(c_Set_OCollect(U_9420),hAPP(hAPP(c_COMBC(U_9420,U_9420,tc_HOL_Obool),c_fequal),U_9421)) = hAPP(hAPP(c_Set_Oinsert(U_9420),U_9421),c_Orderings_Obot__class_Obot(tc_fun(U_9420,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2668_1]) ).
fof(f_2668_3,plain,
! [U_9420,U_9421] : hAPP(c_Set_OCollect(U_9420),hAPP(hAPP(c_COMBC(U_9420,U_9420,tc_HOL_Obool),c_fequal),U_9421)) = hAPP(hAPP(c_Set_Oinsert(U_9420),U_9421),c_Orderings_Obot__class_Obot(tc_fun(U_9420,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2668_2]) ).
cnf(f_2668_4,plain,
hAPP(c_Set_OCollect(U_9420),hAPP(hAPP(c_COMBC(U_9420,U_9420,tc_HOL_Obool),c_fequal),U_9421)) = hAPP(hAPP(c_Set_Oinsert(U_9420),U_9421),c_Orderings_Obot__class_Obot(tc_fun(U_9420,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2668_3]) ).
fof(f_2669_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_singleton__conv2]) ).
fof(f_2669_2,plain,
! [U_9423,U_9422] : hAPP(c_Set_OCollect(U_9422),hAPP(c_fequal,U_9423)) = hAPP(hAPP(c_Set_Oinsert(U_9422),U_9423),c_Orderings_Obot__class_Obot(tc_fun(U_9422,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2669_1]) ).
fof(f_2669_3,plain,
! [U_9422,U_9423] : hAPP(c_Set_OCollect(U_9422),hAPP(c_fequal,U_9423)) = hAPP(hAPP(c_Set_Oinsert(U_9422),U_9423),c_Orderings_Obot__class_Obot(tc_fun(U_9422,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2669_2]) ).
cnf(f_2669_4,plain,
hAPP(c_Set_OCollect(U_9422),hAPP(c_fequal,U_9423)) = hAPP(hAPP(c_Set_Oinsert(U_9422),U_9423),c_Orderings_Obot__class_Obot(tc_fun(U_9422,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2669_3]) ).
fof(f_2670_1,plain,
! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib]) ).
fof(f_2670_2,plain,
! [U_9429,U_9428,U_9427,U_9426,U_9425,U_9424] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9424,tc_fun(U_9427,tc_HOL_Obool)),U_9426),hAPP(hAPP(c_COMBB(tc_fun(U_9427,tc_HOL_Obool),tc_fun(U_9427,tc_HOL_Obool),U_9424),hAPP(c_Set_Oinsert(U_9427),U_9428)),U_9429)) = hAPP(hAPP(c_Set_Oinsert(U_9427),U_9428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9424,tc_fun(U_9427,tc_HOL_Obool)),U_9426),U_9429))
| ~ hBOOL(hAPP(hAPP(c_member(U_9424),U_9425),U_9426)) ),
inference(variable_rename,[status(thm)],[f_2670_1]) ).
fof(f_2670_3,plain,
! [U_9424,U_9425,U_9426,U_9427,U_9428,U_9429] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9424,tc_fun(U_9427,tc_HOL_Obool)),U_9426),hAPP(hAPP(c_COMBB(tc_fun(U_9427,tc_HOL_Obool),tc_fun(U_9427,tc_HOL_Obool),U_9424),hAPP(c_Set_Oinsert(U_9427),U_9428)),U_9429)) = hAPP(hAPP(c_Set_Oinsert(U_9427),U_9428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9424,tc_fun(U_9427,tc_HOL_Obool)),U_9426),U_9429))
| ~ hBOOL(hAPP(hAPP(c_member(U_9424),U_9425),U_9426)) ),
inference(definitional_conversion,[status(esa)],[f_2670_2]) ).
cnf(f_2670_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9424,tc_fun(U_9427,tc_HOL_Obool)),U_9426),hAPP(hAPP(c_COMBB(tc_fun(U_9427,tc_HOL_Obool),tc_fun(U_9427,tc_HOL_Obool),U_9424),hAPP(c_Set_Oinsert(U_9427),U_9428)),U_9429)) = hAPP(hAPP(c_Set_Oinsert(U_9427),U_9428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9424,tc_fun(U_9427,tc_HOL_Obool)),U_9426),U_9429))
| ~ hBOOL(hAPP(hAPP(c_member(U_9424),U_9425),U_9426)) ),
inference(clausify,[status(thm)],[f_2670_3]) ).
fof(f_2671_1,plain,
! [V_ca_2,T_c,T_b,V_A_2] :
( ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__constant__conv]) ).
fof(f_2671_2,plain,
! [U_9433,U_9432,U_9431,U_9430] :
( ( hAPP(c_Set_Oimage(U_9431,U_9432,hAPP(c_COMBK(U_9432,U_9431),U_9433)),U_9430) = hAPP(hAPP(c_Set_Oinsert(U_9432),U_9433),c_Orderings_Obot__class_Obot(tc_fun(U_9432,tc_HOL_Obool)))
| U_9430 = c_Orderings_Obot__class_Obot(tc_fun(U_9431,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(U_9431,U_9432,hAPP(c_COMBK(U_9432,U_9431),U_9433)),U_9430) = c_Orderings_Obot__class_Obot(tc_fun(U_9432,tc_HOL_Obool))
| U_9430 != c_Orderings_Obot__class_Obot(tc_fun(U_9431,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2671_1]) ).
fof(f_2671_3,plain,
( ! [U_9441,U_9439,U_9437,U_9435] :
( hAPP(c_Set_Oimage(U_9437,U_9439,hAPP(c_COMBK(U_9439,U_9437),U_9441)),U_9435) = hAPP(hAPP(c_Set_Oinsert(U_9439),U_9441),c_Orderings_Obot__class_Obot(tc_fun(U_9439,tc_HOL_Obool)))
| U_9435 = c_Orderings_Obot__class_Obot(tc_fun(U_9437,tc_HOL_Obool)) )
& ! [U_9440,U_9438,U_9436,U_9434] :
( hAPP(c_Set_Oimage(U_9436,U_9438,hAPP(c_COMBK(U_9438,U_9436),U_9440)),U_9434) = c_Orderings_Obot__class_Obot(tc_fun(U_9438,tc_HOL_Obool))
| U_9434 != c_Orderings_Obot__class_Obot(tc_fun(U_9436,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2671_2]) ).
fof(f_2671_4,plain,
( ! [U_9441,U_9435,U_9437,U_9439] :
( hAPP(c_Set_Oimage(U_9437,U_9439,hAPP(c_COMBK(U_9439,U_9437),U_9441)),U_9435) = hAPP(hAPP(c_Set_Oinsert(U_9439),U_9441),c_Orderings_Obot__class_Obot(tc_fun(U_9439,tc_HOL_Obool)))
| U_9435 = c_Orderings_Obot__class_Obot(tc_fun(U_9437,tc_HOL_Obool)) )
& ! [U_9440,U_9436,U_9438,U_9434] :
( hAPP(c_Set_Oimage(U_9436,U_9438,hAPP(c_COMBK(U_9438,U_9436),U_9440)),U_9434) = c_Orderings_Obot__class_Obot(tc_fun(U_9438,tc_HOL_Obool))
| U_9434 != c_Orderings_Obot__class_Obot(tc_fun(U_9436,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2671_3]) ).
cnf(f_2671_5,plain,
( hAPP(c_Set_Oimage(U_9436,U_9438,hAPP(c_COMBK(U_9438,U_9436),U_9440)),U_9434) = c_Orderings_Obot__class_Obot(tc_fun(U_9438,tc_HOL_Obool))
| U_9434 != c_Orderings_Obot__class_Obot(tc_fun(U_9436,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2671_4]) ).
cnf(f_2671_6,plain,
( hAPP(c_Set_Oimage(U_9437,U_9439,hAPP(c_COMBK(U_9439,U_9437),U_9441)),U_9435) = hAPP(hAPP(c_Set_Oinsert(U_9439),U_9441),c_Orderings_Obot__class_Obot(tc_fun(U_9439,tc_HOL_Obool)))
| U_9435 = c_Orderings_Obot__class_Obot(tc_fun(U_9437,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2671_4]) ).
fof(f_2672_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__setprod]) ).
fof(f_2672_2,plain,
! [U_9445,U_9444,U_9443,U_9442] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9442),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9443,U_9442),U_9444),U_9445)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9443,U_9442),hAPP(hAPP(c_COMBB(U_9442,U_9442,U_9443),c_Groups_Oabs__class_Oabs(U_9442)),U_9444)),U_9445)
| ~ class_Fields_Olinordered__field(U_9442) ),
inference(variable_rename,[status(thm)],[f_2672_1]) ).
fof(f_2672_3,plain,
! [U_9442,U_9443,U_9444,U_9445] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9442),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9443,U_9442),U_9444),U_9445)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9443,U_9442),hAPP(hAPP(c_COMBB(U_9442,U_9442,U_9443),c_Groups_Oabs__class_Oabs(U_9442)),U_9444)),U_9445)
| ~ class_Fields_Olinordered__field(U_9442) ),
inference(definitional_conversion,[status(esa)],[f_2672_2]) ).
cnf(f_2672_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9442),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9443,U_9442),U_9444),U_9445)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9443,U_9442),hAPP(hAPP(c_COMBB(U_9442,U_9442,U_9443),c_Groups_Oabs__class_Oabs(U_9442)),U_9444)),U_9445)
| ~ class_Fields_Olinordered__field(U_9442) ),
inference(clausify,[status(thm)],[f_2672_3]) ).
fof(f_2673_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs]) ).
fof(f_2673_2,plain,
! [U_9449,U_9448,U_9447,U_9446] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9446),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9447,U_9446),hAPP(hAPP(c_COMBB(U_9446,U_9446,U_9447),c_Groups_Oabs__class_Oabs(U_9446)),U_9448)),U_9449)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9447,U_9446),hAPP(hAPP(c_COMBB(U_9446,U_9446,U_9447),c_Groups_Oabs__class_Oabs(U_9446)),U_9448)),U_9449)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9446) ),
inference(variable_rename,[status(thm)],[f_2673_1]) ).
fof(f_2673_3,plain,
! [U_9446,U_9447,U_9448,U_9449] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9446),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9447,U_9446),hAPP(hAPP(c_COMBB(U_9446,U_9446,U_9447),c_Groups_Oabs__class_Oabs(U_9446)),U_9448)),U_9449)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9447,U_9446),hAPP(hAPP(c_COMBB(U_9446,U_9446,U_9447),c_Groups_Oabs__class_Oabs(U_9446)),U_9448)),U_9449)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9446) ),
inference(definitional_conversion,[status(esa)],[f_2673_2]) ).
cnf(f_2673_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9446),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9447,U_9446),hAPP(hAPP(c_COMBB(U_9446,U_9446,U_9447),c_Groups_Oabs__class_Oabs(U_9446)),U_9448)),U_9449)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9447,U_9446),hAPP(hAPP(c_COMBB(U_9446,U_9446,U_9447),c_Groups_Oabs__class_Oabs(U_9446)),U_9448)),U_9449)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9446) ),
inference(clausify,[status(thm)],[f_2673_3]) ).
fof(f_2674_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INTER__eq__Inter__image]) ).
fof(f_2674_2,plain,
! [U_9453,U_9452,U_9451,U_9450] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9450,tc_fun(U_9451,tc_HOL_Obool)),U_9452),U_9453) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9451,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9450,tc_fun(U_9451,tc_HOL_Obool),U_9453),U_9452)),
inference(variable_rename,[status(thm)],[f_2674_1]) ).
fof(f_2674_3,plain,
! [U_9450,U_9451,U_9452,U_9453] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9450,tc_fun(U_9451,tc_HOL_Obool)),U_9452),U_9453) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9451,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9450,tc_fun(U_9451,tc_HOL_Obool),U_9453),U_9452)),
inference(definitional_conversion,[status(esa)],[f_2674_2]) ).
cnf(f_2674_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9450,tc_fun(U_9451,tc_HOL_Obool)),U_9452),U_9453) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9451,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9450,tc_fun(U_9451,tc_HOL_Obool),U_9453),U_9452)),
inference(clausify,[status(thm)],[f_2674_3]) ).
fof(f_2675_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_Inter__image__eq]) ).
fof(f_2675_2,plain,
! [U_9457,U_9456,U_9455,U_9454] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9454,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9455,tc_fun(U_9454,tc_HOL_Obool),U_9456),U_9457)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9455,tc_fun(U_9454,tc_HOL_Obool)),U_9457),U_9456),
inference(variable_rename,[status(thm)],[f_2675_1]) ).
fof(f_2675_3,plain,
! [U_9454,U_9455,U_9456,U_9457] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9454,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9455,tc_fun(U_9454,tc_HOL_Obool),U_9456),U_9457)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9455,tc_fun(U_9454,tc_HOL_Obool)),U_9457),U_9456),
inference(definitional_conversion,[status(esa)],[f_2675_2]) ).
cnf(f_2675_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9454,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9455,tc_fun(U_9454,tc_HOL_Obool),U_9456),U_9457)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9455,tc_fun(U_9454,tc_HOL_Obool)),U_9457),U_9456),
inference(clausify,[status(thm)],[f_2675_3]) ).
fof(f_2676_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__Union]) ).
fof(f_2676_2,plain,
! [U_9461,U_9460,U_9459,U_9458] : hAPP(c_Set_Oimage(U_9458,U_9459,U_9460),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9458,tc_HOL_Obool),U_9461)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9458,tc_HOL_Obool),tc_fun(U_9459,tc_HOL_Obool)),U_9461),c_Set_Oimage(U_9458,U_9459,U_9460)),
inference(variable_rename,[status(thm)],[f_2676_1]) ).
fof(f_2676_3,plain,
! [U_9458,U_9459,U_9460,U_9461] : hAPP(c_Set_Oimage(U_9458,U_9459,U_9460),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9458,tc_HOL_Obool),U_9461)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9458,tc_HOL_Obool),tc_fun(U_9459,tc_HOL_Obool)),U_9461),c_Set_Oimage(U_9458,U_9459,U_9460)),
inference(definitional_conversion,[status(esa)],[f_2676_2]) ).
cnf(f_2676_4,plain,
hAPP(c_Set_Oimage(U_9458,U_9459,U_9460),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9458,tc_HOL_Obool),U_9461)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9458,tc_HOL_Obool),tc_fun(U_9459,tc_HOL_Obool)),U_9461),c_Set_Oimage(U_9458,U_9459,U_9460)),
inference(clausify,[status(thm)],[f_2676_3]) ).
fof(f_2677_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I10_J]) ).
fof(f_2677_2,plain,
! [U_9467,U_9466,U_9465,U_9464,U_9463,U_9462] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9462,tc_fun(U_9463,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9464,U_9462,U_9465),U_9466)),U_9467) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9464,tc_fun(U_9463,tc_HOL_Obool)),U_9466),hAPP(hAPP(c_COMBB(U_9462,tc_fun(U_9463,tc_HOL_Obool),U_9464),U_9467),U_9465)),
inference(variable_rename,[status(thm)],[f_2677_1]) ).
fof(f_2677_3,plain,
! [U_9462,U_9463,U_9464,U_9465,U_9466,U_9467] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9462,tc_fun(U_9463,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9464,U_9462,U_9465),U_9466)),U_9467) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9464,tc_fun(U_9463,tc_HOL_Obool)),U_9466),hAPP(hAPP(c_COMBB(U_9462,tc_fun(U_9463,tc_HOL_Obool),U_9464),U_9467),U_9465)),
inference(definitional_conversion,[status(esa)],[f_2677_2]) ).
cnf(f_2677_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9462,tc_fun(U_9463,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9464,U_9462,U_9465),U_9466)),U_9467) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9464,tc_fun(U_9463,tc_HOL_Obool)),U_9466),hAPP(hAPP(c_COMBB(U_9462,tc_fun(U_9463,tc_HOL_Obool),U_9464),U_9467),U_9465)),
inference(clausify,[status(thm)],[f_2677_3]) ).
fof(f_2678_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__UN]) ).
fof(f_2678_2,plain,
! [U_9473,U_9472,U_9471,U_9470,U_9469,U_9468] : hAPP(c_Set_Oimage(U_9468,U_9469,U_9470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9471,tc_fun(U_9468,tc_HOL_Obool)),U_9472),U_9473)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9471,tc_fun(U_9469,tc_HOL_Obool)),U_9472),hAPP(hAPP(c_COMBB(tc_fun(U_9468,tc_HOL_Obool),tc_fun(U_9469,tc_HOL_Obool),U_9471),c_Set_Oimage(U_9468,U_9469,U_9470)),U_9473)),
inference(variable_rename,[status(thm)],[f_2678_1]) ).
fof(f_2678_3,plain,
! [U_9468,U_9469,U_9470,U_9471,U_9472,U_9473] : hAPP(c_Set_Oimage(U_9468,U_9469,U_9470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9471,tc_fun(U_9468,tc_HOL_Obool)),U_9472),U_9473)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9471,tc_fun(U_9469,tc_HOL_Obool)),U_9472),hAPP(hAPP(c_COMBB(tc_fun(U_9468,tc_HOL_Obool),tc_fun(U_9469,tc_HOL_Obool),U_9471),c_Set_Oimage(U_9468,U_9469,U_9470)),U_9473)),
inference(definitional_conversion,[status(esa)],[f_2678_2]) ).
cnf(f_2678_4,plain,
hAPP(c_Set_Oimage(U_9468,U_9469,U_9470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9471,tc_fun(U_9468,tc_HOL_Obool)),U_9472),U_9473)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9471,tc_fun(U_9469,tc_HOL_Obool)),U_9472),hAPP(hAPP(c_COMBB(tc_fun(U_9468,tc_HOL_Obool),tc_fun(U_9469,tc_HOL_Obool),U_9471),c_Set_Oimage(U_9468,U_9469,U_9470)),U_9473)),
inference(clausify,[status(thm)],[f_2678_3]) ).
fof(f_2679_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I10_J]) ).
fof(f_2679_2,plain,
! [U_9479,U_9478,U_9477,U_9476,U_9475,U_9474] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9474,tc_fun(U_9475,tc_HOL_Obool)),U_9476),hAPP(hAPP(c_COMBB(U_9477,tc_fun(U_9475,tc_HOL_Obool),U_9474),U_9478),U_9479)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9477,tc_fun(U_9475,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9474,U_9477,U_9479),U_9476)),U_9478),
inference(variable_rename,[status(thm)],[f_2679_1]) ).
fof(f_2679_3,plain,
! [U_9474,U_9475,U_9476,U_9477,U_9478,U_9479] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9474,tc_fun(U_9475,tc_HOL_Obool)),U_9476),hAPP(hAPP(c_COMBB(U_9477,tc_fun(U_9475,tc_HOL_Obool),U_9474),U_9478),U_9479)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9477,tc_fun(U_9475,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9474,U_9477,U_9479),U_9476)),U_9478),
inference(definitional_conversion,[status(esa)],[f_2679_2]) ).
cnf(f_2679_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9474,tc_fun(U_9475,tc_HOL_Obool)),U_9476),hAPP(hAPP(c_COMBB(U_9477,tc_fun(U_9475,tc_HOL_Obool),U_9474),U_9478),U_9479)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9477,tc_fun(U_9475,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9474,U_9477,U_9479),U_9476)),U_9478),
inference(clausify,[status(thm)],[f_2679_3]) ).
fof(f_2680_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_image__image]) ).
fof(f_2680_2,plain,
! [U_9485,U_9484,U_9483,U_9482,U_9481,U_9480] : hAPP(c_Set_Oimage(U_9480,U_9481,U_9482),hAPP(c_Set_Oimage(U_9483,U_9480,U_9484),U_9485)) = hAPP(c_Set_Oimage(U_9483,U_9481,hAPP(hAPP(c_COMBB(U_9480,U_9481,U_9483),U_9482),U_9484)),U_9485),
inference(variable_rename,[status(thm)],[f_2680_1]) ).
fof(f_2680_3,plain,
! [U_9481,U_9480,U_9482,U_9483,U_9484,U_9485] : hAPP(c_Set_Oimage(U_9480,U_9481,U_9482),hAPP(c_Set_Oimage(U_9483,U_9480,U_9484),U_9485)) = hAPP(c_Set_Oimage(U_9483,U_9481,hAPP(hAPP(c_COMBB(U_9480,U_9481,U_9483),U_9482),U_9484)),U_9485),
inference(definitional_conversion,[status(esa)],[f_2680_2]) ).
cnf(f_2680_4,plain,
hAPP(c_Set_Oimage(U_9480,U_9481,U_9482),hAPP(c_Set_Oimage(U_9483,U_9480,U_9484),U_9485)) = hAPP(c_Set_Oimage(U_9483,U_9481,hAPP(hAPP(c_COMBB(U_9480,U_9481,U_9483),U_9482),U_9484)),U_9485),
inference(clausify,[status(thm)],[f_2680_3]) ).
fof(f_2681_1,plain,
! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
inference(fof_nnf,[status(thm)],[fact_image__ident]) ).
fof(f_2681_2,plain,
! [U_9487,U_9486] : hAPP(c_Set_Oimage(U_9486,U_9486,c_COMBI(U_9486)),U_9487) = U_9487,
inference(variable_rename,[status(thm)],[f_2681_1]) ).
fof(f_2681_3,plain,
! [U_9487,U_9486] : hAPP(c_Set_Oimage(U_9486,U_9486,c_COMBI(U_9486)),U_9487) = U_9487,
inference(definitional_conversion,[status(esa)],[f_2681_2]) ).
cnf(f_2681_4,plain,
hAPP(c_Set_Oimage(U_9486,U_9486,c_COMBI(U_9486)),U_9487) = U_9487,
inference(clausify,[status(thm)],[f_2681_3]) ).
fof(f_2682_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I10_J]) ).
fof(f_2682_2,plain,
! [U_9493,U_9492,U_9491,U_9490,U_9489,U_9488] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9488,tc_fun(U_9489,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9490,U_9488,U_9491),U_9492)),U_9493) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9490,tc_fun(U_9489,tc_HOL_Obool)),U_9492),hAPP(hAPP(c_COMBB(U_9488,tc_fun(U_9489,tc_HOL_Obool),U_9490),U_9493),U_9491)),
inference(variable_rename,[status(thm)],[f_2682_1]) ).
fof(f_2682_3,plain,
! [U_9488,U_9489,U_9490,U_9491,U_9492,U_9493] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9488,tc_fun(U_9489,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9490,U_9488,U_9491),U_9492)),U_9493) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9490,tc_fun(U_9489,tc_HOL_Obool)),U_9492),hAPP(hAPP(c_COMBB(U_9488,tc_fun(U_9489,tc_HOL_Obool),U_9490),U_9493),U_9491)),
inference(definitional_conversion,[status(esa)],[f_2682_2]) ).
cnf(f_2682_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9488,tc_fun(U_9489,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9490,U_9488,U_9491),U_9492)),U_9493) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9490,tc_fun(U_9489,tc_HOL_Obool)),U_9492),hAPP(hAPP(c_COMBB(U_9488,tc_fun(U_9489,tc_HOL_Obool),U_9490),U_9493),U_9491)),
inference(clausify,[status(thm)],[f_2682_3]) ).
fof(f_2683_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I10_J]) ).
fof(f_2683_2,plain,
! [U_9499,U_9498,U_9497,U_9496,U_9495,U_9494] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9494,tc_fun(U_9495,tc_HOL_Obool)),U_9496),hAPP(hAPP(c_COMBB(U_9497,tc_fun(U_9495,tc_HOL_Obool),U_9494),U_9498),U_9499)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9497,tc_fun(U_9495,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9494,U_9497,U_9499),U_9496)),U_9498),
inference(variable_rename,[status(thm)],[f_2683_1]) ).
fof(f_2683_3,plain,
! [U_9494,U_9495,U_9496,U_9497,U_9498,U_9499] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9494,tc_fun(U_9495,tc_HOL_Obool)),U_9496),hAPP(hAPP(c_COMBB(U_9497,tc_fun(U_9495,tc_HOL_Obool),U_9494),U_9498),U_9499)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9497,tc_fun(U_9495,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9494,U_9497,U_9499),U_9496)),U_9498),
inference(definitional_conversion,[status(esa)],[f_2683_2]) ).
cnf(f_2683_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9494,tc_fun(U_9495,tc_HOL_Obool)),U_9496),hAPP(hAPP(c_COMBB(U_9497,tc_fun(U_9495,tc_HOL_Obool),U_9494),U_9498),U_9499)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9497,tc_fun(U_9495,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9494,U_9497,U_9499),U_9496)),U_9498),
inference(clausify,[status(thm)],[f_2683_3]) ).
fof(f_2684_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_int__setsum]) ).
fof(f_2684_2,plain,
! [U_9502,U_9501,U_9500] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9500,tc_Nat_Onat),U_9501),U_9502)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9500,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9500),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9501)),U_9502),
inference(variable_rename,[status(thm)],[f_2684_1]) ).
fof(f_2684_3,plain,
! [U_9500,U_9501,U_9502] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9500,tc_Nat_Onat),U_9501),U_9502)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9500,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9500),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9501)),U_9502),
inference(definitional_conversion,[status(esa)],[f_2684_2]) ).
cnf(f_2684_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9500,tc_Nat_Onat),U_9501),U_9502)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9500,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9500),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9501)),U_9502),
inference(clausify,[status(thm)],[f_2684_3]) ).
fof(f_2685_1,plain,
! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib]) ).
fof(f_2685_2,plain,
! [U_9508,U_9507,U_9506,U_9505,U_9504,U_9503] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9503,tc_fun(U_9506,tc_HOL_Obool)),U_9505),hAPP(hAPP(c_COMBB(tc_fun(U_9506,tc_HOL_Obool),tc_fun(U_9506,tc_HOL_Obool),U_9503),hAPP(c_Set_Oinsert(U_9506),U_9507)),U_9508)) = hAPP(hAPP(c_Set_Oinsert(U_9506),U_9507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9503,tc_fun(U_9506,tc_HOL_Obool)),U_9505),U_9508))
| ~ hBOOL(hAPP(hAPP(c_member(U_9503),U_9504),U_9505)) ),
inference(variable_rename,[status(thm)],[f_2685_1]) ).
fof(f_2685_3,plain,
! [U_9503,U_9504,U_9505,U_9506,U_9507,U_9508] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9503,tc_fun(U_9506,tc_HOL_Obool)),U_9505),hAPP(hAPP(c_COMBB(tc_fun(U_9506,tc_HOL_Obool),tc_fun(U_9506,tc_HOL_Obool),U_9503),hAPP(c_Set_Oinsert(U_9506),U_9507)),U_9508)) = hAPP(hAPP(c_Set_Oinsert(U_9506),U_9507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9503,tc_fun(U_9506,tc_HOL_Obool)),U_9505),U_9508))
| ~ hBOOL(hAPP(hAPP(c_member(U_9503),U_9504),U_9505)) ),
inference(definitional_conversion,[status(esa)],[f_2685_2]) ).
cnf(f_2685_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9503,tc_fun(U_9506,tc_HOL_Obool)),U_9505),hAPP(hAPP(c_COMBB(tc_fun(U_9506,tc_HOL_Obool),tc_fun(U_9506,tc_HOL_Obool),U_9503),hAPP(c_Set_Oinsert(U_9506),U_9507)),U_9508)) = hAPP(hAPP(c_Set_Oinsert(U_9506),U_9507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9503,tc_fun(U_9506,tc_HOL_Obool)),U_9505),U_9508))
| ~ hBOOL(hAPP(hAPP(c_member(U_9503),U_9504),U_9505)) ),
inference(clausify,[status(thm)],[f_2685_3]) ).
fof(f_2686_1,plain,
! [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))
| ~ 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)))) )
& ( 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))))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2]) ).
fof(f_2686_2,plain,
! [U_9512,U_9511,U_9510,U_9509] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_fun(U_9510,tc_HOL_Obool))),U_9511),U_9512))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9509,U_9510)),hAPP(hAPP(c_Product__Type_OPair(U_9509,U_9510),U_9511),U_9512)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9509,U_9510),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9509,U_9510)),hAPP(hAPP(c_Product__Type_OPair(U_9509,U_9510),U_9511),U_9512)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9509,U_9510),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_fun(U_9510,tc_HOL_Obool))),U_9511),U_9512)) ) ),
inference(variable_rename,[status(thm)],[f_2686_1]) ).
fof(f_2686_3,plain,
( ! [U_9520,U_9518,U_9516,U_9514] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9514,tc_fun(U_9516,tc_HOL_Obool))),U_9518),U_9520))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9514,U_9516)),hAPP(hAPP(c_Product__Type_OPair(U_9514,U_9516),U_9518),U_9520)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9514,U_9516),tc_HOL_Obool)))) )
& ! [U_9519,U_9517,U_9515,U_9513] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9513,U_9515)),hAPP(hAPP(c_Product__Type_OPair(U_9513,U_9515),U_9517),U_9519)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9513,U_9515),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9513,tc_fun(U_9515,tc_HOL_Obool))),U_9517),U_9519)) ) ),
inference(miniscope,[status(thm)],[f_2686_2]) ).
fof(f_2686_4,plain,
( ! [U_9514,U_9516,U_9518,U_9520] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9514,tc_fun(U_9516,tc_HOL_Obool))),U_9518),U_9520))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9514,U_9516)),hAPP(hAPP(c_Product__Type_OPair(U_9514,U_9516),U_9518),U_9520)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9514,U_9516),tc_HOL_Obool)))) )
& ! [U_9519,U_9515,U_9513,U_9517] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9513,U_9515)),hAPP(hAPP(c_Product__Type_OPair(U_9513,U_9515),U_9517),U_9519)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9513,U_9515),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9513,tc_fun(U_9515,tc_HOL_Obool))),U_9517),U_9519)) ) ),
inference(definitional_conversion,[status(esa)],[f_2686_3]) ).
cnf(f_2686_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9513,U_9515)),hAPP(hAPP(c_Product__Type_OPair(U_9513,U_9515),U_9517),U_9519)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9513,U_9515),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9513,tc_fun(U_9515,tc_HOL_Obool))),U_9517),U_9519)) ),
inference(clausify,[status(thm)],[f_2686_4]) ).
cnf(f_2686_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9514,tc_fun(U_9516,tc_HOL_Obool))),U_9518),U_9520))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9514,U_9516)),hAPP(hAPP(c_Product__Type_OPair(U_9514,U_9516),U_9518),U_9520)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9514,U_9516),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2686_4]) ).
fof(f_2687_1,plain,
! [V_x_2,T_b] :
( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_bot__empty__eq]) ).
fof(f_2687_2,plain,
! [U_9522,U_9521] :
( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9521,tc_HOL_Obool)),U_9522))
| ~ hBOOL(hAPP(hAPP(c_member(U_9521),U_9522),c_Orderings_Obot__class_Obot(tc_fun(U_9521,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(U_9521),U_9522),c_Orderings_Obot__class_Obot(tc_fun(U_9521,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9521,tc_HOL_Obool)),U_9522)) ) ),
inference(variable_rename,[status(thm)],[f_2687_1]) ).
fof(f_2687_3,plain,
( ! [U_9526,U_9524] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9524,tc_HOL_Obool)),U_9526))
| ~ hBOOL(hAPP(hAPP(c_member(U_9524),U_9526),c_Orderings_Obot__class_Obot(tc_fun(U_9524,tc_HOL_Obool)))) )
& ! [U_9525,U_9523] :
( hBOOL(hAPP(hAPP(c_member(U_9523),U_9525),c_Orderings_Obot__class_Obot(tc_fun(U_9523,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9523,tc_HOL_Obool)),U_9525)) ) ),
inference(miniscope,[status(thm)],[f_2687_2]) ).
fof(f_2687_4,plain,
( ! [U_9524,U_9526] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9524,tc_HOL_Obool)),U_9526))
| ~ hBOOL(hAPP(hAPP(c_member(U_9524),U_9526),c_Orderings_Obot__class_Obot(tc_fun(U_9524,tc_HOL_Obool)))) )
& ! [U_9525,U_9523] :
( hBOOL(hAPP(hAPP(c_member(U_9523),U_9525),c_Orderings_Obot__class_Obot(tc_fun(U_9523,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9523,tc_HOL_Obool)),U_9525)) ) ),
inference(definitional_conversion,[status(esa)],[f_2687_3]) ).
cnf(f_2687_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9523),U_9525),c_Orderings_Obot__class_Obot(tc_fun(U_9523,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9523,tc_HOL_Obool)),U_9525)) ),
inference(clausify,[status(thm)],[f_2687_4]) ).
cnf(f_2687_6,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9524,tc_HOL_Obool)),U_9526))
| ~ hBOOL(hAPP(hAPP(c_member(U_9524),U_9526),c_Orderings_Obot__class_Obot(tc_fun(U_9524,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2687_4]) ).
fof(f_2688_1,plain,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( ( 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)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__iff]) ).
fof(f_2688_2,plain,
! [U_9533,U_9532,U_9531,U_9530,U_9529] :
( ( hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9531,tc_fun(U_9529,tc_HOL_Obool)),U_9532),U_9533)))
| ! [U_9528] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),hAPP(U_9533,U_9528)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9531),U_9528),U_9532)) ) )
& ( ? [U_9527] :
( hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),hAPP(U_9533,U_9527)))
& hBOOL(hAPP(hAPP(c_member(U_9531),U_9527),U_9532)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9531,tc_fun(U_9529,tc_HOL_Obool)),U_9532),U_9533))) ) ),
inference(variable_rename,[status(thm)],[f_2688_1]) ).
fof(f_2688_3,plain,
( ! [U_9543,U_9541,U_9539,U_9537,U_9535] :
( hBOOL(hAPP(hAPP(c_member(U_9535),U_9537),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9539,tc_fun(U_9535,tc_HOL_Obool)),U_9541),U_9543)))
| ! [U_9528] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9535),U_9537),hAPP(U_9543,U_9528)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9539),U_9528),U_9541)) ) )
& ! [U_9542,U_9540,U_9538,U_9536,U_9534] :
( ? [U_9527] :
( hBOOL(hAPP(hAPP(c_member(U_9534),U_9536),hAPP(U_9542,U_9527)))
& hBOOL(hAPP(hAPP(c_member(U_9538),U_9527),U_9540)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9534),U_9536),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9538,tc_fun(U_9534,tc_HOL_Obool)),U_9540),U_9542))) ) ),
inference(miniscope,[status(thm)],[f_2688_2]) ).
fof(f_2688_4,plain,
( ! [U_9543,U_9541,U_9539,U_9537,U_9535] :
( hBOOL(hAPP(hAPP(c_member(U_9535),U_9537),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9539,tc_fun(U_9535,tc_HOL_Obool)),U_9541),U_9543)))
| ! [U_9528] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9535),U_9537),hAPP(U_9543,U_9528)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9539),U_9528),U_9541)) ) )
& ! [U_9542,U_9540,U_9538,U_9536,U_9534] :
( ( hBOOL(hAPP(hAPP(c_member(U_9534),U_9536),hAPP(U_9542,sK251(U_9542,U_9540,U_9538,U_9536,U_9534))))
& hBOOL(hAPP(hAPP(c_member(U_9538),sK251(U_9542,U_9540,U_9538,U_9536,U_9534)),U_9540)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9534),U_9536),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9538,tc_fun(U_9534,tc_HOL_Obool)),U_9540),U_9542))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_9527,sK251(U_9542,U_9540,U_9538,U_9536,U_9534))],[f_2688_3]) ).
fof(f_2688_5,plain,
( ! [U_9536,U_9534,U_9538,U_9542,U_9540] :
( hBOOL(hAPP(hAPP(c_member(U_9534),U_9536),hAPP(U_9542,sK251(U_9542,U_9540,U_9538,U_9536,U_9534))))
| ~ sP789(U_9536,U_9534,U_9538,U_9542,U_9540) )
& ! [U_9536,U_9534,U_9538,U_9542,U_9540] :
( hBOOL(hAPP(hAPP(c_member(U_9538),sK251(U_9542,U_9540,U_9538,U_9536,U_9534)),U_9540))
| ~ sP789(U_9536,U_9534,U_9538,U_9542,U_9540) )
& ! [U_9528,U_9537,U_9535,U_9541,U_9543,U_9539] :
( hBOOL(hAPP(hAPP(c_member(U_9535),U_9537),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9539,tc_fun(U_9535,tc_HOL_Obool)),U_9541),U_9543)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9535),U_9537),hAPP(U_9543,U_9528)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9539),U_9528),U_9541)) )
& ! [U_9536,U_9534,U_9538,U_9542,U_9540] :
( sP789(U_9536,U_9534,U_9538,U_9542,U_9540)
| ~ hBOOL(hAPP(hAPP(c_member(U_9534),U_9536),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9538,tc_fun(U_9534,tc_HOL_Obool)),U_9540),U_9542))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP789])],[f_2688_4]) ).
cnf(f_2688_6,plain,
( sP789(U_9536,U_9534,U_9538,U_9542,U_9540)
| ~ hBOOL(hAPP(hAPP(c_member(U_9534),U_9536),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9538,tc_fun(U_9534,tc_HOL_Obool)),U_9540),U_9542))) ),
inference(clausify,[status(thm)],[f_2688_5]) ).
cnf(f_2688_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_9535),U_9537),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9539,tc_fun(U_9535,tc_HOL_Obool)),U_9541),U_9543)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9535),U_9537),hAPP(U_9543,U_9528)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9539),U_9528),U_9541)) ),
inference(clausify,[status(thm)],[f_2688_5]) ).
cnf(f_2688_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9538),sK251(U_9542,U_9540,U_9538,U_9536,U_9534)),U_9540))
| ~ sP789(U_9536,U_9534,U_9538,U_9542,U_9540) ),
inference(clausify,[status(thm)],[f_2688_5]) ).
cnf(f_2688_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_9534),U_9536),hAPP(U_9542,sK251(U_9542,U_9540,U_9538,U_9536,U_9534))))
| ~ sP789(U_9536,U_9534,U_9538,U_9542,U_9540) ),
inference(clausify,[status(thm)],[f_2688_5]) ).
fof(f_2689_1,plain,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( ( 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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__iff]) ).
fof(f_2689_2,plain,
! [U_9550,U_9549,U_9548,U_9547,U_9546] :
( ( hBOOL(hAPP(hAPP(c_member(U_9546),U_9547),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9548,tc_fun(U_9546,tc_HOL_Obool)),U_9549),U_9550)))
| ? [U_9545] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9546),U_9547),hAPP(U_9550,U_9545)))
& hBOOL(hAPP(hAPP(c_member(U_9548),U_9545),U_9549)) ) )
& ( ! [U_9544] :
( hBOOL(hAPP(hAPP(c_member(U_9546),U_9547),hAPP(U_9550,U_9544)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9548),U_9544),U_9549)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9546),U_9547),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9548,tc_fun(U_9546,tc_HOL_Obool)),U_9549),U_9550))) ) ),
inference(variable_rename,[status(thm)],[f_2689_1]) ).
fof(f_2689_3,plain,
( ! [U_9560,U_9558,U_9556,U_9554,U_9552] :
( hBOOL(hAPP(hAPP(c_member(U_9552),U_9554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9556,tc_fun(U_9552,tc_HOL_Obool)),U_9558),U_9560)))
| ? [U_9545] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9552),U_9554),hAPP(U_9560,U_9545)))
& hBOOL(hAPP(hAPP(c_member(U_9556),U_9545),U_9558)) ) )
& ! [U_9559,U_9557,U_9555,U_9553,U_9551] :
( ! [U_9544] :
( hBOOL(hAPP(hAPP(c_member(U_9551),U_9553),hAPP(U_9559,U_9544)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9555),U_9544),U_9557)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9551),U_9553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9555,tc_fun(U_9551,tc_HOL_Obool)),U_9557),U_9559))) ) ),
inference(miniscope,[status(thm)],[f_2689_2]) ).
fof(f_2689_4,plain,
( ! [U_9560,U_9558,U_9556,U_9554,U_9552] :
( hBOOL(hAPP(hAPP(c_member(U_9552),U_9554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9556,tc_fun(U_9552,tc_HOL_Obool)),U_9558),U_9560)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_9552),U_9554),hAPP(U_9560,sK252(U_9560,U_9558,U_9556,U_9554,U_9552))))
& hBOOL(hAPP(hAPP(c_member(U_9556),sK252(U_9560,U_9558,U_9556,U_9554,U_9552)),U_9558)) ) )
& ! [U_9559,U_9557,U_9555,U_9553,U_9551] :
( ! [U_9544] :
( hBOOL(hAPP(hAPP(c_member(U_9551),U_9553),hAPP(U_9559,U_9544)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9555),U_9544),U_9557)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9551),U_9553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9555,tc_fun(U_9551,tc_HOL_Obool)),U_9557),U_9559))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_9545,sK252(U_9560,U_9558,U_9556,U_9554,U_9552))],[f_2689_3]) ).
fof(f_2689_5,plain,
( ! [U_9552,U_9554,U_9558,U_9560,U_9556] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9552),U_9554),hAPP(U_9560,sK252(U_9560,U_9558,U_9556,U_9554,U_9552))))
| ~ sP790(U_9552,U_9554,U_9558,U_9560,U_9556) )
& ! [U_9552,U_9554,U_9558,U_9560,U_9556] :
( hBOOL(hAPP(hAPP(c_member(U_9556),sK252(U_9560,U_9558,U_9556,U_9554,U_9552)),U_9558))
| ~ sP790(U_9552,U_9554,U_9558,U_9560,U_9556) )
& ! [U_9552,U_9554,U_9558,U_9560,U_9556] :
( hBOOL(hAPP(hAPP(c_member(U_9552),U_9554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9556,tc_fun(U_9552,tc_HOL_Obool)),U_9558),U_9560)))
| sP790(U_9552,U_9554,U_9558,U_9560,U_9556) )
& ! [U_9555,U_9553,U_9544,U_9551,U_9559,U_9557] :
( hBOOL(hAPP(hAPP(c_member(U_9551),U_9553),hAPP(U_9559,U_9544)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9555),U_9544),U_9557))
| ~ hBOOL(hAPP(hAPP(c_member(U_9551),U_9553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9555,tc_fun(U_9551,tc_HOL_Obool)),U_9557),U_9559))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP790])],[f_2689_4]) ).
cnf(f_2689_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9551),U_9553),hAPP(U_9559,U_9544)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9555),U_9544),U_9557))
| ~ hBOOL(hAPP(hAPP(c_member(U_9551),U_9553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9555,tc_fun(U_9551,tc_HOL_Obool)),U_9557),U_9559))) ),
inference(clausify,[status(thm)],[f_2689_5]) ).
cnf(f_2689_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_9552),U_9554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9556,tc_fun(U_9552,tc_HOL_Obool)),U_9558),U_9560)))
| sP790(U_9552,U_9554,U_9558,U_9560,U_9556) ),
inference(clausify,[status(thm)],[f_2689_5]) ).
cnf(f_2689_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9556),sK252(U_9560,U_9558,U_9556,U_9554,U_9552)),U_9558))
| ~ sP790(U_9552,U_9554,U_9558,U_9560,U_9556) ),
inference(clausify,[status(thm)],[f_2689_5]) ).
cnf(f_2689_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9552),U_9554),hAPP(U_9560,sK252(U_9560,U_9558,U_9556,U_9554,U_9552))))
| ~ sP790(U_9552,U_9554,U_9558,U_9560,U_9556) ),
inference(clausify,[status(thm)],[f_2689_5]) ).
fof(f_2690_1,plain,
! [V_S_2,V_R_2,T_b] :
( ( 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_R_2 != V_S_2 )
& ( V_R_2 = V_S_2
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__equals__eq]) ).
fof(f_2690_2,plain,
! [U_9563,U_9562,U_9561] :
( ( hAPP(hAPP(c_COMBC(U_9561,tc_fun(U_9561,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9561)),U_9562) = hAPP(hAPP(c_COMBC(U_9561,tc_fun(U_9561,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9561)),U_9563)
| U_9562 != U_9563 )
& ( U_9562 = U_9563
| hAPP(hAPP(c_COMBC(U_9561,tc_fun(U_9561,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9561)),U_9562) != hAPP(hAPP(c_COMBC(U_9561,tc_fun(U_9561,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9561)),U_9563) ) ),
inference(variable_rename,[status(thm)],[f_2690_1]) ).
fof(f_2690_3,plain,
( ! [U_9569,U_9567] :
( ! [U_9565] : hAPP(hAPP(c_COMBC(U_9565,tc_fun(U_9565,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9565)),U_9567) = hAPP(hAPP(c_COMBC(U_9565,tc_fun(U_9565,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9565)),U_9569)
| U_9567 != U_9569 )
& ! [U_9568,U_9566] :
( ! [U_9564] : hAPP(hAPP(c_COMBC(U_9564,tc_fun(U_9564,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9564)),U_9566) != hAPP(hAPP(c_COMBC(U_9564,tc_fun(U_9564,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9564)),U_9568)
| U_9566 = U_9568 ) ),
inference(miniscope,[status(thm)],[f_2690_2]) ).
fof(f_2690_4,plain,
( ! [U_9565,U_9569,U_9567] :
( hAPP(hAPP(c_COMBC(U_9565,tc_fun(U_9565,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9565)),U_9567) = hAPP(hAPP(c_COMBC(U_9565,tc_fun(U_9565,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9565)),U_9569)
| U_9567 != U_9569 )
& ! [U_9564,U_9566,U_9568] :
( hAPP(hAPP(c_COMBC(U_9564,tc_fun(U_9564,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9564)),U_9566) != hAPP(hAPP(c_COMBC(U_9564,tc_fun(U_9564,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9564)),U_9568)
| U_9566 = U_9568 ) ),
inference(definitional_conversion,[status(esa)],[f_2690_3]) ).
cnf(f_2690_5,plain,
( hAPP(hAPP(c_COMBC(U_9564,tc_fun(U_9564,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9564)),U_9566) != hAPP(hAPP(c_COMBC(U_9564,tc_fun(U_9564,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9564)),U_9568)
| U_9566 = U_9568 ),
inference(clausify,[status(thm)],[f_2690_4]) ).
cnf(f_2690_6,plain,
( hAPP(hAPP(c_COMBC(U_9565,tc_fun(U_9565,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9565)),U_9567) = hAPP(hAPP(c_COMBC(U_9565,tc_fun(U_9565,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9565)),U_9569)
| U_9567 != U_9569 ),
inference(clausify,[status(thm)],[f_2690_4]) ).
fof(f_2691_1,plain,
! [V_S_2,V_R_2,T_c,T_b] :
( ( 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_R_2 != V_S_2 )
& ( V_R_2 = V_S_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_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) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2]) ).
fof(f_2691_2,plain,
! [U_9573,U_9572,U_9571,U_9570] :
( ( hAPP(hAPP(c_COMBC(U_9570,tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9571,tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_fun(U_9571,tc_HOL_Obool)),U_9570),c_COMBC(U_9571,tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9571,tc_prod(U_9570,U_9571)),tc_fun(U_9571,tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),U_9570),hAPP(c_COMBB(tc_prod(U_9570,U_9571),tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool),U_9571),c_member(tc_prod(U_9570,U_9571)))),c_Product__Type_OPair(U_9570,U_9571)))),U_9572) = hAPP(hAPP(c_COMBC(U_9570,tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9571,tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_fun(U_9571,tc_HOL_Obool)),U_9570),c_COMBC(U_9571,tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9571,tc_prod(U_9570,U_9571)),tc_fun(U_9571,tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),U_9570),hAPP(c_COMBB(tc_prod(U_9570,U_9571),tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool),U_9571),c_member(tc_prod(U_9570,U_9571)))),c_Product__Type_OPair(U_9570,U_9571)))),U_9573)
| U_9572 != U_9573 )
& ( U_9572 = U_9573
| hAPP(hAPP(c_COMBC(U_9570,tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9571,tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_fun(U_9571,tc_HOL_Obool)),U_9570),c_COMBC(U_9571,tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9571,tc_prod(U_9570,U_9571)),tc_fun(U_9571,tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),U_9570),hAPP(c_COMBB(tc_prod(U_9570,U_9571),tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool),U_9571),c_member(tc_prod(U_9570,U_9571)))),c_Product__Type_OPair(U_9570,U_9571)))),U_9572) != hAPP(hAPP(c_COMBC(U_9570,tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9571,tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_fun(U_9571,tc_HOL_Obool)),U_9570),c_COMBC(U_9571,tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9571,tc_prod(U_9570,U_9571)),tc_fun(U_9571,tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool)),U_9570),hAPP(c_COMBB(tc_prod(U_9570,U_9571),tc_fun(tc_fun(tc_prod(U_9570,U_9571),tc_HOL_Obool),tc_HOL_Obool),U_9571),c_member(tc_prod(U_9570,U_9571)))),c_Product__Type_OPair(U_9570,U_9571)))),U_9573) ) ),
inference(variable_rename,[status(thm)],[f_2691_1]) ).
fof(f_2691_3,plain,
( ! [U_9581,U_9579] :
( ! [U_9577,U_9575] : hAPP(hAPP(c_COMBC(U_9575,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9575),c_COMBC(U_9577,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_prod(U_9575,U_9577)),tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),U_9575),hAPP(c_COMBB(tc_prod(U_9575,U_9577),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool),U_9577),c_member(tc_prod(U_9575,U_9577)))),c_Product__Type_OPair(U_9575,U_9577)))),U_9579) = hAPP(hAPP(c_COMBC(U_9575,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9575),c_COMBC(U_9577,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_prod(U_9575,U_9577)),tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),U_9575),hAPP(c_COMBB(tc_prod(U_9575,U_9577),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool),U_9577),c_member(tc_prod(U_9575,U_9577)))),c_Product__Type_OPair(U_9575,U_9577)))),U_9581)
| U_9579 != U_9581 )
& ! [U_9580,U_9578] :
( ! [U_9576,U_9574] : hAPP(hAPP(c_COMBC(U_9574,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),U_9574),c_COMBC(U_9576,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_prod(U_9574,U_9576)),tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),U_9574),hAPP(c_COMBB(tc_prod(U_9574,U_9576),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool),U_9576),c_member(tc_prod(U_9574,U_9576)))),c_Product__Type_OPair(U_9574,U_9576)))),U_9578) != hAPP(hAPP(c_COMBC(U_9574,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),U_9574),c_COMBC(U_9576,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_prod(U_9574,U_9576)),tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),U_9574),hAPP(c_COMBB(tc_prod(U_9574,U_9576),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool),U_9576),c_member(tc_prod(U_9574,U_9576)))),c_Product__Type_OPair(U_9574,U_9576)))),U_9580)
| U_9578 = U_9580 ) ),
inference(miniscope,[status(thm)],[f_2691_2]) ).
fof(f_2691_4,plain,
( ! [U_9579,U_9581,U_9575,U_9577] :
( hAPP(hAPP(c_COMBC(U_9575,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9575),c_COMBC(U_9577,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_prod(U_9575,U_9577)),tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),U_9575),hAPP(c_COMBB(tc_prod(U_9575,U_9577),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool),U_9577),c_member(tc_prod(U_9575,U_9577)))),c_Product__Type_OPair(U_9575,U_9577)))),U_9579) = hAPP(hAPP(c_COMBC(U_9575,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9575),c_COMBC(U_9577,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_prod(U_9575,U_9577)),tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),U_9575),hAPP(c_COMBB(tc_prod(U_9575,U_9577),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool),U_9577),c_member(tc_prod(U_9575,U_9577)))),c_Product__Type_OPair(U_9575,U_9577)))),U_9581)
| U_9579 != U_9581 )
& ! [U_9578,U_9576,U_9574,U_9580] :
( hAPP(hAPP(c_COMBC(U_9574,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),U_9574),c_COMBC(U_9576,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_prod(U_9574,U_9576)),tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),U_9574),hAPP(c_COMBB(tc_prod(U_9574,U_9576),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool),U_9576),c_member(tc_prod(U_9574,U_9576)))),c_Product__Type_OPair(U_9574,U_9576)))),U_9578) != hAPP(hAPP(c_COMBC(U_9574,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),U_9574),c_COMBC(U_9576,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_prod(U_9574,U_9576)),tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),U_9574),hAPP(c_COMBB(tc_prod(U_9574,U_9576),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool),U_9576),c_member(tc_prod(U_9574,U_9576)))),c_Product__Type_OPair(U_9574,U_9576)))),U_9580)
| U_9578 = U_9580 ) ),
inference(definitional_conversion,[status(esa)],[f_2691_3]) ).
cnf(f_2691_5,plain,
( hAPP(hAPP(c_COMBC(U_9574,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),U_9574),c_COMBC(U_9576,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_prod(U_9574,U_9576)),tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),U_9574),hAPP(c_COMBB(tc_prod(U_9574,U_9576),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool),U_9576),c_member(tc_prod(U_9574,U_9576)))),c_Product__Type_OPair(U_9574,U_9576)))),U_9578) != hAPP(hAPP(c_COMBC(U_9574,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_fun(U_9576,tc_HOL_Obool)),U_9574),c_COMBC(U_9576,tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9576,tc_prod(U_9574,U_9576)),tc_fun(U_9576,tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool)),U_9574),hAPP(c_COMBB(tc_prod(U_9574,U_9576),tc_fun(tc_fun(tc_prod(U_9574,U_9576),tc_HOL_Obool),tc_HOL_Obool),U_9576),c_member(tc_prod(U_9574,U_9576)))),c_Product__Type_OPair(U_9574,U_9576)))),U_9580)
| U_9578 = U_9580 ),
inference(clausify,[status(thm)],[f_2691_4]) ).
cnf(f_2691_6,plain,
( hAPP(hAPP(c_COMBC(U_9575,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9575),c_COMBC(U_9577,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_prod(U_9575,U_9577)),tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),U_9575),hAPP(c_COMBB(tc_prod(U_9575,U_9577),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool),U_9577),c_member(tc_prod(U_9575,U_9577)))),c_Product__Type_OPair(U_9575,U_9577)))),U_9579) = hAPP(hAPP(c_COMBC(U_9575,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9575),c_COMBC(U_9577,tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_prod(U_9575,U_9577)),tc_fun(U_9577,tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool)),U_9575),hAPP(c_COMBB(tc_prod(U_9575,U_9577),tc_fun(tc_fun(tc_prod(U_9575,U_9577),tc_HOL_Obool),tc_HOL_Obool),U_9577),c_member(tc_prod(U_9575,U_9577)))),c_Product__Type_OPair(U_9575,U_9577)))),U_9581)
| U_9579 != U_9581 ),
inference(clausify,[status(thm)],[f_2691_4]) ).
fof(f_2692_1,plain,
! [V_Pa_2,V_a_2,T_b] :
( hBOOL(hAPP(V_Pa_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_CollectE]) ).
fof(f_2692_2,plain,
! [U_9584,U_9583,U_9582] :
( hBOOL(hAPP(U_9584,U_9583))
| ~ hBOOL(hAPP(hAPP(c_member(U_9582),U_9583),hAPP(c_Set_OCollect(U_9582),U_9584))) ),
inference(variable_rename,[status(thm)],[f_2692_1]) ).
fof(f_2692_3,plain,
! [U_9584,U_9583] :
( ! [U_9582] : ~ hBOOL(hAPP(hAPP(c_member(U_9582),U_9583),hAPP(c_Set_OCollect(U_9582),U_9584)))
| hBOOL(hAPP(U_9584,U_9583)) ),
inference(miniscope,[status(thm)],[f_2692_2]) ).
fof(f_2692_4,plain,
! [U_9582,U_9583,U_9584] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9582),U_9583),hAPP(c_Set_OCollect(U_9582),U_9584)))
| hBOOL(hAPP(U_9584,U_9583)) ),
inference(definitional_conversion,[status(esa)],[f_2692_3]) ).
cnf(f_2692_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9582),U_9583),hAPP(c_Set_OCollect(U_9582),U_9584)))
| hBOOL(hAPP(U_9584,U_9583)) ),
inference(clausify,[status(thm)],[f_2692_4]) ).
fof(f_2693_1,plain,
! [V_Pa_2,V_a_2,T_b] :
( hBOOL(hAPP(V_Pa_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_CollectD]) ).
fof(f_2693_2,plain,
! [U_9587,U_9586,U_9585] :
( hBOOL(hAPP(U_9587,U_9586))
| ~ hBOOL(hAPP(hAPP(c_member(U_9585),U_9586),hAPP(c_Set_OCollect(U_9585),U_9587))) ),
inference(variable_rename,[status(thm)],[f_2693_1]) ).
fof(f_2693_3,plain,
! [U_9587,U_9586] :
( ! [U_9585] : ~ hBOOL(hAPP(hAPP(c_member(U_9585),U_9586),hAPP(c_Set_OCollect(U_9585),U_9587)))
| hBOOL(hAPP(U_9587,U_9586)) ),
inference(miniscope,[status(thm)],[f_2693_2]) ).
fof(f_2693_4,plain,
! [U_9585,U_9586,U_9587] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9585),U_9586),hAPP(c_Set_OCollect(U_9585),U_9587)))
| hBOOL(hAPP(U_9587,U_9586)) ),
inference(definitional_conversion,[status(esa)],[f_2693_3]) ).
cnf(f_2693_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9585),U_9586),hAPP(c_Set_OCollect(U_9585),U_9587)))
| hBOOL(hAPP(U_9587,U_9586)) ),
inference(clausify,[status(thm)],[f_2693_4]) ).
fof(f_2694_1,plain,
! [V_Pa_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
| ~ hBOOL(hAPP(V_Pa_2,V_a_2)) )
& ( hBOOL(hAPP(V_Pa_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).
fof(f_2694_2,plain,
! [U_9590,U_9589,U_9588] :
( ( hBOOL(hAPP(hAPP(c_member(U_9588),U_9589),hAPP(c_Set_OCollect(U_9588),U_9590)))
| ~ hBOOL(hAPP(U_9590,U_9589)) )
& ( hBOOL(hAPP(U_9590,U_9589))
| ~ hBOOL(hAPP(hAPP(c_member(U_9588),U_9589),hAPP(c_Set_OCollect(U_9588),U_9590))) ) ),
inference(variable_rename,[status(thm)],[f_2694_1]) ).
fof(f_2694_3,plain,
( ! [U_9596,U_9594] :
( ! [U_9592] : hBOOL(hAPP(hAPP(c_member(U_9592),U_9594),hAPP(c_Set_OCollect(U_9592),U_9596)))
| ~ hBOOL(hAPP(U_9596,U_9594)) )
& ! [U_9595,U_9593] :
( ! [U_9591] : ~ hBOOL(hAPP(hAPP(c_member(U_9591),U_9593),hAPP(c_Set_OCollect(U_9591),U_9595)))
| hBOOL(hAPP(U_9595,U_9593)) ) ),
inference(miniscope,[status(thm)],[f_2694_2]) ).
fof(f_2694_4,plain,
( ! [U_9596,U_9592,U_9594] :
( hBOOL(hAPP(hAPP(c_member(U_9592),U_9594),hAPP(c_Set_OCollect(U_9592),U_9596)))
| ~ hBOOL(hAPP(U_9596,U_9594)) )
& ! [U_9591,U_9593,U_9595] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9591),U_9593),hAPP(c_Set_OCollect(U_9591),U_9595)))
| hBOOL(hAPP(U_9595,U_9593)) ) ),
inference(definitional_conversion,[status(esa)],[f_2694_3]) ).
cnf(f_2694_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9591),U_9593),hAPP(c_Set_OCollect(U_9591),U_9595)))
| hBOOL(hAPP(U_9595,U_9593)) ),
inference(clausify,[status(thm)],[f_2694_4]) ).
cnf(f_2694_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9592),U_9594),hAPP(c_Set_OCollect(U_9592),U_9596)))
| ~ hBOOL(hAPP(U_9596,U_9594)) ),
inference(clausify,[status(thm)],[f_2694_4]) ).
fof(f_2695_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_Collect__mem__eq]) ).
fof(f_2695_2,plain,
! [U_9598,U_9597] : hAPP(c_Set_OCollect(U_9597),hAPP(hAPP(c_COMBC(U_9597,tc_fun(U_9597,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9597)),U_9598)) = U_9598,
inference(variable_rename,[status(thm)],[f_2695_1]) ).
fof(f_2695_3,plain,
! [U_9597,U_9598] : hAPP(c_Set_OCollect(U_9597),hAPP(hAPP(c_COMBC(U_9597,tc_fun(U_9597,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9597)),U_9598)) = U_9598,
inference(definitional_conversion,[status(esa)],[f_2695_2]) ).
cnf(f_2695_4,plain,
hAPP(c_Set_OCollect(U_9597),hAPP(hAPP(c_COMBC(U_9597,tc_fun(U_9597,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9597)),U_9598)) = U_9598,
inference(clausify,[status(thm)],[f_2695_3]) ).
fof(f_2696_1,plain,
! [V_Qa_2,V_Pa_2,T_b] :
( ( 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))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) )
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).
fof(f_2696_2,plain,
! [U_9601,U_9600,U_9599] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9599),hAPP(c_Set_OCollect(U_9599),hAPP(hAPP(c_COMBS(U_9599,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9599),c_fdisj),U_9600)),U_9601))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9599),hAPP(c_Set_OCollect(U_9599),U_9601)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9599),hAPP(c_Set_OCollect(U_9599),U_9600))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9599),hAPP(c_Set_OCollect(U_9599),U_9601)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_9599),hAPP(c_Set_OCollect(U_9599),U_9600))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9599),hAPP(c_Set_OCollect(U_9599),hAPP(hAPP(c_COMBS(U_9599,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9599),c_fdisj),U_9600)),U_9601)))) ) ),
inference(variable_rename,[status(thm)],[f_2696_1]) ).
fof(f_2696_3,plain,
( ! [U_9607,U_9605,U_9603] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),hAPP(hAPP(c_COMBS(U_9603,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9603),c_fdisj),U_9605)),U_9607))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),U_9607)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),U_9605))) )
& ! [U_9606,U_9604,U_9602] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),U_9606)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),U_9604))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),hAPP(hAPP(c_COMBS(U_9602,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9602),c_fdisj),U_9604)),U_9606)))) ) ),
inference(miniscope,[status(thm)],[f_2696_2]) ).
fof(f_2696_4,plain,
( ! [U_9604,U_9602,U_9606] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),U_9606)))
| ~ sP791(U_9604,U_9602,U_9606) )
& ! [U_9604,U_9602,U_9606] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),U_9604)))
| ~ sP791(U_9604,U_9602,U_9606) )
& ! [U_9603,U_9607,U_9605] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),hAPP(hAPP(c_COMBS(U_9603,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9603),c_fdisj),U_9605)),U_9607))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),U_9607)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),U_9605))) )
& ! [U_9604,U_9602,U_9606] :
( sP791(U_9604,U_9602,U_9606)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),hAPP(hAPP(c_COMBS(U_9602,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9602),c_fdisj),U_9604)),U_9606)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP791])],[f_2696_3]) ).
cnf(f_2696_5,plain,
( sP791(U_9604,U_9602,U_9606)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),hAPP(hAPP(c_COMBS(U_9602,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9602),c_fdisj),U_9604)),U_9606)))) ),
inference(clausify,[status(thm)],[f_2696_4]) ).
cnf(f_2696_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),hAPP(hAPP(c_COMBS(U_9603,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9603),c_fdisj),U_9605)),U_9607))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),U_9607)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),hAPP(c_Set_OCollect(U_9603),U_9605))) ),
inference(clausify,[status(thm)],[f_2696_4]) ).
cnf(f_2696_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),U_9604)))
| ~ sP791(U_9604,U_9602,U_9606) ),
inference(clausify,[status(thm)],[f_2696_4]) ).
cnf(f_2696_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),hAPP(c_Set_OCollect(U_9602),U_9606)))
| ~ sP791(U_9604,U_9602,U_9606) ),
inference(clausify,[status(thm)],[f_2696_4]) ).
fof(f_2697_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I5_J]) ).
fof(f_2697_2,plain,
! [U_9612,U_9611,U_9610,U_9609,U_9608] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9608,tc_fun(U_9609,tc_HOL_Obool)),U_9610),hAPP(hAPP(c_COMBB(tc_fun(U_9609,tc_HOL_Obool),tc_fun(U_9609,tc_HOL_Obool),U_9608),hAPP(c_Set_Oinsert(U_9609),U_9611)),U_9612)) = hAPP(hAPP(c_Set_Oinsert(U_9609),U_9611),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9608,tc_fun(U_9609,tc_HOL_Obool)),U_9610),U_9612)),
inference(variable_rename,[status(thm)],[f_2697_1]) ).
fof(f_2697_3,plain,
! [U_9609,U_9608,U_9610,U_9611,U_9612] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9608,tc_fun(U_9609,tc_HOL_Obool)),U_9610),hAPP(hAPP(c_COMBB(tc_fun(U_9609,tc_HOL_Obool),tc_fun(U_9609,tc_HOL_Obool),U_9608),hAPP(c_Set_Oinsert(U_9609),U_9611)),U_9612)) = hAPP(hAPP(c_Set_Oinsert(U_9609),U_9611),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9608,tc_fun(U_9609,tc_HOL_Obool)),U_9610),U_9612)),
inference(definitional_conversion,[status(esa)],[f_2697_2]) ).
cnf(f_2697_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9608,tc_fun(U_9609,tc_HOL_Obool)),U_9610),hAPP(hAPP(c_COMBB(tc_fun(U_9609,tc_HOL_Obool),tc_fun(U_9609,tc_HOL_Obool),U_9608),hAPP(c_Set_Oinsert(U_9609),U_9611)),U_9612)) = hAPP(hAPP(c_Set_Oinsert(U_9609),U_9611),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9608,tc_fun(U_9609,tc_HOL_Obool)),U_9610),U_9612)),
inference(clausify,[status(thm)],[f_2697_3]) ).
fof(f_2698_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I5_J]) ).
fof(f_2698_2,plain,
! [U_9617,U_9616,U_9615,U_9614,U_9613] : hAPP(hAPP(c_Set_Oinsert(U_9613),U_9614),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9615,tc_fun(U_9613,tc_HOL_Obool)),U_9616),U_9617)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9615,tc_fun(U_9613,tc_HOL_Obool)),U_9616),hAPP(hAPP(c_COMBB(tc_fun(U_9613,tc_HOL_Obool),tc_fun(U_9613,tc_HOL_Obool),U_9615),hAPP(c_Set_Oinsert(U_9613),U_9614)),U_9617)),
inference(variable_rename,[status(thm)],[f_2698_1]) ).
fof(f_2698_3,plain,
! [U_9613,U_9614,U_9615,U_9616,U_9617] : hAPP(hAPP(c_Set_Oinsert(U_9613),U_9614),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9615,tc_fun(U_9613,tc_HOL_Obool)),U_9616),U_9617)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9615,tc_fun(U_9613,tc_HOL_Obool)),U_9616),hAPP(hAPP(c_COMBB(tc_fun(U_9613,tc_HOL_Obool),tc_fun(U_9613,tc_HOL_Obool),U_9615),hAPP(c_Set_Oinsert(U_9613),U_9614)),U_9617)),
inference(definitional_conversion,[status(esa)],[f_2698_2]) ).
cnf(f_2698_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_9613),U_9614),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9615,tc_fun(U_9613,tc_HOL_Obool)),U_9616),U_9617)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9615,tc_fun(U_9613,tc_HOL_Obool)),U_9616),hAPP(hAPP(c_COMBB(tc_fun(U_9613,tc_HOL_Obool),tc_fun(U_9613,tc_HOL_Obool),U_9615),hAPP(c_Set_Oinsert(U_9613),U_9614)),U_9617)),
inference(clausify,[status(thm)],[f_2698_3]) ).
fof(f_2699_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).
fof(f_2699_2,plain,
! [U_9620,U_9619,U_9618] : hAPP(hAPP(c_Set_Oinsert(U_9618),U_9619),hAPP(c_Set_OCollect(U_9618),U_9620)) = hAPP(c_Set_OCollect(U_9618),hAPP(hAPP(c_COMBS(U_9618,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9618),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9618),c_fNot),hAPP(hAPP(c_COMBC(U_9618,U_9618,tc_HOL_Obool),c_fequal),U_9619)))),U_9620)),
inference(variable_rename,[status(thm)],[f_2699_1]) ).
fof(f_2699_3,plain,
! [U_9618,U_9619,U_9620] : hAPP(hAPP(c_Set_Oinsert(U_9618),U_9619),hAPP(c_Set_OCollect(U_9618),U_9620)) = hAPP(c_Set_OCollect(U_9618),hAPP(hAPP(c_COMBS(U_9618,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9618),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9618),c_fNot),hAPP(hAPP(c_COMBC(U_9618,U_9618,tc_HOL_Obool),c_fequal),U_9619)))),U_9620)),
inference(definitional_conversion,[status(esa)],[f_2699_2]) ).
cnf(f_2699_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_9618),U_9619),hAPP(c_Set_OCollect(U_9618),U_9620)) = hAPP(c_Set_OCollect(U_9618),hAPP(hAPP(c_COMBS(U_9618,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9618),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9618),c_fNot),hAPP(hAPP(c_COMBC(U_9618,U_9618,tc_HOL_Obool),c_fequal),U_9619)))),U_9620)),
inference(clausify,[status(thm)],[f_2699_3]) ).
fof(f_2700_1,plain,
! [V_x_2,T_c,T_b] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
| ~ class_Orderings_Obot(T_b) ),
inference(fof_nnf,[status(thm)],[fact_bot__fun__def]) ).
fof(f_2700_2,plain,
! [U_9623,U_9622,U_9621] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9622,U_9621)),U_9623) = c_Orderings_Obot__class_Obot(U_9621)
| ~ class_Orderings_Obot(U_9621) ),
inference(variable_rename,[status(thm)],[f_2700_1]) ).
fof(f_2700_3,plain,
! [U_9621,U_9622,U_9623] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9622,U_9621)),U_9623) = c_Orderings_Obot__class_Obot(U_9621)
| ~ class_Orderings_Obot(U_9621) ),
inference(definitional_conversion,[status(esa)],[f_2700_2]) ).
cnf(f_2700_4,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9622,U_9621)),U_9623) = c_Orderings_Obot__class_Obot(U_9621)
| ~ class_Orderings_Obot(U_9621) ),
inference(clausify,[status(thm)],[f_2700_3]) ).
fof(f_2701_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_empty__def]) ).
fof(f_2701_2,plain,
! [U_9624] : c_Orderings_Obot__class_Obot(tc_fun(U_9624,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9624),hAPP(c_COMBK(tc_HOL_Obool,U_9624),c_fFalse)),
inference(variable_rename,[status(thm)],[f_2701_1]) ).
fof(f_2701_3,plain,
! [U_9624] : c_Orderings_Obot__class_Obot(tc_fun(U_9624,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9624),hAPP(c_COMBK(tc_HOL_Obool,U_9624),c_fFalse)),
inference(definitional_conversion,[status(esa)],[f_2701_2]) ).
cnf(f_2701_4,plain,
c_Orderings_Obot__class_Obot(tc_fun(U_9624,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9624),hAPP(c_COMBK(tc_HOL_Obool,U_9624),c_fFalse)),
inference(clausify,[status(thm)],[f_2701_3]) ).
fof(f_2702_1,plain,
! [V_M_2,T_b,V_A_2,T_c] :
( 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
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INF__const]) ).
fof(f_2702_2,plain,
! [U_9628,U_9627,U_9626,U_9625] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9627,U_9625),U_9626),hAPP(c_COMBK(U_9625,U_9627),U_9628)) = U_9628
| U_9626 = c_Orderings_Obot__class_Obot(tc_fun(U_9627,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9625) ),
inference(variable_rename,[status(thm)],[f_2702_1]) ).
fof(f_2702_3,plain,
! [U_9625,U_9626,U_9627,U_9628] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9627,U_9625),U_9626),hAPP(c_COMBK(U_9625,U_9627),U_9628)) = U_9628
| U_9626 = c_Orderings_Obot__class_Obot(tc_fun(U_9627,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9625) ),
inference(definitional_conversion,[status(esa)],[f_2702_2]) ).
cnf(f_2702_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9627,U_9625),U_9626),hAPP(c_COMBK(U_9625,U_9627),U_9628)) = U_9628
| U_9626 = c_Orderings_Obot__class_Obot(tc_fun(U_9627,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9625) ),
inference(clausify,[status(thm)],[f_2702_3]) ).
fof(f_2703_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( 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)
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I1_J]) ).
fof(f_2703_2,plain,
! [U_9634,U_9633,U_9632,U_9631] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9632,tc_fun(U_9631,tc_HOL_Obool)),U_9633),U_9634)
| ? [U_9630] :
( hAPP(U_9634,U_9630) != c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9632),U_9630),U_9633)) ) )
& ( ! [U_9629] :
( hAPP(U_9634,U_9629) = c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9632),U_9629),U_9633)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9632,tc_fun(U_9631,tc_HOL_Obool)),U_9633),U_9634) ) ),
inference(variable_rename,[status(thm)],[f_2703_1]) ).
fof(f_2703_3,plain,
( ! [U_9642,U_9640,U_9638,U_9636] :
( c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9638,tc_fun(U_9636,tc_HOL_Obool)),U_9640),U_9642)
| ? [U_9630] :
( hAPP(U_9642,U_9630) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9638),U_9630),U_9640)) ) )
& ! [U_9641,U_9639,U_9637,U_9635] :
( ! [U_9629] :
( hAPP(U_9641,U_9629) = c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9637),U_9629),U_9639)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9637,tc_fun(U_9635,tc_HOL_Obool)),U_9639),U_9641) ) ),
inference(miniscope,[status(thm)],[f_2703_2]) ).
fof(f_2703_4,plain,
( ! [U_9642,U_9640,U_9638,U_9636] :
( c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9638,tc_fun(U_9636,tc_HOL_Obool)),U_9640),U_9642)
| ( hAPP(U_9642,sK253(U_9642,U_9640,U_9638,U_9636)) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9638),sK253(U_9642,U_9640,U_9638,U_9636)),U_9640)) ) )
& ! [U_9641,U_9639,U_9637,U_9635] :
( ! [U_9629] :
( hAPP(U_9641,U_9629) = c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9637),U_9629),U_9639)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9637,tc_fun(U_9635,tc_HOL_Obool)),U_9639),U_9641) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_9630,sK253(U_9642,U_9640,U_9638,U_9636))],[f_2703_3]) ).
fof(f_2703_5,plain,
( ! [U_9640,U_9636,U_9642,U_9638] :
( hAPP(U_9642,sK253(U_9642,U_9640,U_9638,U_9636)) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
| ~ sP792(U_9640,U_9636,U_9642,U_9638) )
& ! [U_9640,U_9636,U_9642,U_9638] :
( hBOOL(hAPP(hAPP(c_member(U_9638),sK253(U_9642,U_9640,U_9638,U_9636)),U_9640))
| ~ sP792(U_9640,U_9636,U_9642,U_9638) )
& ! [U_9640,U_9636,U_9642,U_9638] :
( c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9638,tc_fun(U_9636,tc_HOL_Obool)),U_9640),U_9642)
| sP792(U_9640,U_9636,U_9642,U_9638) )
& ! [U_9641,U_9637,U_9639,U_9629,U_9635] :
( hAPP(U_9641,U_9629) = c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9637),U_9629),U_9639))
| c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9637,tc_fun(U_9635,tc_HOL_Obool)),U_9639),U_9641) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP792])],[f_2703_4]) ).
cnf(f_2703_6,plain,
( hAPP(U_9641,U_9629) = c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9637),U_9629),U_9639))
| c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9637,tc_fun(U_9635,tc_HOL_Obool)),U_9639),U_9641) ),
inference(clausify,[status(thm)],[f_2703_5]) ).
cnf(f_2703_7,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9638,tc_fun(U_9636,tc_HOL_Obool)),U_9640),U_9642)
| sP792(U_9640,U_9636,U_9642,U_9638) ),
inference(clausify,[status(thm)],[f_2703_5]) ).
cnf(f_2703_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9638),sK253(U_9642,U_9640,U_9638,U_9636)),U_9640))
| ~ sP792(U_9640,U_9636,U_9642,U_9638) ),
inference(clausify,[status(thm)],[f_2703_5]) ).
cnf(f_2703_9,plain,
( hAPP(U_9642,sK253(U_9642,U_9640,U_9638,U_9636)) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
| ~ sP792(U_9640,U_9636,U_9642,U_9638) ),
inference(clausify,[status(thm)],[f_2703_5]) ).
fof(f_2704_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__empty2]) ).
fof(f_2704_2,plain,
! [U_9645,U_9644,U_9643] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9643,tc_fun(U_9644,tc_HOL_Obool)),U_9645),hAPP(c_COMBK(tc_fun(U_9644,tc_HOL_Obool),U_9643),c_Orderings_Obot__class_Obot(tc_fun(U_9644,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9644,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2704_1]) ).
fof(f_2704_3,plain,
! [U_9643,U_9644,U_9645] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9643,tc_fun(U_9644,tc_HOL_Obool)),U_9645),hAPP(c_COMBK(tc_fun(U_9644,tc_HOL_Obool),U_9643),c_Orderings_Obot__class_Obot(tc_fun(U_9644,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9644,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_2704_2]) ).
cnf(f_2704_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9643,tc_fun(U_9644,tc_HOL_Obool)),U_9645),hAPP(c_COMBK(tc_fun(U_9644,tc_HOL_Obool),U_9643),c_Orderings_Obot__class_Obot(tc_fun(U_9644,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9644,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2704_3]) ).
fof(f_2705_1,plain,
! [V_ca_2,T_c,T_b,V_A_2] :
( ( 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_ca_2)) = V_ca_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__constant]) ).
fof(f_2705_2,plain,
! [U_9649,U_9648,U_9647,U_9646] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9647,tc_fun(U_9648,tc_HOL_Obool)),U_9646),hAPP(c_COMBK(tc_fun(U_9648,tc_HOL_Obool),U_9647),U_9649)) = U_9649
| U_9646 = c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9647,tc_fun(U_9648,tc_HOL_Obool)),U_9646),hAPP(c_COMBK(tc_fun(U_9648,tc_HOL_Obool),U_9647),U_9649)) = c_Orderings_Obot__class_Obot(tc_fun(U_9648,tc_HOL_Obool))
| U_9646 != c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2705_1]) ).
fof(f_2705_3,plain,
( ! [U_9657,U_9655,U_9653,U_9651] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9653,tc_fun(U_9655,tc_HOL_Obool)),U_9651),hAPP(c_COMBK(tc_fun(U_9655,tc_HOL_Obool),U_9653),U_9657)) = U_9657
| U_9651 = c_Orderings_Obot__class_Obot(tc_fun(U_9653,tc_HOL_Obool)) )
& ! [U_9656,U_9654,U_9652,U_9650] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9652,tc_fun(U_9654,tc_HOL_Obool)),U_9650),hAPP(c_COMBK(tc_fun(U_9654,tc_HOL_Obool),U_9652),U_9656)) = c_Orderings_Obot__class_Obot(tc_fun(U_9654,tc_HOL_Obool))
| U_9650 != c_Orderings_Obot__class_Obot(tc_fun(U_9652,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2705_2]) ).
fof(f_2705_4,plain,
( ! [U_9651,U_9653,U_9655,U_9657] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9653,tc_fun(U_9655,tc_HOL_Obool)),U_9651),hAPP(c_COMBK(tc_fun(U_9655,tc_HOL_Obool),U_9653),U_9657)) = U_9657
| U_9651 = c_Orderings_Obot__class_Obot(tc_fun(U_9653,tc_HOL_Obool)) )
& ! [U_9654,U_9652,U_9656,U_9650] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9652,tc_fun(U_9654,tc_HOL_Obool)),U_9650),hAPP(c_COMBK(tc_fun(U_9654,tc_HOL_Obool),U_9652),U_9656)) = c_Orderings_Obot__class_Obot(tc_fun(U_9654,tc_HOL_Obool))
| U_9650 != c_Orderings_Obot__class_Obot(tc_fun(U_9652,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2705_3]) ).
cnf(f_2705_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9652,tc_fun(U_9654,tc_HOL_Obool)),U_9650),hAPP(c_COMBK(tc_fun(U_9654,tc_HOL_Obool),U_9652),U_9656)) = c_Orderings_Obot__class_Obot(tc_fun(U_9654,tc_HOL_Obool))
| U_9650 != c_Orderings_Obot__class_Obot(tc_fun(U_9652,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2705_4]) ).
cnf(f_2705_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9653,tc_fun(U_9655,tc_HOL_Obool)),U_9651),hAPP(c_COMBK(tc_fun(U_9655,tc_HOL_Obool),U_9653),U_9657)) = U_9657
| U_9651 = c_Orderings_Obot__class_Obot(tc_fun(U_9653,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2705_4]) ).
fof(f_2706_1,plain,
! [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_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),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) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I2_J]) ).
fof(f_2706_2,plain,
! [U_9663,U_9662,U_9661,U_9660] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9660,tc_fun(U_9661,tc_HOL_Obool)),U_9662),U_9663) = c_Orderings_Obot__class_Obot(tc_fun(U_9661,tc_HOL_Obool))
| ? [U_9659] :
( hAPP(U_9663,U_9659) != c_Orderings_Obot__class_Obot(tc_fun(U_9661,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9660),U_9659),U_9662)) ) )
& ( ! [U_9658] :
( hAPP(U_9663,U_9658) = c_Orderings_Obot__class_Obot(tc_fun(U_9661,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9660),U_9658),U_9662)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9660,tc_fun(U_9661,tc_HOL_Obool)),U_9662),U_9663) != c_Orderings_Obot__class_Obot(tc_fun(U_9661,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2706_1]) ).
fof(f_2706_3,plain,
( ! [U_9671,U_9669,U_9667,U_9665] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9665,tc_fun(U_9667,tc_HOL_Obool)),U_9669),U_9671) = c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
| ? [U_9659] :
( hAPP(U_9671,U_9659) != c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9665),U_9659),U_9669)) ) )
& ! [U_9670,U_9668,U_9666,U_9664] :
( ! [U_9658] :
( hAPP(U_9670,U_9658) = c_Orderings_Obot__class_Obot(tc_fun(U_9666,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9664),U_9658),U_9668)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9664,tc_fun(U_9666,tc_HOL_Obool)),U_9668),U_9670) != c_Orderings_Obot__class_Obot(tc_fun(U_9666,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2706_2]) ).
fof(f_2706_4,plain,
( ! [U_9671,U_9669,U_9667,U_9665] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9665,tc_fun(U_9667,tc_HOL_Obool)),U_9669),U_9671) = c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
| ( hAPP(U_9671,sK254(U_9671,U_9669,U_9667,U_9665)) != c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9665),sK254(U_9671,U_9669,U_9667,U_9665)),U_9669)) ) )
& ! [U_9670,U_9668,U_9666,U_9664] :
( ! [U_9658] :
( hAPP(U_9670,U_9658) = c_Orderings_Obot__class_Obot(tc_fun(U_9666,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9664),U_9658),U_9668)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9664,tc_fun(U_9666,tc_HOL_Obool)),U_9668),U_9670) != c_Orderings_Obot__class_Obot(tc_fun(U_9666,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_9659,sK254(U_9671,U_9669,U_9667,U_9665))],[f_2706_3]) ).
fof(f_2706_5,plain,
( ! [U_9669,U_9665,U_9667,U_9671] :
( hAPP(U_9671,sK254(U_9671,U_9669,U_9667,U_9665)) != c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
| ~ sP793(U_9669,U_9665,U_9667,U_9671) )
& ! [U_9669,U_9665,U_9667,U_9671] :
( hBOOL(hAPP(hAPP(c_member(U_9665),sK254(U_9671,U_9669,U_9667,U_9665)),U_9669))
| ~ sP793(U_9669,U_9665,U_9667,U_9671) )
& ! [U_9669,U_9665,U_9667,U_9671] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9665,tc_fun(U_9667,tc_HOL_Obool)),U_9669),U_9671) = c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
| sP793(U_9669,U_9665,U_9667,U_9671) )
& ! [U_9658,U_9670,U_9664,U_9668,U_9666] :
( hAPP(U_9670,U_9658) = c_Orderings_Obot__class_Obot(tc_fun(U_9666,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9664),U_9658),U_9668))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9664,tc_fun(U_9666,tc_HOL_Obool)),U_9668),U_9670) != c_Orderings_Obot__class_Obot(tc_fun(U_9666,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP793])],[f_2706_4]) ).
cnf(f_2706_6,plain,
( hAPP(U_9670,U_9658) = c_Orderings_Obot__class_Obot(tc_fun(U_9666,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9664),U_9658),U_9668))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9664,tc_fun(U_9666,tc_HOL_Obool)),U_9668),U_9670) != c_Orderings_Obot__class_Obot(tc_fun(U_9666,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2706_5]) ).
cnf(f_2706_7,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9665,tc_fun(U_9667,tc_HOL_Obool)),U_9669),U_9671) = c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
| sP793(U_9669,U_9665,U_9667,U_9671) ),
inference(clausify,[status(thm)],[f_2706_5]) ).
cnf(f_2706_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9665),sK254(U_9671,U_9669,U_9667,U_9665)),U_9669))
| ~ sP793(U_9669,U_9665,U_9667,U_9671) ),
inference(clausify,[status(thm)],[f_2706_5]) ).
cnf(f_2706_9,plain,
( hAPP(U_9671,sK254(U_9671,U_9669,U_9667,U_9665)) != c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
| ~ sP793(U_9669,U_9665,U_9667,U_9671) ),
inference(clausify,[status(thm)],[f_2706_5]) ).
fof(f_2707_1,plain,
! [V_M_2,T_b,V_A_2,T_c] :
( 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
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUP__const]) ).
fof(f_2707_2,plain,
! [U_9675,U_9674,U_9673,U_9672] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9674,U_9672),U_9673),hAPP(c_COMBK(U_9672,U_9674),U_9675)) = U_9675
| U_9673 = c_Orderings_Obot__class_Obot(tc_fun(U_9674,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9672) ),
inference(variable_rename,[status(thm)],[f_2707_1]) ).
fof(f_2707_3,plain,
! [U_9673,U_9674,U_9672,U_9675] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9674,U_9672),U_9673),hAPP(c_COMBK(U_9672,U_9674),U_9675)) = U_9675
| U_9673 = c_Orderings_Obot__class_Obot(tc_fun(U_9674,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9672) ),
inference(definitional_conversion,[status(esa)],[f_2707_2]) ).
cnf(f_2707_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9674,U_9672),U_9673),hAPP(c_COMBK(U_9672,U_9674),U_9675)) = U_9675
| U_9673 = c_Orderings_Obot__class_Obot(tc_fun(U_9674,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9672) ),
inference(clausify,[status(thm)],[f_2707_3]) ).
fof(f_2708_1,plain,
! [V_A_2,V_f_2,T_c,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_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))
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__negf]) ).
fof(f_2708_2,plain,
! [U_9679,U_9678,U_9677,U_9676] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9677,U_9676),hAPP(hAPP(c_COMBB(U_9676,U_9676,U_9677),c_Groups_Ouminus__class_Ouminus(U_9676)),U_9678)),U_9679) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9677,U_9676),U_9678),U_9679))
| ~ class_Groups_Oab__group__add(U_9676) ),
inference(variable_rename,[status(thm)],[f_2708_1]) ).
fof(f_2708_3,plain,
! [U_9676,U_9677,U_9678,U_9679] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9677,U_9676),hAPP(hAPP(c_COMBB(U_9676,U_9676,U_9677),c_Groups_Ouminus__class_Ouminus(U_9676)),U_9678)),U_9679) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9677,U_9676),U_9678),U_9679))
| ~ class_Groups_Oab__group__add(U_9676) ),
inference(definitional_conversion,[status(esa)],[f_2708_2]) ).
cnf(f_2708_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9677,U_9676),hAPP(hAPP(c_COMBB(U_9676,U_9676,U_9677),c_Groups_Ouminus__class_Ouminus(U_9676)),U_9678)),U_9679) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9677,U_9676),U_9678),U_9679))
| ~ class_Groups_Oab__group__add(U_9676) ),
inference(clausify,[status(thm)],[f_2708_3]) ).
fof(f_2709_1,plain,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( 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))
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod__timesf]) ).
fof(f_2709_2,plain,
! [U_9684,U_9683,U_9682,U_9681,U_9680] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),hAPP(hAPP(c_COMBS(U_9681,U_9680,U_9680),hAPP(hAPP(c_COMBB(U_9680,tc_fun(U_9680,U_9680),U_9681),c_Groups_Otimes__class_Otimes(U_9680)),U_9682)),U_9683)),U_9684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9680),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),U_9682),U_9684)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),U_9683),U_9684))
| ~ class_Groups_Ocomm__monoid__mult(U_9680) ),
inference(variable_rename,[status(thm)],[f_2709_1]) ).
fof(f_2709_3,plain,
! [U_9680,U_9681,U_9682,U_9683,U_9684] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),hAPP(hAPP(c_COMBS(U_9681,U_9680,U_9680),hAPP(hAPP(c_COMBB(U_9680,tc_fun(U_9680,U_9680),U_9681),c_Groups_Otimes__class_Otimes(U_9680)),U_9682)),U_9683)),U_9684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9680),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),U_9682),U_9684)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),U_9683),U_9684))
| ~ class_Groups_Ocomm__monoid__mult(U_9680) ),
inference(definitional_conversion,[status(esa)],[f_2709_2]) ).
cnf(f_2709_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),hAPP(hAPP(c_COMBS(U_9681,U_9680,U_9680),hAPP(hAPP(c_COMBB(U_9680,tc_fun(U_9680,U_9680),U_9681),c_Groups_Otimes__class_Otimes(U_9680)),U_9682)),U_9683)),U_9684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9680),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),U_9682),U_9684)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9681,U_9680),U_9683),U_9684))
| ~ class_Groups_Ocomm__monoid__mult(U_9680) ),
inference(clausify,[status(thm)],[f_2709_3]) ).
fof(f_2710_1,plain,
! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Rings_Osemiring__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__product]) ).
fof(f_2710_2,plain,
! [U_9691,U_9690,U_9689,U_9688,U_9687,U_9686,U_9685] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9685),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9686,U_9685),U_9687),U_9688)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9689,U_9685),U_9690),U_9691)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9686,U_9685),hAPP(hAPP(c_COMBC(U_9686,tc_fun(U_9689,tc_HOL_Obool),U_9685),hAPP(hAPP(c_COMBB(tc_fun(U_9689,U_9685),tc_fun(tc_fun(U_9689,tc_HOL_Obool),U_9685),U_9686),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9689,U_9685)),hAPP(hAPP(c_COMBC(U_9686,tc_fun(U_9689,U_9685),tc_fun(U_9689,U_9685)),hAPP(hAPP(c_COMBB(tc_fun(U_9685,U_9685),tc_fun(tc_fun(U_9689,U_9685),tc_fun(U_9689,U_9685)),U_9686),c_COMBB(U_9685,U_9685,U_9689)),hAPP(hAPP(c_COMBB(U_9685,tc_fun(U_9685,U_9685),U_9686),c_Groups_Otimes__class_Otimes(U_9685)),U_9687))),U_9690))),U_9691)),U_9688)
| ~ class_Rings_Osemiring__0(U_9685) ),
inference(variable_rename,[status(thm)],[f_2710_1]) ).
fof(f_2710_3,plain,
! [U_9685,U_9686,U_9687,U_9688,U_9689,U_9690,U_9691] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9685),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9686,U_9685),U_9687),U_9688)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9689,U_9685),U_9690),U_9691)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9686,U_9685),hAPP(hAPP(c_COMBC(U_9686,tc_fun(U_9689,tc_HOL_Obool),U_9685),hAPP(hAPP(c_COMBB(tc_fun(U_9689,U_9685),tc_fun(tc_fun(U_9689,tc_HOL_Obool),U_9685),U_9686),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9689,U_9685)),hAPP(hAPP(c_COMBC(U_9686,tc_fun(U_9689,U_9685),tc_fun(U_9689,U_9685)),hAPP(hAPP(c_COMBB(tc_fun(U_9685,U_9685),tc_fun(tc_fun(U_9689,U_9685),tc_fun(U_9689,U_9685)),U_9686),c_COMBB(U_9685,U_9685,U_9689)),hAPP(hAPP(c_COMBB(U_9685,tc_fun(U_9685,U_9685),U_9686),c_Groups_Otimes__class_Otimes(U_9685)),U_9687))),U_9690))),U_9691)),U_9688)
| ~ class_Rings_Osemiring__0(U_9685) ),
inference(definitional_conversion,[status(esa)],[f_2710_2]) ).
cnf(f_2710_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9685),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9686,U_9685),U_9687),U_9688)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9689,U_9685),U_9690),U_9691)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9686,U_9685),hAPP(hAPP(c_COMBC(U_9686,tc_fun(U_9689,tc_HOL_Obool),U_9685),hAPP(hAPP(c_COMBB(tc_fun(U_9689,U_9685),tc_fun(tc_fun(U_9689,tc_HOL_Obool),U_9685),U_9686),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9689,U_9685)),hAPP(hAPP(c_COMBC(U_9686,tc_fun(U_9689,U_9685),tc_fun(U_9689,U_9685)),hAPP(hAPP(c_COMBB(tc_fun(U_9685,U_9685),tc_fun(tc_fun(U_9689,U_9685),tc_fun(U_9689,U_9685)),U_9686),c_COMBB(U_9685,U_9685,U_9689)),hAPP(hAPP(c_COMBB(U_9685,tc_fun(U_9685,U_9685),U_9686),c_Groups_Otimes__class_Otimes(U_9685)),U_9687))),U_9690))),U_9691)),U_9688)
| ~ class_Rings_Osemiring__0(U_9685) ),
inference(clausify,[status(thm)],[f_2710_3]) ).
fof(f_2711_1,plain,
! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Rings_Osemiring__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib]) ).
fof(f_2711_2,plain,
! [U_9696,U_9695,U_9694,U_9693,U_9692] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9692),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9693,U_9692),U_9694),U_9695)),U_9696) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9693,U_9692),hAPP(hAPP(c_COMBC(U_9693,U_9692,U_9692),hAPP(hAPP(c_COMBB(U_9692,tc_fun(U_9692,U_9692),U_9693),c_Groups_Otimes__class_Otimes(U_9692)),U_9694)),U_9696)),U_9695)
| ~ class_Rings_Osemiring__0(U_9692) ),
inference(variable_rename,[status(thm)],[f_2711_1]) ).
fof(f_2711_3,plain,
! [U_9692,U_9693,U_9694,U_9695,U_9696] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9692),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9693,U_9692),U_9694),U_9695)),U_9696) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9693,U_9692),hAPP(hAPP(c_COMBC(U_9693,U_9692,U_9692),hAPP(hAPP(c_COMBB(U_9692,tc_fun(U_9692,U_9692),U_9693),c_Groups_Otimes__class_Otimes(U_9692)),U_9694)),U_9696)),U_9695)
| ~ class_Rings_Osemiring__0(U_9692) ),
inference(definitional_conversion,[status(esa)],[f_2711_2]) ).
cnf(f_2711_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9692),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9693,U_9692),U_9694),U_9695)),U_9696) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9693,U_9692),hAPP(hAPP(c_COMBC(U_9693,U_9692,U_9692),hAPP(hAPP(c_COMBB(U_9692,tc_fun(U_9692,U_9692),U_9693),c_Groups_Otimes__class_Otimes(U_9692)),U_9694)),U_9696)),U_9695)
| ~ class_Rings_Osemiring__0(U_9692) ),
inference(clausify,[status(thm)],[f_2711_3]) ).
fof(f_2712_1,plain,
! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
( 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)
| ~ class_Rings_Osemiring__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib]) ).
fof(f_2712_2,plain,
! [U_9701,U_9700,U_9699,U_9698,U_9697] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9697),U_9698),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9699,U_9697),U_9700),U_9701)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9699,U_9697),hAPP(hAPP(c_COMBB(U_9697,U_9697,U_9699),hAPP(c_Groups_Otimes__class_Otimes(U_9697),U_9698)),U_9700)),U_9701)
| ~ class_Rings_Osemiring__0(U_9697) ),
inference(variable_rename,[status(thm)],[f_2712_1]) ).
fof(f_2712_3,plain,
! [U_9697,U_9698,U_9699,U_9700,U_9701] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9697),U_9698),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9699,U_9697),U_9700),U_9701)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9699,U_9697),hAPP(hAPP(c_COMBB(U_9697,U_9697,U_9699),hAPP(c_Groups_Otimes__class_Otimes(U_9697),U_9698)),U_9700)),U_9701)
| ~ class_Rings_Osemiring__0(U_9697) ),
inference(definitional_conversion,[status(esa)],[f_2712_2]) ).
cnf(f_2712_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9697),U_9698),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9699,U_9697),U_9700),U_9701)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9699,U_9697),hAPP(hAPP(c_COMBB(U_9697,U_9697,U_9699),hAPP(c_Groups_Otimes__class_Otimes(U_9697),U_9698)),U_9700)),U_9701)
| ~ class_Rings_Osemiring__0(U_9697) ),
inference(clausify,[status(thm)],[f_2712_3]) ).
fof(f_2713_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).
fof(f_2713_2,plain,
! [U_9703,U_9702] : hAPP(c_Set_OCollect(U_9702),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9702),c_fNot),U_9703)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9702,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9702),U_9703)),
inference(variable_rename,[status(thm)],[f_2713_1]) ).
fof(f_2713_3,plain,
! [U_9702,U_9703] : hAPP(c_Set_OCollect(U_9702),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9702),c_fNot),U_9703)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9702,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9702),U_9703)),
inference(definitional_conversion,[status(esa)],[f_2713_2]) ).
cnf(f_2713_4,plain,
hAPP(c_Set_OCollect(U_9702),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9702),c_fNot),U_9703)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9702,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9702),U_9703)),
inference(clausify,[status(thm)],[f_2713_3]) ).
fof(f_2714_1,plain,
! [V_x_2,V_A_2,T_c,T_b] :
( 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))
| ~ class_Groups_Ouminus(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__Compl__def]) ).
fof(f_2714_2,plain,
! [U_9707,U_9706,U_9705,U_9704] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9705,U_9704)),U_9706),U_9707) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9704),hAPP(U_9706,U_9707))
| ~ class_Groups_Ouminus(U_9704) ),
inference(variable_rename,[status(thm)],[f_2714_1]) ).
fof(f_2714_3,plain,
! [U_9704,U_9705,U_9706,U_9707] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9705,U_9704)),U_9706),U_9707) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9704),hAPP(U_9706,U_9707))
| ~ class_Groups_Ouminus(U_9704) ),
inference(definitional_conversion,[status(esa)],[f_2714_2]) ).
cnf(f_2714_4,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9705,U_9704)),U_9706),U_9707) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9704),hAPP(U_9706,U_9707))
| ~ class_Groups_Ouminus(U_9704) ),
inference(clausify,[status(thm)],[f_2714_3]) ).
fof(f_2715_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__UN]) ).
fof(f_2715_2,plain,
! [U_9711,U_9710,U_9709,U_9708] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9709,tc_fun(U_9708,tc_HOL_Obool)),U_9710),U_9711)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9709,tc_fun(U_9708,tc_HOL_Obool)),U_9710),hAPP(hAPP(c_COMBB(tc_fun(U_9708,tc_HOL_Obool),tc_fun(U_9708,tc_HOL_Obool),U_9709),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9708,tc_HOL_Obool))),U_9711)),
inference(variable_rename,[status(thm)],[f_2715_1]) ).
fof(f_2715_3,plain,
! [U_9708,U_9709,U_9710,U_9711] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9709,tc_fun(U_9708,tc_HOL_Obool)),U_9710),U_9711)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9709,tc_fun(U_9708,tc_HOL_Obool)),U_9710),hAPP(hAPP(c_COMBB(tc_fun(U_9708,tc_HOL_Obool),tc_fun(U_9708,tc_HOL_Obool),U_9709),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9708,tc_HOL_Obool))),U_9711)),
inference(definitional_conversion,[status(esa)],[f_2715_2]) ).
cnf(f_2715_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9709,tc_fun(U_9708,tc_HOL_Obool)),U_9710),U_9711)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9709,tc_fun(U_9708,tc_HOL_Obool)),U_9710),hAPP(hAPP(c_COMBB(tc_fun(U_9708,tc_HOL_Obool),tc_fun(U_9708,tc_HOL_Obool),U_9709),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9708,tc_HOL_Obool))),U_9711)),
inference(clausify,[status(thm)],[f_2715_3]) ).
fof(f_2716_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Compl__INT]) ).
fof(f_2716_2,plain,
! [U_9715,U_9714,U_9713,U_9712] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9712,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9713,tc_fun(U_9712,tc_HOL_Obool)),U_9714),U_9715)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9713,tc_fun(U_9712,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_COMBB(tc_fun(U_9712,tc_HOL_Obool),tc_fun(U_9712,tc_HOL_Obool),U_9713),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9712,tc_HOL_Obool))),U_9715)),
inference(variable_rename,[status(thm)],[f_2716_1]) ).
fof(f_2716_3,plain,
! [U_9712,U_9713,U_9714,U_9715] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9712,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9713,tc_fun(U_9712,tc_HOL_Obool)),U_9714),U_9715)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9713,tc_fun(U_9712,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_COMBB(tc_fun(U_9712,tc_HOL_Obool),tc_fun(U_9712,tc_HOL_Obool),U_9713),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9712,tc_HOL_Obool))),U_9715)),
inference(definitional_conversion,[status(esa)],[f_2716_2]) ).
cnf(f_2716_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9712,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9713,tc_fun(U_9712,tc_HOL_Obool)),U_9714),U_9715)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9713,tc_fun(U_9712,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_COMBB(tc_fun(U_9712,tc_HOL_Obool),tc_fun(U_9712,tc_HOL_Obool),U_9713),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9712,tc_HOL_Obool))),U_9715)),
inference(clausify,[status(thm)],[f_2716_3]) ).
fof(f_2717_1,plain,
! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
( 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))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_SUPR__apply]) ).
fof(f_2717_2,plain,
! [U_9721,U_9720,U_9719,U_9718,U_9717,U_9716] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9717,tc_fun(U_9718,U_9716)),U_9719),U_9720),U_9721) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9717,U_9716),U_9719),hAPP(hAPP(c_COMBC(U_9717,U_9718,U_9716),U_9720),U_9721))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9716) ),
inference(variable_rename,[status(thm)],[f_2717_1]) ).
fof(f_2717_3,plain,
! [U_9716,U_9717,U_9718,U_9719,U_9720,U_9721] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9717,tc_fun(U_9718,U_9716)),U_9719),U_9720),U_9721) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9717,U_9716),U_9719),hAPP(hAPP(c_COMBC(U_9717,U_9718,U_9716),U_9720),U_9721))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9716) ),
inference(definitional_conversion,[status(esa)],[f_2717_2]) ).
cnf(f_2717_4,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9717,tc_fun(U_9718,U_9716)),U_9719),U_9720),U_9721) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9717,U_9716),U_9719),hAPP(hAPP(c_COMBC(U_9717,U_9718,U_9716),U_9720),U_9721))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9716) ),
inference(clausify,[status(thm)],[f_2717_3]) ).
fof(f_2718_1,plain,
! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Fields_Ofield(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib]) ).
fof(f_2718_2,plain,
! [U_9726,U_9725,U_9724,U_9723,U_9722] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9722),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9723,U_9722),U_9724),U_9725)),U_9726) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9723,U_9722),hAPP(hAPP(c_COMBC(U_9723,U_9722,U_9722),hAPP(hAPP(c_COMBB(U_9722,tc_fun(U_9722,U_9722),U_9723),c_Rings_Oinverse__class_Odivide(U_9722)),U_9724)),U_9726)),U_9725)
| ~ class_Fields_Ofield(U_9722) ),
inference(variable_rename,[status(thm)],[f_2718_1]) ).
fof(f_2718_3,plain,
! [U_9722,U_9723,U_9724,U_9725,U_9726] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9722),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9723,U_9722),U_9724),U_9725)),U_9726) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9723,U_9722),hAPP(hAPP(c_COMBC(U_9723,U_9722,U_9722),hAPP(hAPP(c_COMBB(U_9722,tc_fun(U_9722,U_9722),U_9723),c_Rings_Oinverse__class_Odivide(U_9722)),U_9724)),U_9726)),U_9725)
| ~ class_Fields_Ofield(U_9722) ),
inference(definitional_conversion,[status(esa)],[f_2718_2]) ).
cnf(f_2718_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9722),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9723,U_9722),U_9724),U_9725)),U_9726) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9723,U_9722),hAPP(hAPP(c_COMBC(U_9723,U_9722,U_9722),hAPP(hAPP(c_COMBB(U_9722,tc_fun(U_9722,U_9722),U_9723),c_Rings_Oinverse__class_Odivide(U_9722)),U_9724)),U_9726)),U_9725)
| ~ class_Fields_Ofield(U_9722) ),
inference(clausify,[status(thm)],[f_2718_3]) ).
fof(f_2719_1,plain,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( 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))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply]) ).
fof(f_2719_2,plain,
! [U_9731,U_9730,U_9729,U_9728,U_9727] :
( c_Finite__Set_Ofun__left__comm__idem(U_9730,U_9728,hAPP(hAPP(c_COMBB(U_9727,tc_fun(U_9728,U_9728),U_9730),U_9729),U_9731))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_9727,U_9728,U_9729) ),
inference(variable_rename,[status(thm)],[f_2719_1]) ).
fof(f_2719_3,plain,
! [U_9728,U_9727,U_9729,U_9730,U_9731] :
( c_Finite__Set_Ofun__left__comm__idem(U_9730,U_9728,hAPP(hAPP(c_COMBB(U_9727,tc_fun(U_9728,U_9728),U_9730),U_9729),U_9731))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_9727,U_9728,U_9729) ),
inference(definitional_conversion,[status(esa)],[f_2719_2]) ).
cnf(f_2719_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_9730,U_9728,hAPP(hAPP(c_COMBB(U_9727,tc_fun(U_9728,U_9728),U_9730),U_9729),U_9731))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_9727,U_9728,U_9729) ),
inference(clausify,[status(thm)],[f_2719_3]) ).
fof(f_2720_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Pow__INT__eq]) ).
fof(f_2720_2,plain,
! [U_9735,U_9734,U_9733,U_9732] : hAPP(c_Set_OPow(U_9732),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9733,tc_fun(U_9732,tc_HOL_Obool)),U_9734),U_9735)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9733,tc_fun(tc_fun(U_9732,tc_HOL_Obool),tc_HOL_Obool)),U_9734),hAPP(hAPP(c_COMBB(tc_fun(U_9732,tc_HOL_Obool),tc_fun(tc_fun(U_9732,tc_HOL_Obool),tc_HOL_Obool),U_9733),c_Set_OPow(U_9732)),U_9735)),
inference(variable_rename,[status(thm)],[f_2720_1]) ).
fof(f_2720_3,plain,
! [U_9732,U_9733,U_9734,U_9735] : hAPP(c_Set_OPow(U_9732),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9733,tc_fun(U_9732,tc_HOL_Obool)),U_9734),U_9735)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9733,tc_fun(tc_fun(U_9732,tc_HOL_Obool),tc_HOL_Obool)),U_9734),hAPP(hAPP(c_COMBB(tc_fun(U_9732,tc_HOL_Obool),tc_fun(tc_fun(U_9732,tc_HOL_Obool),tc_HOL_Obool),U_9733),c_Set_OPow(U_9732)),U_9735)),
inference(definitional_conversion,[status(esa)],[f_2720_2]) ).
cnf(f_2720_4,plain,
hAPP(c_Set_OPow(U_9732),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9733,tc_fun(U_9732,tc_HOL_Obool)),U_9734),U_9735)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9733,tc_fun(tc_fun(U_9732,tc_HOL_Obool),tc_HOL_Obool)),U_9734),hAPP(hAPP(c_COMBB(tc_fun(U_9732,tc_HOL_Obool),tc_fun(tc_fun(U_9732,tc_HOL_Obool),tc_HOL_Obool),U_9733),c_Set_OPow(U_9732)),U_9735)),
inference(clausify,[status(thm)],[f_2720_3]) ).
fof(f_2721_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Inter__def]) ).
fof(f_2721_2,plain,
! [U_9737,U_9736] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9736,tc_HOL_Obool),U_9737) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9736,tc_HOL_Obool),tc_fun(U_9736,tc_HOL_Obool)),U_9737),c_COMBI(tc_fun(U_9736,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2721_1]) ).
fof(f_2721_3,plain,
! [U_9736,U_9737] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9736,tc_HOL_Obool),U_9737) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9736,tc_HOL_Obool),tc_fun(U_9736,tc_HOL_Obool)),U_9737),c_COMBI(tc_fun(U_9736,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2721_2]) ).
cnf(f_2721_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9736,tc_HOL_Obool),U_9737) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9736,tc_HOL_Obool),tc_fun(U_9736,tc_HOL_Obool)),U_9737),c_COMBI(tc_fun(U_9736,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2721_3]) ).
fof(f_2722_1,plain,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( 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)))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_INF__commute]) ).
fof(f_2722_2,plain,
! [U_9743,U_9742,U_9741,U_9740,U_9739,U_9738] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9739,U_9738),U_9740),hAPP(hAPP(c_COMBB(tc_fun(U_9741,U_9738),U_9738,U_9739),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9741,U_9738),U_9742)),U_9743)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9741,U_9738),U_9742),hAPP(hAPP(c_COMBB(tc_fun(U_9739,U_9738),U_9738,U_9741),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9739,U_9738),U_9740)),hAPP(c_COMBC(U_9739,U_9741,U_9738),U_9743)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9738) ),
inference(variable_rename,[status(thm)],[f_2722_1]) ).
fof(f_2722_3,plain,
! [U_9738,U_9739,U_9740,U_9741,U_9742,U_9743] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9739,U_9738),U_9740),hAPP(hAPP(c_COMBB(tc_fun(U_9741,U_9738),U_9738,U_9739),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9741,U_9738),U_9742)),U_9743)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9741,U_9738),U_9742),hAPP(hAPP(c_COMBB(tc_fun(U_9739,U_9738),U_9738,U_9741),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9739,U_9738),U_9740)),hAPP(c_COMBC(U_9739,U_9741,U_9738),U_9743)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9738) ),
inference(definitional_conversion,[status(esa)],[f_2722_2]) ).
cnf(f_2722_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9739,U_9738),U_9740),hAPP(hAPP(c_COMBB(tc_fun(U_9741,U_9738),U_9738,U_9739),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9741,U_9738),U_9742)),U_9743)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9741,U_9738),U_9742),hAPP(hAPP(c_COMBB(tc_fun(U_9739,U_9738),U_9738,U_9741),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9739,U_9738),U_9740)),hAPP(c_COMBC(U_9739,U_9741,U_9738),U_9743)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9738) ),
inference(clausify,[status(thm)],[f_2722_3]) ).
fof(f_2723_1,plain,
! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
( 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))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_INFI__apply]) ).
fof(f_2723_2,plain,
! [U_9749,U_9748,U_9747,U_9746,U_9745,U_9744] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9746,U_9744)),U_9747),U_9748),U_9749) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,U_9744),U_9747),hAPP(hAPP(c_COMBC(U_9745,U_9746,U_9744),U_9748),U_9749))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9744) ),
inference(variable_rename,[status(thm)],[f_2723_1]) ).
fof(f_2723_3,plain,
! [U_9744,U_9745,U_9746,U_9747,U_9748,U_9749] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9746,U_9744)),U_9747),U_9748),U_9749) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,U_9744),U_9747),hAPP(hAPP(c_COMBC(U_9745,U_9746,U_9744),U_9748),U_9749))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9744) ),
inference(definitional_conversion,[status(esa)],[f_2723_2]) ).
cnf(f_2723_4,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9746,U_9744)),U_9747),U_9748),U_9749) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,U_9744),U_9747),hAPP(hAPP(c_COMBC(U_9745,U_9746,U_9744),U_9748),U_9749))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9744) ),
inference(clausify,[status(thm)],[f_2723_3]) ).
fof(f_2724_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I8_J]) ).
fof(f_2724_2,plain,
! [U_9753,U_9752,U_9751,U_9750] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9750,tc_fun(U_9751,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9750,tc_HOL_Obool),U_9752)),U_9753) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9750,tc_HOL_Obool),tc_fun(U_9751,tc_HOL_Obool)),U_9752),hAPP(hAPP(c_COMBC(tc_fun(U_9750,tc_HOL_Obool),tc_fun(U_9750,tc_fun(U_9751,tc_HOL_Obool)),tc_fun(U_9751,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9750,tc_fun(U_9751,tc_HOL_Obool))),U_9753)),
inference(variable_rename,[status(thm)],[f_2724_1]) ).
fof(f_2724_3,plain,
! [U_9750,U_9751,U_9752,U_9753] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9750,tc_fun(U_9751,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9750,tc_HOL_Obool),U_9752)),U_9753) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9750,tc_HOL_Obool),tc_fun(U_9751,tc_HOL_Obool)),U_9752),hAPP(hAPP(c_COMBC(tc_fun(U_9750,tc_HOL_Obool),tc_fun(U_9750,tc_fun(U_9751,tc_HOL_Obool)),tc_fun(U_9751,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9750,tc_fun(U_9751,tc_HOL_Obool))),U_9753)),
inference(definitional_conversion,[status(esa)],[f_2724_2]) ).
cnf(f_2724_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9750,tc_fun(U_9751,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9750,tc_HOL_Obool),U_9752)),U_9753) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9750,tc_HOL_Obool),tc_fun(U_9751,tc_HOL_Obool)),U_9752),hAPP(hAPP(c_COMBC(tc_fun(U_9750,tc_HOL_Obool),tc_fun(U_9750,tc_fun(U_9751,tc_HOL_Obool)),tc_fun(U_9751,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9750,tc_fun(U_9751,tc_HOL_Obool))),U_9753)),
inference(clausify,[status(thm)],[f_2724_3]) ).
fof(f_2725_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I8_J]) ).
fof(f_2725_2,plain,
! [U_9757,U_9756,U_9755,U_9754] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9754,tc_HOL_Obool),tc_fun(U_9755,tc_HOL_Obool)),U_9756),hAPP(hAPP(c_COMBC(tc_fun(U_9754,tc_HOL_Obool),tc_fun(U_9754,tc_fun(U_9755,tc_HOL_Obool)),tc_fun(U_9755,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9754,tc_fun(U_9755,tc_HOL_Obool))),U_9757)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9754,tc_fun(U_9755,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9754,tc_HOL_Obool),U_9756)),U_9757),
inference(variable_rename,[status(thm)],[f_2725_1]) ).
fof(f_2725_3,plain,
! [U_9754,U_9755,U_9756,U_9757] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9754,tc_HOL_Obool),tc_fun(U_9755,tc_HOL_Obool)),U_9756),hAPP(hAPP(c_COMBC(tc_fun(U_9754,tc_HOL_Obool),tc_fun(U_9754,tc_fun(U_9755,tc_HOL_Obool)),tc_fun(U_9755,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9754,tc_fun(U_9755,tc_HOL_Obool))),U_9757)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9754,tc_fun(U_9755,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9754,tc_HOL_Obool),U_9756)),U_9757),
inference(definitional_conversion,[status(esa)],[f_2725_2]) ).
cnf(f_2725_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9754,tc_HOL_Obool),tc_fun(U_9755,tc_HOL_Obool)),U_9756),hAPP(hAPP(c_COMBC(tc_fun(U_9754,tc_HOL_Obool),tc_fun(U_9754,tc_fun(U_9755,tc_HOL_Obool)),tc_fun(U_9755,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9754,tc_fun(U_9755,tc_HOL_Obool))),U_9757)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9754,tc_fun(U_9755,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9754,tc_HOL_Obool),U_9756)),U_9757),
inference(clausify,[status(thm)],[f_2725_3]) ).
fof(f_2726_1,plain,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( ( 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)
| V_b_2 != V_b_H_2
| V_a_2 != V_a_H_2 )
& ( ( V_b_2 = V_b_H_2
& V_a_2 = V_a_H_2 )
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject]) ).
fof(f_2726_2,plain,
! [U_9763,U_9762,U_9761,U_9760,U_9759,U_9758] :
( ( c_Nitpick_Opair__box_OPairBox(U_9758,U_9759,U_9760,U_9761) = c_Nitpick_Opair__box_OPairBox(U_9758,U_9759,U_9762,U_9763)
| U_9761 != U_9763
| U_9760 != U_9762 )
& ( ( U_9761 = U_9763
& U_9760 = U_9762 )
| c_Nitpick_Opair__box_OPairBox(U_9758,U_9759,U_9760,U_9761) != c_Nitpick_Opair__box_OPairBox(U_9758,U_9759,U_9762,U_9763) ) ),
inference(variable_rename,[status(thm)],[f_2726_1]) ).
fof(f_2726_3,plain,
( ! [U_9775,U_9773,U_9771,U_9769] :
( ! [U_9767,U_9765] : c_Nitpick_Opair__box_OPairBox(U_9765,U_9767,U_9769,U_9771) = c_Nitpick_Opair__box_OPairBox(U_9765,U_9767,U_9773,U_9775)
| U_9771 != U_9775
| U_9769 != U_9773 )
& ! [U_9774,U_9772,U_9770,U_9768] :
( ! [U_9766,U_9764] : c_Nitpick_Opair__box_OPairBox(U_9764,U_9766,U_9768,U_9770) != c_Nitpick_Opair__box_OPairBox(U_9764,U_9766,U_9772,U_9774)
| ( U_9770 = U_9774
& U_9768 = U_9772 ) ) ),
inference(miniscope,[status(thm)],[f_2726_2]) ).
fof(f_2726_4,plain,
( ! [U_9772,U_9774,U_9768,U_9770] :
( U_9770 = U_9774
| ~ sP794(U_9772,U_9774,U_9768,U_9770) )
& ! [U_9772,U_9774,U_9768,U_9770] :
( U_9768 = U_9772
| ~ sP794(U_9772,U_9774,U_9768,U_9770) )
& ! [U_9771,U_9769,U_9773,U_9765,U_9775,U_9767] :
( c_Nitpick_Opair__box_OPairBox(U_9765,U_9767,U_9769,U_9771) = c_Nitpick_Opair__box_OPairBox(U_9765,U_9767,U_9773,U_9775)
| U_9771 != U_9775
| U_9769 != U_9773 )
& ! [U_9772,U_9774,U_9768,U_9764,U_9766,U_9770] :
( c_Nitpick_Opair__box_OPairBox(U_9764,U_9766,U_9768,U_9770) != c_Nitpick_Opair__box_OPairBox(U_9764,U_9766,U_9772,U_9774)
| sP794(U_9772,U_9774,U_9768,U_9770) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP794])],[f_2726_3]) ).
cnf(f_2726_5,plain,
( c_Nitpick_Opair__box_OPairBox(U_9764,U_9766,U_9768,U_9770) != c_Nitpick_Opair__box_OPairBox(U_9764,U_9766,U_9772,U_9774)
| sP794(U_9772,U_9774,U_9768,U_9770) ),
inference(clausify,[status(thm)],[f_2726_4]) ).
cnf(f_2726_6,plain,
( c_Nitpick_Opair__box_OPairBox(U_9765,U_9767,U_9769,U_9771) = c_Nitpick_Opair__box_OPairBox(U_9765,U_9767,U_9773,U_9775)
| U_9771 != U_9775
| U_9769 != U_9773 ),
inference(clausify,[status(thm)],[f_2726_4]) ).
cnf(f_2726_7,plain,
( U_9768 = U_9772
| ~ sP794(U_9772,U_9774,U_9768,U_9770) ),
inference(clausify,[status(thm)],[f_2726_4]) ).
cnf(f_2726_8,plain,
( U_9770 = U_9774
| ~ sP794(U_9772,U_9774,U_9768,U_9770) ),
inference(clausify,[status(thm)],[f_2726_4]) ).
fof(f_2727_1,plain,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( 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))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply]) ).
fof(f_2727_2,plain,
! [U_9780,U_9779,U_9778,U_9777,U_9776] :
( c_Finite__Set_Ofun__left__comm(U_9779,U_9777,hAPP(hAPP(c_COMBB(U_9776,tc_fun(U_9777,U_9777),U_9779),U_9778),U_9780))
| ~ c_Finite__Set_Ofun__left__comm(U_9776,U_9777,U_9778) ),
inference(variable_rename,[status(thm)],[f_2727_1]) ).
fof(f_2727_3,plain,
! [U_9780,U_9778,U_9779,U_9777,U_9776] :
( c_Finite__Set_Ofun__left__comm(U_9779,U_9777,hAPP(hAPP(c_COMBB(U_9776,tc_fun(U_9777,U_9777),U_9779),U_9778),U_9780))
| ~ c_Finite__Set_Ofun__left__comm(U_9776,U_9777,U_9778) ),
inference(definitional_conversion,[status(esa)],[f_2727_2]) ).
cnf(f_2727_4,plain,
( c_Finite__Set_Ofun__left__comm(U_9779,U_9777,hAPP(hAPP(c_COMBB(U_9776,tc_fun(U_9777,U_9777),U_9779),U_9778),U_9780))
| ~ c_Finite__Set_Ofun__left__comm(U_9776,U_9777,U_9778) ),
inference(clausify,[status(thm)],[f_2727_3]) ).
fof(f_2728_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Union__def]) ).
fof(f_2728_2,plain,
! [U_9782,U_9781] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9781,tc_HOL_Obool),U_9782) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9781,tc_HOL_Obool),tc_fun(U_9781,tc_HOL_Obool)),U_9782),c_COMBI(tc_fun(U_9781,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2728_1]) ).
fof(f_2728_3,plain,
! [U_9781,U_9782] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9781,tc_HOL_Obool),U_9782) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9781,tc_HOL_Obool),tc_fun(U_9781,tc_HOL_Obool)),U_9782),c_COMBI(tc_fun(U_9781,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2728_2]) ).
cnf(f_2728_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9781,tc_HOL_Obool),U_9782) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9781,tc_HOL_Obool),tc_fun(U_9781,tc_HOL_Obool)),U_9782),c_COMBI(tc_fun(U_9781,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2728_3]) ).
fof(f_2729_1,plain,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( ( 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))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP1__iff]) ).
fof(f_2729_2,plain,
! [U_9789,U_9788,U_9787,U_9786,U_9785] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9785,tc_fun(U_9786,tc_HOL_Obool)),U_9787),U_9788),U_9789))
| ! [U_9784] :
( ~ hBOOL(hAPP(hAPP(U_9788,U_9784),U_9789))
| ~ hBOOL(hAPP(hAPP(c_member(U_9785),U_9784),U_9787)) ) )
& ( ? [U_9783] :
( hBOOL(hAPP(hAPP(U_9788,U_9783),U_9789))
& hBOOL(hAPP(hAPP(c_member(U_9785),U_9783),U_9787)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9785,tc_fun(U_9786,tc_HOL_Obool)),U_9787),U_9788),U_9789)) ) ),
inference(variable_rename,[status(thm)],[f_2729_1]) ).
fof(f_2729_3,plain,
( ! [U_9799,U_9797,U_9795,U_9793,U_9791] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9793,tc_HOL_Obool)),U_9795),U_9797),U_9799))
| ! [U_9784] :
( ~ hBOOL(hAPP(hAPP(U_9797,U_9784),U_9799))
| ~ hBOOL(hAPP(hAPP(c_member(U_9791),U_9784),U_9795)) ) )
& ! [U_9798,U_9796,U_9794,U_9792,U_9790] :
( ? [U_9783] :
( hBOOL(hAPP(hAPP(U_9796,U_9783),U_9798))
& hBOOL(hAPP(hAPP(c_member(U_9790),U_9783),U_9794)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9790,tc_fun(U_9792,tc_HOL_Obool)),U_9794),U_9796),U_9798)) ) ),
inference(miniscope,[status(thm)],[f_2729_2]) ).
fof(f_2729_4,plain,
( ! [U_9799,U_9797,U_9795,U_9793,U_9791] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9793,tc_HOL_Obool)),U_9795),U_9797),U_9799))
| ! [U_9784] :
( ~ hBOOL(hAPP(hAPP(U_9797,U_9784),U_9799))
| ~ hBOOL(hAPP(hAPP(c_member(U_9791),U_9784),U_9795)) ) )
& ! [U_9798,U_9796,U_9794,U_9792,U_9790] :
( ( hBOOL(hAPP(hAPP(U_9796,sK255(U_9798,U_9796,U_9794,U_9792,U_9790)),U_9798))
& hBOOL(hAPP(hAPP(c_member(U_9790),sK255(U_9798,U_9796,U_9794,U_9792,U_9790)),U_9794)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9790,tc_fun(U_9792,tc_HOL_Obool)),U_9794),U_9796),U_9798)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_9783,sK255(U_9798,U_9796,U_9794,U_9792,U_9790))],[f_2729_3]) ).
fof(f_2729_5,plain,
( ! [U_9796,U_9790,U_9794,U_9792,U_9798] :
( hBOOL(hAPP(hAPP(U_9796,sK255(U_9798,U_9796,U_9794,U_9792,U_9790)),U_9798))
| ~ sP795(U_9796,U_9790,U_9794,U_9792,U_9798) )
& ! [U_9796,U_9790,U_9794,U_9792,U_9798] :
( hBOOL(hAPP(hAPP(c_member(U_9790),sK255(U_9798,U_9796,U_9794,U_9792,U_9790)),U_9794))
| ~ sP795(U_9796,U_9790,U_9794,U_9792,U_9798) )
& ! [U_9795,U_9784,U_9791,U_9793,U_9797,U_9799] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9793,tc_HOL_Obool)),U_9795),U_9797),U_9799))
| ~ hBOOL(hAPP(hAPP(U_9797,U_9784),U_9799))
| ~ hBOOL(hAPP(hAPP(c_member(U_9791),U_9784),U_9795)) )
& ! [U_9796,U_9790,U_9794,U_9792,U_9798] :
( sP795(U_9796,U_9790,U_9794,U_9792,U_9798)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9790,tc_fun(U_9792,tc_HOL_Obool)),U_9794),U_9796),U_9798)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP795])],[f_2729_4]) ).
cnf(f_2729_6,plain,
( sP795(U_9796,U_9790,U_9794,U_9792,U_9798)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9790,tc_fun(U_9792,tc_HOL_Obool)),U_9794),U_9796),U_9798)) ),
inference(clausify,[status(thm)],[f_2729_5]) ).
cnf(f_2729_7,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9793,tc_HOL_Obool)),U_9795),U_9797),U_9799))
| ~ hBOOL(hAPP(hAPP(U_9797,U_9784),U_9799))
| ~ hBOOL(hAPP(hAPP(c_member(U_9791),U_9784),U_9795)) ),
inference(clausify,[status(thm)],[f_2729_5]) ).
cnf(f_2729_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9790),sK255(U_9798,U_9796,U_9794,U_9792,U_9790)),U_9794))
| ~ sP795(U_9796,U_9790,U_9794,U_9792,U_9798) ),
inference(clausify,[status(thm)],[f_2729_5]) ).
cnf(f_2729_9,plain,
( hBOOL(hAPP(hAPP(U_9796,sK255(U_9798,U_9796,U_9794,U_9792,U_9790)),U_9798))
| ~ sP795(U_9796,U_9790,U_9794,U_9792,U_9798) ),
inference(clausify,[status(thm)],[f_2729_5]) ).
fof(f_2730_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__UN__flatten]) ).
fof(f_2730_2,plain,
! [U_9805,U_9804,U_9803,U_9802,U_9801,U_9800] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9802,tc_fun(U_9800,tc_HOL_Obool)),U_9803),U_9804)),U_9805) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9802,tc_fun(U_9801,tc_HOL_Obool)),U_9803),hAPP(hAPP(c_COMBC(U_9802,tc_fun(U_9800,tc_fun(U_9801,tc_HOL_Obool)),tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9800,tc_HOL_Obool),tc_fun(tc_fun(U_9800,tc_fun(U_9801,tc_HOL_Obool)),tc_fun(U_9801,tc_HOL_Obool)),U_9802),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9801,tc_HOL_Obool))),U_9804)),U_9805)),
inference(variable_rename,[status(thm)],[f_2730_1]) ).
fof(f_2730_3,plain,
! [U_9800,U_9801,U_9802,U_9803,U_9804,U_9805] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9802,tc_fun(U_9800,tc_HOL_Obool)),U_9803),U_9804)),U_9805) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9802,tc_fun(U_9801,tc_HOL_Obool)),U_9803),hAPP(hAPP(c_COMBC(U_9802,tc_fun(U_9800,tc_fun(U_9801,tc_HOL_Obool)),tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9800,tc_HOL_Obool),tc_fun(tc_fun(U_9800,tc_fun(U_9801,tc_HOL_Obool)),tc_fun(U_9801,tc_HOL_Obool)),U_9802),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9801,tc_HOL_Obool))),U_9804)),U_9805)),
inference(definitional_conversion,[status(esa)],[f_2730_2]) ).
cnf(f_2730_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9802,tc_fun(U_9800,tc_HOL_Obool)),U_9803),U_9804)),U_9805) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9802,tc_fun(U_9801,tc_HOL_Obool)),U_9803),hAPP(hAPP(c_COMBC(U_9802,tc_fun(U_9800,tc_fun(U_9801,tc_HOL_Obool)),tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9800,tc_HOL_Obool),tc_fun(tc_fun(U_9800,tc_fun(U_9801,tc_HOL_Obool)),tc_fun(U_9801,tc_HOL_Obool)),U_9802),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9801,tc_HOL_Obool))),U_9804)),U_9805)),
inference(clausify,[status(thm)],[f_2730_3]) ).
fof(f_2731_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I9_J]) ).
fof(f_2731_2,plain,
! [U_9811,U_9810,U_9809,U_9808,U_9807,U_9806] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9806,tc_fun(U_9807,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9806,tc_HOL_Obool)),U_9809),U_9810)),U_9811) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9807,tc_HOL_Obool)),U_9809),hAPP(hAPP(c_COMBC(U_9808,tc_fun(U_9806,tc_fun(U_9807,tc_HOL_Obool)),tc_fun(U_9807,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9806,tc_HOL_Obool),tc_fun(tc_fun(U_9806,tc_fun(U_9807,tc_HOL_Obool)),tc_fun(U_9807,tc_HOL_Obool)),U_9808),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9806,tc_fun(U_9807,tc_HOL_Obool))),U_9810)),U_9811)),
inference(variable_rename,[status(thm)],[f_2731_1]) ).
fof(f_2731_3,plain,
! [U_9806,U_9807,U_9808,U_9809,U_9810,U_9811] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9806,tc_fun(U_9807,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9806,tc_HOL_Obool)),U_9809),U_9810)),U_9811) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9807,tc_HOL_Obool)),U_9809),hAPP(hAPP(c_COMBC(U_9808,tc_fun(U_9806,tc_fun(U_9807,tc_HOL_Obool)),tc_fun(U_9807,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9806,tc_HOL_Obool),tc_fun(tc_fun(U_9806,tc_fun(U_9807,tc_HOL_Obool)),tc_fun(U_9807,tc_HOL_Obool)),U_9808),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9806,tc_fun(U_9807,tc_HOL_Obool))),U_9810)),U_9811)),
inference(definitional_conversion,[status(esa)],[f_2731_2]) ).
cnf(f_2731_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9806,tc_fun(U_9807,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9806,tc_HOL_Obool)),U_9809),U_9810)),U_9811) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9807,tc_HOL_Obool)),U_9809),hAPP(hAPP(c_COMBC(U_9808,tc_fun(U_9806,tc_fun(U_9807,tc_HOL_Obool)),tc_fun(U_9807,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9806,tc_HOL_Obool),tc_fun(tc_fun(U_9806,tc_fun(U_9807,tc_HOL_Obool)),tc_fun(U_9807,tc_HOL_Obool)),U_9808),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9806,tc_fun(U_9807,tc_HOL_Obool))),U_9810)),U_9811)),
inference(clausify,[status(thm)],[f_2731_3]) ).
fof(f_2732_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I9_J]) ).
fof(f_2732_2,plain,
! [U_9817,U_9816,U_9815,U_9814,U_9813,U_9812] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9812,tc_fun(U_9813,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9814,tc_fun(U_9812,tc_HOL_Obool)),U_9815),U_9816)),U_9817) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9814,tc_fun(U_9813,tc_HOL_Obool)),U_9815),hAPP(hAPP(c_COMBC(U_9814,tc_fun(U_9812,tc_fun(U_9813,tc_HOL_Obool)),tc_fun(U_9813,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9812,tc_HOL_Obool),tc_fun(tc_fun(U_9812,tc_fun(U_9813,tc_HOL_Obool)),tc_fun(U_9813,tc_HOL_Obool)),U_9814),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9812,tc_fun(U_9813,tc_HOL_Obool))),U_9816)),U_9817)),
inference(variable_rename,[status(thm)],[f_2732_1]) ).
fof(f_2732_3,plain,
! [U_9812,U_9813,U_9814,U_9815,U_9816,U_9817] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9812,tc_fun(U_9813,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9814,tc_fun(U_9812,tc_HOL_Obool)),U_9815),U_9816)),U_9817) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9814,tc_fun(U_9813,tc_HOL_Obool)),U_9815),hAPP(hAPP(c_COMBC(U_9814,tc_fun(U_9812,tc_fun(U_9813,tc_HOL_Obool)),tc_fun(U_9813,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9812,tc_HOL_Obool),tc_fun(tc_fun(U_9812,tc_fun(U_9813,tc_HOL_Obool)),tc_fun(U_9813,tc_HOL_Obool)),U_9814),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9812,tc_fun(U_9813,tc_HOL_Obool))),U_9816)),U_9817)),
inference(definitional_conversion,[status(esa)],[f_2732_2]) ).
cnf(f_2732_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9812,tc_fun(U_9813,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9814,tc_fun(U_9812,tc_HOL_Obool)),U_9815),U_9816)),U_9817) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9814,tc_fun(U_9813,tc_HOL_Obool)),U_9815),hAPP(hAPP(c_COMBC(U_9814,tc_fun(U_9812,tc_fun(U_9813,tc_HOL_Obool)),tc_fun(U_9813,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9812,tc_HOL_Obool),tc_fun(tc_fun(U_9812,tc_fun(U_9813,tc_HOL_Obool)),tc_fun(U_9813,tc_HOL_Obool)),U_9814),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9812,tc_fun(U_9813,tc_HOL_Obool))),U_9816)),U_9817)),
inference(clausify,[status(thm)],[f_2732_3]) ).
fof(f_2733_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I9_J]) ).
fof(f_2733_2,plain,
! [U_9823,U_9822,U_9821,U_9820,U_9819,U_9818] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9818,tc_fun(U_9819,tc_HOL_Obool)),U_9820),hAPP(hAPP(c_COMBC(U_9818,tc_fun(U_9821,tc_fun(U_9819,tc_HOL_Obool)),tc_fun(U_9819,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9821,tc_HOL_Obool),tc_fun(tc_fun(U_9821,tc_fun(U_9819,tc_HOL_Obool)),tc_fun(U_9819,tc_HOL_Obool)),U_9818),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9821,tc_fun(U_9819,tc_HOL_Obool))),U_9822)),U_9823)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9821,tc_fun(U_9819,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9818,tc_fun(U_9821,tc_HOL_Obool)),U_9820),U_9822)),U_9823),
inference(variable_rename,[status(thm)],[f_2733_1]) ).
fof(f_2733_3,plain,
! [U_9818,U_9819,U_9820,U_9821,U_9822,U_9823] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9818,tc_fun(U_9819,tc_HOL_Obool)),U_9820),hAPP(hAPP(c_COMBC(U_9818,tc_fun(U_9821,tc_fun(U_9819,tc_HOL_Obool)),tc_fun(U_9819,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9821,tc_HOL_Obool),tc_fun(tc_fun(U_9821,tc_fun(U_9819,tc_HOL_Obool)),tc_fun(U_9819,tc_HOL_Obool)),U_9818),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9821,tc_fun(U_9819,tc_HOL_Obool))),U_9822)),U_9823)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9821,tc_fun(U_9819,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9818,tc_fun(U_9821,tc_HOL_Obool)),U_9820),U_9822)),U_9823),
inference(definitional_conversion,[status(esa)],[f_2733_2]) ).
cnf(f_2733_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9818,tc_fun(U_9819,tc_HOL_Obool)),U_9820),hAPP(hAPP(c_COMBC(U_9818,tc_fun(U_9821,tc_fun(U_9819,tc_HOL_Obool)),tc_fun(U_9819,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9821,tc_HOL_Obool),tc_fun(tc_fun(U_9821,tc_fun(U_9819,tc_HOL_Obool)),tc_fun(U_9819,tc_HOL_Obool)),U_9818),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9821,tc_fun(U_9819,tc_HOL_Obool))),U_9822)),U_9823)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9821,tc_fun(U_9819,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9818,tc_fun(U_9821,tc_HOL_Obool)),U_9820),U_9822)),U_9823),
inference(clausify,[status(thm)],[f_2733_3]) ).
fof(f_2734_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I9_J]) ).
fof(f_2734_2,plain,
! [U_9829,U_9828,U_9827,U_9826,U_9825,U_9824] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9824,tc_fun(U_9825,tc_HOL_Obool)),U_9826),hAPP(hAPP(c_COMBC(U_9824,tc_fun(U_9827,tc_fun(U_9825,tc_HOL_Obool)),tc_fun(U_9825,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9827,tc_HOL_Obool),tc_fun(tc_fun(U_9827,tc_fun(U_9825,tc_HOL_Obool)),tc_fun(U_9825,tc_HOL_Obool)),U_9824),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9827,tc_fun(U_9825,tc_HOL_Obool))),U_9828)),U_9829)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9827,tc_fun(U_9825,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9824,tc_fun(U_9827,tc_HOL_Obool)),U_9826),U_9828)),U_9829),
inference(variable_rename,[status(thm)],[f_2734_1]) ).
fof(f_2734_3,plain,
! [U_9824,U_9825,U_9826,U_9827,U_9828,U_9829] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9824,tc_fun(U_9825,tc_HOL_Obool)),U_9826),hAPP(hAPP(c_COMBC(U_9824,tc_fun(U_9827,tc_fun(U_9825,tc_HOL_Obool)),tc_fun(U_9825,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9827,tc_HOL_Obool),tc_fun(tc_fun(U_9827,tc_fun(U_9825,tc_HOL_Obool)),tc_fun(U_9825,tc_HOL_Obool)),U_9824),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9827,tc_fun(U_9825,tc_HOL_Obool))),U_9828)),U_9829)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9827,tc_fun(U_9825,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9824,tc_fun(U_9827,tc_HOL_Obool)),U_9826),U_9828)),U_9829),
inference(definitional_conversion,[status(esa)],[f_2734_2]) ).
cnf(f_2734_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9824,tc_fun(U_9825,tc_HOL_Obool)),U_9826),hAPP(hAPP(c_COMBC(U_9824,tc_fun(U_9827,tc_fun(U_9825,tc_HOL_Obool)),tc_fun(U_9825,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9827,tc_HOL_Obool),tc_fun(tc_fun(U_9827,tc_fun(U_9825,tc_HOL_Obool)),tc_fun(U_9825,tc_HOL_Obool)),U_9824),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9827,tc_fun(U_9825,tc_HOL_Obool))),U_9828)),U_9829)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9827,tc_fun(U_9825,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9824,tc_fun(U_9827,tc_HOL_Obool)),U_9826),U_9828)),U_9829),
inference(clausify,[status(thm)],[f_2734_3]) ).
fof(f_2735_1,plain,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( 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)))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_SUP__commute]) ).
fof(f_2735_2,plain,
! [U_9835,U_9834,U_9833,U_9832,U_9831,U_9830] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9831,U_9830),U_9832),hAPP(hAPP(c_COMBB(tc_fun(U_9833,U_9830),U_9830,U_9831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9833,U_9830),U_9834)),U_9835)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9833,U_9830),U_9834),hAPP(hAPP(c_COMBB(tc_fun(U_9831,U_9830),U_9830,U_9833),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9831,U_9830),U_9832)),hAPP(c_COMBC(U_9831,U_9833,U_9830),U_9835)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9830) ),
inference(variable_rename,[status(thm)],[f_2735_1]) ).
fof(f_2735_3,plain,
! [U_9830,U_9831,U_9832,U_9833,U_9834,U_9835] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9831,U_9830),U_9832),hAPP(hAPP(c_COMBB(tc_fun(U_9833,U_9830),U_9830,U_9831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9833,U_9830),U_9834)),U_9835)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9833,U_9830),U_9834),hAPP(hAPP(c_COMBB(tc_fun(U_9831,U_9830),U_9830,U_9833),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9831,U_9830),U_9832)),hAPP(c_COMBC(U_9831,U_9833,U_9830),U_9835)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9830) ),
inference(definitional_conversion,[status(esa)],[f_2735_2]) ).
cnf(f_2735_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9831,U_9830),U_9832),hAPP(hAPP(c_COMBB(tc_fun(U_9833,U_9830),U_9830,U_9831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9833,U_9830),U_9834)),U_9835)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9833,U_9830),U_9834),hAPP(hAPP(c_COMBB(tc_fun(U_9831,U_9830),U_9830,U_9833),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9831,U_9830),U_9832)),hAPP(c_COMBC(U_9831,U_9833,U_9830),U_9835)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9830) ),
inference(clausify,[status(thm)],[f_2735_3]) ).
fof(f_2736_1,plain,
! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
( ( 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)
| V_x_2 = V_a_2 )
& ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2
| V_x_2 != V_a_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__def]) ).
fof(f_2736_2,plain,
! [U_9841,U_9840,U_9839,U_9838,U_9837,U_9836] :
( ( hAPP(c_Fun_Ofun__upd(U_9838,U_9839,U_9840,U_9837,U_9841),U_9836) = hAPP(U_9840,U_9836)
| U_9836 = U_9837 )
& ( hAPP(c_Fun_Ofun__upd(U_9838,U_9839,U_9840,U_9837,U_9841),U_9836) = U_9841
| U_9836 != U_9837 ) ),
inference(variable_rename,[status(thm)],[f_2736_1]) ).
fof(f_2736_3,plain,
( ! [U_9853,U_9851,U_9849,U_9847,U_9845,U_9843] :
( hAPP(c_Fun_Ofun__upd(U_9847,U_9849,U_9851,U_9845,U_9853),U_9843) = hAPP(U_9851,U_9843)
| U_9843 = U_9845 )
& ! [U_9852,U_9850,U_9848,U_9846,U_9844,U_9842] :
( hAPP(c_Fun_Ofun__upd(U_9846,U_9848,U_9850,U_9844,U_9852),U_9842) = U_9852
| U_9842 != U_9844 ) ),
inference(miniscope,[status(thm)],[f_2736_2]) ).
fof(f_2736_4,plain,
( ! [U_9843,U_9845,U_9847,U_9849,U_9851,U_9853] :
( hAPP(c_Fun_Ofun__upd(U_9847,U_9849,U_9851,U_9845,U_9853),U_9843) = hAPP(U_9851,U_9843)
| U_9843 = U_9845 )
& ! [U_9848,U_9844,U_9842,U_9846,U_9850,U_9852] :
( hAPP(c_Fun_Ofun__upd(U_9846,U_9848,U_9850,U_9844,U_9852),U_9842) = U_9852
| U_9842 != U_9844 ) ),
inference(definitional_conversion,[status(esa)],[f_2736_3]) ).
cnf(f_2736_5,plain,
( hAPP(c_Fun_Ofun__upd(U_9846,U_9848,U_9850,U_9844,U_9852),U_9842) = U_9852
| U_9842 != U_9844 ),
inference(clausify,[status(thm)],[f_2736_4]) ).
cnf(f_2736_6,plain,
( hAPP(c_Fun_Ofun__upd(U_9847,U_9849,U_9851,U_9845,U_9853),U_9843) = hAPP(U_9851,U_9843)
| U_9843 = U_9845 ),
inference(clausify,[status(thm)],[f_2736_4]) ).
fof(f_2737_1,plain,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( 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)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__commute]) ).
fof(f_2737_2,plain,
! [U_9859,U_9858,U_9857,U_9856,U_9855,U_9854] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9855,U_9854),hAPP(hAPP(c_COMBC(U_9855,tc_fun(U_9856,tc_HOL_Obool),U_9854),hAPP(hAPP(c_COMBB(tc_fun(U_9856,U_9854),tc_fun(tc_fun(U_9856,tc_HOL_Obool),U_9854),U_9855),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9856,U_9854)),U_9857)),U_9858)),U_9859) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9856,U_9854),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9855,tc_HOL_Obool),U_9854),hAPP(hAPP(c_COMBB(tc_fun(U_9855,U_9854),tc_fun(tc_fun(U_9855,tc_HOL_Obool),U_9854),U_9856),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9855,U_9854)),hAPP(c_COMBC(U_9855,U_9856,U_9854),U_9857))),U_9859)),U_9858)
| ~ class_Groups_Ocomm__monoid__add(U_9854) ),
inference(variable_rename,[status(thm)],[f_2737_1]) ).
fof(f_2737_3,plain,
! [U_9855,U_9854,U_9856,U_9857,U_9858,U_9859] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9855,U_9854),hAPP(hAPP(c_COMBC(U_9855,tc_fun(U_9856,tc_HOL_Obool),U_9854),hAPP(hAPP(c_COMBB(tc_fun(U_9856,U_9854),tc_fun(tc_fun(U_9856,tc_HOL_Obool),U_9854),U_9855),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9856,U_9854)),U_9857)),U_9858)),U_9859) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9856,U_9854),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9855,tc_HOL_Obool),U_9854),hAPP(hAPP(c_COMBB(tc_fun(U_9855,U_9854),tc_fun(tc_fun(U_9855,tc_HOL_Obool),U_9854),U_9856),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9855,U_9854)),hAPP(c_COMBC(U_9855,U_9856,U_9854),U_9857))),U_9859)),U_9858)
| ~ class_Groups_Ocomm__monoid__add(U_9854) ),
inference(definitional_conversion,[status(esa)],[f_2737_2]) ).
cnf(f_2737_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9855,U_9854),hAPP(hAPP(c_COMBC(U_9855,tc_fun(U_9856,tc_HOL_Obool),U_9854),hAPP(hAPP(c_COMBB(tc_fun(U_9856,U_9854),tc_fun(tc_fun(U_9856,tc_HOL_Obool),U_9854),U_9855),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9856,U_9854)),U_9857)),U_9858)),U_9859) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9856,U_9854),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9855,tc_HOL_Obool),U_9854),hAPP(hAPP(c_COMBB(tc_fun(U_9855,U_9854),tc_fun(tc_fun(U_9855,tc_HOL_Obool),U_9854),U_9856),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9855,U_9854)),hAPP(c_COMBC(U_9855,U_9856,U_9854),U_9857))),U_9859)),U_9858)
| ~ class_Groups_Ocomm__monoid__add(U_9854) ),
inference(clausify,[status(thm)],[f_2737_3]) ).
fof(f_2738_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_fold__image__def]) ).
fof(f_2738_2,plain,
! [U_9863,U_9862,U_9861,U_9860] : hAPP(c_Finite__Set_Ofold__image(U_9860,U_9861,U_9862),U_9863) = c_Finite__Set_Ofold(U_9861,U_9860,hAPP(hAPP(c_COMBB(U_9860,tc_fun(U_9860,U_9860),U_9861),U_9862),U_9863)),
inference(variable_rename,[status(thm)],[f_2738_1]) ).
fof(f_2738_3,plain,
! [U_9860,U_9861,U_9862,U_9863] : hAPP(c_Finite__Set_Ofold__image(U_9860,U_9861,U_9862),U_9863) = c_Finite__Set_Ofold(U_9861,U_9860,hAPP(hAPP(c_COMBB(U_9860,tc_fun(U_9860,U_9860),U_9861),U_9862),U_9863)),
inference(definitional_conversion,[status(esa)],[f_2738_2]) ).
cnf(f_2738_4,plain,
hAPP(c_Finite__Set_Ofold__image(U_9860,U_9861,U_9862),U_9863) = c_Finite__Set_Ofold(U_9861,U_9860,hAPP(hAPP(c_COMBB(U_9860,tc_fun(U_9860,U_9860),U_9861),U_9862),U_9863)),
inference(clausify,[status(thm)],[f_2738_3]) ).
fof(f_2739_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I8_J]) ).
fof(f_2739_2,plain,
! [U_9867,U_9866,U_9865,U_9864] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9865,tc_HOL_Obool)),U_9866),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_fun(U_9865,tc_HOL_Obool)),tc_fun(U_9865,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9864,tc_fun(U_9865,tc_HOL_Obool))),U_9867)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9864,tc_fun(U_9865,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9864,tc_HOL_Obool),U_9866)),U_9867),
inference(variable_rename,[status(thm)],[f_2739_1]) ).
fof(f_2739_3,plain,
! [U_9864,U_9865,U_9866,U_9867] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9865,tc_HOL_Obool)),U_9866),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_fun(U_9865,tc_HOL_Obool)),tc_fun(U_9865,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9864,tc_fun(U_9865,tc_HOL_Obool))),U_9867)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9864,tc_fun(U_9865,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9864,tc_HOL_Obool),U_9866)),U_9867),
inference(definitional_conversion,[status(esa)],[f_2739_2]) ).
cnf(f_2739_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9865,tc_HOL_Obool)),U_9866),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_fun(U_9865,tc_HOL_Obool)),tc_fun(U_9865,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9864,tc_fun(U_9865,tc_HOL_Obool))),U_9867)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9864,tc_fun(U_9865,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9864,tc_HOL_Obool),U_9866)),U_9867),
inference(clausify,[status(thm)],[f_2739_3]) ).
fof(f_2740_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I8_J]) ).
fof(f_2740_2,plain,
! [U_9871,U_9870,U_9869,U_9868] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9868,tc_fun(U_9869,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9868,tc_HOL_Obool),U_9870)),U_9871) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9869,tc_HOL_Obool)),U_9870),hAPP(hAPP(c_COMBC(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_fun(U_9869,tc_HOL_Obool)),tc_fun(U_9869,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9868,tc_fun(U_9869,tc_HOL_Obool))),U_9871)),
inference(variable_rename,[status(thm)],[f_2740_1]) ).
fof(f_2740_3,plain,
! [U_9868,U_9869,U_9870,U_9871] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9868,tc_fun(U_9869,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9868,tc_HOL_Obool),U_9870)),U_9871) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9869,tc_HOL_Obool)),U_9870),hAPP(hAPP(c_COMBC(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_fun(U_9869,tc_HOL_Obool)),tc_fun(U_9869,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9868,tc_fun(U_9869,tc_HOL_Obool))),U_9871)),
inference(definitional_conversion,[status(esa)],[f_2740_2]) ).
cnf(f_2740_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9868,tc_fun(U_9869,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9868,tc_HOL_Obool),U_9870)),U_9871) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9869,tc_HOL_Obool)),U_9870),hAPP(hAPP(c_COMBC(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_fun(U_9869,tc_HOL_Obool)),tc_fun(U_9869,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9868,tc_fun(U_9869,tc_HOL_Obool))),U_9871)),
inference(clausify,[status(thm)],[f_2740_3]) ).
fof(f_2741_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_int__setprod]) ).
fof(f_2741_2,plain,
! [U_9874,U_9873,U_9872] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9872,tc_Nat_Onat),U_9873),U_9874)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9872,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9872),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9873)),U_9874),
inference(variable_rename,[status(thm)],[f_2741_1]) ).
fof(f_2741_3,plain,
! [U_9872,U_9873,U_9874] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9872,tc_Nat_Onat),U_9873),U_9874)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9872,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9872),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9873)),U_9874),
inference(definitional_conversion,[status(esa)],[f_2741_2]) ).
cnf(f_2741_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9872,tc_Nat_Onat),U_9873),U_9874)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9872,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9872),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9873)),U_9874),
inference(clausify,[status(thm)],[f_2741_3]) ).
fof(f_2742_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__setsum]) ).
fof(f_2742_2,plain,
! [U_9878,U_9877,U_9876,U_9875] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_9875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9876,tc_Int_Oint),U_9877),U_9878)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9876,U_9875),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9875,U_9876),c_Int_Oring__1__class_Oof__int(U_9875)),U_9877)),U_9878)
| ~ class_Rings_Oring__1(U_9875) ),
inference(variable_rename,[status(thm)],[f_2742_1]) ).
fof(f_2742_3,plain,
! [U_9875,U_9876,U_9877,U_9878] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_9875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9876,tc_Int_Oint),U_9877),U_9878)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9876,U_9875),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9875,U_9876),c_Int_Oring__1__class_Oof__int(U_9875)),U_9877)),U_9878)
| ~ class_Rings_Oring__1(U_9875) ),
inference(definitional_conversion,[status(esa)],[f_2742_2]) ).
cnf(f_2742_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_9875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9876,tc_Int_Oint),U_9877),U_9878)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9876,U_9875),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9875,U_9876),c_Int_Oring__1__class_Oof__int(U_9875)),U_9877)),U_9878)
| ~ class_Rings_Oring__1(U_9875) ),
inference(clausify,[status(thm)],[f_2742_3]) ).
fof(f_2743_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Rings_Oring__1(T_b)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__setprod]) ).
fof(f_2743_2,plain,
! [U_9882,U_9881,U_9880,U_9879] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_9879),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9880,tc_Int_Oint),U_9881),U_9882)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9880,U_9879),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9879,U_9880),c_Int_Oring__1__class_Oof__int(U_9879)),U_9881)),U_9882)
| ~ class_Rings_Oring__1(U_9879)
| ~ class_Groups_Ocomm__monoid__mult(U_9879) ),
inference(variable_rename,[status(thm)],[f_2743_1]) ).
fof(f_2743_3,plain,
! [U_9879,U_9880,U_9881,U_9882] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_9879),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9880,tc_Int_Oint),U_9881),U_9882)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9880,U_9879),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9879,U_9880),c_Int_Oring__1__class_Oof__int(U_9879)),U_9881)),U_9882)
| ~ class_Rings_Oring__1(U_9879)
| ~ class_Groups_Ocomm__monoid__mult(U_9879) ),
inference(definitional_conversion,[status(esa)],[f_2743_2]) ).
cnf(f_2743_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_9879),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9880,tc_Int_Oint),U_9881),U_9882)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9880,U_9879),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9879,U_9880),c_Int_Oring__1__class_Oof__int(U_9879)),U_9881)),U_9882)
| ~ class_Rings_Oring__1(U_9879)
| ~ class_Groups_Ocomm__monoid__mult(U_9879) ),
inference(clausify,[status(thm)],[f_2743_3]) ).
fof(f_2744_1,plain,
! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Fields_Ofield__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__dividef]) ).
fof(f_2744_2,plain,
! [U_9887,U_9886,U_9885,U_9884,U_9883] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),hAPP(hAPP(c_COMBS(U_9884,U_9883,U_9883),hAPP(hAPP(c_COMBB(U_9883,tc_fun(U_9883,U_9883),U_9884),c_Rings_Oinverse__class_Odivide(U_9883)),U_9886)),U_9887)),U_9885) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9883),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),U_9886),U_9885)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),U_9887),U_9885))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Fields_Ofield__inverse__zero(U_9883) ),
inference(variable_rename,[status(thm)],[f_2744_1]) ).
fof(f_2744_3,plain,
! [U_9883,U_9884,U_9885,U_9886,U_9887] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),hAPP(hAPP(c_COMBS(U_9884,U_9883,U_9883),hAPP(hAPP(c_COMBB(U_9883,tc_fun(U_9883,U_9883),U_9884),c_Rings_Oinverse__class_Odivide(U_9883)),U_9886)),U_9887)),U_9885) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9883),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),U_9886),U_9885)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),U_9887),U_9885))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Fields_Ofield__inverse__zero(U_9883) ),
inference(definitional_conversion,[status(esa)],[f_2744_2]) ).
cnf(f_2744_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),hAPP(hAPP(c_COMBS(U_9884,U_9883,U_9883),hAPP(hAPP(c_COMBB(U_9883,tc_fun(U_9883,U_9883),U_9884),c_Rings_Oinverse__class_Odivide(U_9883)),U_9886)),U_9887)),U_9885) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9883),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),U_9886),U_9885)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),U_9887),U_9885))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Fields_Ofield__inverse__zero(U_9883) ),
inference(clausify,[status(thm)],[f_2744_3]) ).
fof(f_2745_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Compl__eq]) ).
fof(f_2745_2,plain,
! [U_9889,U_9888] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9888,tc_HOL_Obool)),U_9889) = hAPP(c_Set_OCollect(U_9888),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9888),c_fNot),hAPP(hAPP(c_COMBC(U_9888,tc_fun(U_9888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9888)),U_9889))),
inference(variable_rename,[status(thm)],[f_2745_1]) ).
fof(f_2745_3,plain,
! [U_9888,U_9889] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9888,tc_HOL_Obool)),U_9889) = hAPP(c_Set_OCollect(U_9888),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9888),c_fNot),hAPP(hAPP(c_COMBC(U_9888,tc_fun(U_9888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9888)),U_9889))),
inference(definitional_conversion,[status(esa)],[f_2745_2]) ).
cnf(f_2745_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9888,tc_HOL_Obool)),U_9889) = hAPP(c_Set_OCollect(U_9888),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9888),c_fNot),hAPP(hAPP(c_COMBC(U_9888,tc_fun(U_9888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9888)),U_9889))),
inference(clausify,[status(thm)],[f_2745_3]) ).
fof(f_2746_1,plain,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib]) ).
fof(f_2746_2,plain,
! [U_9894,U_9893,U_9892,U_9891,U_9890] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),hAPP(hAPP(c_COMBS(U_9891,U_9890,U_9890),hAPP(hAPP(c_COMBB(U_9890,tc_fun(U_9890,U_9890),U_9891),c_Groups_Otimes__class_Otimes(U_9890)),U_9893)),U_9894)),U_9892) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9890),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),U_9893),U_9892)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),U_9894),U_9892))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9891),U_9892))
| ~ class_Groups_Ocomm__monoid__mult(U_9890) ),
inference(variable_rename,[status(thm)],[f_2746_1]) ).
fof(f_2746_3,plain,
! [U_9890,U_9891,U_9892,U_9893,U_9894] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),hAPP(hAPP(c_COMBS(U_9891,U_9890,U_9890),hAPP(hAPP(c_COMBB(U_9890,tc_fun(U_9890,U_9890),U_9891),c_Groups_Otimes__class_Otimes(U_9890)),U_9893)),U_9894)),U_9892) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9890),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),U_9893),U_9892)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),U_9894),U_9892))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9891),U_9892))
| ~ class_Groups_Ocomm__monoid__mult(U_9890) ),
inference(definitional_conversion,[status(esa)],[f_2746_2]) ).
cnf(f_2746_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),hAPP(hAPP(c_COMBS(U_9891,U_9890,U_9890),hAPP(hAPP(c_COMBB(U_9890,tc_fun(U_9890,U_9890),U_9891),c_Groups_Otimes__class_Otimes(U_9890)),U_9893)),U_9894)),U_9892) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9890),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),U_9893),U_9892)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9891,U_9890),U_9894),U_9892))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9891),U_9892))
| ~ class_Groups_Ocomm__monoid__mult(U_9890) ),
inference(clausify,[status(thm)],[f_2746_3]) ).
fof(f_2747_1,plain,
! [V_B_2,V_a_2,T_c,T_b,V_C_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)) = 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))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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)))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J]) ).
fof(f_2747_2,plain,
! [U_9899,U_9898,U_9897,U_9896,U_9895] :
( ( hAPP(hAPP(c_Set_Oinsert(U_9897),U_9898),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9896,tc_fun(U_9897,tc_HOL_Obool)),U_9895),U_9899)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9896,tc_fun(U_9897,tc_HOL_Obool)),U_9895),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool),U_9896),hAPP(c_Set_Oinsert(U_9897),U_9898)),U_9899))
| U_9895 = c_Orderings_Obot__class_Obot(tc_fun(U_9896,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Set_Oinsert(U_9897),U_9898),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9896,tc_fun(U_9897,tc_HOL_Obool)),U_9895),U_9899)) = hAPP(hAPP(c_Set_Oinsert(U_9897),U_9898),c_Orderings_Obot__class_Obot(tc_fun(U_9897,tc_HOL_Obool)))
| U_9895 != c_Orderings_Obot__class_Obot(tc_fun(U_9896,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2747_1]) ).
fof(f_2747_3,plain,
( ! [U_9909,U_9907,U_9905,U_9903,U_9901] :
( hAPP(hAPP(c_Set_Oinsert(U_9905),U_9907),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9903,tc_fun(U_9905,tc_HOL_Obool)),U_9901),U_9909)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9903,tc_fun(U_9905,tc_HOL_Obool)),U_9901),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),hAPP(c_Set_Oinsert(U_9905),U_9907)),U_9909))
| U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool)) )
& ! [U_9908,U_9906,U_9904,U_9902,U_9900] :
( hAPP(hAPP(c_Set_Oinsert(U_9904),U_9906),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9902,tc_fun(U_9904,tc_HOL_Obool)),U_9900),U_9908)) = hAPP(hAPP(c_Set_Oinsert(U_9904),U_9906),c_Orderings_Obot__class_Obot(tc_fun(U_9904,tc_HOL_Obool)))
| U_9900 != c_Orderings_Obot__class_Obot(tc_fun(U_9902,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2747_2]) ).
fof(f_2747_4,plain,
( ! [U_9901,U_9903,U_9905,U_9907,U_9909] :
( hAPP(hAPP(c_Set_Oinsert(U_9905),U_9907),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9903,tc_fun(U_9905,tc_HOL_Obool)),U_9901),U_9909)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9903,tc_fun(U_9905,tc_HOL_Obool)),U_9901),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),hAPP(c_Set_Oinsert(U_9905),U_9907)),U_9909))
| U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool)) )
& ! [U_9902,U_9906,U_9900,U_9904,U_9908] :
( hAPP(hAPP(c_Set_Oinsert(U_9904),U_9906),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9902,tc_fun(U_9904,tc_HOL_Obool)),U_9900),U_9908)) = hAPP(hAPP(c_Set_Oinsert(U_9904),U_9906),c_Orderings_Obot__class_Obot(tc_fun(U_9904,tc_HOL_Obool)))
| U_9900 != c_Orderings_Obot__class_Obot(tc_fun(U_9902,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2747_3]) ).
cnf(f_2747_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_9904),U_9906),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9902,tc_fun(U_9904,tc_HOL_Obool)),U_9900),U_9908)) = hAPP(hAPP(c_Set_Oinsert(U_9904),U_9906),c_Orderings_Obot__class_Obot(tc_fun(U_9904,tc_HOL_Obool)))
| U_9900 != c_Orderings_Obot__class_Obot(tc_fun(U_9902,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2747_4]) ).
cnf(f_2747_6,plain,
( hAPP(hAPP(c_Set_Oinsert(U_9905),U_9907),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9903,tc_fun(U_9905,tc_HOL_Obool)),U_9901),U_9909)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9903,tc_fun(U_9905,tc_HOL_Obool)),U_9901),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),hAPP(c_Set_Oinsert(U_9905),U_9907)),U_9909))
| U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2747_4]) ).
fof(f_2748_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_UN__singleton]) ).
fof(f_2748_2,plain,
! [U_9911,U_9910] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9910,tc_fun(U_9910,tc_HOL_Obool)),U_9911),hAPP(hAPP(c_COMBC(U_9910,tc_fun(U_9910,tc_HOL_Obool),tc_fun(U_9910,tc_HOL_Obool)),c_Set_Oinsert(U_9910)),c_Orderings_Obot__class_Obot(tc_fun(U_9910,tc_HOL_Obool)))) = U_9911,
inference(variable_rename,[status(thm)],[f_2748_1]) ).
fof(f_2748_3,plain,
! [U_9910,U_9911] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9910,tc_fun(U_9910,tc_HOL_Obool)),U_9911),hAPP(hAPP(c_COMBC(U_9910,tc_fun(U_9910,tc_HOL_Obool),tc_fun(U_9910,tc_HOL_Obool)),c_Set_Oinsert(U_9910)),c_Orderings_Obot__class_Obot(tc_fun(U_9910,tc_HOL_Obool)))) = U_9911,
inference(definitional_conversion,[status(esa)],[f_2748_2]) ).
cnf(f_2748_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9910,tc_fun(U_9910,tc_HOL_Obool)),U_9911),hAPP(hAPP(c_COMBC(U_9910,tc_fun(U_9910,tc_HOL_Obool),tc_fun(U_9910,tc_HOL_Obool)),c_Set_Oinsert(U_9910)),c_Orderings_Obot__class_Obot(tc_fun(U_9910,tc_HOL_Obool)))) = U_9911,
inference(clausify,[status(thm)],[f_2748_3]) ).
fof(f_2749_1,plain,
! [V_B_2,V_a_2,T_c,T_b,V_C_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)) = 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))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J]) ).
fof(f_2749_2,plain,
! [U_9916,U_9915,U_9914,U_9913,U_9912] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9913,tc_fun(U_9914,tc_HOL_Obool)),U_9912),hAPP(hAPP(c_COMBB(tc_fun(U_9914,tc_HOL_Obool),tc_fun(U_9914,tc_HOL_Obool),U_9913),hAPP(c_Set_Oinsert(U_9914),U_9915)),U_9916)) = hAPP(hAPP(c_Set_Oinsert(U_9914),U_9915),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9913,tc_fun(U_9914,tc_HOL_Obool)),U_9912),U_9916))
| U_9912 = c_Orderings_Obot__class_Obot(tc_fun(U_9913,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9913,tc_fun(U_9914,tc_HOL_Obool)),U_9912),hAPP(hAPP(c_COMBB(tc_fun(U_9914,tc_HOL_Obool),tc_fun(U_9914,tc_HOL_Obool),U_9913),hAPP(c_Set_Oinsert(U_9914),U_9915)),U_9916)) = c_Orderings_Obot__class_Obot(tc_fun(U_9914,tc_HOL_Obool))
| U_9912 != c_Orderings_Obot__class_Obot(tc_fun(U_9913,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2749_1]) ).
fof(f_2749_3,plain,
( ! [U_9926,U_9924,U_9922,U_9920,U_9918] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9920,tc_fun(U_9922,tc_HOL_Obool)),U_9918),hAPP(hAPP(c_COMBB(tc_fun(U_9922,tc_HOL_Obool),tc_fun(U_9922,tc_HOL_Obool),U_9920),hAPP(c_Set_Oinsert(U_9922),U_9924)),U_9926)) = hAPP(hAPP(c_Set_Oinsert(U_9922),U_9924),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9920,tc_fun(U_9922,tc_HOL_Obool)),U_9918),U_9926))
| U_9918 = c_Orderings_Obot__class_Obot(tc_fun(U_9920,tc_HOL_Obool)) )
& ! [U_9925,U_9923,U_9921,U_9919,U_9917] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9919,tc_fun(U_9921,tc_HOL_Obool)),U_9917),hAPP(hAPP(c_COMBB(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool),U_9919),hAPP(c_Set_Oinsert(U_9921),U_9923)),U_9925)) = c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))
| U_9917 != c_Orderings_Obot__class_Obot(tc_fun(U_9919,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2749_2]) ).
fof(f_2749_4,plain,
( ! [U_9918,U_9920,U_9922,U_9924,U_9926] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9920,tc_fun(U_9922,tc_HOL_Obool)),U_9918),hAPP(hAPP(c_COMBB(tc_fun(U_9922,tc_HOL_Obool),tc_fun(U_9922,tc_HOL_Obool),U_9920),hAPP(c_Set_Oinsert(U_9922),U_9924)),U_9926)) = hAPP(hAPP(c_Set_Oinsert(U_9922),U_9924),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9920,tc_fun(U_9922,tc_HOL_Obool)),U_9918),U_9926))
| U_9918 = c_Orderings_Obot__class_Obot(tc_fun(U_9920,tc_HOL_Obool)) )
& ! [U_9919,U_9923,U_9917,U_9921,U_9925] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9919,tc_fun(U_9921,tc_HOL_Obool)),U_9917),hAPP(hAPP(c_COMBB(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool),U_9919),hAPP(c_Set_Oinsert(U_9921),U_9923)),U_9925)) = c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))
| U_9917 != c_Orderings_Obot__class_Obot(tc_fun(U_9919,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2749_3]) ).
cnf(f_2749_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9919,tc_fun(U_9921,tc_HOL_Obool)),U_9917),hAPP(hAPP(c_COMBB(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool),U_9919),hAPP(c_Set_Oinsert(U_9921),U_9923)),U_9925)) = c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))
| U_9917 != c_Orderings_Obot__class_Obot(tc_fun(U_9919,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2749_4]) ).
cnf(f_2749_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9920,tc_fun(U_9922,tc_HOL_Obool)),U_9918),hAPP(hAPP(c_COMBB(tc_fun(U_9922,tc_HOL_Obool),tc_fun(U_9922,tc_HOL_Obool),U_9920),hAPP(c_Set_Oinsert(U_9922),U_9924)),U_9926)) = hAPP(hAPP(c_Set_Oinsert(U_9922),U_9924),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9920,tc_fun(U_9922,tc_HOL_Obool)),U_9918),U_9926))
| U_9918 = c_Orderings_Obot__class_Obot(tc_fun(U_9920,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2749_4]) ).
fof(f_2750_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_UN__atMost__UNIV]) ).
fof(f_2750_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_2750_1]) ).
cnf(f_2750_3,plain,
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)),
inference(clausify,[status(thm)],[f_2750_2]) ).
fof(f_2751_1,plain,
! [V_ca_2,T_c,T_b,V_A_2] :
( ( 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_ca_2)) = V_ca_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__constant]) ).
fof(f_2751_2,plain,
! [U_9930,U_9929,U_9928,U_9927] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9928,tc_fun(U_9929,tc_HOL_Obool)),U_9927),hAPP(c_COMBK(tc_fun(U_9929,tc_HOL_Obool),U_9928),U_9930)) = U_9930
| U_9927 = c_Orderings_Obot__class_Obot(tc_fun(U_9928,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9928,tc_fun(U_9929,tc_HOL_Obool)),U_9927),hAPP(c_COMBK(tc_fun(U_9929,tc_HOL_Obool),U_9928),U_9930)) = c_Orderings_Otop__class_Otop(tc_fun(U_9929,tc_HOL_Obool))
| U_9927 != c_Orderings_Obot__class_Obot(tc_fun(U_9928,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2751_1]) ).
fof(f_2751_3,plain,
( ! [U_9938,U_9936,U_9934,U_9932] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9934,tc_fun(U_9936,tc_HOL_Obool)),U_9932),hAPP(c_COMBK(tc_fun(U_9936,tc_HOL_Obool),U_9934),U_9938)) = U_9938
| U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9934,tc_HOL_Obool)) )
& ! [U_9937,U_9935,U_9933,U_9931] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9933,tc_fun(U_9935,tc_HOL_Obool)),U_9931),hAPP(c_COMBK(tc_fun(U_9935,tc_HOL_Obool),U_9933),U_9937)) = c_Orderings_Otop__class_Otop(tc_fun(U_9935,tc_HOL_Obool))
| U_9931 != c_Orderings_Obot__class_Obot(tc_fun(U_9933,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2751_2]) ).
fof(f_2751_4,plain,
( ! [U_9932,U_9934,U_9936,U_9938] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9934,tc_fun(U_9936,tc_HOL_Obool)),U_9932),hAPP(c_COMBK(tc_fun(U_9936,tc_HOL_Obool),U_9934),U_9938)) = U_9938
| U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9934,tc_HOL_Obool)) )
& ! [U_9937,U_9933,U_9931,U_9935] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9933,tc_fun(U_9935,tc_HOL_Obool)),U_9931),hAPP(c_COMBK(tc_fun(U_9935,tc_HOL_Obool),U_9933),U_9937)) = c_Orderings_Otop__class_Otop(tc_fun(U_9935,tc_HOL_Obool))
| U_9931 != c_Orderings_Obot__class_Obot(tc_fun(U_9933,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2751_3]) ).
cnf(f_2751_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9933,tc_fun(U_9935,tc_HOL_Obool)),U_9931),hAPP(c_COMBK(tc_fun(U_9935,tc_HOL_Obool),U_9933),U_9937)) = c_Orderings_Otop__class_Otop(tc_fun(U_9935,tc_HOL_Obool))
| U_9931 != c_Orderings_Obot__class_Obot(tc_fun(U_9933,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2751_4]) ).
cnf(f_2751_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9934,tc_fun(U_9936,tc_HOL_Obool)),U_9932),hAPP(c_COMBK(tc_fun(U_9936,tc_HOL_Obool),U_9934),U_9938)) = U_9938
| U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9934,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2751_4]) ).
fof(f_2752_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_INT__empty]) ).
fof(f_2752_2,plain,
! [U_9941,U_9940,U_9939] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9939,tc_fun(U_9940,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9939,tc_HOL_Obool))),U_9941) = c_Orderings_Otop__class_Otop(tc_fun(U_9940,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2752_1]) ).
fof(f_2752_3,plain,
! [U_9939,U_9940,U_9941] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9939,tc_fun(U_9940,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9939,tc_HOL_Obool))),U_9941) = c_Orderings_Otop__class_Otop(tc_fun(U_9940,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_2752_2]) ).
cnf(f_2752_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9939,tc_fun(U_9940,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9939,tc_HOL_Obool))),U_9941) = c_Orderings_Otop__class_Otop(tc_fun(U_9940,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2752_3]) ).
fof(f_2753_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( 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)
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J]) ).
fof(f_2753_2,plain,
! [U_9947,U_9946,U_9945,U_9944] :
( ( c_Orderings_Otop__class_Otop(tc_fun(U_9944,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9945,tc_fun(U_9944,tc_HOL_Obool)),U_9946),U_9947)
| ? [U_9943] :
( hAPP(U_9947,U_9943) != c_Orderings_Otop__class_Otop(tc_fun(U_9944,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9945),U_9943),U_9946)) ) )
& ( ! [U_9942] :
( hAPP(U_9947,U_9942) = c_Orderings_Otop__class_Otop(tc_fun(U_9944,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9945),U_9942),U_9946)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_9944,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9945,tc_fun(U_9944,tc_HOL_Obool)),U_9946),U_9947) ) ),
inference(variable_rename,[status(thm)],[f_2753_1]) ).
fof(f_2753_3,plain,
( ! [U_9955,U_9953,U_9951,U_9949] :
( c_Orderings_Otop__class_Otop(tc_fun(U_9949,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9951,tc_fun(U_9949,tc_HOL_Obool)),U_9953),U_9955)
| ? [U_9943] :
( hAPP(U_9955,U_9943) != c_Orderings_Otop__class_Otop(tc_fun(U_9949,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9951),U_9943),U_9953)) ) )
& ! [U_9954,U_9952,U_9950,U_9948] :
( ! [U_9942] :
( hAPP(U_9954,U_9942) = c_Orderings_Otop__class_Otop(tc_fun(U_9948,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9950),U_9942),U_9952)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_9948,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9950,tc_fun(U_9948,tc_HOL_Obool)),U_9952),U_9954) ) ),
inference(miniscope,[status(thm)],[f_2753_2]) ).
fof(f_2753_4,plain,
( ! [U_9955,U_9953,U_9951,U_9949] :
( c_Orderings_Otop__class_Otop(tc_fun(U_9949,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9951,tc_fun(U_9949,tc_HOL_Obool)),U_9953),U_9955)
| ( hAPP(U_9955,sK256(U_9955,U_9953,U_9951,U_9949)) != c_Orderings_Otop__class_Otop(tc_fun(U_9949,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9951),sK256(U_9955,U_9953,U_9951,U_9949)),U_9953)) ) )
& ! [U_9954,U_9952,U_9950,U_9948] :
( ! [U_9942] :
( hAPP(U_9954,U_9942) = c_Orderings_Otop__class_Otop(tc_fun(U_9948,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9950),U_9942),U_9952)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_9948,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9950,tc_fun(U_9948,tc_HOL_Obool)),U_9952),U_9954) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_9943,sK256(U_9955,U_9953,U_9951,U_9949))],[f_2753_3]) ).
fof(f_2753_5,plain,
( ! [U_9951,U_9949,U_9955,U_9953] :
( hAPP(U_9955,sK256(U_9955,U_9953,U_9951,U_9949)) != c_Orderings_Otop__class_Otop(tc_fun(U_9949,tc_HOL_Obool))
| ~ sP796(U_9951,U_9949,U_9955,U_9953) )
& ! [U_9951,U_9949,U_9955,U_9953] :
( hBOOL(hAPP(hAPP(c_member(U_9951),sK256(U_9955,U_9953,U_9951,U_9949)),U_9953))
| ~ sP796(U_9951,U_9949,U_9955,U_9953) )
& ! [U_9951,U_9949,U_9955,U_9953] :
( c_Orderings_Otop__class_Otop(tc_fun(U_9949,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9951,tc_fun(U_9949,tc_HOL_Obool)),U_9953),U_9955)
| sP796(U_9951,U_9949,U_9955,U_9953) )
& ! [U_9954,U_9942,U_9948,U_9952,U_9950] :
( hAPP(U_9954,U_9942) = c_Orderings_Otop__class_Otop(tc_fun(U_9948,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9950),U_9942),U_9952))
| c_Orderings_Otop__class_Otop(tc_fun(U_9948,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9950,tc_fun(U_9948,tc_HOL_Obool)),U_9952),U_9954) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP796])],[f_2753_4]) ).
cnf(f_2753_6,plain,
( hAPP(U_9954,U_9942) = c_Orderings_Otop__class_Otop(tc_fun(U_9948,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9950),U_9942),U_9952))
| c_Orderings_Otop__class_Otop(tc_fun(U_9948,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9950,tc_fun(U_9948,tc_HOL_Obool)),U_9952),U_9954) ),
inference(clausify,[status(thm)],[f_2753_5]) ).
cnf(f_2753_7,plain,
( c_Orderings_Otop__class_Otop(tc_fun(U_9949,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9951,tc_fun(U_9949,tc_HOL_Obool)),U_9953),U_9955)
| sP796(U_9951,U_9949,U_9955,U_9953) ),
inference(clausify,[status(thm)],[f_2753_5]) ).
cnf(f_2753_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9951),sK256(U_9955,U_9953,U_9951,U_9949)),U_9953))
| ~ sP796(U_9951,U_9949,U_9955,U_9953) ),
inference(clausify,[status(thm)],[f_2753_5]) ).
cnf(f_2753_9,plain,
( hAPP(U_9955,sK256(U_9955,U_9953,U_9951,U_9949)) != c_Orderings_Otop__class_Otop(tc_fun(U_9949,tc_HOL_Obool))
| ~ sP796(U_9951,U_9949,U_9955,U_9953) ),
inference(clausify,[status(thm)],[f_2753_5]) ).
fof(f_2754_1,plain,
! [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_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),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) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I2_J]) ).
fof(f_2754_2,plain,
! [U_9961,U_9960,U_9959,U_9958] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9958,tc_fun(U_9959,tc_HOL_Obool)),U_9960),U_9961) = c_Orderings_Otop__class_Otop(tc_fun(U_9959,tc_HOL_Obool))
| ? [U_9957] :
( hAPP(U_9961,U_9957) != c_Orderings_Otop__class_Otop(tc_fun(U_9959,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9958),U_9957),U_9960)) ) )
& ( ! [U_9956] :
( hAPP(U_9961,U_9956) = c_Orderings_Otop__class_Otop(tc_fun(U_9959,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9958),U_9956),U_9960)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9958,tc_fun(U_9959,tc_HOL_Obool)),U_9960),U_9961) != c_Orderings_Otop__class_Otop(tc_fun(U_9959,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2754_1]) ).
fof(f_2754_3,plain,
( ! [U_9969,U_9967,U_9965,U_9963] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9963,tc_fun(U_9965,tc_HOL_Obool)),U_9967),U_9969) = c_Orderings_Otop__class_Otop(tc_fun(U_9965,tc_HOL_Obool))
| ? [U_9957] :
( hAPP(U_9969,U_9957) != c_Orderings_Otop__class_Otop(tc_fun(U_9965,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9963),U_9957),U_9967)) ) )
& ! [U_9968,U_9966,U_9964,U_9962] :
( ! [U_9956] :
( hAPP(U_9968,U_9956) = c_Orderings_Otop__class_Otop(tc_fun(U_9964,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9962),U_9956),U_9966)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9962,tc_fun(U_9964,tc_HOL_Obool)),U_9966),U_9968) != c_Orderings_Otop__class_Otop(tc_fun(U_9964,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2754_2]) ).
fof(f_2754_4,plain,
( ! [U_9969,U_9967,U_9965,U_9963] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9963,tc_fun(U_9965,tc_HOL_Obool)),U_9967),U_9969) = c_Orderings_Otop__class_Otop(tc_fun(U_9965,tc_HOL_Obool))
| ( hAPP(U_9969,sK257(U_9969,U_9967,U_9965,U_9963)) != c_Orderings_Otop__class_Otop(tc_fun(U_9965,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9963),sK257(U_9969,U_9967,U_9965,U_9963)),U_9967)) ) )
& ! [U_9968,U_9966,U_9964,U_9962] :
( ! [U_9956] :
( hAPP(U_9968,U_9956) = c_Orderings_Otop__class_Otop(tc_fun(U_9964,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9962),U_9956),U_9966)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9962,tc_fun(U_9964,tc_HOL_Obool)),U_9966),U_9968) != c_Orderings_Otop__class_Otop(tc_fun(U_9964,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_9957,sK257(U_9969,U_9967,U_9965,U_9963))],[f_2754_3]) ).
fof(f_2754_5,plain,
( ! [U_9967,U_9965,U_9963,U_9969] :
( hAPP(U_9969,sK257(U_9969,U_9967,U_9965,U_9963)) != c_Orderings_Otop__class_Otop(tc_fun(U_9965,tc_HOL_Obool))
| ~ sP797(U_9967,U_9965,U_9963,U_9969) )
& ! [U_9967,U_9965,U_9963,U_9969] :
( hBOOL(hAPP(hAPP(c_member(U_9963),sK257(U_9969,U_9967,U_9965,U_9963)),U_9967))
| ~ sP797(U_9967,U_9965,U_9963,U_9969) )
& ! [U_9967,U_9965,U_9963,U_9969] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9963,tc_fun(U_9965,tc_HOL_Obool)),U_9967),U_9969) = c_Orderings_Otop__class_Otop(tc_fun(U_9965,tc_HOL_Obool))
| sP797(U_9967,U_9965,U_9963,U_9969) )
& ! [U_9956,U_9968,U_9962,U_9966,U_9964] :
( hAPP(U_9968,U_9956) = c_Orderings_Otop__class_Otop(tc_fun(U_9964,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9962),U_9956),U_9966))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9962,tc_fun(U_9964,tc_HOL_Obool)),U_9966),U_9968) != c_Orderings_Otop__class_Otop(tc_fun(U_9964,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP797])],[f_2754_4]) ).
cnf(f_2754_6,plain,
( hAPP(U_9968,U_9956) = c_Orderings_Otop__class_Otop(tc_fun(U_9964,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9962),U_9956),U_9966))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9962,tc_fun(U_9964,tc_HOL_Obool)),U_9966),U_9968) != c_Orderings_Otop__class_Otop(tc_fun(U_9964,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2754_5]) ).
cnf(f_2754_7,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9963,tc_fun(U_9965,tc_HOL_Obool)),U_9967),U_9969) = c_Orderings_Otop__class_Otop(tc_fun(U_9965,tc_HOL_Obool))
| sP797(U_9967,U_9965,U_9963,U_9969) ),
inference(clausify,[status(thm)],[f_2754_5]) ).
cnf(f_2754_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9963),sK257(U_9969,U_9967,U_9965,U_9963)),U_9967))
| ~ sP797(U_9967,U_9965,U_9963,U_9969) ),
inference(clausify,[status(thm)],[f_2754_5]) ).
cnf(f_2754_9,plain,
( hAPP(U_9969,sK257(U_9969,U_9967,U_9965,U_9963)) != c_Orderings_Otop__class_Otop(tc_fun(U_9965,tc_HOL_Obool))
| ~ sP797(U_9967,U_9965,U_9963,U_9969) ),
inference(clausify,[status(thm)],[f_2754_5]) ).
fof(f_2755_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_UNIV__def]) ).
fof(f_2755_2,plain,
! [U_9970] : c_Orderings_Otop__class_Otop(tc_fun(U_9970,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9970),hAPP(c_COMBK(tc_HOL_Obool,U_9970),c_fTrue)),
inference(variable_rename,[status(thm)],[f_2755_1]) ).
fof(f_2755_3,plain,
! [U_9970] : c_Orderings_Otop__class_Otop(tc_fun(U_9970,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9970),hAPP(c_COMBK(tc_HOL_Obool,U_9970),c_fTrue)),
inference(definitional_conversion,[status(esa)],[f_2755_2]) ).
cnf(f_2755_4,plain,
c_Orderings_Otop__class_Otop(tc_fun(U_9970,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9970),hAPP(c_COMBK(tc_HOL_Obool,U_9970),c_fTrue)),
inference(clausify,[status(thm)],[f_2755_3]) ).
fof(f_2756_1,plain,
! [V_A_2,T_c,T_b] :
( 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)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod__1]) ).
fof(f_2756_2,plain,
! [U_9973,U_9972,U_9971] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9972,U_9971),hAPP(c_COMBK(U_9971,U_9972),c_Groups_Oone__class_Oone(U_9971))),U_9973) = c_Groups_Oone__class_Oone(U_9971)
| ~ class_Groups_Ocomm__monoid__mult(U_9971) ),
inference(variable_rename,[status(thm)],[f_2756_1]) ).
fof(f_2756_3,plain,
! [U_9971,U_9973,U_9972] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9972,U_9971),hAPP(c_COMBK(U_9971,U_9972),c_Groups_Oone__class_Oone(U_9971))),U_9973) = c_Groups_Oone__class_Oone(U_9971)
| ~ class_Groups_Ocomm__monoid__mult(U_9971) ),
inference(definitional_conversion,[status(esa)],[f_2756_2]) ).
cnf(f_2756_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9972,U_9971),hAPP(c_COMBK(U_9971,U_9972),c_Groups_Oone__class_Oone(U_9971))),U_9973) = c_Groups_Oone__class_Oone(U_9971)
| ~ class_Groups_Ocomm__monoid__mult(U_9971) ),
inference(clausify,[status(thm)],[f_2756_3]) ).
fof(f_2757_1,plain,
! [V_A_2,T_c,T_b] :
( 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)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__0]) ).
fof(f_2757_2,plain,
! [U_9976,U_9975,U_9974] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9975,U_9974),hAPP(c_COMBK(U_9974,U_9975),c_Groups_Ozero__class_Ozero(U_9974))),U_9976) = c_Groups_Ozero__class_Ozero(U_9974)
| ~ class_Groups_Ocomm__monoid__add(U_9974) ),
inference(variable_rename,[status(thm)],[f_2757_1]) ).
fof(f_2757_3,plain,
! [U_9974,U_9975,U_9976] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9975,U_9974),hAPP(c_COMBK(U_9974,U_9975),c_Groups_Ozero__class_Ozero(U_9974))),U_9976) = c_Groups_Ozero__class_Ozero(U_9974)
| ~ class_Groups_Ocomm__monoid__add(U_9974) ),
inference(definitional_conversion,[status(esa)],[f_2757_2]) ).
cnf(f_2757_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9975,U_9974),hAPP(c_COMBK(U_9974,U_9975),c_Groups_Ozero__class_Ozero(U_9974))),U_9976) = c_Groups_Ozero__class_Ozero(U_9974)
| ~ class_Groups_Ocomm__monoid__add(U_9974) ),
inference(clausify,[status(thm)],[f_2757_3]) ).
fof(f_2758_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_UN__lessThan__UNIV]) ).
fof(f_2758_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_2758_1]) ).
cnf(f_2758_3,plain,
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)),
inference(clausify,[status(thm)],[f_2758_2]) ).
fof(f_2759_1,plain,
! [V_x_2,V_r_2,T_c,T_b] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF__INT__eq]) ).
fof(f_2759_2,plain,
! [U_9980,U_9979,U_9978,U_9977] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9977,tc_fun(U_9978,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9977,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9978,tc_HOL_Obool),tc_fun(U_9978,tc_HOL_Obool),U_9977),hAPP(c_COMBC(U_9978,tc_fun(U_9978,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9978))),U_9979)),U_9980))
| ~ hBOOL(hAPP(hAPP(c_member(U_9978),U_9980),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9977,tc_fun(U_9978,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9977,tc_HOL_Obool))),U_9979))) )
& ( hBOOL(hAPP(hAPP(c_member(U_9978),U_9980),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9977,tc_fun(U_9978,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9977,tc_HOL_Obool))),U_9979)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9977,tc_fun(U_9978,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9977,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9978,tc_HOL_Obool),tc_fun(U_9978,tc_HOL_Obool),U_9977),hAPP(c_COMBC(U_9978,tc_fun(U_9978,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9978))),U_9979)),U_9980)) ) ),
inference(variable_rename,[status(thm)],[f_2759_1]) ).
fof(f_2759_3,plain,
( ! [U_9988,U_9986,U_9984,U_9982] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9982,tc_fun(U_9984,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9982,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9984,tc_HOL_Obool),U_9982),hAPP(c_COMBC(U_9984,tc_fun(U_9984,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9984))),U_9986)),U_9988))
| ~ hBOOL(hAPP(hAPP(c_member(U_9984),U_9988),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9982,tc_fun(U_9984,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9982,tc_HOL_Obool))),U_9986))) )
& ! [U_9987,U_9985,U_9983,U_9981] :
( hBOOL(hAPP(hAPP(c_member(U_9983),U_9987),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9981,tc_fun(U_9983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9981,tc_HOL_Obool))),U_9985)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9981,tc_fun(U_9983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9981,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9983,tc_HOL_Obool),tc_fun(U_9983,tc_HOL_Obool),U_9981),hAPP(c_COMBC(U_9983,tc_fun(U_9983,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9983))),U_9985)),U_9987)) ) ),
inference(miniscope,[status(thm)],[f_2759_2]) ).
fof(f_2759_4,plain,
( ! [U_9988,U_9982,U_9984,U_9986] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9982,tc_fun(U_9984,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9982,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9984,tc_HOL_Obool),U_9982),hAPP(c_COMBC(U_9984,tc_fun(U_9984,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9984))),U_9986)),U_9988))
| ~ hBOOL(hAPP(hAPP(c_member(U_9984),U_9988),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9982,tc_fun(U_9984,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9982,tc_HOL_Obool))),U_9986))) )
& ! [U_9983,U_9987,U_9981,U_9985] :
( hBOOL(hAPP(hAPP(c_member(U_9983),U_9987),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9981,tc_fun(U_9983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9981,tc_HOL_Obool))),U_9985)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9981,tc_fun(U_9983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9981,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9983,tc_HOL_Obool),tc_fun(U_9983,tc_HOL_Obool),U_9981),hAPP(c_COMBC(U_9983,tc_fun(U_9983,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9983))),U_9985)),U_9987)) ) ),
inference(definitional_conversion,[status(esa)],[f_2759_3]) ).
cnf(f_2759_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9983),U_9987),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9981,tc_fun(U_9983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9981,tc_HOL_Obool))),U_9985)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9981,tc_fun(U_9983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9981,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9983,tc_HOL_Obool),tc_fun(U_9983,tc_HOL_Obool),U_9981),hAPP(c_COMBC(U_9983,tc_fun(U_9983,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9983))),U_9985)),U_9987)) ),
inference(clausify,[status(thm)],[f_2759_4]) ).
cnf(f_2759_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9982,tc_fun(U_9984,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9982,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9984,tc_HOL_Obool),U_9982),hAPP(c_COMBC(U_9984,tc_fun(U_9984,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9984))),U_9986)),U_9988))
| ~ hBOOL(hAPP(hAPP(c_member(U_9984),U_9988),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9982,tc_fun(U_9984,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9982,tc_HOL_Obool))),U_9986))) ),
inference(clausify,[status(thm)],[f_2759_4]) ).
fof(f_2760_1,plain,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2]) ).
fof(f_2760_2,plain,
! [U_9994,U_9993,U_9992,U_9991,U_9990,U_9989] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9989,tc_fun(U_9990,tc_fun(U_9991,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9989,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_fun(U_9990,tc_fun(U_9991,tc_HOL_Obool)),U_9989),hAPP(c_COMBC(U_9990,tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_fun(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),U_9990),c_COMBC(U_9991,tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_prod(U_9990,U_9991)),tc_fun(U_9991,tc_fun(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_HOL_Obool)),U_9990),hAPP(c_COMBB(tc_prod(U_9990,U_9991),tc_fun(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_HOL_Obool),U_9991),c_member(tc_prod(U_9990,U_9991)))),c_Product__Type_OPair(U_9990,U_9991))))),U_9992)),U_9993),U_9994))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9990,U_9991)),hAPP(hAPP(c_Product__Type_OPair(U_9990,U_9991),U_9993),U_9994)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9989,tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9989,tc_HOL_Obool))),U_9992))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9990,U_9991)),hAPP(hAPP(c_Product__Type_OPair(U_9990,U_9991),U_9993),U_9994)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9989,tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9989,tc_HOL_Obool))),U_9992)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9989,tc_fun(U_9990,tc_fun(U_9991,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9989,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_fun(U_9990,tc_fun(U_9991,tc_HOL_Obool)),U_9989),hAPP(c_COMBC(U_9990,tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_fun(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),U_9990),c_COMBC(U_9991,tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_prod(U_9990,U_9991)),tc_fun(U_9991,tc_fun(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_HOL_Obool)),U_9990),hAPP(c_COMBB(tc_prod(U_9990,U_9991),tc_fun(tc_fun(tc_prod(U_9990,U_9991),tc_HOL_Obool),tc_HOL_Obool),U_9991),c_member(tc_prod(U_9990,U_9991)))),c_Product__Type_OPair(U_9990,U_9991))))),U_9992)),U_9993),U_9994)) ) ),
inference(variable_rename,[status(thm)],[f_2760_1]) ).
fof(f_2760_3,plain,
( ! [U_10006,U_10004,U_10002,U_10000,U_9998,U_9996] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9996,tc_fun(U_9998,tc_fun(U_10000,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9996,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_9998,tc_fun(U_10000,tc_HOL_Obool)),U_9996),hAPP(c_COMBC(U_9998,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_10000,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10000,tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_10000,tc_HOL_Obool)),U_9998),c_COMBC(U_10000,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10000,tc_prod(U_9998,U_10000)),tc_fun(U_10000,tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),U_9998),hAPP(c_COMBB(tc_prod(U_9998,U_10000),tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool),U_10000),c_member(tc_prod(U_9998,U_10000)))),c_Product__Type_OPair(U_9998,U_10000))))),U_10002)),U_10004),U_10006))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9998,U_10000)),hAPP(hAPP(c_Product__Type_OPair(U_9998,U_10000),U_10004),U_10006)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9996,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9996,tc_HOL_Obool))),U_10002))) )
& ! [U_10005,U_10003,U_10001,U_9999,U_9997,U_9995] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9997,U_9999)),hAPP(hAPP(c_Product__Type_OPair(U_9997,U_9999),U_10003),U_10005)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9995,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9995,tc_HOL_Obool))),U_10001)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9995,tc_fun(U_9997,tc_fun(U_9999,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9995,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9997,tc_fun(U_9999,tc_HOL_Obool)),U_9995),hAPP(c_COMBC(U_9997,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9999,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9999,tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9999,tc_HOL_Obool)),U_9997),c_COMBC(U_9999,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9999,tc_prod(U_9997,U_9999)),tc_fun(U_9999,tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),U_9997),hAPP(c_COMBB(tc_prod(U_9997,U_9999),tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool),U_9999),c_member(tc_prod(U_9997,U_9999)))),c_Product__Type_OPair(U_9997,U_9999))))),U_10001)),U_10003),U_10005)) ) ),
inference(miniscope,[status(thm)],[f_2760_2]) ).
fof(f_2760_4,plain,
( ! [U_9996,U_9998,U_10000,U_10002,U_10004,U_10006] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9996,tc_fun(U_9998,tc_fun(U_10000,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9996,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_9998,tc_fun(U_10000,tc_HOL_Obool)),U_9996),hAPP(c_COMBC(U_9998,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_10000,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10000,tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_10000,tc_HOL_Obool)),U_9998),c_COMBC(U_10000,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10000,tc_prod(U_9998,U_10000)),tc_fun(U_10000,tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),U_9998),hAPP(c_COMBB(tc_prod(U_9998,U_10000),tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool),U_10000),c_member(tc_prod(U_9998,U_10000)))),c_Product__Type_OPair(U_9998,U_10000))))),U_10002)),U_10004),U_10006))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9998,U_10000)),hAPP(hAPP(c_Product__Type_OPair(U_9998,U_10000),U_10004),U_10006)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9996,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9996,tc_HOL_Obool))),U_10002))) )
& ! [U_9995,U_10003,U_10005,U_9997,U_10001,U_9999] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9997,U_9999)),hAPP(hAPP(c_Product__Type_OPair(U_9997,U_9999),U_10003),U_10005)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9995,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9995,tc_HOL_Obool))),U_10001)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9995,tc_fun(U_9997,tc_fun(U_9999,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9995,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9997,tc_fun(U_9999,tc_HOL_Obool)),U_9995),hAPP(c_COMBC(U_9997,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9999,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9999,tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9999,tc_HOL_Obool)),U_9997),c_COMBC(U_9999,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9999,tc_prod(U_9997,U_9999)),tc_fun(U_9999,tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),U_9997),hAPP(c_COMBB(tc_prod(U_9997,U_9999),tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool),U_9999),c_member(tc_prod(U_9997,U_9999)))),c_Product__Type_OPair(U_9997,U_9999))))),U_10001)),U_10003),U_10005)) ) ),
inference(definitional_conversion,[status(esa)],[f_2760_3]) ).
cnf(f_2760_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9997,U_9999)),hAPP(hAPP(c_Product__Type_OPair(U_9997,U_9999),U_10003),U_10005)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9995,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9995,tc_HOL_Obool))),U_10001)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9995,tc_fun(U_9997,tc_fun(U_9999,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9995,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9997,tc_fun(U_9999,tc_HOL_Obool)),U_9995),hAPP(c_COMBC(U_9997,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9999,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9999,tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_fun(U_9999,tc_HOL_Obool)),U_9997),c_COMBC(U_9999,tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9999,tc_prod(U_9997,U_9999)),tc_fun(U_9999,tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool)),U_9997),hAPP(c_COMBB(tc_prod(U_9997,U_9999),tc_fun(tc_fun(tc_prod(U_9997,U_9999),tc_HOL_Obool),tc_HOL_Obool),U_9999),c_member(tc_prod(U_9997,U_9999)))),c_Product__Type_OPair(U_9997,U_9999))))),U_10001)),U_10003),U_10005)) ),
inference(clausify,[status(thm)],[f_2760_4]) ).
cnf(f_2760_6,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9996,tc_fun(U_9998,tc_fun(U_10000,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9996,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_9998,tc_fun(U_10000,tc_HOL_Obool)),U_9996),hAPP(c_COMBC(U_9998,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_10000,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10000,tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_fun(U_10000,tc_HOL_Obool)),U_9998),c_COMBC(U_10000,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10000,tc_prod(U_9998,U_10000)),tc_fun(U_10000,tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool)),U_9998),hAPP(c_COMBB(tc_prod(U_9998,U_10000),tc_fun(tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool),tc_HOL_Obool),U_10000),c_member(tc_prod(U_9998,U_10000)))),c_Product__Type_OPair(U_9998,U_10000))))),U_10002)),U_10004),U_10006))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9998,U_10000)),hAPP(hAPP(c_Product__Type_OPair(U_9998,U_10000),U_10004),U_10006)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9996,tc_fun(tc_prod(U_9998,U_10000),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9996,tc_HOL_Obool))),U_10002))) ),
inference(clausify,[status(thm)],[f_2760_4]) ).
fof(f_2761_1,plain,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2]) ).
fof(f_2761_2,plain,
! [U_10012,U_10011,U_10010,U_10009,U_10008,U_10007] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10007,tc_fun(U_10008,tc_fun(U_10009,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10007,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_fun(U_10008,tc_fun(U_10009,tc_HOL_Obool)),U_10007),hAPP(c_COMBC(U_10008,tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_fun(U_10009,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10009,tc_fun(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_fun(U_10009,tc_HOL_Obool)),U_10008),c_COMBC(U_10009,tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10009,tc_prod(U_10008,U_10009)),tc_fun(U_10009,tc_fun(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_HOL_Obool)),U_10008),hAPP(c_COMBB(tc_prod(U_10008,U_10009),tc_fun(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_HOL_Obool),U_10009),c_member(tc_prod(U_10008,U_10009)))),c_Product__Type_OPair(U_10008,U_10009))))),U_10010)),U_10011),U_10012))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10008,U_10009)),hAPP(hAPP(c_Product__Type_OPair(U_10008,U_10009),U_10011),U_10012)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10007,tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10007,tc_HOL_Obool))),U_10010))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10008,U_10009)),hAPP(hAPP(c_Product__Type_OPair(U_10008,U_10009),U_10011),U_10012)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10007,tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10007,tc_HOL_Obool))),U_10010)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10007,tc_fun(U_10008,tc_fun(U_10009,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10007,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_fun(U_10008,tc_fun(U_10009,tc_HOL_Obool)),U_10007),hAPP(c_COMBC(U_10008,tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_fun(U_10009,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10009,tc_fun(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_fun(U_10009,tc_HOL_Obool)),U_10008),c_COMBC(U_10009,tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10009,tc_prod(U_10008,U_10009)),tc_fun(U_10009,tc_fun(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_HOL_Obool)),U_10008),hAPP(c_COMBB(tc_prod(U_10008,U_10009),tc_fun(tc_fun(tc_prod(U_10008,U_10009),tc_HOL_Obool),tc_HOL_Obool),U_10009),c_member(tc_prod(U_10008,U_10009)))),c_Product__Type_OPair(U_10008,U_10009))))),U_10010)),U_10011),U_10012)) ) ),
inference(variable_rename,[status(thm)],[f_2761_1]) ).
fof(f_2761_3,plain,
( ! [U_10024,U_10022,U_10020,U_10018,U_10016,U_10014] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10014,tc_fun(U_10016,tc_fun(U_10018,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10014,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10016,tc_fun(U_10018,tc_HOL_Obool)),U_10014),hAPP(c_COMBC(U_10016,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10018,tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),U_10016),c_COMBC(U_10018,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10018,tc_prod(U_10016,U_10018)),tc_fun(U_10018,tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),U_10016),hAPP(c_COMBB(tc_prod(U_10016,U_10018),tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool),U_10018),c_member(tc_prod(U_10016,U_10018)))),c_Product__Type_OPair(U_10016,U_10018))))),U_10020)),U_10022),U_10024))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10016,U_10018)),hAPP(hAPP(c_Product__Type_OPair(U_10016,U_10018),U_10022),U_10024)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10014,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10014,tc_HOL_Obool))),U_10020))) )
& ! [U_10023,U_10021,U_10019,U_10017,U_10015,U_10013] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10015,U_10017)),hAPP(hAPP(c_Product__Type_OPair(U_10015,U_10017),U_10021),U_10023)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10013,tc_HOL_Obool))),U_10019)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10015,tc_fun(U_10017,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10013,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10015,tc_fun(U_10017,tc_HOL_Obool)),U_10013),hAPP(c_COMBC(U_10015,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10017,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10017,tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10017,tc_HOL_Obool)),U_10015),c_COMBC(U_10017,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10017,tc_prod(U_10015,U_10017)),tc_fun(U_10017,tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),U_10015),hAPP(c_COMBB(tc_prod(U_10015,U_10017),tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool),U_10017),c_member(tc_prod(U_10015,U_10017)))),c_Product__Type_OPair(U_10015,U_10017))))),U_10019)),U_10021),U_10023)) ) ),
inference(miniscope,[status(thm)],[f_2761_2]) ).
fof(f_2761_4,plain,
( ! [U_10014,U_10016,U_10018,U_10020,U_10022,U_10024] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10014,tc_fun(U_10016,tc_fun(U_10018,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10014,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10016,tc_fun(U_10018,tc_HOL_Obool)),U_10014),hAPP(c_COMBC(U_10016,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10018,tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),U_10016),c_COMBC(U_10018,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10018,tc_prod(U_10016,U_10018)),tc_fun(U_10018,tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),U_10016),hAPP(c_COMBB(tc_prod(U_10016,U_10018),tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool),U_10018),c_member(tc_prod(U_10016,U_10018)))),c_Product__Type_OPair(U_10016,U_10018))))),U_10020)),U_10022),U_10024))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10016,U_10018)),hAPP(hAPP(c_Product__Type_OPair(U_10016,U_10018),U_10022),U_10024)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10014,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10014,tc_HOL_Obool))),U_10020))) )
& ! [U_10015,U_10019,U_10013,U_10021,U_10017,U_10023] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10015,U_10017)),hAPP(hAPP(c_Product__Type_OPair(U_10015,U_10017),U_10021),U_10023)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10013,tc_HOL_Obool))),U_10019)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10015,tc_fun(U_10017,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10013,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10015,tc_fun(U_10017,tc_HOL_Obool)),U_10013),hAPP(c_COMBC(U_10015,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10017,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10017,tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10017,tc_HOL_Obool)),U_10015),c_COMBC(U_10017,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10017,tc_prod(U_10015,U_10017)),tc_fun(U_10017,tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),U_10015),hAPP(c_COMBB(tc_prod(U_10015,U_10017),tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool),U_10017),c_member(tc_prod(U_10015,U_10017)))),c_Product__Type_OPair(U_10015,U_10017))))),U_10019)),U_10021),U_10023)) ) ),
inference(definitional_conversion,[status(esa)],[f_2761_3]) ).
cnf(f_2761_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10015,U_10017)),hAPP(hAPP(c_Product__Type_OPair(U_10015,U_10017),U_10021),U_10023)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10013,tc_HOL_Obool))),U_10019)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10015,tc_fun(U_10017,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10013,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10015,tc_fun(U_10017,tc_HOL_Obool)),U_10013),hAPP(c_COMBC(U_10015,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10017,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10017,tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_fun(U_10017,tc_HOL_Obool)),U_10015),c_COMBC(U_10017,tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10017,tc_prod(U_10015,U_10017)),tc_fun(U_10017,tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool)),U_10015),hAPP(c_COMBB(tc_prod(U_10015,U_10017),tc_fun(tc_fun(tc_prod(U_10015,U_10017),tc_HOL_Obool),tc_HOL_Obool),U_10017),c_member(tc_prod(U_10015,U_10017)))),c_Product__Type_OPair(U_10015,U_10017))))),U_10019)),U_10021),U_10023)) ),
inference(clausify,[status(thm)],[f_2761_4]) ).
cnf(f_2761_6,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10014,tc_fun(U_10016,tc_fun(U_10018,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10014,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10016,tc_fun(U_10018,tc_HOL_Obool)),U_10014),hAPP(c_COMBC(U_10016,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10018,tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),U_10016),c_COMBC(U_10018,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10018,tc_prod(U_10016,U_10018)),tc_fun(U_10018,tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool)),U_10016),hAPP(c_COMBB(tc_prod(U_10016,U_10018),tc_fun(tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool),tc_HOL_Obool),U_10018),c_member(tc_prod(U_10016,U_10018)))),c_Product__Type_OPair(U_10016,U_10018))))),U_10020)),U_10022),U_10024))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10016,U_10018)),hAPP(hAPP(c_Product__Type_OPair(U_10016,U_10018),U_10022),U_10024)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10014,tc_fun(tc_prod(U_10016,U_10018),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10014,tc_HOL_Obool))),U_10020))) ),
inference(clausify,[status(thm)],[f_2761_4]) ).
fof(f_2762_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_range__composition]) ).
fof(f_2762_2,plain,
! [U_10029,U_10028,U_10027,U_10026,U_10025] : hAPP(c_Set_Oimage(U_10025,U_10026,hAPP(hAPP(c_COMBB(U_10027,U_10026,U_10025),U_10028),U_10029)),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_10027,U_10026,U_10028),hAPP(c_Set_Oimage(U_10025,U_10027,U_10029),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2762_1]) ).
fof(f_2762_3,plain,
! [U_10025,U_10026,U_10027,U_10028,U_10029] : hAPP(c_Set_Oimage(U_10025,U_10026,hAPP(hAPP(c_COMBB(U_10027,U_10026,U_10025),U_10028),U_10029)),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_10027,U_10026,U_10028),hAPP(c_Set_Oimage(U_10025,U_10027,U_10029),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_2762_2]) ).
cnf(f_2762_4,plain,
hAPP(c_Set_Oimage(U_10025,U_10026,hAPP(hAPP(c_COMBB(U_10027,U_10026,U_10025),U_10028),U_10029)),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_10027,U_10026,U_10028),hAPP(c_Set_Oimage(U_10025,U_10027,U_10029),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2762_3]) ).
fof(f_2763_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_UN__atLeast__UNIV]) ).
fof(f_2763_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_2763_1]) ).
cnf(f_2763_3,plain,
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)),
inference(clausify,[status(thm)],[f_2763_2]) ).
fof(f_2764_1,plain,
! [V_f_2,T_d,V_g_2,T_c,T_b] :
( 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)))))
| ~ 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))))) ),
inference(fof_nnf,[status(thm)],[fact_finite__range__imageI]) ).
fof(f_2764_2,plain,
! [U_10034,U_10033,U_10032,U_10031,U_10030] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10033),hAPP(c_Set_Oimage(U_10031,U_10033,hAPP(hAPP(c_COMBB(U_10030,U_10033,U_10031),U_10034),U_10032)),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10030),hAPP(c_Set_Oimage(U_10031,U_10030,U_10032),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_2764_1]) ).
fof(f_2764_3,plain,
! [U_10030,U_10031,U_10032,U_10033,U_10034] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10033),hAPP(c_Set_Oimage(U_10031,U_10033,hAPP(hAPP(c_COMBB(U_10030,U_10033,U_10031),U_10034),U_10032)),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10030),hAPP(c_Set_Oimage(U_10031,U_10030,U_10032),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool))))) ),
inference(definitional_conversion,[status(esa)],[f_2764_2]) ).
cnf(f_2764_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10033),hAPP(c_Set_Oimage(U_10031,U_10033,hAPP(hAPP(c_COMBB(U_10030,U_10033,U_10031),U_10034),U_10032)),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10030),hAPP(c_Set_Oimage(U_10031,U_10030,U_10032),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_2764_3]) ).
fof(f_2765_1,plain,
! [V_x_2,V_r_2,T_c,T_b] :
( ( 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))
| ~ 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))) )
& ( 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)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq]) ).
fof(f_2765_2,plain,
! [U_10038,U_10037,U_10036,U_10035] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10035,tc_fun(U_10036,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10035,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10036,tc_HOL_Obool),tc_fun(U_10036,tc_HOL_Obool),U_10035),hAPP(c_COMBC(U_10036,tc_fun(U_10036,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10036))),U_10037)),U_10038))
| ~ hBOOL(hAPP(hAPP(c_member(U_10036),U_10038),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10035,tc_fun(U_10036,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10035,tc_HOL_Obool))),U_10037))) )
& ( hBOOL(hAPP(hAPP(c_member(U_10036),U_10038),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10035,tc_fun(U_10036,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10035,tc_HOL_Obool))),U_10037)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10035,tc_fun(U_10036,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10035,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10036,tc_HOL_Obool),tc_fun(U_10036,tc_HOL_Obool),U_10035),hAPP(c_COMBC(U_10036,tc_fun(U_10036,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10036))),U_10037)),U_10038)) ) ),
inference(variable_rename,[status(thm)],[f_2765_1]) ).
fof(f_2765_3,plain,
( ! [U_10046,U_10044,U_10042,U_10040] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10042,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10040,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10042,tc_HOL_Obool),tc_fun(U_10042,tc_HOL_Obool),U_10040),hAPP(c_COMBC(U_10042,tc_fun(U_10042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10042))),U_10044)),U_10046))
| ~ hBOOL(hAPP(hAPP(c_member(U_10042),U_10046),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10042,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10040,tc_HOL_Obool))),U_10044))) )
& ! [U_10045,U_10043,U_10041,U_10039] :
( hBOOL(hAPP(hAPP(c_member(U_10041),U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10041,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10039,tc_HOL_Obool))),U_10043)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10041,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10039,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10041,tc_HOL_Obool),tc_fun(U_10041,tc_HOL_Obool),U_10039),hAPP(c_COMBC(U_10041,tc_fun(U_10041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10041))),U_10043)),U_10045)) ) ),
inference(miniscope,[status(thm)],[f_2765_2]) ).
fof(f_2765_4,plain,
( ! [U_10040,U_10042,U_10044,U_10046] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10042,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10040,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10042,tc_HOL_Obool),tc_fun(U_10042,tc_HOL_Obool),U_10040),hAPP(c_COMBC(U_10042,tc_fun(U_10042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10042))),U_10044)),U_10046))
| ~ hBOOL(hAPP(hAPP(c_member(U_10042),U_10046),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10042,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10040,tc_HOL_Obool))),U_10044))) )
& ! [U_10045,U_10041,U_10039,U_10043] :
( hBOOL(hAPP(hAPP(c_member(U_10041),U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10041,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10039,tc_HOL_Obool))),U_10043)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10041,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10039,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10041,tc_HOL_Obool),tc_fun(U_10041,tc_HOL_Obool),U_10039),hAPP(c_COMBC(U_10041,tc_fun(U_10041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10041))),U_10043)),U_10045)) ) ),
inference(definitional_conversion,[status(esa)],[f_2765_3]) ).
cnf(f_2765_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10041),U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10041,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10039,tc_HOL_Obool))),U_10043)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10041,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10039,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10041,tc_HOL_Obool),tc_fun(U_10041,tc_HOL_Obool),U_10039),hAPP(c_COMBC(U_10041,tc_fun(U_10041,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10041))),U_10043)),U_10045)) ),
inference(clausify,[status(thm)],[f_2765_4]) ).
cnf(f_2765_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10042,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10040,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10042,tc_HOL_Obool),tc_fun(U_10042,tc_HOL_Obool),U_10040),hAPP(c_COMBC(U_10042,tc_fun(U_10042,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10042))),U_10044)),U_10046))
| ~ hBOOL(hAPP(hAPP(c_member(U_10042),U_10046),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10042,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10040,tc_HOL_Obool))),U_10044))) ),
inference(clausify,[status(thm)],[f_2765_4]) ).
fof(f_2766_1,plain,
! [V_Pa_2,T_b] :
( ( ( 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))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ 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)))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).
fof(f_2766_2,plain,
! [U_10048,U_10047] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10047),c_fNot),U_10048))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),c_Orderings_Otop__class_Otop(tc_fun(U_10047,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),c_Orderings_Otop__class_Otop(tc_fun(U_10047,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10047),c_fNot),U_10048)))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),U_10048))) ),
inference(variable_rename,[status(thm)],[f_2766_1]) ).
fof(f_2766_3,plain,
( ! [U_10047,U_10048] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10047),c_fNot),U_10048))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),c_Orderings_Otop__class_Otop(tc_fun(U_10047,tc_HOL_Obool))))
| ~ sP798(U_10047,U_10048) )
& ! [U_10047,U_10048] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),c_Orderings_Otop__class_Otop(tc_fun(U_10047,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10047),c_fNot),U_10048))))
| ~ sP798(U_10047,U_10048) )
& ! [U_10047,U_10048] :
( sP798(U_10047,U_10048)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),U_10048))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP798])],[f_2766_2]) ).
cnf(f_2766_4,plain,
( sP798(U_10047,U_10048)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),U_10048))) ),
inference(clausify,[status(thm)],[f_2766_3]) ).
cnf(f_2766_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),c_Orderings_Otop__class_Otop(tc_fun(U_10047,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10047),c_fNot),U_10048))))
| ~ sP798(U_10047,U_10048) ),
inference(clausify,[status(thm)],[f_2766_3]) ).
cnf(f_2766_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),hAPP(c_Set_OCollect(U_10047),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10047),c_fNot),U_10048))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),c_Orderings_Otop__class_Otop(tc_fun(U_10047,tc_HOL_Obool))))
| ~ sP798(U_10047,U_10048) ),
inference(clausify,[status(thm)],[f_2766_3]) ).
fof(f_2767_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).
fof(f_2767_2,plain,
! [U_10051,U_10050,U_10049] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10049,tc_Nat_Onat),U_10050),U_10051) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10049,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10049),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10050)),U_10051)),
inference(variable_rename,[status(thm)],[f_2767_1]) ).
fof(f_2767_3,plain,
! [U_10050,U_10049,U_10051] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10049,tc_Nat_Onat),U_10050),U_10051) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10049,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10049),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10050)),U_10051)),
inference(definitional_conversion,[status(esa)],[f_2767_2]) ).
cnf(f_2767_4,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10049,tc_Nat_Onat),U_10050),U_10051) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10049,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10049),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10050)),U_10051)),
inference(clausify,[status(thm)],[f_2767_3]) ).
fof(f_2768_1,plain,
! [V_n_2,V_m_2,V_f_2,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,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))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl]) ).
fof(f_2768_2,plain,
! [U_10055,U_10054,U_10053,U_10052] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10052),U_10053),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10054)),hAPP(c_Nat_OSuc,U_10055))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10052),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10052,tc_Nat_Onat),U_10053),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10054),U_10055))
| ~ class_Groups_Ocomm__monoid__add(U_10052) ),
inference(variable_rename,[status(thm)],[f_2768_1]) ).
fof(f_2768_3,plain,
! [U_10052,U_10053,U_10054,U_10055] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10052),U_10053),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10054)),hAPP(c_Nat_OSuc,U_10055))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10052),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10052,tc_Nat_Onat),U_10053),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10054),U_10055))
| ~ class_Groups_Ocomm__monoid__add(U_10052) ),
inference(definitional_conversion,[status(esa)],[f_2768_2]) ).
cnf(f_2768_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10052),U_10053),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10054)),hAPP(c_Nat_OSuc,U_10055))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10052),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10052,tc_Nat_Onat),U_10053),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10054),U_10055))
| ~ class_Groups_Ocomm__monoid__add(U_10052) ),
inference(clausify,[status(thm)],[f_2768_3]) ).
fof(f_2769_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__setsum]) ).
fof(f_2769_2,plain,
! [U_10059,U_10058,U_10057,U_10056] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10056),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10057,tc_Nat_Onat),U_10058),U_10059)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10057,U_10056),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10056,U_10057),c_Nat_Osemiring__1__class_Oof__nat(U_10056)),U_10058)),U_10059)
| ~ class_Rings_Osemiring__1(U_10056) ),
inference(variable_rename,[status(thm)],[f_2769_1]) ).
fof(f_2769_3,plain,
! [U_10056,U_10057,U_10058,U_10059] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10056),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10057,tc_Nat_Onat),U_10058),U_10059)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10057,U_10056),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10056,U_10057),c_Nat_Osemiring__1__class_Oof__nat(U_10056)),U_10058)),U_10059)
| ~ class_Rings_Osemiring__1(U_10056) ),
inference(definitional_conversion,[status(esa)],[f_2769_2]) ).
cnf(f_2769_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10056),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10057,tc_Nat_Onat),U_10058),U_10059)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10057,U_10056),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10056,U_10057),c_Nat_Osemiring__1__class_Oof__nat(U_10056)),U_10058)),U_10059)
| ~ class_Rings_Osemiring__1(U_10056) ),
inference(clausify,[status(thm)],[f_2769_3]) ).
fof(f_2770_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Int__Inter__image]) ).
fof(f_2770_2,plain,
! [U_10064,U_10063,U_10062,U_10061,U_10060] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10060,tc_fun(U_10061,tc_HOL_Obool)),U_10062),hAPP(hAPP(c_COMBS(U_10060,tc_fun(U_10061,tc_HOL_Obool),tc_fun(U_10061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10061,tc_HOL_Obool),tc_fun(tc_fun(U_10061,tc_HOL_Obool),tc_fun(U_10061,tc_HOL_Obool)),U_10060),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10061,tc_HOL_Obool))),U_10063)),U_10064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10061,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10061,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10060,tc_fun(U_10061,tc_HOL_Obool),U_10063),U_10062))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10061,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10060,tc_fun(U_10061,tc_HOL_Obool),U_10064),U_10062))),
inference(variable_rename,[status(thm)],[f_2770_1]) ).
fof(f_2770_3,plain,
! [U_10060,U_10061,U_10062,U_10063,U_10064] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10060,tc_fun(U_10061,tc_HOL_Obool)),U_10062),hAPP(hAPP(c_COMBS(U_10060,tc_fun(U_10061,tc_HOL_Obool),tc_fun(U_10061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10061,tc_HOL_Obool),tc_fun(tc_fun(U_10061,tc_HOL_Obool),tc_fun(U_10061,tc_HOL_Obool)),U_10060),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10061,tc_HOL_Obool))),U_10063)),U_10064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10061,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10061,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10060,tc_fun(U_10061,tc_HOL_Obool),U_10063),U_10062))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10061,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10060,tc_fun(U_10061,tc_HOL_Obool),U_10064),U_10062))),
inference(definitional_conversion,[status(esa)],[f_2770_2]) ).
cnf(f_2770_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10060,tc_fun(U_10061,tc_HOL_Obool)),U_10062),hAPP(hAPP(c_COMBS(U_10060,tc_fun(U_10061,tc_HOL_Obool),tc_fun(U_10061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10061,tc_HOL_Obool),tc_fun(tc_fun(U_10061,tc_HOL_Obool),tc_fun(U_10061,tc_HOL_Obool)),U_10060),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10061,tc_HOL_Obool))),U_10063)),U_10064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10061,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10061,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10060,tc_fun(U_10061,tc_HOL_Obool),U_10063),U_10062))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10061,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10060,tc_fun(U_10061,tc_HOL_Obool),U_10064),U_10062))),
inference(clausify,[status(thm)],[f_2770_3]) ).
fof(f_2771_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_UN__le__add__shift]) ).
fof(f_2771_2,plain,
! [U_10068,U_10067,U_10066,U_10065] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10066)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool),tc_Nat_Onat),U_10067),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10068))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10068,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10066),U_10068))),U_10067),
inference(variable_rename,[status(thm)],[f_2771_1]) ).
fof(f_2771_3,plain,
! [U_10065,U_10066,U_10067,U_10068] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10066)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool),tc_Nat_Onat),U_10067),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10068))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10068,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10066),U_10068))),U_10067),
inference(definitional_conversion,[status(esa)],[f_2771_2]) ).
cnf(f_2771_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10066)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool),tc_Nat_Onat),U_10067),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10068))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10065,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10068,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10066),U_10068))),U_10067),
inference(clausify,[status(thm)],[f_2771_3]) ).
fof(f_2772_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_UN__Pow__subset]) ).
fof(f_2772_2,plain,
! [U_10072,U_10071,U_10070,U_10069] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10070,tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool)),U_10071),hAPP(hAPP(c_COMBB(tc_fun(U_10069,tc_HOL_Obool),tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool),U_10070),c_Set_OPow(U_10069)),U_10072))),hAPP(c_Set_OPow(U_10069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10070,tc_fun(U_10069,tc_HOL_Obool)),U_10071),U_10072)))),
inference(variable_rename,[status(thm)],[f_2772_1]) ).
fof(f_2772_3,plain,
! [U_10069,U_10070,U_10071,U_10072] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10070,tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool)),U_10071),hAPP(hAPP(c_COMBB(tc_fun(U_10069,tc_HOL_Obool),tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool),U_10070),c_Set_OPow(U_10069)),U_10072))),hAPP(c_Set_OPow(U_10069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10070,tc_fun(U_10069,tc_HOL_Obool)),U_10071),U_10072)))),
inference(definitional_conversion,[status(esa)],[f_2772_2]) ).
cnf(f_2772_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10070,tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool)),U_10071),hAPP(hAPP(c_COMBB(tc_fun(U_10069,tc_HOL_Obool),tc_fun(tc_fun(U_10069,tc_HOL_Obool),tc_HOL_Obool),U_10070),c_Set_OPow(U_10069)),U_10072))),hAPP(c_Set_OPow(U_10069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10070,tc_fun(U_10069,tc_HOL_Obool)),U_10071),U_10072)))),
inference(clausify,[status(thm)],[f_2772_3]) ).
fof(f_2773_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( 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)
| ~ class_Rings_Osemiring__1(T_b)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__setprod]) ).
fof(f_2773_2,plain,
! [U_10076,U_10075,U_10074,U_10073] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10073),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10074,tc_Nat_Onat),U_10075),U_10076)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10074,U_10073),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10073,U_10074),c_Nat_Osemiring__1__class_Oof__nat(U_10073)),U_10075)),U_10076)
| ~ class_Rings_Osemiring__1(U_10073)
| ~ class_Groups_Ocomm__monoid__mult(U_10073) ),
inference(variable_rename,[status(thm)],[f_2773_1]) ).
fof(f_2773_3,plain,
! [U_10073,U_10074,U_10075,U_10076] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10073),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10074,tc_Nat_Onat),U_10075),U_10076)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10074,U_10073),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10073,U_10074),c_Nat_Osemiring__1__class_Oof__nat(U_10073)),U_10075)),U_10076)
| ~ class_Rings_Osemiring__1(U_10073)
| ~ class_Groups_Ocomm__monoid__mult(U_10073) ),
inference(definitional_conversion,[status(esa)],[f_2773_2]) ).
cnf(f_2773_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10073),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10074,tc_Nat_Onat),U_10075),U_10076)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10074,U_10073),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10073,U_10074),c_Nat_Osemiring__1__class_Oof__nat(U_10073)),U_10075)),U_10076)
| ~ class_Rings_Osemiring__1(U_10073)
| ~ class_Groups_Ocomm__monoid__mult(U_10073) ),
inference(clausify,[status(thm)],[f_2773_3]) ).
fof(f_2774_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).
fof(f_2774_2,plain,
! [U_10079,U_10078,U_10077] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10077,tc_Nat_Onat),U_10078),U_10079) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10077,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10077),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10078)),U_10079)),
inference(variable_rename,[status(thm)],[f_2774_1]) ).
fof(f_2774_3,plain,
! [U_10077,U_10078,U_10079] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10077,tc_Nat_Onat),U_10078),U_10079) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10077,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10077),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10078)),U_10079)),
inference(definitional_conversion,[status(esa)],[f_2774_2]) ).
cnf(f_2774_4,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10077,tc_Nat_Onat),U_10078),U_10079) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10077,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10077),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10078)),U_10079)),
inference(clausify,[status(thm)],[f_2774_3]) ).
fof(f_2775_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__add__atLeastLessThan]) ).
fof(f_2775_2,plain,
! [U_10082,U_10081,U_10080] : 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)),U_10080)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10081),U_10082)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10081),U_10080)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10082),U_10080)),
inference(variable_rename,[status(thm)],[f_2775_1]) ).
fof(f_2775_3,plain,
! [U_10080,U_10081,U_10082] : 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)),U_10080)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10081),U_10082)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10081),U_10080)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10082),U_10080)),
inference(definitional_conversion,[status(esa)],[f_2775_2]) ).
cnf(f_2775_4,plain,
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)),U_10080)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10081),U_10082)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10081),U_10080)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10082),U_10080)),
inference(clausify,[status(thm)],[f_2775_3]) ).
fof(f_2776_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_image__add__atLeastAtMost]) ).
fof(f_2776_2,plain,
! [U_10085,U_10084,U_10083] : 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)),U_10083)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10084,U_10085)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10084),U_10083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10085),U_10083)),
inference(variable_rename,[status(thm)],[f_2776_1]) ).
fof(f_2776_3,plain,
! [U_10083,U_10084,U_10085] : 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)),U_10083)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10084,U_10085)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10084),U_10083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10085),U_10083)),
inference(definitional_conversion,[status(esa)],[f_2776_2]) ).
cnf(f_2776_4,plain,
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)),U_10083)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10084,U_10085)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10084),U_10083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10085),U_10083)),
inference(clausify,[status(thm)],[f_2776_3]) ).
fof(f_2777_1,plain,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_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(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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__delta_H]) ).
fof(f_2777_2,plain,
! [U_10090,U_10089,U_10088,U_10087,U_10086] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10087,U_10086),hAPP(hAPP(c_COMBC(U_10087,U_10086,U_10086),hAPP(hAPP(c_COMBS(U_10087,U_10086,tc_fun(U_10086,U_10086)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10086,tc_fun(U_10086,U_10086)),U_10087),c_If(U_10086)),hAPP(c_fequal,U_10089))),U_10090)),c_Groups_Ozero__class_Ozero(U_10086))),U_10088) = c_Groups_Ozero__class_Ozero(U_10086)
| hBOOL(hAPP(hAPP(c_member(U_10087),U_10089),U_10088)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10087,U_10086),hAPP(hAPP(c_COMBC(U_10087,U_10086,U_10086),hAPP(hAPP(c_COMBS(U_10087,U_10086,tc_fun(U_10086,U_10086)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10086,tc_fun(U_10086,U_10086)),U_10087),c_If(U_10086)),hAPP(c_fequal,U_10089))),U_10090)),c_Groups_Ozero__class_Ozero(U_10086))),U_10088) = hAPP(U_10090,U_10089)
| ~ hBOOL(hAPP(hAPP(c_member(U_10087),U_10089),U_10088)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10087),U_10088))
| ~ class_Groups_Ocomm__monoid__add(U_10086) ),
inference(variable_rename,[status(thm)],[f_2777_1]) ).
fof(f_2777_3,plain,
( ! [U_10086,U_10087,U_10088,U_10089,U_10090] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10087,U_10086),hAPP(hAPP(c_COMBC(U_10087,U_10086,U_10086),hAPP(hAPP(c_COMBS(U_10087,U_10086,tc_fun(U_10086,U_10086)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10086,tc_fun(U_10086,U_10086)),U_10087),c_If(U_10086)),hAPP(c_fequal,U_10089))),U_10090)),c_Groups_Ozero__class_Ozero(U_10086))),U_10088) = c_Groups_Ozero__class_Ozero(U_10086)
| hBOOL(hAPP(hAPP(c_member(U_10087),U_10089),U_10088))
| ~ sP799(U_10086,U_10087,U_10088,U_10089,U_10090) )
& ! [U_10086,U_10087,U_10088,U_10089,U_10090] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10087,U_10086),hAPP(hAPP(c_COMBC(U_10087,U_10086,U_10086),hAPP(hAPP(c_COMBS(U_10087,U_10086,tc_fun(U_10086,U_10086)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10086,tc_fun(U_10086,U_10086)),U_10087),c_If(U_10086)),hAPP(c_fequal,U_10089))),U_10090)),c_Groups_Ozero__class_Ozero(U_10086))),U_10088) = hAPP(U_10090,U_10089)
| ~ hBOOL(hAPP(hAPP(c_member(U_10087),U_10089),U_10088))
| ~ sP799(U_10086,U_10087,U_10088,U_10089,U_10090) )
& ! [U_10086,U_10087,U_10088,U_10089,U_10090] :
( sP799(U_10086,U_10087,U_10088,U_10089,U_10090)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10087),U_10088))
| ~ class_Groups_Ocomm__monoid__add(U_10086) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP799])],[f_2777_2]) ).
cnf(f_2777_4,plain,
( sP799(U_10086,U_10087,U_10088,U_10089,U_10090)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10087),U_10088))
| ~ class_Groups_Ocomm__monoid__add(U_10086) ),
inference(clausify,[status(thm)],[f_2777_3]) ).
cnf(f_2777_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10087,U_10086),hAPP(hAPP(c_COMBC(U_10087,U_10086,U_10086),hAPP(hAPP(c_COMBS(U_10087,U_10086,tc_fun(U_10086,U_10086)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10086,tc_fun(U_10086,U_10086)),U_10087),c_If(U_10086)),hAPP(c_fequal,U_10089))),U_10090)),c_Groups_Ozero__class_Ozero(U_10086))),U_10088) = hAPP(U_10090,U_10089)
| ~ hBOOL(hAPP(hAPP(c_member(U_10087),U_10089),U_10088))
| ~ sP799(U_10086,U_10087,U_10088,U_10089,U_10090) ),
inference(clausify,[status(thm)],[f_2777_3]) ).
cnf(f_2777_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10087,U_10086),hAPP(hAPP(c_COMBC(U_10087,U_10086,U_10086),hAPP(hAPP(c_COMBS(U_10087,U_10086,tc_fun(U_10086,U_10086)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10086,tc_fun(U_10086,U_10086)),U_10087),c_If(U_10086)),hAPP(c_fequal,U_10089))),U_10090)),c_Groups_Ozero__class_Ozero(U_10086))),U_10088) = c_Groups_Ozero__class_Ozero(U_10086)
| hBOOL(hAPP(hAPP(c_member(U_10087),U_10089),U_10088))
| ~ sP799(U_10086,U_10087,U_10088,U_10089,U_10090) ),
inference(clausify,[status(thm)],[f_2777_3]) ).
fof(f_2778_1,plain,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_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,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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__delta]) ).
fof(f_2778_2,plain,
! [U_10095,U_10094,U_10093,U_10092,U_10091] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10092,U_10091),hAPP(hAPP(c_COMBC(U_10092,U_10091,U_10091),hAPP(hAPP(c_COMBS(U_10092,U_10091,tc_fun(U_10091,U_10091)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10091,tc_fun(U_10091,U_10091)),U_10092),c_If(U_10091)),hAPP(hAPP(c_COMBC(U_10092,U_10092,tc_HOL_Obool),c_fequal),U_10094))),U_10095)),c_Groups_Ozero__class_Ozero(U_10091))),U_10093) = c_Groups_Ozero__class_Ozero(U_10091)
| hBOOL(hAPP(hAPP(c_member(U_10092),U_10094),U_10093)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10092,U_10091),hAPP(hAPP(c_COMBC(U_10092,U_10091,U_10091),hAPP(hAPP(c_COMBS(U_10092,U_10091,tc_fun(U_10091,U_10091)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10091,tc_fun(U_10091,U_10091)),U_10092),c_If(U_10091)),hAPP(hAPP(c_COMBC(U_10092,U_10092,tc_HOL_Obool),c_fequal),U_10094))),U_10095)),c_Groups_Ozero__class_Ozero(U_10091))),U_10093) = hAPP(U_10095,U_10094)
| ~ hBOOL(hAPP(hAPP(c_member(U_10092),U_10094),U_10093)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10092),U_10093))
| ~ class_Groups_Ocomm__monoid__add(U_10091) ),
inference(variable_rename,[status(thm)],[f_2778_1]) ).
fof(f_2778_3,plain,
( ! [U_10092,U_10091,U_10093,U_10094,U_10095] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10092,U_10091),hAPP(hAPP(c_COMBC(U_10092,U_10091,U_10091),hAPP(hAPP(c_COMBS(U_10092,U_10091,tc_fun(U_10091,U_10091)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10091,tc_fun(U_10091,U_10091)),U_10092),c_If(U_10091)),hAPP(hAPP(c_COMBC(U_10092,U_10092,tc_HOL_Obool),c_fequal),U_10094))),U_10095)),c_Groups_Ozero__class_Ozero(U_10091))),U_10093) = c_Groups_Ozero__class_Ozero(U_10091)
| hBOOL(hAPP(hAPP(c_member(U_10092),U_10094),U_10093))
| ~ sP800(U_10092,U_10091,U_10093,U_10094,U_10095) )
& ! [U_10092,U_10091,U_10093,U_10094,U_10095] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10092,U_10091),hAPP(hAPP(c_COMBC(U_10092,U_10091,U_10091),hAPP(hAPP(c_COMBS(U_10092,U_10091,tc_fun(U_10091,U_10091)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10091,tc_fun(U_10091,U_10091)),U_10092),c_If(U_10091)),hAPP(hAPP(c_COMBC(U_10092,U_10092,tc_HOL_Obool),c_fequal),U_10094))),U_10095)),c_Groups_Ozero__class_Ozero(U_10091))),U_10093) = hAPP(U_10095,U_10094)
| ~ hBOOL(hAPP(hAPP(c_member(U_10092),U_10094),U_10093))
| ~ sP800(U_10092,U_10091,U_10093,U_10094,U_10095) )
& ! [U_10092,U_10091,U_10093,U_10094,U_10095] :
( sP800(U_10092,U_10091,U_10093,U_10094,U_10095)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10092),U_10093))
| ~ class_Groups_Ocomm__monoid__add(U_10091) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP800])],[f_2778_2]) ).
cnf(f_2778_4,plain,
( sP800(U_10092,U_10091,U_10093,U_10094,U_10095)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10092),U_10093))
| ~ class_Groups_Ocomm__monoid__add(U_10091) ),
inference(clausify,[status(thm)],[f_2778_3]) ).
cnf(f_2778_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10092,U_10091),hAPP(hAPP(c_COMBC(U_10092,U_10091,U_10091),hAPP(hAPP(c_COMBS(U_10092,U_10091,tc_fun(U_10091,U_10091)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10091,tc_fun(U_10091,U_10091)),U_10092),c_If(U_10091)),hAPP(hAPP(c_COMBC(U_10092,U_10092,tc_HOL_Obool),c_fequal),U_10094))),U_10095)),c_Groups_Ozero__class_Ozero(U_10091))),U_10093) = hAPP(U_10095,U_10094)
| ~ hBOOL(hAPP(hAPP(c_member(U_10092),U_10094),U_10093))
| ~ sP800(U_10092,U_10091,U_10093,U_10094,U_10095) ),
inference(clausify,[status(thm)],[f_2778_3]) ).
cnf(f_2778_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10092,U_10091),hAPP(hAPP(c_COMBC(U_10092,U_10091,U_10091),hAPP(hAPP(c_COMBS(U_10092,U_10091,tc_fun(U_10091,U_10091)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10091,tc_fun(U_10091,U_10091)),U_10092),c_If(U_10091)),hAPP(hAPP(c_COMBC(U_10092,U_10092,tc_HOL_Obool),c_fequal),U_10094))),U_10095)),c_Groups_Ozero__class_Ozero(U_10091))),U_10093) = c_Groups_Ozero__class_Ozero(U_10091)
| hBOOL(hAPP(hAPP(c_member(U_10092),U_10094),U_10093))
| ~ sP800(U_10092,U_10091,U_10093,U_10094,U_10095) ),
inference(clausify,[status(thm)],[f_2778_3]) ).
fof(f_2779_1,plain,
! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__constant]) ).
fof(f_2779_2,plain,
! [U_10100,U_10099,U_10098,U_10097,U_10096] :
( hAPP(c_Set_Oimage(U_10096,U_10099,hAPP(c_COMBK(U_10099,U_10096),U_10100)),U_10098) = hAPP(hAPP(c_Set_Oinsert(U_10099),U_10100),c_Orderings_Obot__class_Obot(tc_fun(U_10099,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10096),U_10097),U_10098)) ),
inference(variable_rename,[status(thm)],[f_2779_1]) ).
fof(f_2779_3,plain,
! [U_10097,U_10100,U_10098,U_10096,U_10099] :
( hAPP(c_Set_Oimage(U_10096,U_10099,hAPP(c_COMBK(U_10099,U_10096),U_10100)),U_10098) = hAPP(hAPP(c_Set_Oinsert(U_10099),U_10100),c_Orderings_Obot__class_Obot(tc_fun(U_10099,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10096),U_10097),U_10098)) ),
inference(definitional_conversion,[status(esa)],[f_2779_2]) ).
cnf(f_2779_4,plain,
( hAPP(c_Set_Oimage(U_10096,U_10099,hAPP(c_COMBK(U_10099,U_10096),U_10100)),U_10098) = hAPP(hAPP(c_Set_Oinsert(U_10099),U_10100),c_Orderings_Obot__class_Obot(tc_fun(U_10099,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10096),U_10097),U_10098)) ),
inference(clausify,[status(thm)],[f_2779_3]) ).
fof(f_2780_1,plain,
! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict]) ).
fof(f_2780_2,plain,
! [U_10107,U_10106,U_10105,U_10104,U_10103,U_10102,U_10101] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10102,U_10101),hAPP(hAPP(c_COMBS(U_10102,tc_fun(U_10104,tc_HOL_Obool),U_10101),hAPP(hAPP(c_COMBB(tc_fun(U_10104,U_10101),tc_fun(tc_fun(U_10104,tc_HOL_Obool),U_10101),U_10102),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10104,U_10101)),U_10106)),hAPP(hAPP(c_COMBB(tc_fun(U_10104,tc_HOL_Obool),tc_fun(U_10104,tc_HOL_Obool),U_10102),c_Set_OCollect(U_10104)),hAPP(hAPP(c_COMBB(tc_fun(U_10104,tc_HOL_Obool),tc_fun(U_10104,tc_HOL_Obool),U_10102),hAPP(c_COMBS(U_10104,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10104),c_fconj),hAPP(hAPP(c_COMBC(U_10104,tc_fun(U_10104,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10104)),U_10105)))),U_10107)))),U_10103) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10104,U_10101),hAPP(hAPP(c_COMBS(U_10104,tc_fun(U_10102,tc_HOL_Obool),U_10101),hAPP(hAPP(c_COMBB(tc_fun(U_10102,U_10101),tc_fun(tc_fun(U_10102,tc_HOL_Obool),U_10101),U_10104),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10102,U_10101)),hAPP(c_COMBC(U_10102,U_10104,U_10101),U_10106))),hAPP(hAPP(c_COMBB(tc_fun(U_10102,tc_HOL_Obool),tc_fun(U_10102,tc_HOL_Obool),U_10104),c_Set_OCollect(U_10102)),hAPP(hAPP(c_COMBB(tc_fun(U_10102,tc_HOL_Obool),tc_fun(U_10102,tc_HOL_Obool),U_10104),hAPP(c_COMBS(U_10102,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10102),c_fconj),hAPP(hAPP(c_COMBC(U_10102,tc_fun(U_10102,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10102)),U_10103)))),hAPP(c_COMBC(U_10102,U_10104,tc_HOL_Obool),U_10107))))),U_10105)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10104),U_10105))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10102),U_10103))
| ~ class_Groups_Ocomm__monoid__add(U_10101) ),
inference(variable_rename,[status(thm)],[f_2780_1]) ).
fof(f_2780_3,plain,
! [U_10101,U_10102,U_10103,U_10104,U_10105,U_10106,U_10107] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10102,U_10101),hAPP(hAPP(c_COMBS(U_10102,tc_fun(U_10104,tc_HOL_Obool),U_10101),hAPP(hAPP(c_COMBB(tc_fun(U_10104,U_10101),tc_fun(tc_fun(U_10104,tc_HOL_Obool),U_10101),U_10102),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10104,U_10101)),U_10106)),hAPP(hAPP(c_COMBB(tc_fun(U_10104,tc_HOL_Obool),tc_fun(U_10104,tc_HOL_Obool),U_10102),c_Set_OCollect(U_10104)),hAPP(hAPP(c_COMBB(tc_fun(U_10104,tc_HOL_Obool),tc_fun(U_10104,tc_HOL_Obool),U_10102),hAPP(c_COMBS(U_10104,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10104),c_fconj),hAPP(hAPP(c_COMBC(U_10104,tc_fun(U_10104,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10104)),U_10105)))),U_10107)))),U_10103) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10104,U_10101),hAPP(hAPP(c_COMBS(U_10104,tc_fun(U_10102,tc_HOL_Obool),U_10101),hAPP(hAPP(c_COMBB(tc_fun(U_10102,U_10101),tc_fun(tc_fun(U_10102,tc_HOL_Obool),U_10101),U_10104),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10102,U_10101)),hAPP(c_COMBC(U_10102,U_10104,U_10101),U_10106))),hAPP(hAPP(c_COMBB(tc_fun(U_10102,tc_HOL_Obool),tc_fun(U_10102,tc_HOL_Obool),U_10104),c_Set_OCollect(U_10102)),hAPP(hAPP(c_COMBB(tc_fun(U_10102,tc_HOL_Obool),tc_fun(U_10102,tc_HOL_Obool),U_10104),hAPP(c_COMBS(U_10102,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10102),c_fconj),hAPP(hAPP(c_COMBC(U_10102,tc_fun(U_10102,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10102)),U_10103)))),hAPP(c_COMBC(U_10102,U_10104,tc_HOL_Obool),U_10107))))),U_10105)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10104),U_10105))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10102),U_10103))
| ~ class_Groups_Ocomm__monoid__add(U_10101) ),
inference(definitional_conversion,[status(esa)],[f_2780_2]) ).
cnf(f_2780_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10102,U_10101),hAPP(hAPP(c_COMBS(U_10102,tc_fun(U_10104,tc_HOL_Obool),U_10101),hAPP(hAPP(c_COMBB(tc_fun(U_10104,U_10101),tc_fun(tc_fun(U_10104,tc_HOL_Obool),U_10101),U_10102),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10104,U_10101)),U_10106)),hAPP(hAPP(c_COMBB(tc_fun(U_10104,tc_HOL_Obool),tc_fun(U_10104,tc_HOL_Obool),U_10102),c_Set_OCollect(U_10104)),hAPP(hAPP(c_COMBB(tc_fun(U_10104,tc_HOL_Obool),tc_fun(U_10104,tc_HOL_Obool),U_10102),hAPP(c_COMBS(U_10104,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10104),c_fconj),hAPP(hAPP(c_COMBC(U_10104,tc_fun(U_10104,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10104)),U_10105)))),U_10107)))),U_10103) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10104,U_10101),hAPP(hAPP(c_COMBS(U_10104,tc_fun(U_10102,tc_HOL_Obool),U_10101),hAPP(hAPP(c_COMBB(tc_fun(U_10102,U_10101),tc_fun(tc_fun(U_10102,tc_HOL_Obool),U_10101),U_10104),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10102,U_10101)),hAPP(c_COMBC(U_10102,U_10104,U_10101),U_10106))),hAPP(hAPP(c_COMBB(tc_fun(U_10102,tc_HOL_Obool),tc_fun(U_10102,tc_HOL_Obool),U_10104),c_Set_OCollect(U_10102)),hAPP(hAPP(c_COMBB(tc_fun(U_10102,tc_HOL_Obool),tc_fun(U_10102,tc_HOL_Obool),U_10104),hAPP(c_COMBS(U_10102,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10102),c_fconj),hAPP(hAPP(c_COMBC(U_10102,tc_fun(U_10102,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10102)),U_10103)))),hAPP(c_COMBC(U_10102,U_10104,tc_HOL_Obool),U_10107))))),U_10105)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10104),U_10105))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10102),U_10103))
| ~ class_Groups_Ocomm__monoid__add(U_10101) ),
inference(clausify,[status(thm)],[f_2780_3]) ).
fof(f_2781_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_INT__greaterThan__UNIV]) ).
fof(f_2781_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_2781_1]) ).
cnf(f_2781_3,plain,
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)),
inference(clausify,[status(thm)],[f_2781_2]) ).
fof(f_2782_1,plain,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__delta_H]) ).
fof(f_2782_2,plain,
! [U_10112,U_10111,U_10110,U_10109,U_10108] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10109,U_10108),hAPP(hAPP(c_COMBC(U_10109,U_10108,U_10108),hAPP(hAPP(c_COMBS(U_10109,U_10108,tc_fun(U_10108,U_10108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10108,tc_fun(U_10108,U_10108)),U_10109),c_If(U_10108)),hAPP(c_fequal,U_10111))),U_10112)),c_Groups_Oone__class_Oone(U_10108))),U_10110) = c_Groups_Oone__class_Oone(U_10108)
| hBOOL(hAPP(hAPP(c_member(U_10109),U_10111),U_10110)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10109,U_10108),hAPP(hAPP(c_COMBC(U_10109,U_10108,U_10108),hAPP(hAPP(c_COMBS(U_10109,U_10108,tc_fun(U_10108,U_10108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10108,tc_fun(U_10108,U_10108)),U_10109),c_If(U_10108)),hAPP(c_fequal,U_10111))),U_10112)),c_Groups_Oone__class_Oone(U_10108))),U_10110) = hAPP(U_10112,U_10111)
| ~ hBOOL(hAPP(hAPP(c_member(U_10109),U_10111),U_10110)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10109),U_10110))
| ~ class_Groups_Ocomm__monoid__mult(U_10108) ),
inference(variable_rename,[status(thm)],[f_2782_1]) ).
fof(f_2782_3,plain,
( ! [U_10108,U_10109,U_10110,U_10111,U_10112] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10109,U_10108),hAPP(hAPP(c_COMBC(U_10109,U_10108,U_10108),hAPP(hAPP(c_COMBS(U_10109,U_10108,tc_fun(U_10108,U_10108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10108,tc_fun(U_10108,U_10108)),U_10109),c_If(U_10108)),hAPP(c_fequal,U_10111))),U_10112)),c_Groups_Oone__class_Oone(U_10108))),U_10110) = c_Groups_Oone__class_Oone(U_10108)
| hBOOL(hAPP(hAPP(c_member(U_10109),U_10111),U_10110))
| ~ sP801(U_10108,U_10109,U_10110,U_10111,U_10112) )
& ! [U_10108,U_10109,U_10110,U_10111,U_10112] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10109,U_10108),hAPP(hAPP(c_COMBC(U_10109,U_10108,U_10108),hAPP(hAPP(c_COMBS(U_10109,U_10108,tc_fun(U_10108,U_10108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10108,tc_fun(U_10108,U_10108)),U_10109),c_If(U_10108)),hAPP(c_fequal,U_10111))),U_10112)),c_Groups_Oone__class_Oone(U_10108))),U_10110) = hAPP(U_10112,U_10111)
| ~ hBOOL(hAPP(hAPP(c_member(U_10109),U_10111),U_10110))
| ~ sP801(U_10108,U_10109,U_10110,U_10111,U_10112) )
& ! [U_10108,U_10109,U_10110,U_10111,U_10112] :
( sP801(U_10108,U_10109,U_10110,U_10111,U_10112)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10109),U_10110))
| ~ class_Groups_Ocomm__monoid__mult(U_10108) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP801])],[f_2782_2]) ).
cnf(f_2782_4,plain,
( sP801(U_10108,U_10109,U_10110,U_10111,U_10112)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10109),U_10110))
| ~ class_Groups_Ocomm__monoid__mult(U_10108) ),
inference(clausify,[status(thm)],[f_2782_3]) ).
cnf(f_2782_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10109,U_10108),hAPP(hAPP(c_COMBC(U_10109,U_10108,U_10108),hAPP(hAPP(c_COMBS(U_10109,U_10108,tc_fun(U_10108,U_10108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10108,tc_fun(U_10108,U_10108)),U_10109),c_If(U_10108)),hAPP(c_fequal,U_10111))),U_10112)),c_Groups_Oone__class_Oone(U_10108))),U_10110) = hAPP(U_10112,U_10111)
| ~ hBOOL(hAPP(hAPP(c_member(U_10109),U_10111),U_10110))
| ~ sP801(U_10108,U_10109,U_10110,U_10111,U_10112) ),
inference(clausify,[status(thm)],[f_2782_3]) ).
cnf(f_2782_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10109,U_10108),hAPP(hAPP(c_COMBC(U_10109,U_10108,U_10108),hAPP(hAPP(c_COMBS(U_10109,U_10108,tc_fun(U_10108,U_10108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10108,tc_fun(U_10108,U_10108)),U_10109),c_If(U_10108)),hAPP(c_fequal,U_10111))),U_10112)),c_Groups_Oone__class_Oone(U_10108))),U_10110) = c_Groups_Oone__class_Oone(U_10108)
| hBOOL(hAPP(hAPP(c_member(U_10109),U_10111),U_10110))
| ~ sP801(U_10108,U_10109,U_10110,U_10111,U_10112) ),
inference(clausify,[status(thm)],[f_2782_3]) ).
fof(f_2783_1,plain,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__delta]) ).
fof(f_2783_2,plain,
! [U_10117,U_10116,U_10115,U_10114,U_10113] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10114,U_10113),hAPP(hAPP(c_COMBC(U_10114,U_10113,U_10113),hAPP(hAPP(c_COMBS(U_10114,U_10113,tc_fun(U_10113,U_10113)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10113,tc_fun(U_10113,U_10113)),U_10114),c_If(U_10113)),hAPP(hAPP(c_COMBC(U_10114,U_10114,tc_HOL_Obool),c_fequal),U_10116))),U_10117)),c_Groups_Oone__class_Oone(U_10113))),U_10115) = c_Groups_Oone__class_Oone(U_10113)
| hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10114,U_10113),hAPP(hAPP(c_COMBC(U_10114,U_10113,U_10113),hAPP(hAPP(c_COMBS(U_10114,U_10113,tc_fun(U_10113,U_10113)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10113,tc_fun(U_10113,U_10113)),U_10114),c_If(U_10113)),hAPP(hAPP(c_COMBC(U_10114,U_10114,tc_HOL_Obool),c_fequal),U_10116))),U_10117)),c_Groups_Oone__class_Oone(U_10113))),U_10115) = hAPP(U_10117,U_10116)
| ~ hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10114),U_10115))
| ~ class_Groups_Ocomm__monoid__mult(U_10113) ),
inference(variable_rename,[status(thm)],[f_2783_1]) ).
fof(f_2783_3,plain,
( ! [U_10114,U_10113,U_10115,U_10116,U_10117] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10114,U_10113),hAPP(hAPP(c_COMBC(U_10114,U_10113,U_10113),hAPP(hAPP(c_COMBS(U_10114,U_10113,tc_fun(U_10113,U_10113)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10113,tc_fun(U_10113,U_10113)),U_10114),c_If(U_10113)),hAPP(hAPP(c_COMBC(U_10114,U_10114,tc_HOL_Obool),c_fequal),U_10116))),U_10117)),c_Groups_Oone__class_Oone(U_10113))),U_10115) = c_Groups_Oone__class_Oone(U_10113)
| hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115))
| ~ sP802(U_10114,U_10113,U_10115,U_10116,U_10117) )
& ! [U_10114,U_10113,U_10115,U_10116,U_10117] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10114,U_10113),hAPP(hAPP(c_COMBC(U_10114,U_10113,U_10113),hAPP(hAPP(c_COMBS(U_10114,U_10113,tc_fun(U_10113,U_10113)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10113,tc_fun(U_10113,U_10113)),U_10114),c_If(U_10113)),hAPP(hAPP(c_COMBC(U_10114,U_10114,tc_HOL_Obool),c_fequal),U_10116))),U_10117)),c_Groups_Oone__class_Oone(U_10113))),U_10115) = hAPP(U_10117,U_10116)
| ~ hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115))
| ~ sP802(U_10114,U_10113,U_10115,U_10116,U_10117) )
& ! [U_10114,U_10113,U_10115,U_10116,U_10117] :
( sP802(U_10114,U_10113,U_10115,U_10116,U_10117)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10114),U_10115))
| ~ class_Groups_Ocomm__monoid__mult(U_10113) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP802])],[f_2783_2]) ).
cnf(f_2783_4,plain,
( sP802(U_10114,U_10113,U_10115,U_10116,U_10117)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10114),U_10115))
| ~ class_Groups_Ocomm__monoid__mult(U_10113) ),
inference(clausify,[status(thm)],[f_2783_3]) ).
cnf(f_2783_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10114,U_10113),hAPP(hAPP(c_COMBC(U_10114,U_10113,U_10113),hAPP(hAPP(c_COMBS(U_10114,U_10113,tc_fun(U_10113,U_10113)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10113,tc_fun(U_10113,U_10113)),U_10114),c_If(U_10113)),hAPP(hAPP(c_COMBC(U_10114,U_10114,tc_HOL_Obool),c_fequal),U_10116))),U_10117)),c_Groups_Oone__class_Oone(U_10113))),U_10115) = hAPP(U_10117,U_10116)
| ~ hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115))
| ~ sP802(U_10114,U_10113,U_10115,U_10116,U_10117) ),
inference(clausify,[status(thm)],[f_2783_3]) ).
cnf(f_2783_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10114,U_10113),hAPP(hAPP(c_COMBC(U_10114,U_10113,U_10113),hAPP(hAPP(c_COMBS(U_10114,U_10113,tc_fun(U_10113,U_10113)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10113,tc_fun(U_10113,U_10113)),U_10114),c_If(U_10113)),hAPP(hAPP(c_COMBC(U_10114,U_10114,tc_HOL_Obool),c_fequal),U_10116))),U_10117)),c_Groups_Oone__class_Oone(U_10113))),U_10115) = c_Groups_Oone__class_Oone(U_10113)
| hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115))
| ~ sP802(U_10114,U_10113,U_10115,U_10116,U_10117) ),
inference(clausify,[status(thm)],[f_2783_3]) ).
fof(f_2784_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_image__eq__UN]) ).
fof(f_2784_2,plain,
! [U_10121,U_10120,U_10119,U_10118] : hAPP(c_Set_Oimage(U_10118,U_10119,U_10120),U_10121) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10118,tc_fun(U_10119,tc_HOL_Obool)),U_10121),hAPP(hAPP(c_COMBC(U_10118,tc_fun(U_10119,tc_HOL_Obool),tc_fun(U_10119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10119,tc_fun(tc_fun(U_10119,tc_HOL_Obool),tc_fun(U_10119,tc_HOL_Obool)),U_10118),c_Set_Oinsert(U_10119)),U_10120)),c_Orderings_Obot__class_Obot(tc_fun(U_10119,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2784_1]) ).
fof(f_2784_3,plain,
! [U_10119,U_10118,U_10120,U_10121] : hAPP(c_Set_Oimage(U_10118,U_10119,U_10120),U_10121) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10118,tc_fun(U_10119,tc_HOL_Obool)),U_10121),hAPP(hAPP(c_COMBC(U_10118,tc_fun(U_10119,tc_HOL_Obool),tc_fun(U_10119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10119,tc_fun(tc_fun(U_10119,tc_HOL_Obool),tc_fun(U_10119,tc_HOL_Obool)),U_10118),c_Set_Oinsert(U_10119)),U_10120)),c_Orderings_Obot__class_Obot(tc_fun(U_10119,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_2784_2]) ).
cnf(f_2784_4,plain,
hAPP(c_Set_Oimage(U_10118,U_10119,U_10120),U_10121) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10118,tc_fun(U_10119,tc_HOL_Obool)),U_10121),hAPP(hAPP(c_COMBC(U_10118,tc_fun(U_10119,tc_HOL_Obool),tc_fun(U_10119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10119,tc_fun(tc_fun(U_10119,tc_HOL_Obool),tc_fun(U_10119,tc_HOL_Obool)),U_10118),c_Set_Oinsert(U_10119)),U_10120)),c_Orderings_Obot__class_Obot(tc_fun(U_10119,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2784_3]) ).
fof(f_2785_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).
fof(f_2785_2,plain,
! [U_10127,U_10126,U_10125,U_10124,U_10123,U_10122] : hAPP(c_Set_Oimage(U_10122,U_10123,hAPP(hAPP(c_COMBS(U_10122,U_10123,U_10123),hAPP(hAPP(c_COMBS(U_10122,U_10123,tc_fun(U_10123,U_10123)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10123,tc_fun(U_10123,U_10123)),U_10122),c_If(U_10123)),U_10124)),U_10125)),U_10126)),U_10127) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10123,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10122,U_10123,U_10125),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10127),hAPP(c_Set_OCollect(U_10122),U_10124)))),hAPP(c_Set_Oimage(U_10122,U_10123,U_10126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10127),hAPP(c_Set_OCollect(U_10122),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10122),c_fNot),U_10124))))),
inference(variable_rename,[status(thm)],[f_2785_1]) ).
fof(f_2785_3,plain,
! [U_10122,U_10123,U_10124,U_10125,U_10126,U_10127] : hAPP(c_Set_Oimage(U_10122,U_10123,hAPP(hAPP(c_COMBS(U_10122,U_10123,U_10123),hAPP(hAPP(c_COMBS(U_10122,U_10123,tc_fun(U_10123,U_10123)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10123,tc_fun(U_10123,U_10123)),U_10122),c_If(U_10123)),U_10124)),U_10125)),U_10126)),U_10127) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10123,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10122,U_10123,U_10125),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10127),hAPP(c_Set_OCollect(U_10122),U_10124)))),hAPP(c_Set_Oimage(U_10122,U_10123,U_10126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10127),hAPP(c_Set_OCollect(U_10122),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10122),c_fNot),U_10124))))),
inference(definitional_conversion,[status(esa)],[f_2785_2]) ).
cnf(f_2785_4,plain,
hAPP(c_Set_Oimage(U_10122,U_10123,hAPP(hAPP(c_COMBS(U_10122,U_10123,U_10123),hAPP(hAPP(c_COMBS(U_10122,U_10123,tc_fun(U_10123,U_10123)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10123,tc_fun(U_10123,U_10123)),U_10122),c_If(U_10123)),U_10124)),U_10125)),U_10126)),U_10127) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10123,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10122,U_10123,U_10125),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10127),hAPP(c_Set_OCollect(U_10122),U_10124)))),hAPP(c_Set_Oimage(U_10122,U_10123,U_10126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10127),hAPP(c_Set_OCollect(U_10122),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10122),c_fNot),U_10124))))),
inference(clausify,[status(thm)],[f_2785_3]) ).
fof(f_2786_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_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)) = 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_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( 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))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J]) ).
fof(f_2786_2,plain,
! [U_10132,U_10131,U_10130,U_10129,U_10128] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10129,tc_fun(U_10130,tc_HOL_Obool)),U_10128),hAPP(hAPP(c_COMBB(tc_fun(U_10130,tc_HOL_Obool),tc_fun(U_10130,tc_HOL_Obool),U_10129),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10130,tc_HOL_Obool)),U_10131)),U_10132)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10130,tc_HOL_Obool)),U_10131),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10129,tc_fun(U_10130,tc_HOL_Obool)),U_10128),U_10132))
| U_10128 = c_Orderings_Obot__class_Obot(tc_fun(U_10129,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10129,tc_fun(U_10130,tc_HOL_Obool)),U_10128),hAPP(hAPP(c_COMBB(tc_fun(U_10130,tc_HOL_Obool),tc_fun(U_10130,tc_HOL_Obool),U_10129),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10130,tc_HOL_Obool)),U_10131)),U_10132)) = c_Orderings_Otop__class_Otop(tc_fun(U_10130,tc_HOL_Obool))
| U_10128 != c_Orderings_Obot__class_Obot(tc_fun(U_10129,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2786_1]) ).
fof(f_2786_3,plain,
( ! [U_10142,U_10140,U_10138,U_10136,U_10134] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10136,tc_fun(U_10138,tc_HOL_Obool)),U_10134),hAPP(hAPP(c_COMBB(tc_fun(U_10138,tc_HOL_Obool),tc_fun(U_10138,tc_HOL_Obool),U_10136),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10138,tc_HOL_Obool)),U_10140)),U_10142)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10138,tc_HOL_Obool)),U_10140),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10136,tc_fun(U_10138,tc_HOL_Obool)),U_10134),U_10142))
| U_10134 = c_Orderings_Obot__class_Obot(tc_fun(U_10136,tc_HOL_Obool)) )
& ! [U_10141,U_10139,U_10137,U_10135,U_10133] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10135,tc_fun(U_10137,tc_HOL_Obool)),U_10133),hAPP(hAPP(c_COMBB(tc_fun(U_10137,tc_HOL_Obool),tc_fun(U_10137,tc_HOL_Obool),U_10135),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10137,tc_HOL_Obool)),U_10139)),U_10141)) = c_Orderings_Otop__class_Otop(tc_fun(U_10137,tc_HOL_Obool))
| U_10133 != c_Orderings_Obot__class_Obot(tc_fun(U_10135,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2786_2]) ).
fof(f_2786_4,plain,
( ! [U_10134,U_10136,U_10138,U_10140,U_10142] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10136,tc_fun(U_10138,tc_HOL_Obool)),U_10134),hAPP(hAPP(c_COMBB(tc_fun(U_10138,tc_HOL_Obool),tc_fun(U_10138,tc_HOL_Obool),U_10136),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10138,tc_HOL_Obool)),U_10140)),U_10142)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10138,tc_HOL_Obool)),U_10140),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10136,tc_fun(U_10138,tc_HOL_Obool)),U_10134),U_10142))
| U_10134 = c_Orderings_Obot__class_Obot(tc_fun(U_10136,tc_HOL_Obool)) )
& ! [U_10139,U_10135,U_10133,U_10137,U_10141] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10135,tc_fun(U_10137,tc_HOL_Obool)),U_10133),hAPP(hAPP(c_COMBB(tc_fun(U_10137,tc_HOL_Obool),tc_fun(U_10137,tc_HOL_Obool),U_10135),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10137,tc_HOL_Obool)),U_10139)),U_10141)) = c_Orderings_Otop__class_Otop(tc_fun(U_10137,tc_HOL_Obool))
| U_10133 != c_Orderings_Obot__class_Obot(tc_fun(U_10135,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2786_3]) ).
cnf(f_2786_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10135,tc_fun(U_10137,tc_HOL_Obool)),U_10133),hAPP(hAPP(c_COMBB(tc_fun(U_10137,tc_HOL_Obool),tc_fun(U_10137,tc_HOL_Obool),U_10135),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10137,tc_HOL_Obool)),U_10139)),U_10141)) = c_Orderings_Otop__class_Otop(tc_fun(U_10137,tc_HOL_Obool))
| U_10133 != c_Orderings_Obot__class_Obot(tc_fun(U_10135,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2786_4]) ).
cnf(f_2786_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10136,tc_fun(U_10138,tc_HOL_Obool)),U_10134),hAPP(hAPP(c_COMBB(tc_fun(U_10138,tc_HOL_Obool),tc_fun(U_10138,tc_HOL_Obool),U_10136),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10138,tc_HOL_Obool)),U_10140)),U_10142)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10138,tc_HOL_Obool)),U_10140),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10136,tc_fun(U_10138,tc_HOL_Obool)),U_10134),U_10142))
| U_10134 = c_Orderings_Obot__class_Obot(tc_fun(U_10136,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2786_4]) ).
fof(f_2787_1,plain,
! [V_A_2,V_y_2,T_c,T_b] :
( 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)
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__constant]) ).
fof(f_2787_2,plain,
! [U_10146,U_10145,U_10144,U_10143] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10144,U_10143),hAPP(c_COMBK(U_10143,U_10144),U_10145)),U_10146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10143),hAPP(c_Finite__Set_Ocard(U_10144),U_10146))),U_10145)
| ~ class_Rings_Osemiring__1(U_10143) ),
inference(variable_rename,[status(thm)],[f_2787_1]) ).
fof(f_2787_3,plain,
! [U_10143,U_10144,U_10145,U_10146] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10144,U_10143),hAPP(c_COMBK(U_10143,U_10144),U_10145)),U_10146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10143),hAPP(c_Finite__Set_Ocard(U_10144),U_10146))),U_10145)
| ~ class_Rings_Osemiring__1(U_10143) ),
inference(definitional_conversion,[status(esa)],[f_2787_2]) ).
cnf(f_2787_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10144,U_10143),hAPP(c_COMBK(U_10143,U_10144),U_10145)),U_10146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10143),hAPP(c_Finite__Set_Ocard(U_10144),U_10146))),U_10145)
| ~ class_Rings_Osemiring__1(U_10143) ),
inference(clausify,[status(thm)],[f_2787_3]) ).
fof(f_2788_1,plain,
! [V_w_2,V_z_2,T_b] :
( 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)))
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__even]) ).
fof(f_2788_2,plain,
! [U_10149,U_10148,U_10147] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10147),U_10148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10149))) = hAPP(hAPP(c_HOL_OLet(U_10147,U_10147),hAPP(hAPP(c_Power_Opower__class_Opower(U_10147),U_10148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10149))),hAPP(hAPP(c_COMBS(U_10147,U_10147,U_10147),c_Groups_Otimes__class_Otimes(U_10147)),c_COMBI(U_10147)))
| ~ class_Int_Onumber__ring(U_10147) ),
inference(variable_rename,[status(thm)],[f_2788_1]) ).
fof(f_2788_3,plain,
! [U_10147,U_10148,U_10149] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10147),U_10148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10149))) = hAPP(hAPP(c_HOL_OLet(U_10147,U_10147),hAPP(hAPP(c_Power_Opower__class_Opower(U_10147),U_10148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10149))),hAPP(hAPP(c_COMBS(U_10147,U_10147,U_10147),c_Groups_Otimes__class_Otimes(U_10147)),c_COMBI(U_10147)))
| ~ class_Int_Onumber__ring(U_10147) ),
inference(definitional_conversion,[status(esa)],[f_2788_2]) ).
cnf(f_2788_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10147),U_10148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10149))) = hAPP(hAPP(c_HOL_OLet(U_10147,U_10147),hAPP(hAPP(c_Power_Opower__class_Opower(U_10147),U_10148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10149))),hAPP(hAPP(c_COMBS(U_10147,U_10147,U_10147),c_Groups_Otimes__class_Otimes(U_10147)),c_COMBI(U_10147)))
| ~ class_Int_Onumber__ring(U_10147) ),
inference(clausify,[status(thm)],[f_2788_3]) ).
fof(f_2789_1,plain,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__distrib]) ).
fof(f_2789_2,plain,
! [U_10154,U_10153,U_10152,U_10151,U_10150] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),hAPP(hAPP(c_COMBS(U_10151,U_10150,U_10150),hAPP(hAPP(c_COMBB(U_10150,tc_fun(U_10150,U_10150),U_10151),c_Groups_Otimes__class_Otimes(U_10150)),U_10153)),U_10154)),c_Groups_Oone__class_Oone(U_10150)),U_10152) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10150),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),U_10153),c_Groups_Oone__class_Oone(U_10150)),U_10152)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),U_10154),c_Groups_Oone__class_Oone(U_10150)),U_10152))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10151),U_10152))
| ~ class_Groups_Ocomm__monoid__mult(U_10150) ),
inference(variable_rename,[status(thm)],[f_2789_1]) ).
fof(f_2789_3,plain,
! [U_10150,U_10151,U_10152,U_10153,U_10154] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),hAPP(hAPP(c_COMBS(U_10151,U_10150,U_10150),hAPP(hAPP(c_COMBB(U_10150,tc_fun(U_10150,U_10150),U_10151),c_Groups_Otimes__class_Otimes(U_10150)),U_10153)),U_10154)),c_Groups_Oone__class_Oone(U_10150)),U_10152) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10150),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),U_10153),c_Groups_Oone__class_Oone(U_10150)),U_10152)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),U_10154),c_Groups_Oone__class_Oone(U_10150)),U_10152))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10151),U_10152))
| ~ class_Groups_Ocomm__monoid__mult(U_10150) ),
inference(definitional_conversion,[status(esa)],[f_2789_2]) ).
cnf(f_2789_4,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),hAPP(hAPP(c_COMBS(U_10151,U_10150,U_10150),hAPP(hAPP(c_COMBB(U_10150,tc_fun(U_10150,U_10150),U_10151),c_Groups_Otimes__class_Otimes(U_10150)),U_10153)),U_10154)),c_Groups_Oone__class_Oone(U_10150)),U_10152) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10150),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),U_10153),c_Groups_Oone__class_Oone(U_10150)),U_10152)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10150,U_10151,c_Groups_Otimes__class_Otimes(U_10150)),U_10154),c_Groups_Oone__class_Oone(U_10150)),U_10152))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10151),U_10152))
| ~ class_Groups_Ocomm__monoid__mult(U_10150) ),
inference(clausify,[status(thm)],[f_2789_3]) ).
fof(f_2790_1,plain,
! [T_b] :
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dual__max]) ).
fof(f_2790_2,plain,
! [U_10155] :
( c_Orderings_Oord_Omax(U_10155,hAPP(c_COMBC(U_10155,U_10155,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10155))) = c_Orderings_Oord__class_Omin(U_10155)
| ~ class_Orderings_Olinorder(U_10155) ),
inference(variable_rename,[status(thm)],[f_2790_1]) ).
fof(f_2790_3,plain,
! [U_10155] :
( c_Orderings_Oord_Omax(U_10155,hAPP(c_COMBC(U_10155,U_10155,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10155))) = c_Orderings_Oord__class_Omin(U_10155)
| ~ class_Orderings_Olinorder(U_10155) ),
inference(definitional_conversion,[status(esa)],[f_2790_2]) ).
cnf(f_2790_4,plain,
( c_Orderings_Oord_Omax(U_10155,hAPP(c_COMBC(U_10155,U_10155,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10155))) = c_Orderings_Oord__class_Omin(U_10155)
| ~ class_Orderings_Olinorder(U_10155) ),
inference(clausify,[status(thm)],[f_2790_3]) ).
fof(f_2791_1,plain,
! [T_b] :
( 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)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dual__min]) ).
fof(f_2791_2,plain,
! [U_10156] :
( c_Orderings_Oord_Omin(U_10156,hAPP(c_COMBC(U_10156,U_10156,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10156))) = c_Orderings_Oord__class_Omax(U_10156)
| ~ class_Orderings_Olinorder(U_10156) ),
inference(variable_rename,[status(thm)],[f_2791_1]) ).
fof(f_2791_3,plain,
! [U_10156] :
( c_Orderings_Oord_Omin(U_10156,hAPP(c_COMBC(U_10156,U_10156,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10156))) = c_Orderings_Oord__class_Omax(U_10156)
| ~ class_Orderings_Olinorder(U_10156) ),
inference(definitional_conversion,[status(esa)],[f_2791_2]) ).
cnf(f_2791_4,plain,
( c_Orderings_Oord_Omin(U_10156,hAPP(c_COMBC(U_10156,U_10156,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10156))) = c_Orderings_Oord__class_Omax(U_10156)
| ~ class_Orderings_Olinorder(U_10156) ),
inference(clausify,[status(thm)],[f_2791_3]) ).
fof(f_2792_1,plain,
! [V_y_2,V_A_2,T_b,T_c] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__constant]) ).
fof(f_2792_2,plain,
! [U_10160,U_10159,U_10158,U_10157] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10158,U_10157),hAPP(c_COMBK(U_10157,U_10158),U_10160)),U_10159) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10157),U_10160),hAPP(c_Finite__Set_Ocard(U_10158),U_10159))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159))
| ~ class_Groups_Ocomm__monoid__mult(U_10157) ),
inference(variable_rename,[status(thm)],[f_2792_1]) ).
fof(f_2792_3,plain,
! [U_10157,U_10158,U_10159,U_10160] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10158,U_10157),hAPP(c_COMBK(U_10157,U_10158),U_10160)),U_10159) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10157),U_10160),hAPP(c_Finite__Set_Ocard(U_10158),U_10159))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159))
| ~ class_Groups_Ocomm__monoid__mult(U_10157) ),
inference(definitional_conversion,[status(esa)],[f_2792_2]) ).
cnf(f_2792_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10158,U_10157),hAPP(c_COMBK(U_10157,U_10158),U_10160)),U_10159) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10157),U_10160),hAPP(c_Finite__Set_Ocard(U_10158),U_10159))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159))
| ~ class_Groups_Ocomm__monoid__mult(U_10157) ),
inference(clausify,[status(thm)],[f_2792_3]) ).
fof(f_2793_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup]) ).
fof(f_2793_2,plain,
! [U_10165,U_10164,U_10163,U_10162,U_10161] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10161),U_10164),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10162,U_10161),U_10163),U_10165)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10162,U_10161,hAPP(hAPP(c_COMBB(U_10161,tc_fun(U_10161,U_10161),U_10162),c_Lattices_Osemilattice__sup__class_Osup(U_10161)),U_10165)),U_10164),U_10163)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10162),U_10163))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10161) ),
inference(variable_rename,[status(thm)],[f_2793_1]) ).
fof(f_2793_3,plain,
! [U_10161,U_10162,U_10163,U_10164,U_10165] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10161),U_10164),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10162,U_10161),U_10163),U_10165)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10162,U_10161,hAPP(hAPP(c_COMBB(U_10161,tc_fun(U_10161,U_10161),U_10162),c_Lattices_Osemilattice__sup__class_Osup(U_10161)),U_10165)),U_10164),U_10163)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10162),U_10163))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10161) ),
inference(definitional_conversion,[status(esa)],[f_2793_2]) ).
cnf(f_2793_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10161),U_10164),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10162,U_10161),U_10163),U_10165)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10162,U_10161,hAPP(hAPP(c_COMBB(U_10161,tc_fun(U_10161,U_10161),U_10162),c_Lattices_Osemilattice__sup__class_Osup(U_10161)),U_10165)),U_10164),U_10163)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10162),U_10163))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10161) ),
inference(clausify,[status(thm)],[f_2793_3]) ).
fof(f_2794_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf]) ).
fof(f_2794_2,plain,
! [U_10170,U_10169,U_10168,U_10167,U_10166] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10166),U_10169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10167,U_10166),U_10168),U_10170)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10167,U_10166,hAPP(hAPP(c_COMBB(U_10166,tc_fun(U_10166,U_10166),U_10167),c_Lattices_Osemilattice__inf__class_Oinf(U_10166)),U_10170)),U_10169),U_10168)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10167),U_10168))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10166) ),
inference(variable_rename,[status(thm)],[f_2794_1]) ).
fof(f_2794_3,plain,
! [U_10167,U_10166,U_10168,U_10169,U_10170] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10166),U_10169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10167,U_10166),U_10168),U_10170)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10167,U_10166,hAPP(hAPP(c_COMBB(U_10166,tc_fun(U_10166,U_10166),U_10167),c_Lattices_Osemilattice__inf__class_Oinf(U_10166)),U_10170)),U_10169),U_10168)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10167),U_10168))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10166) ),
inference(definitional_conversion,[status(esa)],[f_2794_2]) ).
cnf(f_2794_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10166),U_10169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10167,U_10166),U_10168),U_10170)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10167,U_10166,hAPP(hAPP(c_COMBB(U_10166,tc_fun(U_10166,U_10166),U_10167),c_Lattices_Osemilattice__inf__class_Oinf(U_10166)),U_10170)),U_10169),U_10168)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10167),U_10168))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10166) ),
inference(clausify,[status(thm)],[f_2794_3]) ).
fof(f_2795_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).
fof(f_2795_2,plain,
! [U_10171] : 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)))),U_10171)) = 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),U_10171),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_2795_1]) ).
fof(f_2795_3,plain,
! [U_10171] : 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)))),U_10171)) = 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),U_10171),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(definitional_conversion,[status(esa)],[f_2795_2]) ).
cnf(f_2795_4,plain,
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)))),U_10171)) = 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),U_10171),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_2795_3]) ).
fof(f_2796_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).
fof(f_2796_2,plain,
! [U_10172] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_10172) = 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),U_10172),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2796_1]) ).
fof(f_2796_3,plain,
! [U_10172] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_10172) = 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),U_10172),c_Int_Onat)))),
inference(definitional_conversion,[status(esa)],[f_2796_2]) ).
cnf(f_2796_4,plain,
hAPP(c_Set_OCollect(tc_Nat_Onat),U_10172) = 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),U_10172),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2796_3]) ).
fof(f_2797_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_zpower__number__of__even]) ).
fof(f_2797_2,plain,
! [U_10174,U_10173] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10173),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10174))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10173),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10174))),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))),
inference(variable_rename,[status(thm)],[f_2797_1]) ).
fof(f_2797_3,plain,
! [U_10173,U_10174] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10173),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10174))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10173),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10174))),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))),
inference(definitional_conversion,[status(esa)],[f_2797_2]) ).
cnf(f_2797_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10173),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10174))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10173),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10174))),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))),
inference(clausify,[status(thm)],[f_2797_3]) ).
fof(f_2798_1,plain,
! [V_n_2,V_f_2,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),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))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc]) ).
fof(f_2798_2,plain,
! [U_10177,U_10176,U_10175] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10175),U_10176),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10177))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10175),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10175),U_10176),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10177))),hAPP(U_10176,U_10177))
| ~ class_Groups_Ocomm__monoid__add(U_10175) ),
inference(variable_rename,[status(thm)],[f_2798_1]) ).
fof(f_2798_3,plain,
! [U_10175,U_10176,U_10177] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10175),U_10176),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10177))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10175),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10175),U_10176),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10177))),hAPP(U_10176,U_10177))
| ~ class_Groups_Ocomm__monoid__add(U_10175) ),
inference(definitional_conversion,[status(esa)],[f_2798_2]) ).
cnf(f_2798_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10175),U_10176),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10177))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10175),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10175),U_10176),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10177))),hAPP(U_10176,U_10177))
| ~ class_Groups_Ocomm__monoid__add(U_10175) ),
inference(clausify,[status(thm)],[f_2798_3]) ).
fof(f_2799_1,plain,
! [V_n_2,V_f_2,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),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)))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc]) ).
fof(f_2799_2,plain,
! [U_10180,U_10179,U_10178] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10178),U_10179),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10180))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10178),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10178),U_10179),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10180))),hAPP(U_10179,hAPP(c_Nat_OSuc,U_10180)))
| ~ class_Groups_Ocomm__monoid__add(U_10178) ),
inference(variable_rename,[status(thm)],[f_2799_1]) ).
fof(f_2799_3,plain,
! [U_10178,U_10179,U_10180] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10178),U_10179),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10180))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10178),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10178),U_10179),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10180))),hAPP(U_10179,hAPP(c_Nat_OSuc,U_10180)))
| ~ class_Groups_Ocomm__monoid__add(U_10178) ),
inference(definitional_conversion,[status(esa)],[f_2799_2]) ).
cnf(f_2799_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10178),U_10179),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10180))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10178),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10178),U_10179),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10180))),hAPP(U_10179,hAPP(c_Nat_OSuc,U_10180)))
| ~ class_Groups_Ocomm__monoid__add(U_10178) ),
inference(clausify,[status(thm)],[f_2799_3]) ).
fof(f_2800_1,plain,
! [V_A_2,V_f_2,T_b] :
( 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))
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J]) ).
fof(f_2800_2,plain,
! [U_10183,U_10182,U_10181] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10181),U_10182),U_10183) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10181),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10181,tc_Int_Oint),U_10182),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10183))
| ~ class_Groups_Ocomm__monoid__mult(U_10181)
| ~ class_Groups_Ocomm__monoid__add(U_10181) ),
inference(variable_rename,[status(thm)],[f_2800_1]) ).
fof(f_2800_3,plain,
! [U_10181,U_10182,U_10183] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10181),U_10182),U_10183) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10181),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10181,tc_Int_Oint),U_10182),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10183))
| ~ class_Groups_Ocomm__monoid__mult(U_10181)
| ~ class_Groups_Ocomm__monoid__add(U_10181) ),
inference(definitional_conversion,[status(esa)],[f_2800_2]) ).
cnf(f_2800_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10181),U_10182),U_10183) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10181),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10181,tc_Int_Oint),U_10182),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10183))
| ~ class_Groups_Ocomm__monoid__mult(U_10181)
| ~ class_Groups_Ocomm__monoid__add(U_10181) ),
inference(clausify,[status(thm)],[f_2800_3]) ).
fof(f_2801_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Un__Union__image]) ).
fof(f_2801_2,plain,
! [U_10188,U_10187,U_10186,U_10185,U_10184] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10184,tc_fun(U_10185,tc_HOL_Obool)),U_10186),hAPP(hAPP(c_COMBS(U_10184,tc_fun(U_10185,tc_HOL_Obool),tc_fun(U_10185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10185,tc_HOL_Obool),tc_fun(tc_fun(U_10185,tc_HOL_Obool),tc_fun(U_10185,tc_HOL_Obool)),U_10184),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10185,tc_HOL_Obool))),U_10187)),U_10188)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10185,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10185,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10184,tc_fun(U_10185,tc_HOL_Obool),U_10187),U_10186))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10185,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10184,tc_fun(U_10185,tc_HOL_Obool),U_10188),U_10186))),
inference(variable_rename,[status(thm)],[f_2801_1]) ).
fof(f_2801_3,plain,
! [U_10184,U_10185,U_10186,U_10187,U_10188] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10184,tc_fun(U_10185,tc_HOL_Obool)),U_10186),hAPP(hAPP(c_COMBS(U_10184,tc_fun(U_10185,tc_HOL_Obool),tc_fun(U_10185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10185,tc_HOL_Obool),tc_fun(tc_fun(U_10185,tc_HOL_Obool),tc_fun(U_10185,tc_HOL_Obool)),U_10184),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10185,tc_HOL_Obool))),U_10187)),U_10188)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10185,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10185,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10184,tc_fun(U_10185,tc_HOL_Obool),U_10187),U_10186))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10185,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10184,tc_fun(U_10185,tc_HOL_Obool),U_10188),U_10186))),
inference(definitional_conversion,[status(esa)],[f_2801_2]) ).
cnf(f_2801_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10184,tc_fun(U_10185,tc_HOL_Obool)),U_10186),hAPP(hAPP(c_COMBS(U_10184,tc_fun(U_10185,tc_HOL_Obool),tc_fun(U_10185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10185,tc_HOL_Obool),tc_fun(tc_fun(U_10185,tc_HOL_Obool),tc_fun(U_10185,tc_HOL_Obool)),U_10184),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10185,tc_HOL_Obool))),U_10187)),U_10188)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10185,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10185,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10184,tc_fun(U_10185,tc_HOL_Obool),U_10187),U_10186))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10185,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10184,tc_fun(U_10185,tc_HOL_Obool),U_10188),U_10186))),
inference(clausify,[status(thm)],[f_2801_3]) ).
fof(f_2802_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).
fof(f_2802_2,plain,
! [U_10190,U_10189] : 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)),U_10189)),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),U_10190),U_10189))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10189),U_10190),
inference(variable_rename,[status(thm)],[f_2802_1]) ).
fof(f_2802_3,plain,
! [U_10189,U_10190] : 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)),U_10189)),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),U_10190),U_10189))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10189),U_10190),
inference(definitional_conversion,[status(esa)],[f_2802_2]) ).
cnf(f_2802_4,plain,
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)),U_10189)),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),U_10190),U_10189))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10189),U_10190),
inference(clausify,[status(thm)],[f_2802_3]) ).
fof(f_2803_1,plain,
! [V_f_2,V_A_2,T_b] :
( 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))
| ~ c_Nat__Transfer_Onat__set(V_A_2)
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J]) ).
fof(f_2803_2,plain,
! [U_10193,U_10192,U_10191] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10191),U_10193),U_10192) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10191),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10191,tc_Nat_Onat),U_10193),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10192))
| ~ c_Nat__Transfer_Onat__set(U_10192)
| ~ class_Groups_Ocomm__monoid__mult(U_10191)
| ~ class_Groups_Ocomm__monoid__add(U_10191) ),
inference(variable_rename,[status(thm)],[f_2803_1]) ).
fof(f_2803_3,plain,
! [U_10191,U_10192,U_10193] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10191),U_10193),U_10192) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10191),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10191,tc_Nat_Onat),U_10193),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10192))
| ~ c_Nat__Transfer_Onat__set(U_10192)
| ~ class_Groups_Ocomm__monoid__mult(U_10191)
| ~ class_Groups_Ocomm__monoid__add(U_10191) ),
inference(definitional_conversion,[status(esa)],[f_2803_2]) ).
cnf(f_2803_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10191),U_10193),U_10192) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10191),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10191,tc_Nat_Onat),U_10193),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10192))
| ~ c_Nat__Transfer_Onat__set(U_10192)
| ~ class_Groups_Ocomm__monoid__mult(U_10191)
| ~ class_Groups_Ocomm__monoid__add(U_10191) ),
inference(clausify,[status(thm)],[f_2803_3]) ).
fof(f_2804_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( 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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2)))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq]) ).
fof(f_2804_2,plain,
! [U_10196,U_10195,U_10194] :
( ( hBOOL(hAPP(c_Predicate_OPowp(U_10194,hAPP(hAPP(c_COMBC(U_10194,tc_fun(U_10194,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10194)),U_10195)),U_10196))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10194,tc_HOL_Obool)),U_10196),hAPP(c_Set_OPow(U_10194),U_10195))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10194,tc_HOL_Obool)),U_10196),hAPP(c_Set_OPow(U_10194),U_10195)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10194,hAPP(hAPP(c_COMBC(U_10194,tc_fun(U_10194,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10194)),U_10195)),U_10196)) ) ),
inference(variable_rename,[status(thm)],[f_2804_1]) ).
fof(f_2804_3,plain,
( ! [U_10202,U_10200,U_10198] :
( hBOOL(hAPP(c_Predicate_OPowp(U_10198,hAPP(hAPP(c_COMBC(U_10198,tc_fun(U_10198,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10198)),U_10200)),U_10202))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10198,tc_HOL_Obool)),U_10202),hAPP(c_Set_OPow(U_10198),U_10200))) )
& ! [U_10201,U_10199,U_10197] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10197,tc_HOL_Obool)),U_10201),hAPP(c_Set_OPow(U_10197),U_10199)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10197,hAPP(hAPP(c_COMBC(U_10197,tc_fun(U_10197,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10197)),U_10199)),U_10201)) ) ),
inference(miniscope,[status(thm)],[f_2804_2]) ).
fof(f_2804_4,plain,
( ! [U_10198,U_10200,U_10202] :
( hBOOL(hAPP(c_Predicate_OPowp(U_10198,hAPP(hAPP(c_COMBC(U_10198,tc_fun(U_10198,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10198)),U_10200)),U_10202))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10198,tc_HOL_Obool)),U_10202),hAPP(c_Set_OPow(U_10198),U_10200))) )
& ! [U_10201,U_10199,U_10197] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10197,tc_HOL_Obool)),U_10201),hAPP(c_Set_OPow(U_10197),U_10199)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10197,hAPP(hAPP(c_COMBC(U_10197,tc_fun(U_10197,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10197)),U_10199)),U_10201)) ) ),
inference(definitional_conversion,[status(esa)],[f_2804_3]) ).
cnf(f_2804_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10197,tc_HOL_Obool)),U_10201),hAPP(c_Set_OPow(U_10197),U_10199)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10197,hAPP(hAPP(c_COMBC(U_10197,tc_fun(U_10197,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10197)),U_10199)),U_10201)) ),
inference(clausify,[status(thm)],[f_2804_4]) ).
cnf(f_2804_6,plain,
( hBOOL(hAPP(c_Predicate_OPowp(U_10198,hAPP(hAPP(c_COMBC(U_10198,tc_fun(U_10198,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10198)),U_10200)),U_10202))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10198,tc_HOL_Obool)),U_10202),hAPP(c_Set_OPow(U_10198),U_10200))) ),
inference(clausify,[status(thm)],[f_2804_4]) ).
fof(f_2805_1,plain,
! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H]) ).
fof(f_2805_2,plain,
! [U_10207,U_10206,U_10205,U_10204,U_10203] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10204,U_10203),U_10206),hAPP(c_Set_OCollect(U_10204),hAPP(hAPP(c_COMBS(U_10204,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10204),c_fconj),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10205))),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10207)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10204,U_10203),hAPP(hAPP(c_COMBC(U_10204,U_10203,U_10203),hAPP(hAPP(c_COMBS(U_10204,U_10203,tc_fun(U_10203,U_10203)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10203,tc_fun(U_10203,U_10203)),U_10204),c_If(U_10203)),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10207))),U_10206)),c_Groups_Ozero__class_Ozero(U_10203))),U_10205)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205))
| ~ class_Groups_Ocomm__monoid__add(U_10203) ),
inference(variable_rename,[status(thm)],[f_2805_1]) ).
fof(f_2805_3,plain,
! [U_10203,U_10204,U_10205,U_10206,U_10207] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10204,U_10203),U_10206),hAPP(c_Set_OCollect(U_10204),hAPP(hAPP(c_COMBS(U_10204,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10204),c_fconj),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10205))),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10207)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10204,U_10203),hAPP(hAPP(c_COMBC(U_10204,U_10203,U_10203),hAPP(hAPP(c_COMBS(U_10204,U_10203,tc_fun(U_10203,U_10203)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10203,tc_fun(U_10203,U_10203)),U_10204),c_If(U_10203)),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10207))),U_10206)),c_Groups_Ozero__class_Ozero(U_10203))),U_10205)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205))
| ~ class_Groups_Ocomm__monoid__add(U_10203) ),
inference(definitional_conversion,[status(esa)],[f_2805_2]) ).
cnf(f_2805_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10204,U_10203),U_10206),hAPP(c_Set_OCollect(U_10204),hAPP(hAPP(c_COMBS(U_10204,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10204),c_fconj),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10205))),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10207)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10204,U_10203),hAPP(hAPP(c_COMBC(U_10204,U_10203,U_10203),hAPP(hAPP(c_COMBS(U_10204,U_10203,tc_fun(U_10203,U_10203)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10203,tc_fun(U_10203,U_10203)),U_10204),c_If(U_10203)),hAPP(hAPP(c_COMBC(U_10204,tc_fun(U_10204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10204)),U_10207))),U_10206)),c_Groups_Ozero__class_Ozero(U_10203))),U_10205)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205))
| ~ class_Groups_Ocomm__monoid__add(U_10203) ),
inference(clausify,[status(thm)],[f_2805_3]) ).
fof(f_2806_1,plain,
! [V_B_2,V_f_2,V_A_2,T_b,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),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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set]) ).
fof(f_2806_2,plain,
! [U_10212,U_10211,U_10210,U_10209,U_10208] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10209,U_10208),U_10211),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10209,tc_HOL_Obool)),U_10210),U_10212)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10209,U_10208),hAPP(hAPP(c_COMBC(U_10209,U_10208,U_10208),hAPP(hAPP(c_COMBS(U_10209,U_10208,tc_fun(U_10208,U_10208)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10208,tc_fun(U_10208,U_10208)),U_10209),c_If(U_10208)),hAPP(hAPP(c_COMBC(U_10209,tc_fun(U_10209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10209)),U_10212))),U_10211)),c_Groups_Ozero__class_Ozero(U_10208))),U_10210)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10209),U_10210))
| ~ class_Groups_Ocomm__monoid__add(U_10208) ),
inference(variable_rename,[status(thm)],[f_2806_1]) ).
fof(f_2806_3,plain,
! [U_10209,U_10208,U_10210,U_10211,U_10212] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10209,U_10208),U_10211),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10209,tc_HOL_Obool)),U_10210),U_10212)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10209,U_10208),hAPP(hAPP(c_COMBC(U_10209,U_10208,U_10208),hAPP(hAPP(c_COMBS(U_10209,U_10208,tc_fun(U_10208,U_10208)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10208,tc_fun(U_10208,U_10208)),U_10209),c_If(U_10208)),hAPP(hAPP(c_COMBC(U_10209,tc_fun(U_10209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10209)),U_10212))),U_10211)),c_Groups_Ozero__class_Ozero(U_10208))),U_10210)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10209),U_10210))
| ~ class_Groups_Ocomm__monoid__add(U_10208) ),
inference(definitional_conversion,[status(esa)],[f_2806_2]) ).
cnf(f_2806_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10209,U_10208),U_10211),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10209,tc_HOL_Obool)),U_10210),U_10212)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10209,U_10208),hAPP(hAPP(c_COMBC(U_10209,U_10208,U_10208),hAPP(hAPP(c_COMBS(U_10209,U_10208,tc_fun(U_10208,U_10208)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10208,tc_fun(U_10208,U_10208)),U_10209),c_If(U_10208)),hAPP(hAPP(c_COMBC(U_10209,tc_fun(U_10209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10209)),U_10212))),U_10211)),c_Groups_Ozero__class_Ozero(U_10208))),U_10210)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10209),U_10210))
| ~ class_Groups_Ocomm__monoid__add(U_10208) ),
inference(clausify,[status(thm)],[f_2806_3]) ).
fof(f_2807_1,plain,
! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
( 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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__image__gen]) ).
fof(f_2807_2,plain,
! [U_10218,U_10217,U_10216,U_10215,U_10214,U_10213] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10214,U_10213),U_10216),U_10215) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10217,U_10213),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),U_10213,U_10217),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10214,U_10213),U_10216)),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),tc_fun(U_10214,tc_HOL_Obool),U_10217),c_Set_OCollect(U_10214)),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),tc_fun(U_10214,tc_HOL_Obool),U_10217),hAPP(c_COMBS(U_10214,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10214),c_fconj),hAPP(hAPP(c_COMBC(U_10214,tc_fun(U_10214,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10214)),U_10215)))),hAPP(c_COMBC(U_10214,U_10217,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_10217,tc_fun(U_10217,tc_HOL_Obool),U_10214),c_fequal),U_10218)))))),hAPP(c_Set_Oimage(U_10214,U_10217,U_10218),U_10215))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10214),U_10215))
| ~ class_Groups_Ocomm__monoid__add(U_10213) ),
inference(variable_rename,[status(thm)],[f_2807_1]) ).
fof(f_2807_3,plain,
! [U_10213,U_10214,U_10215,U_10216,U_10217,U_10218] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10214,U_10213),U_10216),U_10215) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10217,U_10213),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),U_10213,U_10217),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10214,U_10213),U_10216)),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),tc_fun(U_10214,tc_HOL_Obool),U_10217),c_Set_OCollect(U_10214)),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),tc_fun(U_10214,tc_HOL_Obool),U_10217),hAPP(c_COMBS(U_10214,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10214),c_fconj),hAPP(hAPP(c_COMBC(U_10214,tc_fun(U_10214,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10214)),U_10215)))),hAPP(c_COMBC(U_10214,U_10217,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_10217,tc_fun(U_10217,tc_HOL_Obool),U_10214),c_fequal),U_10218)))))),hAPP(c_Set_Oimage(U_10214,U_10217,U_10218),U_10215))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10214),U_10215))
| ~ class_Groups_Ocomm__monoid__add(U_10213) ),
inference(definitional_conversion,[status(esa)],[f_2807_2]) ).
cnf(f_2807_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10214,U_10213),U_10216),U_10215) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10217,U_10213),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),U_10213,U_10217),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10214,U_10213),U_10216)),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),tc_fun(U_10214,tc_HOL_Obool),U_10217),c_Set_OCollect(U_10214)),hAPP(hAPP(c_COMBB(tc_fun(U_10214,tc_HOL_Obool),tc_fun(U_10214,tc_HOL_Obool),U_10217),hAPP(c_COMBS(U_10214,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10214),c_fconj),hAPP(hAPP(c_COMBC(U_10214,tc_fun(U_10214,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10214)),U_10215)))),hAPP(c_COMBC(U_10214,U_10217,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_10217,tc_fun(U_10217,tc_HOL_Obool),U_10214),c_fequal),U_10218)))))),hAPP(c_Set_Oimage(U_10214,U_10217,U_10218),U_10215))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10214),U_10215))
| ~ class_Groups_Ocomm__monoid__add(U_10213) ),
inference(clausify,[status(thm)],[f_2807_3]) ).
fof(f_2808_1,plain,
! [V_f_2,T_c,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image]) ).
fof(f_2808_2,plain,
! [U_10222,U_10221,U_10220,U_10219] :
( hAPP(c_Set_Oimage(U_10219,U_10221,U_10222),U_10220) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10221,tc_HOL_Obool),U_10219,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10221,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10219,tc_fun(U_10221,tc_HOL_Obool),tc_fun(U_10221,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10221,tc_fun(tc_fun(U_10221,tc_HOL_Obool),tc_fun(U_10221,tc_HOL_Obool)),U_10219),c_Set_Oinsert(U_10221)),U_10222)),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))),U_10220)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10219),U_10220)) ),
inference(variable_rename,[status(thm)],[f_2808_1]) ).
fof(f_2808_3,plain,
! [U_10220,U_10219,U_10221,U_10222] :
( hAPP(c_Set_Oimage(U_10219,U_10221,U_10222),U_10220) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10221,tc_HOL_Obool),U_10219,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10221,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10219,tc_fun(U_10221,tc_HOL_Obool),tc_fun(U_10221,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10221,tc_fun(tc_fun(U_10221,tc_HOL_Obool),tc_fun(U_10221,tc_HOL_Obool)),U_10219),c_Set_Oinsert(U_10221)),U_10222)),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))),U_10220)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10219),U_10220)) ),
inference(definitional_conversion,[status(esa)],[f_2808_2]) ).
cnf(f_2808_4,plain,
( hAPP(c_Set_Oimage(U_10219,U_10221,U_10222),U_10220) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10221,tc_HOL_Obool),U_10219,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10221,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10219,tc_fun(U_10221,tc_HOL_Obool),tc_fun(U_10221,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10221,tc_fun(tc_fun(U_10221,tc_HOL_Obool),tc_fun(U_10221,tc_HOL_Obool)),U_10219),c_Set_Oinsert(U_10221)),U_10222)),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))),U_10220)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10219),U_10220)) ),
inference(clausify,[status(thm)],[f_2808_3]) ).
fof(f_2809_1,plain,
! [V_w_2,V_v_2,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),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)))
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of]) ).
fof(f_2809_2,plain,
! [U_10225,U_10224,U_10223] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10225))) = hAPP(hAPP(c_HOL_OLet(U_10223,U_10223),hAPP(hAPP(c_Power_Opower__class_Opower(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10225))),hAPP(hAPP(c_COMBS(U_10223,U_10223,U_10223),c_Groups_Otimes__class_Otimes(U_10223)),c_COMBI(U_10223)))
| ~ class_Int_Onumber__ring(U_10223) ),
inference(variable_rename,[status(thm)],[f_2809_1]) ).
fof(f_2809_3,plain,
! [U_10223,U_10224,U_10225] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10225))) = hAPP(hAPP(c_HOL_OLet(U_10223,U_10223),hAPP(hAPP(c_Power_Opower__class_Opower(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10225))),hAPP(hAPP(c_COMBS(U_10223,U_10223,U_10223),c_Groups_Otimes__class_Otimes(U_10223)),c_COMBI(U_10223)))
| ~ class_Int_Onumber__ring(U_10223) ),
inference(definitional_conversion,[status(esa)],[f_2809_2]) ).
cnf(f_2809_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10225))) = hAPP(hAPP(c_HOL_OLet(U_10223,U_10223),hAPP(hAPP(c_Power_Opower__class_Opower(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10225))),hAPP(hAPP(c_COMBS(U_10223,U_10223,U_10223),c_Groups_Otimes__class_Otimes(U_10223)),c_COMBI(U_10223)))
| ~ class_Int_Onumber__ring(U_10223) ),
inference(clausify,[status(thm)],[f_2809_3]) ).
fof(f_2810_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup]) ).
fof(f_2810_2,plain,
! [U_10229,U_10228,U_10227,U_10226] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10227,U_10226),U_10228),U_10229) = hAPP(hAPP(c_Finite__Set_Ofold(U_10227,U_10226,hAPP(hAPP(c_COMBB(U_10226,tc_fun(U_10226,U_10226),U_10227),c_Lattices_Osemilattice__sup__class_Osup(U_10226)),U_10229)),c_Orderings_Obot__class_Obot(U_10226)),U_10228)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10228))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10226) ),
inference(variable_rename,[status(thm)],[f_2810_1]) ).
fof(f_2810_3,plain,
! [U_10226,U_10227,U_10228,U_10229] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10227,U_10226),U_10228),U_10229) = hAPP(hAPP(c_Finite__Set_Ofold(U_10227,U_10226,hAPP(hAPP(c_COMBB(U_10226,tc_fun(U_10226,U_10226),U_10227),c_Lattices_Osemilattice__sup__class_Osup(U_10226)),U_10229)),c_Orderings_Obot__class_Obot(U_10226)),U_10228)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10228))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10226) ),
inference(definitional_conversion,[status(esa)],[f_2810_2]) ).
cnf(f_2810_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10227,U_10226),U_10228),U_10229) = hAPP(hAPP(c_Finite__Set_Ofold(U_10227,U_10226,hAPP(hAPP(c_COMBB(U_10226,tc_fun(U_10226,U_10226),U_10227),c_Lattices_Osemilattice__sup__class_Osup(U_10226)),U_10229)),c_Orderings_Obot__class_Obot(U_10226)),U_10228)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10228))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10226) ),
inference(clausify,[status(thm)],[f_2810_3]) ).
fof(f_2811_1,plain,
! [V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g]) ).
fof(f_2811_2,plain,
! [U_10231,U_10230] :
( hAPP(c_Finite__Set_Ocard(U_10230),U_10231) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10230,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10230),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10231)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10231)) ),
inference(variable_rename,[status(thm)],[f_2811_1]) ).
fof(f_2811_3,plain,
! [U_10230,U_10231] :
( hAPP(c_Finite__Set_Ocard(U_10230),U_10231) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10230,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10230),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10231)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10231)) ),
inference(definitional_conversion,[status(esa)],[f_2811_2]) ).
cnf(f_2811_4,plain,
( hAPP(c_Finite__Set_Ocard(U_10230),U_10231) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10230,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10230),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10231)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10231)) ),
inference(clausify,[status(thm)],[f_2811_3]) ).
fof(f_2812_1,plain,
! [V_A_2,T_b] :
( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_card__def]) ).
fof(f_2812_2,plain,
! [U_10233,U_10232] :
( ( hAPP(c_Finite__Set_Ocard(U_10232),U_10233) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10232),U_10233)) )
& ( hAPP(c_Finite__Set_Ocard(U_10232),U_10233) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10232,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10232),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10233)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10232),U_10233)) ) ),
inference(variable_rename,[status(thm)],[f_2812_1]) ).
fof(f_2812_3,plain,
( ! [U_10237,U_10235] :
( hAPP(c_Finite__Set_Ocard(U_10235),U_10237) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10235),U_10237)) )
& ! [U_10236,U_10234] :
( hAPP(c_Finite__Set_Ocard(U_10234),U_10236) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10234,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10234),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10236)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10234),U_10236)) ) ),
inference(miniscope,[status(thm)],[f_2812_2]) ).
fof(f_2812_4,plain,
( ! [U_10235,U_10237] :
( hAPP(c_Finite__Set_Ocard(U_10235),U_10237) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10235),U_10237)) )
& ! [U_10236,U_10234] :
( hAPP(c_Finite__Set_Ocard(U_10234),U_10236) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10234,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10234),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10236)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10234),U_10236)) ) ),
inference(definitional_conversion,[status(esa)],[f_2812_3]) ).
cnf(f_2812_5,plain,
( hAPP(c_Finite__Set_Ocard(U_10234),U_10236) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10234,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10234),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10236)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10234),U_10236)) ),
inference(clausify,[status(thm)],[f_2812_4]) ).
cnf(f_2812_6,plain,
( hAPP(c_Finite__Set_Ocard(U_10235),U_10237) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10235),U_10237)) ),
inference(clausify,[status(thm)],[f_2812_4]) ).
fof(f_2813_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__remove]) ).
fof(f_2813_2,plain,
! [U_10238] : c_Finite__Set_Ofun__left__comm__idem(U_10238,tc_fun(U_10238,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10238,tc_HOL_Obool),tc_fun(tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),U_10238),hAPP(c_COMBC(tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10238,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10238,tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),c_Set_Oinsert(U_10238)),c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2813_1]) ).
fof(f_2813_3,plain,
! [U_10238] : c_Finite__Set_Ofun__left__comm__idem(U_10238,tc_fun(U_10238,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10238,tc_HOL_Obool),tc_fun(tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),U_10238),hAPP(c_COMBC(tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10238,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10238,tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),c_Set_Oinsert(U_10238)),c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_2813_2]) ).
cnf(f_2813_4,plain,
c_Finite__Set_Ofun__left__comm__idem(U_10238,tc_fun(U_10238,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10238,tc_HOL_Obool),tc_fun(tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),U_10238),hAPP(c_COMBC(tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10238,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10238,tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10238,tc_HOL_Obool)),c_Set_Oinsert(U_10238)),c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2813_3]) ).
fof(f_2814_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf]) ).
fof(f_2814_2,plain,
! [U_10242,U_10241,U_10240,U_10239] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10240,U_10239),U_10241),U_10242) = hAPP(hAPP(c_Finite__Set_Ofold(U_10240,U_10239,hAPP(hAPP(c_COMBB(U_10239,tc_fun(U_10239,U_10239),U_10240),c_Lattices_Osemilattice__inf__class_Oinf(U_10239)),U_10242)),c_Orderings_Otop__class_Otop(U_10239)),U_10241)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10239) ),
inference(variable_rename,[status(thm)],[f_2814_1]) ).
fof(f_2814_3,plain,
! [U_10239,U_10240,U_10241,U_10242] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10240,U_10239),U_10241),U_10242) = hAPP(hAPP(c_Finite__Set_Ofold(U_10240,U_10239,hAPP(hAPP(c_COMBB(U_10239,tc_fun(U_10239,U_10239),U_10240),c_Lattices_Osemilattice__inf__class_Oinf(U_10239)),U_10242)),c_Orderings_Otop__class_Otop(U_10239)),U_10241)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10239) ),
inference(definitional_conversion,[status(esa)],[f_2814_2]) ).
cnf(f_2814_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10240,U_10239),U_10241),U_10242) = hAPP(hAPP(c_Finite__Set_Ofold(U_10240,U_10239,hAPP(hAPP(c_COMBB(U_10239,tc_fun(U_10239,U_10239),U_10240),c_Lattices_Osemilattice__inf__class_Oinf(U_10239)),U_10242)),c_Orderings_Otop__class_Otop(U_10239)),U_10241)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10239) ),
inference(clausify,[status(thm)],[f_2814_3]) ).
fof(f_2815_1,plain,
! [V_z_2,V_z_H_2] :
( ( 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))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) )
& ( 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)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__nat__eq__if]) ).
fof(f_2815_2,plain,
! [U_10244,U_10243] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10244)),hAPP(c_Int_Onat,U_10243)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10244),U_10243)),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))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10243)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10244)),hAPP(c_Int_Onat,U_10243)) = hAPP(c_Int_Onat,U_10244)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10243)) ) ),
inference(variable_rename,[status(thm)],[f_2815_1]) ).
fof(f_2815_3,plain,
( ! [U_10248,U_10246] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10248)),hAPP(c_Int_Onat,U_10246)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10248),U_10246)),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))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10246)) )
& ! [U_10247,U_10245] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10247)),hAPP(c_Int_Onat,U_10245)) = hAPP(c_Int_Onat,U_10247)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10245)) ) ),
inference(miniscope,[status(thm)],[f_2815_2]) ).
fof(f_2815_4,plain,
( ! [U_10246,U_10248] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10248)),hAPP(c_Int_Onat,U_10246)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10248),U_10246)),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))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10246)) )
& ! [U_10247,U_10245] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10247)),hAPP(c_Int_Onat,U_10245)) = hAPP(c_Int_Onat,U_10247)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10245)) ) ),
inference(definitional_conversion,[status(esa)],[f_2815_3]) ).
cnf(f_2815_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10247)),hAPP(c_Int_Onat,U_10245)) = hAPP(c_Int_Onat,U_10247)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10245)) ),
inference(clausify,[status(thm)],[f_2815_4]) ).
cnf(f_2815_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10248)),hAPP(c_Int_Onat,U_10246)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10248),U_10246)),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))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10246)) ),
inference(clausify,[status(thm)],[f_2815_4]) ).
fof(f_2816_1,plain,
! [V_l,V_k] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod]) ).
fof(f_2816_2,plain,
! [U_10250,U_10249] :
( c_Divides_OnegDivAlg(U_10249,U_10250) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10249),U_10250)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10249,U_10250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10249),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2816_1]) ).
fof(f_2816_3,plain,
! [U_10249,U_10250] :
( c_Divides_OnegDivAlg(U_10249,U_10250) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10249),U_10250)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10249,U_10250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10249),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2816_2]) ).
cnf(f_2816_4,plain,
( c_Divides_OnegDivAlg(U_10249,U_10250) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10249),U_10250)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10249,U_10250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10249),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2816_3]) ).
fof(f_2817_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_negDivAlg__minus1]) ).
fof(f_2817_2,plain,
! [U_10251] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_10251) = 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),U_10251),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_2817_1]) ).
fof(f_2817_3,plain,
! [U_10251] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_10251) = 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),U_10251),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_2817_2]) ).
cnf(f_2817_4,plain,
c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_10251) = 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),U_10251),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_2817_3]) ).
fof(f_2818_1,plain,
! [V_i_2,V_M_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),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)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__less__Suc2]) ).
fof(f_2818_2,plain,
! [U_10253,U_10252] :
( 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)),U_10252))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_10253)))) = 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)),U_10252))),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,U_10253)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10252)) ),
inference(variable_rename,[status(thm)],[f_2818_1]) ).
fof(f_2818_3,plain,
! [U_10252,U_10253] :
( 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)),U_10252))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_10253)))) = 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)),U_10252))),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,U_10253)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10252)) ),
inference(definitional_conversion,[status(esa)],[f_2818_2]) ).
cnf(f_2818_4,plain,
( 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)),U_10252))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_10253)))) = 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)),U_10252))),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,U_10253)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10252)) ),
inference(clausify,[status(thm)],[f_2818_3]) ).
fof(f_2819_1,plain,
! [V_i_2,V_M_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))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__less]) ).
fof(f_2819_2,plain,
! [U_10255,U_10254] :
( 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)),U_10254))),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,U_10255))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10254)) ),
inference(variable_rename,[status(thm)],[f_2819_1]) ).
fof(f_2819_3,plain,
! [U_10254,U_10255] :
( 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)),U_10254))),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,U_10255))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10254)) ),
inference(definitional_conversion,[status(esa)],[f_2819_2]) ).
cnf(f_2819_4,plain,
( 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)),U_10254))),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,U_10255))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10254)) ),
inference(clausify,[status(thm)],[f_2819_3]) ).
fof(f_2820_1,plain,
! [V_i_2,V_M_2] :
( 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)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__less__Suc]) ).
fof(f_2820_2,plain,
! [U_10257,U_10256] :
( 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)),U_10256))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_10257))))) = 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)),U_10256))),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,U_10257)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10256)) ),
inference(variable_rename,[status(thm)],[f_2820_1]) ).
fof(f_2820_3,plain,
! [U_10256,U_10257] :
( 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)),U_10256))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_10257))))) = 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)),U_10256))),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,U_10257)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10256)) ),
inference(definitional_conversion,[status(esa)],[f_2820_2]) ).
cnf(f_2820_4,plain,
( 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)),U_10256))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_10257))))) = 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)),U_10256))),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,U_10257)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10256)) ),
inference(clausify,[status(thm)],[f_2820_3]) ).
fof(f_2821_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_UN__le__eq__Un0]) ).
fof(f_2821_2,plain,
! [U_10260,U_10259,U_10258] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10259)),U_10260) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10258,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10259)),U_10260)),hAPP(U_10260,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2821_1]) ).
fof(f_2821_3,plain,
! [U_10258,U_10259,U_10260] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10259)),U_10260) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10258,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10259)),U_10260)),hAPP(U_10260,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2821_2]) ).
cnf(f_2821_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10259)),U_10260) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10258,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10259)),U_10260)),hAPP(U_10260,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2821_3]) ).
fof(f_2822_1,plain,
! [V_f_2,V_A_2,T_b] :
( 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))
| ~ c_Nat__Transfer_Onat__set(V_A_2)
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J]) ).
fof(f_2822_2,plain,
! [U_10263,U_10262,U_10261] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10261),U_10263),U_10262) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10261),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10261,tc_Nat_Onat),U_10263),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10262))
| ~ c_Nat__Transfer_Onat__set(U_10262)
| ~ class_Groups_Ocomm__monoid__mult(U_10261)
| ~ class_Groups_Ocomm__monoid__add(U_10261) ),
inference(variable_rename,[status(thm)],[f_2822_1]) ).
fof(f_2822_3,plain,
! [U_10261,U_10262,U_10263] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10261),U_10263),U_10262) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10261),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10261,tc_Nat_Onat),U_10263),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10262))
| ~ c_Nat__Transfer_Onat__set(U_10262)
| ~ class_Groups_Ocomm__monoid__mult(U_10261)
| ~ class_Groups_Ocomm__monoid__add(U_10261) ),
inference(definitional_conversion,[status(esa)],[f_2822_2]) ).
cnf(f_2822_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10261),U_10263),U_10262) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10261),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10261,tc_Nat_Onat),U_10263),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10262))
| ~ c_Nat__Transfer_Onat__set(U_10262)
| ~ class_Groups_Ocomm__monoid__mult(U_10261)
| ~ class_Groups_Ocomm__monoid__add(U_10261) ),
inference(clausify,[status(thm)],[f_2822_3]) ).
fof(f_2823_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_adjust__eq]) ).
fof(f_2823_2,plain,
! [U_10266,U_10265,U_10264] : hAPP(c_Divides_Oadjust(U_10264),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10265),U_10266)) = 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),U_10266),U_10264)),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)))),U_10265)),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)))),U_10265)),U_10266))),
inference(variable_rename,[status(thm)],[f_2823_1]) ).
fof(f_2823_3,plain,
! [U_10264,U_10265,U_10266] : hAPP(c_Divides_Oadjust(U_10264),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10265),U_10266)) = 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),U_10266),U_10264)),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)))),U_10265)),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)))),U_10265)),U_10266))),
inference(definitional_conversion,[status(esa)],[f_2823_2]) ).
cnf(f_2823_4,plain,
hAPP(c_Divides_Oadjust(U_10264),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10265),U_10266)) = 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),U_10266),U_10264)),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)))),U_10265)),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)))),U_10265)),U_10266))),
inference(clausify,[status(thm)],[f_2823_3]) ).
fof(f_2824_1,plain,
! [V_Pa_2,V_n_2,V_m_2,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head]) ).
fof(f_2824_2,plain,
! [U_10270,U_10269,U_10268,U_10267] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10267),U_10270),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10268,U_10269)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10267),hAPP(U_10270,U_10268)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10267),U_10270),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10268,U_10269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10268),U_10269))
| ~ class_Groups_Ocomm__monoid__add(U_10267) ),
inference(variable_rename,[status(thm)],[f_2824_1]) ).
fof(f_2824_3,plain,
! [U_10267,U_10268,U_10269,U_10270] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10267),U_10270),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10268,U_10269)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10267),hAPP(U_10270,U_10268)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10267),U_10270),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10268,U_10269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10268),U_10269))
| ~ class_Groups_Ocomm__monoid__add(U_10267) ),
inference(definitional_conversion,[status(esa)],[f_2824_2]) ).
cnf(f_2824_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10267),U_10270),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10268,U_10269)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10267),hAPP(U_10270,U_10268)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10267),U_10270),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10268,U_10269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10268),U_10269))
| ~ class_Groups_Ocomm__monoid__add(U_10267) ),
inference(clausify,[status(thm)],[f_2824_3]) ).
fof(f_2825_1,plain,
! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
( 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)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__cases]) ).
fof(f_2825_2,plain,
! [U_10276,U_10275,U_10274,U_10273,U_10272,U_10271] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),hAPP(hAPP(c_COMBS(U_10272,U_10271,U_10271),hAPP(hAPP(c_COMBS(U_10272,U_10271,tc_fun(U_10271,U_10271)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10271,tc_fun(U_10271,U_10271)),U_10272),c_If(U_10271)),U_10274)),U_10275)),U_10276)),U_10273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10271),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),U_10275),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10272,tc_HOL_Obool)),U_10273),hAPP(c_Set_OCollect(U_10272),U_10274)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),U_10276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10272,tc_HOL_Obool)),U_10273),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10272,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_10272),U_10274)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10272),U_10273))
| ~ class_Groups_Ocomm__monoid__add(U_10271) ),
inference(variable_rename,[status(thm)],[f_2825_1]) ).
fof(f_2825_3,plain,
! [U_10271,U_10272,U_10273,U_10274,U_10275,U_10276] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),hAPP(hAPP(c_COMBS(U_10272,U_10271,U_10271),hAPP(hAPP(c_COMBS(U_10272,U_10271,tc_fun(U_10271,U_10271)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10271,tc_fun(U_10271,U_10271)),U_10272),c_If(U_10271)),U_10274)),U_10275)),U_10276)),U_10273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10271),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),U_10275),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10272,tc_HOL_Obool)),U_10273),hAPP(c_Set_OCollect(U_10272),U_10274)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),U_10276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10272,tc_HOL_Obool)),U_10273),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10272,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_10272),U_10274)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10272),U_10273))
| ~ class_Groups_Ocomm__monoid__add(U_10271) ),
inference(definitional_conversion,[status(esa)],[f_2825_2]) ).
cnf(f_2825_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),hAPP(hAPP(c_COMBS(U_10272,U_10271,U_10271),hAPP(hAPP(c_COMBS(U_10272,U_10271,tc_fun(U_10271,U_10271)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10271,tc_fun(U_10271,U_10271)),U_10272),c_If(U_10271)),U_10274)),U_10275)),U_10276)),U_10273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10271),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),U_10275),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10272,tc_HOL_Obool)),U_10273),hAPP(c_Set_OCollect(U_10272),U_10274)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10272,U_10271),U_10276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10272,tc_HOL_Obool)),U_10273),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10272,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_10272),U_10274)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10272),U_10273))
| ~ class_Groups_Ocomm__monoid__add(U_10271) ),
inference(clausify,[status(thm)],[f_2825_3]) ).
fof(f_2826_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_minus__fold__remove]) ).
fof(f_2826_2,plain,
! [U_10279,U_10278,U_10277] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10277,tc_HOL_Obool)),U_10279),U_10278) = hAPP(hAPP(c_Finite__Set_Ofold(U_10277,tc_fun(U_10277,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10277,tc_HOL_Obool),tc_fun(tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),U_10277),hAPP(c_COMBC(tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10277,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10277,tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),c_Set_Oinsert(U_10277)),c_Orderings_Obot__class_Obot(tc_fun(U_10277,tc_HOL_Obool))))),U_10279),U_10278)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10277),U_10278)) ),
inference(variable_rename,[status(thm)],[f_2826_1]) ).
fof(f_2826_3,plain,
! [U_10278,U_10277,U_10279] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10277,tc_HOL_Obool)),U_10279),U_10278) = hAPP(hAPP(c_Finite__Set_Ofold(U_10277,tc_fun(U_10277,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10277,tc_HOL_Obool),tc_fun(tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),U_10277),hAPP(c_COMBC(tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10277,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10277,tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),c_Set_Oinsert(U_10277)),c_Orderings_Obot__class_Obot(tc_fun(U_10277,tc_HOL_Obool))))),U_10279),U_10278)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10277),U_10278)) ),
inference(definitional_conversion,[status(esa)],[f_2826_2]) ).
cnf(f_2826_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10277,tc_HOL_Obool)),U_10279),U_10278) = hAPP(hAPP(c_Finite__Set_Ofold(U_10277,tc_fun(U_10277,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10277,tc_HOL_Obool),tc_fun(tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),U_10277),hAPP(c_COMBC(tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10277,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10277,tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),c_Set_Oinsert(U_10277)),c_Orderings_Obot__class_Obot(tc_fun(U_10277,tc_HOL_Obool))))),U_10279),U_10278)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10277),U_10278)) ),
inference(clausify,[status(thm)],[f_2826_3]) ).
fof(f_2827_1,plain,
! [V_v_2,V_n_2] :
( ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
| ~ 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))))) )
& ( 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)))))
| hAPP(c_Nat_OSuc,V_n_2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of]) ).
fof(f_2827_2,plain,
! [U_10281,U_10280] :
( ( hAPP(c_Nat_OSuc,U_10280) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10281)
| ~ 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(U_10281))),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)),U_10280))))) )
& ( 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(U_10281))),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)),U_10280)))))
| hAPP(c_Nat_OSuc,U_10280) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10281) ) ),
inference(variable_rename,[status(thm)],[f_2827_1]) ).
fof(f_2827_3,plain,
( ! [U_10285,U_10283] :
( hAPP(c_Nat_OSuc,U_10283) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10285)
| ~ 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(U_10285))),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)),U_10283))))) )
& ! [U_10284,U_10282] :
( 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(U_10284))),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)),U_10282)))))
| hAPP(c_Nat_OSuc,U_10282) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10284) ) ),
inference(miniscope,[status(thm)],[f_2827_2]) ).
fof(f_2827_4,plain,
( ! [U_10283,U_10285] :
( hAPP(c_Nat_OSuc,U_10283) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10285)
| ~ 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(U_10285))),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)),U_10283))))) )
& ! [U_10284,U_10282] :
( 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(U_10284))),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)),U_10282)))))
| hAPP(c_Nat_OSuc,U_10282) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10284) ) ),
inference(definitional_conversion,[status(esa)],[f_2827_3]) ).
cnf(f_2827_5,plain,
( 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(U_10284))),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)),U_10282)))))
| hAPP(c_Nat_OSuc,U_10282) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10284) ),
inference(clausify,[status(thm)],[f_2827_4]) ).
cnf(f_2827_6,plain,
( hAPP(c_Nat_OSuc,U_10283) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10285)
| ~ 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(U_10285))),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)),U_10283))))) ),
inference(clausify,[status(thm)],[f_2827_4]) ).
fof(f_2828_1,plain,
! [V_n_2,V_v_2] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
| ~ 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))))) )
& ( 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)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != hAPP(c_Nat_OSuc,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc]) ).
fof(f_2828_2,plain,
! [U_10287,U_10286] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10286) = hAPP(c_Nat_OSuc,U_10287)
| ~ 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(U_10286))),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)),U_10287))))) )
& ( 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(U_10286))),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)),U_10287)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10286) != hAPP(c_Nat_OSuc,U_10287) ) ),
inference(variable_rename,[status(thm)],[f_2828_1]) ).
fof(f_2828_3,plain,
( ! [U_10291,U_10289] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10289) = hAPP(c_Nat_OSuc,U_10291)
| ~ 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(U_10289))),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)),U_10291))))) )
& ! [U_10290,U_10288] :
( 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(U_10288))),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)),U_10290)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10288) != hAPP(c_Nat_OSuc,U_10290) ) ),
inference(miniscope,[status(thm)],[f_2828_2]) ).
fof(f_2828_4,plain,
( ! [U_10291,U_10289] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10289) = hAPP(c_Nat_OSuc,U_10291)
| ~ 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(U_10289))),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)),U_10291))))) )
& ! [U_10290,U_10288] :
( 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(U_10288))),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)),U_10290)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10288) != hAPP(c_Nat_OSuc,U_10290) ) ),
inference(definitional_conversion,[status(esa)],[f_2828_3]) ).
cnf(f_2828_5,plain,
( 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(U_10288))),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)),U_10290)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10288) != hAPP(c_Nat_OSuc,U_10290) ),
inference(clausify,[status(thm)],[f_2828_4]) ).
cnf(f_2828_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10289) = hAPP(c_Nat_OSuc,U_10291)
| ~ 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(U_10289))),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)),U_10291))))) ),
inference(clausify,[status(thm)],[f_2828_4]) ).
fof(f_2829_1,plain,
! [V_w_2] :
( ( 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))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__Bit1]) ).
fof(f_2829_2,plain,
! [U_10292] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10292)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10292)),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))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10292))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10292)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10292))) ) ),
inference(variable_rename,[status(thm)],[f_2829_1]) ).
fof(f_2829_3,plain,
( ! [U_10294] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10294)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10294)),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))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10294))) )
& ! [U_10293] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10293)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10293))) ) ),
inference(miniscope,[status(thm)],[f_2829_2]) ).
fof(f_2829_4,plain,
( ! [U_10294] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10294)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10294)),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))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10294))) )
& ! [U_10293] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10293)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10293))) ) ),
inference(definitional_conversion,[status(esa)],[f_2829_3]) ).
cnf(f_2829_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10293)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10293))) ),
inference(clausify,[status(thm)],[f_2829_4]) ).
cnf(f_2829_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10294)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10294)),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))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10294))) ),
inference(clausify,[status(thm)],[f_2829_4]) ).
fof(f_2830_1,plain,
! [V_n_2,V_x_2,T_b] :
( 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)))
| V_x_2 = c_Groups_Oone__class_Oone(T_b)
| ~ class_Fields_Ofield(T_b) ),
inference(fof_nnf,[status(thm)],[fact_geometric__sum]) ).
fof(f_2830_2,plain,
! [U_10297,U_10296,U_10295] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10295),hAPP(c_Power_Opower__class_Opower(U_10295),U_10296)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10297)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10295),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10295),hAPP(hAPP(c_Power_Opower__class_Opower(U_10295),U_10296),U_10297)),c_Groups_Oone__class_Oone(U_10295))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10295),U_10296),c_Groups_Oone__class_Oone(U_10295)))
| U_10296 = c_Groups_Oone__class_Oone(U_10295)
| ~ class_Fields_Ofield(U_10295) ),
inference(variable_rename,[status(thm)],[f_2830_1]) ).
fof(f_2830_3,plain,
! [U_10295,U_10296,U_10297] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10295),hAPP(c_Power_Opower__class_Opower(U_10295),U_10296)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10297)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10295),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10295),hAPP(hAPP(c_Power_Opower__class_Opower(U_10295),U_10296),U_10297)),c_Groups_Oone__class_Oone(U_10295))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10295),U_10296),c_Groups_Oone__class_Oone(U_10295)))
| U_10296 = c_Groups_Oone__class_Oone(U_10295)
| ~ class_Fields_Ofield(U_10295) ),
inference(definitional_conversion,[status(esa)],[f_2830_2]) ).
cnf(f_2830_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10295),hAPP(c_Power_Opower__class_Opower(U_10295),U_10296)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10297)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10295),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10295),hAPP(hAPP(c_Power_Opower__class_Opower(U_10295),U_10296),U_10297)),c_Groups_Oone__class_Oone(U_10295))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10295),U_10296),c_Groups_Oone__class_Oone(U_10295)))
| U_10296 = c_Groups_Oone__class_Oone(U_10295)
| ~ class_Fields_Ofield(U_10295) ),
inference(clausify,[status(thm)],[f_2830_3]) ).
fof(f_2831_1,plain,
! [V_n_2,T_b] :
( 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)))
| ~ class_Rings_Ocomm__semiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gauss__sum]) ).
fof(f_2831_2,plain,
! [U_10299,U_10298] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10298),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10298),c_Groups_Oone__class_Oone(U_10298)),c_Groups_Oone__class_Oone(U_10298))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10298),c_Nat_Osemiring__1__class_Oof__nat(U_10298)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10298),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10298),U_10299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10298),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10298),U_10299)),c_Groups_Oone__class_Oone(U_10298)))
| ~ class_Rings_Ocomm__semiring__1(U_10298) ),
inference(variable_rename,[status(thm)],[f_2831_1]) ).
fof(f_2831_3,plain,
! [U_10298,U_10299] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10298),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10298),c_Groups_Oone__class_Oone(U_10298)),c_Groups_Oone__class_Oone(U_10298))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10298),c_Nat_Osemiring__1__class_Oof__nat(U_10298)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10298),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10298),U_10299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10298),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10298),U_10299)),c_Groups_Oone__class_Oone(U_10298)))
| ~ class_Rings_Ocomm__semiring__1(U_10298) ),
inference(definitional_conversion,[status(esa)],[f_2831_2]) ).
cnf(f_2831_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10298),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10298),c_Groups_Oone__class_Oone(U_10298)),c_Groups_Oone__class_Oone(U_10298))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10298),c_Nat_Osemiring__1__class_Oof__nat(U_10298)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10298),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10298),U_10299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10298),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10298),U_10299)),c_Groups_Oone__class_Oone(U_10298)))
| ~ class_Rings_Ocomm__semiring__1(U_10298) ),
inference(clausify,[status(thm)],[f_2831_3]) ).
fof(f_2832_1,plain,
! [V_f_2,V_n_2,V_m_2,T_b] :
( ( ( 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)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
& ( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) )
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__natinterval__difff]) ).
fof(f_2832_2,plain,
! [U_10303,U_10302,U_10301,U_10300] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10300),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10300,U_10300),hAPP(hAPP(c_COMBB(U_10300,tc_fun(U_10300,U_10300),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10300)),U_10303)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10300,tc_Nat_Onat),U_10303),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,U_10301,U_10302)) = c_Groups_Ozero__class_Ozero(U_10300)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10301),U_10302)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10300),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10300,U_10300),hAPP(hAPP(c_COMBB(U_10300,tc_fun(U_10300,U_10300),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10300)),U_10303)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10300,tc_Nat_Onat),U_10303),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,U_10301,U_10302)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10300),hAPP(U_10303,U_10301)),hAPP(U_10303,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10302),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10301),U_10302)) ) )
| ~ class_Groups_Oab__group__add(U_10300) ),
inference(variable_rename,[status(thm)],[f_2832_1]) ).
fof(f_2832_3,plain,
( ! [U_10300,U_10301,U_10302,U_10303] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10300),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10300,U_10300),hAPP(hAPP(c_COMBB(U_10300,tc_fun(U_10300,U_10300),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10300)),U_10303)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10300,tc_Nat_Onat),U_10303),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,U_10301,U_10302)) = c_Groups_Ozero__class_Ozero(U_10300)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10301),U_10302))
| ~ sP803(U_10300,U_10301,U_10302,U_10303) )
& ! [U_10300,U_10301,U_10302,U_10303] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10300),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10300,U_10300),hAPP(hAPP(c_COMBB(U_10300,tc_fun(U_10300,U_10300),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10300)),U_10303)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10300,tc_Nat_Onat),U_10303),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,U_10301,U_10302)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10300),hAPP(U_10303,U_10301)),hAPP(U_10303,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10302),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10301),U_10302))
| ~ sP803(U_10300,U_10301,U_10302,U_10303) )
& ! [U_10300,U_10301,U_10302,U_10303] :
( sP803(U_10300,U_10301,U_10302,U_10303)
| ~ class_Groups_Oab__group__add(U_10300) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP803])],[f_2832_2]) ).
cnf(f_2832_4,plain,
( sP803(U_10300,U_10301,U_10302,U_10303)
| ~ class_Groups_Oab__group__add(U_10300) ),
inference(clausify,[status(thm)],[f_2832_3]) ).
cnf(f_2832_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10300),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10300,U_10300),hAPP(hAPP(c_COMBB(U_10300,tc_fun(U_10300,U_10300),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10300)),U_10303)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10300,tc_Nat_Onat),U_10303),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,U_10301,U_10302)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10300),hAPP(U_10303,U_10301)),hAPP(U_10303,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10302),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10301),U_10302))
| ~ sP803(U_10300,U_10301,U_10302,U_10303) ),
inference(clausify,[status(thm)],[f_2832_3]) ).
cnf(f_2832_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10300),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10300,U_10300),hAPP(hAPP(c_COMBB(U_10300,tc_fun(U_10300,U_10300),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10300)),U_10303)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10300,tc_Nat_Onat),U_10303),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,U_10301,U_10302)) = c_Groups_Ozero__class_Ozero(U_10300)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10301),U_10302))
| ~ sP803(U_10300,U_10301,U_10302,U_10303) ),
inference(clausify,[status(thm)],[f_2832_3]) ).
fof(f_2833_1,plain,
! [V_v_2,V_n_2] :
( ( 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)))
| ~ 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))))) )
& ( 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)))))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of]) ).
fof(f_2833_2,plain,
! [U_10305,U_10304] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10304)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10305)))
| ~ 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(U_10305))),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),U_10304)),c_Int_Onat))))) )
& ( 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(U_10305))),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),U_10304)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10304)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10305))) ) ),
inference(variable_rename,[status(thm)],[f_2833_1]) ).
fof(f_2833_3,plain,
( ! [U_10309,U_10307] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10309)))
| ~ 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(U_10309))),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),U_10307)),c_Int_Onat))))) )
& ! [U_10308,U_10306] :
( 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(U_10308))),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),U_10306)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10306)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10308))) ) ),
inference(miniscope,[status(thm)],[f_2833_2]) ).
fof(f_2833_4,plain,
( ! [U_10309,U_10307] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10309)))
| ~ 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(U_10309))),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),U_10307)),c_Int_Onat))))) )
& ! [U_10306,U_10308] :
( 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(U_10308))),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),U_10306)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10306)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10308))) ) ),
inference(definitional_conversion,[status(esa)],[f_2833_3]) ).
cnf(f_2833_5,plain,
( 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(U_10308))),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),U_10306)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10306)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10308))) ),
inference(clausify,[status(thm)],[f_2833_4]) ).
cnf(f_2833_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10309)))
| ~ 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(U_10309))),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),U_10307)),c_Int_Onat))))) ),
inference(clausify,[status(thm)],[f_2833_4]) ).
fof(f_2834_1,plain,
! [V_n_2,V_v_2] :
( ( 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)))
| ~ 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)))) )
& ( 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))))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc]) ).
fof(f_2834_2,plain,
! [U_10311,U_10310] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10310)),hAPP(c_Nat_OSuc,U_10311)))
| ~ 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(U_10310))),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)),U_10311)))) )
& ( 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(U_10310))),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)),U_10311))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10310)),hAPP(c_Nat_OSuc,U_10311))) ) ),
inference(variable_rename,[status(thm)],[f_2834_1]) ).
fof(f_2834_3,plain,
( ! [U_10315,U_10313] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10313)),hAPP(c_Nat_OSuc,U_10315)))
| ~ 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(U_10313))),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)),U_10315)))) )
& ! [U_10314,U_10312] :
( 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(U_10312))),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)),U_10314))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10312)),hAPP(c_Nat_OSuc,U_10314))) ) ),
inference(miniscope,[status(thm)],[f_2834_2]) ).
fof(f_2834_4,plain,
( ! [U_10315,U_10313] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10313)),hAPP(c_Nat_OSuc,U_10315)))
| ~ 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(U_10313))),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)),U_10315)))) )
& ! [U_10314,U_10312] :
( 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(U_10312))),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)),U_10314))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10312)),hAPP(c_Nat_OSuc,U_10314))) ) ),
inference(definitional_conversion,[status(esa)],[f_2834_3]) ).
cnf(f_2834_5,plain,
( 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(U_10312))),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)),U_10314))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10312)),hAPP(c_Nat_OSuc,U_10314))) ),
inference(clausify,[status(thm)],[f_2834_4]) ).
cnf(f_2834_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10313)),hAPP(c_Nat_OSuc,U_10315)))
| ~ 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(U_10313))),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)),U_10315)))) ),
inference(clausify,[status(thm)],[f_2834_4]) ).
fof(f_2835_1,plain,
! [V_v_2,V_n_2] :
( ( 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)))
| ~ 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))))) )
& ( 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)))))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of]) ).
fof(f_2835_2,plain,
! [U_10317,U_10316] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10316)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10317)))
| ~ 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(U_10317))),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),U_10316)),c_Int_Onat))))) )
& ( 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(U_10317))),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),U_10316)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10316)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10317))) ) ),
inference(variable_rename,[status(thm)],[f_2835_1]) ).
fof(f_2835_3,plain,
( ! [U_10321,U_10319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10321)))
| ~ 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(U_10321))),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),U_10319)),c_Int_Onat))))) )
& ! [U_10320,U_10318] :
( 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(U_10320))),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),U_10318)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10318)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10320))) ) ),
inference(miniscope,[status(thm)],[f_2835_2]) ).
fof(f_2835_4,plain,
( ! [U_10321,U_10319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10321)))
| ~ 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(U_10321))),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),U_10319)),c_Int_Onat))))) )
& ! [U_10320,U_10318] :
( 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(U_10320))),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),U_10318)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10318)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10320))) ) ),
inference(definitional_conversion,[status(esa)],[f_2835_3]) ).
cnf(f_2835_5,plain,
( 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(U_10320))),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),U_10318)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10318)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10320))) ),
inference(clausify,[status(thm)],[f_2835_4]) ).
cnf(f_2835_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10321)))
| ~ 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(U_10321))),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),U_10319)),c_Int_Onat))))) ),
inference(clausify,[status(thm)],[f_2835_4]) ).
fof(f_2836_1,plain,
! [V_n_2,V_v_2] :
( ( 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)))
| ~ 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)))) )
& ( 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))))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc]) ).
fof(f_2836_2,plain,
! [U_10323,U_10322] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10322)),hAPP(c_Nat_OSuc,U_10323)))
| ~ 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(U_10322))),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)),U_10323)))) )
& ( 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(U_10322))),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)),U_10323))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10322)),hAPP(c_Nat_OSuc,U_10323))) ) ),
inference(variable_rename,[status(thm)],[f_2836_1]) ).
fof(f_2836_3,plain,
( ! [U_10327,U_10325] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10325)),hAPP(c_Nat_OSuc,U_10327)))
| ~ 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(U_10325))),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)),U_10327)))) )
& ! [U_10326,U_10324] :
( 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(U_10324))),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)),U_10326))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10324)),hAPP(c_Nat_OSuc,U_10326))) ) ),
inference(miniscope,[status(thm)],[f_2836_2]) ).
fof(f_2836_4,plain,
( ! [U_10327,U_10325] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10325)),hAPP(c_Nat_OSuc,U_10327)))
| ~ 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(U_10325))),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)),U_10327)))) )
& ! [U_10326,U_10324] :
( 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(U_10324))),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)),U_10326))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10324)),hAPP(c_Nat_OSuc,U_10326))) ) ),
inference(definitional_conversion,[status(esa)],[f_2836_3]) ).
cnf(f_2836_5,plain,
( 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(U_10324))),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)),U_10326))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10324)),hAPP(c_Nat_OSuc,U_10326))) ),
inference(clausify,[status(thm)],[f_2836_4]) ).
cnf(f_2836_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10325)),hAPP(c_Nat_OSuc,U_10327)))
| ~ 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(U_10325))),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)),U_10327)))) ),
inference(clausify,[status(thm)],[f_2836_4]) ).
fof(f_2837_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_max__Suc__number__of]) ).
fof(f_2837_2,plain,
! [U_10329,U_10328] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10328)),hAPP(c_Nat_OSuc,U_10329)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10328))),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,U_10329))),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)),U_10329)))),
inference(variable_rename,[status(thm)],[f_2837_1]) ).
fof(f_2837_3,plain,
! [U_10329,U_10328] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10328)),hAPP(c_Nat_OSuc,U_10329)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10328))),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,U_10329))),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)),U_10329)))),
inference(definitional_conversion,[status(esa)],[f_2837_2]) ).
cnf(f_2837_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10328)),hAPP(c_Nat_OSuc,U_10329)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10328))),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,U_10329))),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)),U_10329)))),
inference(clausify,[status(thm)],[f_2837_3]) ).
fof(f_2838_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_max__number__of__Suc]) ).
fof(f_2838_2,plain,
! [U_10331,U_10330] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10330)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10331)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10331))),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,U_10330))),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),U_10330)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2838_1]) ).
fof(f_2838_3,plain,
! [U_10330,U_10331] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10330)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10331)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10331))),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,U_10330))),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),U_10330)),c_Int_Onat)))),
inference(definitional_conversion,[status(esa)],[f_2838_2]) ).
cnf(f_2838_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10330)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10331)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10331))),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,U_10330))),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),U_10330)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2838_3]) ).
fof(f_2839_1,plain,
! [V_z_2,V_w_2,T_b] :
( ( ( 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)
| 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))) )
& ( 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)))
| ~ 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))) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__odd]) ).
fof(f_2839_2,plain,
! [U_10334,U_10333,U_10332] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10333))) = c_Groups_Oone__class_Oone(U_10332)
| 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),U_10333))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10333))) = hAPP(hAPP(c_HOL_OLet(U_10332,U_10332),hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10333))),hAPP(hAPP(c_COMBS(U_10332,U_10332,U_10332),hAPP(hAPP(c_COMBB(U_10332,tc_fun(U_10332,U_10332),U_10332),c_Groups_Otimes__class_Otimes(U_10332)),hAPP(c_Groups_Otimes__class_Otimes(U_10332),U_10334))),c_COMBI(U_10332)))
| ~ 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),U_10333))) ) )
| ~ class_Int_Onumber__ring(U_10332) ),
inference(variable_rename,[status(thm)],[f_2839_1]) ).
fof(f_2839_3,plain,
( ! [U_10332,U_10333,U_10334] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10333))) = c_Groups_Oone__class_Oone(U_10332)
| 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),U_10333)))
| ~ sP804(U_10332,U_10333,U_10334) )
& ! [U_10332,U_10333,U_10334] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10333))) = hAPP(hAPP(c_HOL_OLet(U_10332,U_10332),hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10333))),hAPP(hAPP(c_COMBS(U_10332,U_10332,U_10332),hAPP(hAPP(c_COMBB(U_10332,tc_fun(U_10332,U_10332),U_10332),c_Groups_Otimes__class_Otimes(U_10332)),hAPP(c_Groups_Otimes__class_Otimes(U_10332),U_10334))),c_COMBI(U_10332)))
| ~ 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),U_10333)))
| ~ sP804(U_10332,U_10333,U_10334) )
& ! [U_10332,U_10333,U_10334] :
( sP804(U_10332,U_10333,U_10334)
| ~ class_Int_Onumber__ring(U_10332) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP804])],[f_2839_2]) ).
cnf(f_2839_4,plain,
( sP804(U_10332,U_10333,U_10334)
| ~ class_Int_Onumber__ring(U_10332) ),
inference(clausify,[status(thm)],[f_2839_3]) ).
cnf(f_2839_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10333))) = hAPP(hAPP(c_HOL_OLet(U_10332,U_10332),hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10333))),hAPP(hAPP(c_COMBS(U_10332,U_10332,U_10332),hAPP(hAPP(c_COMBB(U_10332,tc_fun(U_10332,U_10332),U_10332),c_Groups_Otimes__class_Otimes(U_10332)),hAPP(c_Groups_Otimes__class_Otimes(U_10332),U_10334))),c_COMBI(U_10332)))
| ~ 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),U_10333)))
| ~ sP804(U_10332,U_10333,U_10334) ),
inference(clausify,[status(thm)],[f_2839_3]) ).
cnf(f_2839_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10332),U_10334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10333))) = c_Groups_Oone__class_Oone(U_10332)
| 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),U_10333)))
| ~ sP804(U_10332,U_10333,U_10334) ),
inference(clausify,[status(thm)],[f_2839_3]) ).
fof(f_2840_1,plain,
! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( 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_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( 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_ca_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_ca_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))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__gen__delta]) ).
fof(f_2840_2,plain,
! [U_10340,U_10339,U_10338,U_10337,U_10336,U_10335] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10336,U_10335),hAPP(hAPP(c_COMBC(U_10336,U_10335,U_10335),hAPP(hAPP(c_COMBS(U_10336,U_10335,tc_fun(U_10335,U_10335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10335,tc_fun(U_10335,U_10335)),U_10336),c_If(U_10335)),hAPP(hAPP(c_COMBC(U_10336,U_10336,tc_HOL_Obool),c_fequal),U_10338))),U_10339)),U_10340)),U_10337) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10335),U_10340),hAPP(c_Finite__Set_Ocard(U_10336),U_10337))
| hBOOL(hAPP(hAPP(c_member(U_10336),U_10338),U_10337)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10336,U_10335),hAPP(hAPP(c_COMBC(U_10336,U_10335,U_10335),hAPP(hAPP(c_COMBS(U_10336,U_10335,tc_fun(U_10335,U_10335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10335,tc_fun(U_10335,U_10335)),U_10336),c_If(U_10335)),hAPP(hAPP(c_COMBC(U_10336,U_10336,tc_HOL_Obool),c_fequal),U_10338))),U_10339)),U_10340)),U_10337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10335),hAPP(U_10339,U_10338)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10335),U_10340),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10336),U_10337)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10336),U_10338),U_10337)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10336),U_10337))
| ~ class_Groups_Ocomm__monoid__mult(U_10335) ),
inference(variable_rename,[status(thm)],[f_2840_1]) ).
fof(f_2840_3,plain,
( ! [U_10335,U_10336,U_10337,U_10338,U_10339,U_10340] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10336,U_10335),hAPP(hAPP(c_COMBC(U_10336,U_10335,U_10335),hAPP(hAPP(c_COMBS(U_10336,U_10335,tc_fun(U_10335,U_10335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10335,tc_fun(U_10335,U_10335)),U_10336),c_If(U_10335)),hAPP(hAPP(c_COMBC(U_10336,U_10336,tc_HOL_Obool),c_fequal),U_10338))),U_10339)),U_10340)),U_10337) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10335),U_10340),hAPP(c_Finite__Set_Ocard(U_10336),U_10337))
| hBOOL(hAPP(hAPP(c_member(U_10336),U_10338),U_10337))
| ~ sP805(U_10335,U_10336,U_10337,U_10338,U_10339,U_10340) )
& ! [U_10335,U_10336,U_10337,U_10338,U_10339,U_10340] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10336,U_10335),hAPP(hAPP(c_COMBC(U_10336,U_10335,U_10335),hAPP(hAPP(c_COMBS(U_10336,U_10335,tc_fun(U_10335,U_10335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10335,tc_fun(U_10335,U_10335)),U_10336),c_If(U_10335)),hAPP(hAPP(c_COMBC(U_10336,U_10336,tc_HOL_Obool),c_fequal),U_10338))),U_10339)),U_10340)),U_10337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10335),hAPP(U_10339,U_10338)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10335),U_10340),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10336),U_10337)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10336),U_10338),U_10337))
| ~ sP805(U_10335,U_10336,U_10337,U_10338,U_10339,U_10340) )
& ! [U_10335,U_10336,U_10337,U_10338,U_10339,U_10340] :
( sP805(U_10335,U_10336,U_10337,U_10338,U_10339,U_10340)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10336),U_10337))
| ~ class_Groups_Ocomm__monoid__mult(U_10335) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP805])],[f_2840_2]) ).
cnf(f_2840_4,plain,
( sP805(U_10335,U_10336,U_10337,U_10338,U_10339,U_10340)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10336),U_10337))
| ~ class_Groups_Ocomm__monoid__mult(U_10335) ),
inference(clausify,[status(thm)],[f_2840_3]) ).
cnf(f_2840_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10336,U_10335),hAPP(hAPP(c_COMBC(U_10336,U_10335,U_10335),hAPP(hAPP(c_COMBS(U_10336,U_10335,tc_fun(U_10335,U_10335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10335,tc_fun(U_10335,U_10335)),U_10336),c_If(U_10335)),hAPP(hAPP(c_COMBC(U_10336,U_10336,tc_HOL_Obool),c_fequal),U_10338))),U_10339)),U_10340)),U_10337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10335),hAPP(U_10339,U_10338)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10335),U_10340),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10336),U_10337)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10336),U_10338),U_10337))
| ~ sP805(U_10335,U_10336,U_10337,U_10338,U_10339,U_10340) ),
inference(clausify,[status(thm)],[f_2840_3]) ).
cnf(f_2840_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10336,U_10335),hAPP(hAPP(c_COMBC(U_10336,U_10335,U_10335),hAPP(hAPP(c_COMBS(U_10336,U_10335,tc_fun(U_10335,U_10335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10335,tc_fun(U_10335,U_10335)),U_10336),c_If(U_10335)),hAPP(hAPP(c_COMBC(U_10336,U_10336,tc_HOL_Obool),c_fequal),U_10338))),U_10339)),U_10340)),U_10337) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10335),U_10340),hAPP(c_Finite__Set_Ocard(U_10336),U_10337))
| hBOOL(hAPP(hAPP(c_member(U_10336),U_10338),U_10337))
| ~ sP805(U_10335,U_10336,U_10337,U_10338,U_10339,U_10340) ),
inference(clausify,[status(thm)],[f_2840_3]) ).
fof(f_2841_1,plain,
! [V_x_2,V_y_2,V_ca_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_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_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_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_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_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_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_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat]) ).
fof(f_2841_2,plain,
! [U_10343,U_10342,U_10341] :
( ( ( ( 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)),U_10341)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10343),U_10342)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10343),U_10342)) )
& ( 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)),U_10341)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10343),U_10342)) = 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10343),U_10342)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10341),U_10342)) )
& ( 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)),U_10341)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10343),U_10342)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10343),U_10341)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10342),U_10341))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10341),U_10342)) ) ),
inference(variable_rename,[status(thm)],[f_2841_1]) ).
fof(f_2841_3,plain,
( ! [U_10349,U_10347,U_10345] :
( ( ( 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)),U_10345)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10349),U_10347)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10349),U_10347)) )
& ( 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)),U_10345)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10349),U_10347)) = 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10349),U_10347)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10345),U_10347)) )
& ! [U_10348,U_10346,U_10344] :
( 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)),U_10344)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10348),U_10346)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10348),U_10344)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10346),U_10344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10344),U_10346)) ) ),
inference(miniscope,[status(thm)],[f_2841_2]) ).
fof(f_2841_4,plain,
( ! [U_10349,U_10345,U_10347] :
( 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)),U_10345)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10349),U_10347)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10349),U_10347))
| ~ sP806(U_10349,U_10345,U_10347) )
& ! [U_10349,U_10345,U_10347] :
( 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)),U_10345)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10349),U_10347)) = 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10349),U_10347))
| ~ sP806(U_10349,U_10345,U_10347) )
& ! [U_10349,U_10345,U_10347] :
( sP806(U_10349,U_10345,U_10347)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10345),U_10347)) )
& ! [U_10344,U_10348,U_10346] :
( 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)),U_10344)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10348),U_10346)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10348),U_10344)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10346),U_10344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10344),U_10346)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP806])],[f_2841_3]) ).
cnf(f_2841_5,plain,
( 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)),U_10344)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10348),U_10346)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10348),U_10344)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10346),U_10344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10344),U_10346)) ),
inference(clausify,[status(thm)],[f_2841_4]) ).
cnf(f_2841_6,plain,
( sP806(U_10349,U_10345,U_10347)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10345),U_10347)) ),
inference(clausify,[status(thm)],[f_2841_4]) ).
cnf(f_2841_7,plain,
( 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)),U_10345)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10349),U_10347)) = 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10349),U_10347))
| ~ sP806(U_10349,U_10345,U_10347) ),
inference(clausify,[status(thm)],[f_2841_4]) ).
cnf(f_2841_8,plain,
( 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)),U_10345)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10349),U_10347)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10349),U_10347))
| ~ sP806(U_10349,U_10345,U_10347) ),
inference(clausify,[status(thm)],[f_2841_4]) ).
fof(f_2842_1,plain,
! [V_z_2,V_w_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_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| 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))) )
& ( 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)))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_zpower__number__of__odd]) ).
fof(f_2842_2,plain,
! [U_10351,U_10350] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10351),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10350))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| 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),U_10350))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10351),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10350))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10351),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10350))),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),U_10351))),c_COMBI(tc_Int_Oint)))
| ~ 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),U_10350))) ) ),
inference(variable_rename,[status(thm)],[f_2842_1]) ).
fof(f_2842_3,plain,
( ! [U_10355,U_10353] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10355),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10353))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| 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),U_10353))) )
& ! [U_10354,U_10352] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10354),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10352))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10354),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10352))),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),U_10354))),c_COMBI(tc_Int_Oint)))
| ~ 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),U_10352))) ) ),
inference(miniscope,[status(thm)],[f_2842_2]) ).
fof(f_2842_4,plain,
( ! [U_10353,U_10355] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10355),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10353))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| 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),U_10353))) )
& ! [U_10352,U_10354] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10354),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10352))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10354),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10352))),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),U_10354))),c_COMBI(tc_Int_Oint)))
| ~ 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),U_10352))) ) ),
inference(definitional_conversion,[status(esa)],[f_2842_3]) ).
cnf(f_2842_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10354),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10352))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10354),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10352))),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),U_10354))),c_COMBI(tc_Int_Oint)))
| ~ 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),U_10352))) ),
inference(clausify,[status(thm)],[f_2842_4]) ).
cnf(f_2842_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10355),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10353))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| 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),U_10353))) ),
inference(clausify,[status(thm)],[f_2842_4]) ).
fof(f_2843_1,plain,
! [V_n_2,V_d_2,V_a_2,T_b] :
( 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))))
| ~ class_Rings_Ocomm__semiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_arith__series__general]) ).
fof(f_2843_2,plain,
! [U_10359,U_10358,U_10357,U_10356] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),c_Groups_Oone__class_Oone(U_10356)),c_Groups_Oone__class_Oone(U_10356))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10356),hAPP(hAPP(c_COMBB(U_10356,U_10356,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_10356,U_10356),hAPP(hAPP(c_COMBB(U_10356,tc_fun(U_10356,U_10356),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_10356)),c_Nat_Osemiring__1__class_Oof__nat(U_10356))),U_10358))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10359))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10356),U_10359)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10356),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10359),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10358))))
| ~ class_Rings_Ocomm__semiring__1(U_10356) ),
inference(variable_rename,[status(thm)],[f_2843_1]) ).
fof(f_2843_3,plain,
! [U_10356,U_10357,U_10358,U_10359] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),c_Groups_Oone__class_Oone(U_10356)),c_Groups_Oone__class_Oone(U_10356))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10356),hAPP(hAPP(c_COMBB(U_10356,U_10356,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_10356,U_10356),hAPP(hAPP(c_COMBB(U_10356,tc_fun(U_10356,U_10356),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_10356)),c_Nat_Osemiring__1__class_Oof__nat(U_10356))),U_10358))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10359))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10356),U_10359)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10356),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10359),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10358))))
| ~ class_Rings_Ocomm__semiring__1(U_10356) ),
inference(definitional_conversion,[status(esa)],[f_2843_2]) ).
cnf(f_2843_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),c_Groups_Oone__class_Oone(U_10356)),c_Groups_Oone__class_Oone(U_10356))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10356),hAPP(hAPP(c_COMBB(U_10356,U_10356,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_10356,U_10356),hAPP(hAPP(c_COMBB(U_10356,tc_fun(U_10356,U_10356),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_10356)),c_Nat_Osemiring__1__class_Oof__nat(U_10356))),U_10358))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10359))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10356),U_10359)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10356),U_10357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10356),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10356),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10359),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10358))))
| ~ class_Rings_Ocomm__semiring__1(U_10356) ),
inference(clausify,[status(thm)],[f_2843_3]) ).
fof(f_2844_1,plain,
! [V_b,V_a] :
( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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))) )
& ( 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))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ 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))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps]) ).
fof(f_2844_2,plain,
! [U_10361,U_10360] :
( ( c_Divides_OnegDivAlg(U_10360,U_10361) = hAPP(c_Divides_Oadjust(U_10361),c_Divides_OnegDivAlg(U_10360,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)))),U_10361)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10361),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),U_10360),U_10361))) )
& ( c_Divides_OnegDivAlg(U_10360,U_10361) = 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),U_10360),U_10361))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10361),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ 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),U_10360),U_10361))) ) ) ),
inference(variable_rename,[status(thm)],[f_2844_1]) ).
fof(f_2844_3,plain,
( ! [U_10365,U_10363] :
( c_Divides_OnegDivAlg(U_10363,U_10365) = hAPP(c_Divides_Oadjust(U_10365),c_Divides_OnegDivAlg(U_10363,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)))),U_10365)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10365),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),U_10363),U_10365))) )
& ! [U_10364,U_10362] :
( c_Divides_OnegDivAlg(U_10362,U_10364) = 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),U_10362),U_10364))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10364),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ 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),U_10362),U_10364))) ) ) ),
inference(miniscope,[status(thm)],[f_2844_2]) ).
fof(f_2844_4,plain,
( ! [U_10364,U_10362] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10364),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP807(U_10364,U_10362) )
& ! [U_10364,U_10362] :
( ~ 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),U_10362),U_10364)))
| ~ sP807(U_10364,U_10362) )
& ! [U_10365,U_10363] :
( c_Divides_OnegDivAlg(U_10363,U_10365) = hAPP(c_Divides_Oadjust(U_10365),c_Divides_OnegDivAlg(U_10363,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)))),U_10365)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10365),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),U_10363),U_10365))) )
& ! [U_10364,U_10362] :
( c_Divides_OnegDivAlg(U_10362,U_10364) = 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),U_10362),U_10364))
| sP807(U_10364,U_10362) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP807])],[f_2844_3]) ).
cnf(f_2844_5,plain,
( c_Divides_OnegDivAlg(U_10362,U_10364) = 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),U_10362),U_10364))
| sP807(U_10364,U_10362) ),
inference(clausify,[status(thm)],[f_2844_4]) ).
cnf(f_2844_6,plain,
( c_Divides_OnegDivAlg(U_10363,U_10365) = hAPP(c_Divides_Oadjust(U_10365),c_Divides_OnegDivAlg(U_10363,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)))),U_10365)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10365),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),U_10363),U_10365))) ),
inference(clausify,[status(thm)],[f_2844_4]) ).
cnf(f_2844_7,plain,
( ~ 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),U_10362),U_10364)))
| ~ sP807(U_10364,U_10362) ),
inference(clausify,[status(thm)],[f_2844_4]) ).
cnf(f_2844_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10364),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP807(U_10364,U_10362) ),
inference(clausify,[status(thm)],[f_2844_4]) ).
fof(f_2845_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_min__number__of__Suc]) ).
fof(f_2845_2,plain,
! [U_10367,U_10366] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10367)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10367))),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),U_10366)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2845_1]) ).
fof(f_2845_3,plain,
! [U_10367,U_10366] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10367)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10367))),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),U_10366)),c_Int_Onat)))),
inference(definitional_conversion,[status(esa)],[f_2845_2]) ).
cnf(f_2845_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10367)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10367))),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),U_10366)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2845_3]) ).
fof(f_2846_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_min__Suc__number__of]) ).
fof(f_2846_2,plain,
! [U_10369,U_10368] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10368)),hAPP(c_Nat_OSuc,U_10369)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10368))),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)),U_10369)))),
inference(variable_rename,[status(thm)],[f_2846_1]) ).
fof(f_2846_3,plain,
! [U_10368,U_10369] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10368)),hAPP(c_Nat_OSuc,U_10369)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10368))),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)),U_10369)))),
inference(definitional_conversion,[status(esa)],[f_2846_2]) ).
cnf(f_2846_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10368)),hAPP(c_Nat_OSuc,U_10369)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10368))),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)),U_10369)))),
inference(clausify,[status(thm)],[f_2846_3]) ).
fof(f_2847_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_arith__series__nat]) ).
fof(f_2847_2,plain,
! [U_10372,U_10371,U_10370] : 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),U_10370)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_10371))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10372))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10372),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10372),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_10371)))),
inference(variable_rename,[status(thm)],[f_2847_1]) ).
fof(f_2847_3,plain,
! [U_10372,U_10370,U_10371] : 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),U_10370)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_10371))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10372))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10372),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10372),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_10371)))),
inference(definitional_conversion,[status(esa)],[f_2847_2]) ).
cnf(f_2847_4,plain,
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),U_10370)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_10371))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10372))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10372),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10372),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_10371)))),
inference(clausify,[status(thm)],[f_2847_3]) ).
fof(f_2848_1,plain,
! [V_v_2,V_w_2,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),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)
| 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))) )
& ( 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)))
| ~ 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))) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__odd__number__of]) ).
fof(f_2848_2,plain,
! [U_10375,U_10374,U_10373] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10374))) = c_Groups_Oone__class_Oone(U_10373)
| 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),U_10374))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10374))) = hAPP(hAPP(c_HOL_OLet(U_10373,U_10373),hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10374))),hAPP(hAPP(c_COMBS(U_10373,U_10373,U_10373),hAPP(hAPP(c_COMBB(U_10373,tc_fun(U_10373,U_10373),U_10373),c_Groups_Otimes__class_Otimes(U_10373)),hAPP(c_Groups_Otimes__class_Otimes(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)))),c_COMBI(U_10373)))
| ~ 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),U_10374))) ) )
| ~ class_Int_Onumber__ring(U_10373) ),
inference(variable_rename,[status(thm)],[f_2848_1]) ).
fof(f_2848_3,plain,
( ! [U_10373,U_10374,U_10375] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10374))) = c_Groups_Oone__class_Oone(U_10373)
| 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),U_10374)))
| ~ sP808(U_10373,U_10374,U_10375) )
& ! [U_10373,U_10374,U_10375] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10374))) = hAPP(hAPP(c_HOL_OLet(U_10373,U_10373),hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10374))),hAPP(hAPP(c_COMBS(U_10373,U_10373,U_10373),hAPP(hAPP(c_COMBB(U_10373,tc_fun(U_10373,U_10373),U_10373),c_Groups_Otimes__class_Otimes(U_10373)),hAPP(c_Groups_Otimes__class_Otimes(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)))),c_COMBI(U_10373)))
| ~ 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),U_10374)))
| ~ sP808(U_10373,U_10374,U_10375) )
& ! [U_10373,U_10374,U_10375] :
( sP808(U_10373,U_10374,U_10375)
| ~ class_Int_Onumber__ring(U_10373) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP808])],[f_2848_2]) ).
cnf(f_2848_4,plain,
( sP808(U_10373,U_10374,U_10375)
| ~ class_Int_Onumber__ring(U_10373) ),
inference(clausify,[status(thm)],[f_2848_3]) ).
cnf(f_2848_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10374))) = hAPP(hAPP(c_HOL_OLet(U_10373,U_10373),hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10374))),hAPP(hAPP(c_COMBS(U_10373,U_10373,U_10373),hAPP(hAPP(c_COMBB(U_10373,tc_fun(U_10373,U_10373),U_10373),c_Groups_Otimes__class_Otimes(U_10373)),hAPP(c_Groups_Otimes__class_Otimes(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)))),c_COMBI(U_10373)))
| ~ 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),U_10374)))
| ~ sP808(U_10373,U_10374,U_10375) ),
inference(clausify,[status(thm)],[f_2848_3]) ).
cnf(f_2848_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10373),hAPP(c_Int_Onumber__class_Onumber__of(U_10373),U_10375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10374))) = c_Groups_Oone__class_Oone(U_10373)
| 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),U_10374)))
| ~ sP808(U_10373,U_10374,U_10375) ),
inference(clausify,[status(thm)],[f_2848_3]) ).
fof(f_2849_1,plain,
! [V_w,V_v] :
( ( ( 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))))
| 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)))) )
& ( 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)))
| ~ 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)))) ) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn__number__of]) ).
fof(f_2849_2,plain,
! [U_10377,U_10376] :
( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),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),U_10376))))
| 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)))) )
& ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)) = 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)))
| ~ 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)))) ) )
| ~ 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),U_10376))) ),
inference(variable_rename,[status(thm)],[f_2849_1]) ).
fof(f_2849_3,plain,
( ! [U_10376,U_10377] :
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),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),U_10376))))
| 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376))))
| ~ sP809(U_10376,U_10377) )
& ! [U_10376,U_10377] :
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)) = 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)))
| ~ 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376))))
| ~ sP809(U_10376,U_10377) )
& ! [U_10376,U_10377] :
( sP809(U_10376,U_10377)
| ~ 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),U_10376))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP809])],[f_2849_2]) ).
cnf(f_2849_4,plain,
( sP809(U_10376,U_10377)
| ~ 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),U_10376))) ),
inference(clausify,[status(thm)],[f_2849_3]) ).
cnf(f_2849_5,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)) = 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)))
| ~ 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376))))
| ~ sP809(U_10376,U_10377) ),
inference(clausify,[status(thm)],[f_2849_3]) ).
cnf(f_2849_6,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377),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),U_10376))))
| 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),U_10377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376))))
| ~ sP809(U_10376,U_10377) ),
inference(clausify,[status(thm)],[f_2849_3]) ).
fof(f_2850_1,plain,
! [V_a,V_b] :
( ( ( 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)))
| 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))) )
& ( 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))
| ~ 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))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn]) ).
fof(f_2850_2,plain,
! [U_10379,U_10378] :
( ( ( c_Divides_OnegDivAlg(U_10379,U_10378) = hAPP(c_Divides_Oadjust(U_10378),c_Divides_OnegDivAlg(U_10379,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)))),U_10378)))
| 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),U_10379),U_10378))) )
& ( c_Divides_OnegDivAlg(U_10379,U_10378) = 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),U_10379),U_10378))
| ~ 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),U_10379),U_10378))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10378)) ),
inference(variable_rename,[status(thm)],[f_2850_1]) ).
fof(f_2850_3,plain,
( ! [U_10378,U_10379] :
( c_Divides_OnegDivAlg(U_10379,U_10378) = hAPP(c_Divides_Oadjust(U_10378),c_Divides_OnegDivAlg(U_10379,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)))),U_10378)))
| 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),U_10379),U_10378)))
| ~ sP810(U_10378,U_10379) )
& ! [U_10378,U_10379] :
( c_Divides_OnegDivAlg(U_10379,U_10378) = 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),U_10379),U_10378))
| ~ 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),U_10379),U_10378)))
| ~ sP810(U_10378,U_10379) )
& ! [U_10378,U_10379] :
( sP810(U_10378,U_10379)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10378)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP810])],[f_2850_2]) ).
cnf(f_2850_4,plain,
( sP810(U_10378,U_10379)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10378)) ),
inference(clausify,[status(thm)],[f_2850_3]) ).
cnf(f_2850_5,plain,
( c_Divides_OnegDivAlg(U_10379,U_10378) = 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),U_10379),U_10378))
| ~ 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),U_10379),U_10378)))
| ~ sP810(U_10378,U_10379) ),
inference(clausify,[status(thm)],[f_2850_3]) ).
cnf(f_2850_6,plain,
( c_Divides_OnegDivAlg(U_10379,U_10378) = hAPP(c_Divides_Oadjust(U_10378),c_Divides_OnegDivAlg(U_10379,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)))),U_10378)))
| 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),U_10379),U_10378)))
| ~ sP810(U_10378,U_10379) ),
inference(clausify,[status(thm)],[f_2850_3]) ).
fof(f_2851_1,plain,
! [V_v_2,V_v_H_2] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__nat__number__of]) ).
fof(f_2851_2,plain,
! [U_10381,U_10380] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10381)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10380)) = 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),U_10381),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10380)))),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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10380),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10381)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10380)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10381)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10380),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2851_1]) ).
fof(f_2851_3,plain,
( ! [U_10385,U_10383] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10383)) = 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),U_10385),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10383)))),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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10383),c_Int_OPls)) )
& ! [U_10384,U_10382] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10384)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10382)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10384)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10382),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2851_2]) ).
fof(f_2851_4,plain,
( ! [U_10383,U_10385] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10383)) = 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),U_10385),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10383)))),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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10383),c_Int_OPls)) )
& ! [U_10382,U_10384] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10384)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10382)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10384)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10382),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2851_3]) ).
cnf(f_2851_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10384)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10382)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10384)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10382),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2851_4]) ).
cnf(f_2851_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10383)) = 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),U_10385),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10383)))),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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10383),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2851_4]) ).
fof(f_2852_1,plain,
! [V_a_2,V_b_2] :
( ( ( ( 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)))
| V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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))
| ( V_b_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& V_a_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_norm__frac_Osimps]) ).
fof(f_2852_2,plain,
! [U_10387,U_10386] :
( ( ( ( c_Nitpick_Onorm__frac(U_10387,U_10386) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10387),U_10386)),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),U_10387))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10386)))
| U_10386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10387 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_10387,U_10386) = 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))
| ( U_10386 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_10387 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10386),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(U_10387,U_10386) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10387),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10386))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10386),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2852_1]) ).
fof(f_2852_3,plain,
( ! [U_10391,U_10389] :
( ( ( c_Nitpick_Onorm__frac(U_10391,U_10389) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10391),U_10389)),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),U_10391))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10389)))
| U_10389 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10391 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_10391,U_10389) = 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))
| ( U_10389 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_10391 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10389),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10390,U_10388] :
( c_Nitpick_Onorm__frac(U_10390,U_10388) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10390),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10388))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10388),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2852_2]) ).
fof(f_2852_4,plain,
( ! [U_10391,U_10389] :
( U_10389 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP811(U_10391,U_10389) )
& ! [U_10391,U_10389] :
( U_10391 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP811(U_10391,U_10389) )
& ! [U_10391,U_10389] :
( c_Nitpick_Onorm__frac(U_10391,U_10389) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10391),U_10389)),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),U_10391))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10389)))
| U_10389 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10391 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP812(U_10391,U_10389) )
& ! [U_10391,U_10389] :
( c_Nitpick_Onorm__frac(U_10391,U_10389) = 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))
| sP811(U_10391,U_10389)
| ~ sP812(U_10391,U_10389) )
& ! [U_10391,U_10389] :
( sP812(U_10391,U_10389)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10389),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10390,U_10388] :
( c_Nitpick_Onorm__frac(U_10390,U_10388) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10390),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10388))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10388),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP811,sP812])],[f_2852_3]) ).
cnf(f_2852_5,plain,
( c_Nitpick_Onorm__frac(U_10390,U_10388) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10390),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10388))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10388),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2852_4]) ).
cnf(f_2852_6,plain,
( sP812(U_10391,U_10389)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10389),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2852_4]) ).
cnf(f_2852_7,plain,
( c_Nitpick_Onorm__frac(U_10391,U_10389) = 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))
| sP811(U_10391,U_10389)
| ~ sP812(U_10391,U_10389) ),
inference(clausify,[status(thm)],[f_2852_4]) ).
cnf(f_2852_8,plain,
( c_Nitpick_Onorm__frac(U_10391,U_10389) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10391),U_10389)),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),U_10391))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10389)))
| U_10389 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10391 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP812(U_10391,U_10389) ),
inference(clausify,[status(thm)],[f_2852_4]) ).
cnf(f_2852_9,plain,
( U_10391 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP811(U_10391,U_10389) ),
inference(clausify,[status(thm)],[f_2852_4]) ).
cnf(f_2852_10,plain,
( U_10389 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP811(U_10391,U_10389) ),
inference(clausify,[status(thm)],[f_2852_4]) ).
fof(f_2853_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_nat__case__add__eq__if]) ).
fof(f_2853_2,plain,
! [U_10396,U_10395,U_10394,U_10393,U_10392] : c_Nat_Onat_Onat__case(U_10392,U_10393,U_10394,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10395)),U_10396)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10392),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10395))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10392,U_10392),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10392,tc_fun(U_10392,U_10392)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10392,tc_fun(U_10392,U_10392)),tc_Int_Oint),c_If(U_10392)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10392,U_10393,U_10394,U_10396))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10392,tc_Int_Oint),U_10394),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)),U_10396)))),
inference(variable_rename,[status(thm)],[f_2853_1]) ).
fof(f_2853_3,plain,
! [U_10394,U_10393,U_10392,U_10395,U_10396] : c_Nat_Onat_Onat__case(U_10392,U_10393,U_10394,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10395)),U_10396)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10392),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10395))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10392,U_10392),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10392,tc_fun(U_10392,U_10392)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10392,tc_fun(U_10392,U_10392)),tc_Int_Oint),c_If(U_10392)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10392,U_10393,U_10394,U_10396))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10392,tc_Int_Oint),U_10394),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)),U_10396)))),
inference(definitional_conversion,[status(esa)],[f_2853_2]) ).
cnf(f_2853_4,plain,
c_Nat_Onat_Onat__case(U_10392,U_10393,U_10394,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10395)),U_10396)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10392),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10395))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10392,U_10392),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10392,tc_fun(U_10392,U_10392)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10392,tc_fun(U_10392,U_10392)),tc_Int_Oint),c_If(U_10392)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10392,U_10393,U_10394,U_10396))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10392,tc_Int_Oint),U_10394),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)),U_10396)))),
inference(clausify,[status(thm)],[f_2853_3]) ).
fof(f_2854_1,plain,
! [V_w] :
( ( ( 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))))
| 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))) )
& ( 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))
| ~ 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))) ) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).
fof(f_2854_2,plain,
! [U_10397] :
( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)),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),U_10397))))
| 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),U_10397))) )
& ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)) = 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))
| ~ 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),U_10397))) ) )
| ~ 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),U_10397))) ),
inference(variable_rename,[status(thm)],[f_2854_1]) ).
fof(f_2854_3,plain,
( ! [U_10397] :
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)),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),U_10397))))
| 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),U_10397)))
| ~ sP813(U_10397) )
& ! [U_10397] :
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)) = 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))
| ~ 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),U_10397)))
| ~ sP813(U_10397) )
& ! [U_10397] :
( sP813(U_10397)
| ~ 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),U_10397))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP813])],[f_2854_2]) ).
cnf(f_2854_4,plain,
( sP813(U_10397)
| ~ 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),U_10397))) ),
inference(clausify,[status(thm)],[f_2854_3]) ).
cnf(f_2854_5,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)) = 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))
| ~ 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),U_10397)))
| ~ sP813(U_10397) ),
inference(clausify,[status(thm)],[f_2854_3]) ).
cnf(f_2854_6,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)),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),U_10397))))
| 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),U_10397)))
| ~ sP813(U_10397) ),
inference(clausify,[status(thm)],[f_2854_3]) ).
fof(f_2855_1,plain,
! [V_b,V_a] :
( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
& ( 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)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps]) ).
fof(f_2855_2,plain,
! [U_10399,U_10398] :
( ( c_Divides_OposDivAlg(U_10398,U_10399) = hAPP(c_Divides_Oadjust(U_10399),c_Divides_OposDivAlg(U_10398,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)))),U_10399)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10399),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10398),U_10399)) )
& ( c_Divides_OposDivAlg(U_10398,U_10399) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10398)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10399),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10398),U_10399)) ) ) ),
inference(variable_rename,[status(thm)],[f_2855_1]) ).
fof(f_2855_3,plain,
( ! [U_10403,U_10401] :
( c_Divides_OposDivAlg(U_10401,U_10403) = hAPP(c_Divides_Oadjust(U_10403),c_Divides_OposDivAlg(U_10401,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)))),U_10403)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10403),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10401),U_10403)) )
& ! [U_10402,U_10400] :
( c_Divides_OposDivAlg(U_10400,U_10402) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10400)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10402),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10400),U_10402)) ) ) ),
inference(miniscope,[status(thm)],[f_2855_2]) ).
fof(f_2855_4,plain,
( ! [U_10400,U_10402] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10402),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP814(U_10400,U_10402) )
& ! [U_10400,U_10402] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10400),U_10402))
| ~ sP814(U_10400,U_10402) )
& ! [U_10403,U_10401] :
( c_Divides_OposDivAlg(U_10401,U_10403) = hAPP(c_Divides_Oadjust(U_10403),c_Divides_OposDivAlg(U_10401,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)))),U_10403)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10403),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10401),U_10403)) )
& ! [U_10400,U_10402] :
( c_Divides_OposDivAlg(U_10400,U_10402) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10400)
| sP814(U_10400,U_10402) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP814])],[f_2855_3]) ).
cnf(f_2855_5,plain,
( c_Divides_OposDivAlg(U_10400,U_10402) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10400)
| sP814(U_10400,U_10402) ),
inference(clausify,[status(thm)],[f_2855_4]) ).
cnf(f_2855_6,plain,
( c_Divides_OposDivAlg(U_10401,U_10403) = hAPP(c_Divides_Oadjust(U_10403),c_Divides_OposDivAlg(U_10401,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)))),U_10403)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10403),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10401),U_10403)) ),
inference(clausify,[status(thm)],[f_2855_4]) ).
cnf(f_2855_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10400),U_10402))
| ~ sP814(U_10400,U_10402) ),
inference(clausify,[status(thm)],[f_2855_4]) ).
cnf(f_2855_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10402),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP814(U_10400,U_10402) ),
inference(clausify,[status(thm)],[f_2855_4]) ).
fof(f_2856_1,plain,
! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
( 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))
| ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
& ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup2CI]) ).
fof(f_2856_2,plain,
! [U_10409,U_10408,U_10407,U_10406,U_10405,U_10404] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10408,tc_fun(U_10409,tc_HOL_Obool))),U_10407),U_10404),U_10405),U_10406))
| ( ~ hBOOL(hAPP(hAPP(U_10407,U_10405),U_10406))
& ~ hBOOL(hAPP(hAPP(U_10404,U_10405),U_10406)) ) ),
inference(variable_rename,[status(thm)],[f_2856_1]) ).
fof(f_2856_3,plain,
( ! [U_10404,U_10406,U_10407,U_10405] :
( ~ hBOOL(hAPP(hAPP(U_10407,U_10405),U_10406))
| ~ sP815(U_10404,U_10406,U_10407,U_10405) )
& ! [U_10404,U_10406,U_10407,U_10405] :
( ~ hBOOL(hAPP(hAPP(U_10404,U_10405),U_10406))
| ~ sP815(U_10404,U_10406,U_10407,U_10405) )
& ! [U_10404,U_10406,U_10407,U_10408,U_10405,U_10409] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10408,tc_fun(U_10409,tc_HOL_Obool))),U_10407),U_10404),U_10405),U_10406))
| sP815(U_10404,U_10406,U_10407,U_10405) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP815])],[f_2856_2]) ).
cnf(f_2856_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10408,tc_fun(U_10409,tc_HOL_Obool))),U_10407),U_10404),U_10405),U_10406))
| sP815(U_10404,U_10406,U_10407,U_10405) ),
inference(clausify,[status(thm)],[f_2856_3]) ).
cnf(f_2856_5,plain,
( ~ hBOOL(hAPP(hAPP(U_10404,U_10405),U_10406))
| ~ sP815(U_10404,U_10406,U_10407,U_10405) ),
inference(clausify,[status(thm)],[f_2856_3]) ).
cnf(f_2856_6,plain,
( ~ hBOOL(hAPP(hAPP(U_10407,U_10405),U_10406))
| ~ sP815(U_10404,U_10406,U_10407,U_10405) ),
inference(clausify,[status(thm)],[f_2856_3]) ).
fof(f_2857_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
| hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_sup2E]) ).
fof(f_2857_2,plain,
! [U_10415,U_10414,U_10413,U_10412,U_10411,U_10410] :
( hBOOL(hAPP(hAPP(U_10413,U_10414),U_10415))
| hBOOL(hAPP(hAPP(U_10412,U_10414),U_10415))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10410,tc_fun(U_10411,tc_HOL_Obool))),U_10412),U_10413),U_10414),U_10415)) ),
inference(variable_rename,[status(thm)],[f_2857_1]) ).
fof(f_2857_3,plain,
! [U_10415,U_10414,U_10413,U_10412] :
( ! [U_10411,U_10410] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10410,tc_fun(U_10411,tc_HOL_Obool))),U_10412),U_10413),U_10414),U_10415))
| hBOOL(hAPP(hAPP(U_10413,U_10414),U_10415))
| hBOOL(hAPP(hAPP(U_10412,U_10414),U_10415)) ),
inference(miniscope,[status(thm)],[f_2857_2]) ).
fof(f_2857_4,plain,
! [U_10411,U_10410,U_10412,U_10413,U_10414,U_10415] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10410,tc_fun(U_10411,tc_HOL_Obool))),U_10412),U_10413),U_10414),U_10415))
| hBOOL(hAPP(hAPP(U_10413,U_10414),U_10415))
| hBOOL(hAPP(hAPP(U_10412,U_10414),U_10415)) ),
inference(definitional_conversion,[status(esa)],[f_2857_3]) ).
cnf(f_2857_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10410,tc_fun(U_10411,tc_HOL_Obool))),U_10412),U_10413),U_10414),U_10415))
| hBOOL(hAPP(hAPP(U_10413,U_10414),U_10415))
| hBOOL(hAPP(hAPP(U_10412,U_10414),U_10415)) ),
inference(clausify,[status(thm)],[f_2857_4]) ).
fof(f_2858_1,plain,
! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
( 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))
| ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2I]) ).
fof(f_2858_2,plain,
! [U_10421,U_10420,U_10419,U_10418,U_10417,U_10416] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10420,tc_fun(U_10421,tc_HOL_Obool))),U_10416),U_10419),U_10417),U_10418))
| ~ hBOOL(hAPP(hAPP(U_10419,U_10417),U_10418))
| ~ hBOOL(hAPP(hAPP(U_10416,U_10417),U_10418)) ),
inference(variable_rename,[status(thm)],[f_2858_1]) ).
fof(f_2858_3,plain,
! [U_10417,U_10416,U_10418,U_10419,U_10420,U_10421] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10420,tc_fun(U_10421,tc_HOL_Obool))),U_10416),U_10419),U_10417),U_10418))
| ~ hBOOL(hAPP(hAPP(U_10419,U_10417),U_10418))
| ~ hBOOL(hAPP(hAPP(U_10416,U_10417),U_10418)) ),
inference(definitional_conversion,[status(esa)],[f_2858_2]) ).
cnf(f_2858_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10420,tc_fun(U_10421,tc_HOL_Obool))),U_10416),U_10419),U_10417),U_10418))
| ~ hBOOL(hAPP(hAPP(U_10419,U_10417),U_10418))
| ~ hBOOL(hAPP(hAPP(U_10416,U_10417),U_10418)) ),
inference(clausify,[status(thm)],[f_2858_3]) ).
fof(f_2859_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
& hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_inf2E]) ).
fof(f_2859_2,plain,
! [U_10427,U_10426,U_10425,U_10424,U_10423,U_10422] :
( ( hBOOL(hAPP(hAPP(U_10425,U_10426),U_10427))
& hBOOL(hAPP(hAPP(U_10424,U_10426),U_10427)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10422,tc_fun(U_10423,tc_HOL_Obool))),U_10424),U_10425),U_10426),U_10427)) ),
inference(variable_rename,[status(thm)],[f_2859_1]) ).
fof(f_2859_3,plain,
! [U_10427,U_10426,U_10425,U_10424] :
( ! [U_10423,U_10422] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10422,tc_fun(U_10423,tc_HOL_Obool))),U_10424),U_10425),U_10426),U_10427))
| ( hBOOL(hAPP(hAPP(U_10425,U_10426),U_10427))
& hBOOL(hAPP(hAPP(U_10424,U_10426),U_10427)) ) ),
inference(miniscope,[status(thm)],[f_2859_2]) ).
fof(f_2859_4,plain,
( ! [U_10424,U_10425,U_10426,U_10427] :
( hBOOL(hAPP(hAPP(U_10425,U_10426),U_10427))
| ~ sP816(U_10424,U_10425,U_10426,U_10427) )
& ! [U_10424,U_10425,U_10426,U_10427] :
( hBOOL(hAPP(hAPP(U_10424,U_10426),U_10427))
| ~ sP816(U_10424,U_10425,U_10426,U_10427) )
& ! [U_10423,U_10422,U_10424,U_10425,U_10426,U_10427] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10422,tc_fun(U_10423,tc_HOL_Obool))),U_10424),U_10425),U_10426),U_10427))
| sP816(U_10424,U_10425,U_10426,U_10427) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP816])],[f_2859_3]) ).
cnf(f_2859_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10422,tc_fun(U_10423,tc_HOL_Obool))),U_10424),U_10425),U_10426),U_10427))
| sP816(U_10424,U_10425,U_10426,U_10427) ),
inference(clausify,[status(thm)],[f_2859_4]) ).
cnf(f_2859_6,plain,
( hBOOL(hAPP(hAPP(U_10424,U_10426),U_10427))
| ~ sP816(U_10424,U_10425,U_10426,U_10427) ),
inference(clausify,[status(thm)],[f_2859_4]) ).
cnf(f_2859_7,plain,
( hBOOL(hAPP(hAPP(U_10425,U_10426),U_10427))
| ~ sP816(U_10424,U_10425,U_10426,U_10427) ),
inference(clausify,[status(thm)],[f_2859_4]) ).
fof(f_2860_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_bot2E]) ).
fof(f_2860_2,plain,
! [U_10431,U_10430,U_10429,U_10428] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_10428,tc_fun(U_10429,tc_HOL_Obool))),U_10430),U_10431)),
inference(variable_rename,[status(thm)],[f_2860_1]) ).
fof(f_2860_3,plain,
! [U_10428,U_10430,U_10429,U_10431] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_10428,tc_fun(U_10429,tc_HOL_Obool))),U_10430),U_10431)),
inference(definitional_conversion,[status(esa)],[f_2860_2]) ).
cnf(f_2860_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_10428,tc_fun(U_10429,tc_HOL_Obool))),U_10430),U_10431)),
inference(clausify,[status(thm)],[f_2860_3]) ).
fof(f_2861_1,plain,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( ( 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))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF1__iff]) ).
fof(f_2861_2,plain,
! [U_10438,U_10437,U_10436,U_10435,U_10434] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10434,tc_fun(U_10435,tc_HOL_Obool)),U_10436),U_10437),U_10438))
| ? [U_10433] :
( ~ hBOOL(hAPP(hAPP(U_10437,U_10433),U_10438))
& hBOOL(hAPP(hAPP(c_member(U_10434),U_10433),U_10436)) ) )
& ( ! [U_10432] :
( hBOOL(hAPP(hAPP(U_10437,U_10432),U_10438))
| ~ hBOOL(hAPP(hAPP(c_member(U_10434),U_10432),U_10436)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10434,tc_fun(U_10435,tc_HOL_Obool)),U_10436),U_10437),U_10438)) ) ),
inference(variable_rename,[status(thm)],[f_2861_1]) ).
fof(f_2861_3,plain,
( ! [U_10448,U_10446,U_10444,U_10442,U_10440] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10440,tc_fun(U_10442,tc_HOL_Obool)),U_10444),U_10446),U_10448))
| ? [U_10433] :
( ~ hBOOL(hAPP(hAPP(U_10446,U_10433),U_10448))
& hBOOL(hAPP(hAPP(c_member(U_10440),U_10433),U_10444)) ) )
& ! [U_10447,U_10445,U_10443,U_10441,U_10439] :
( ! [U_10432] :
( hBOOL(hAPP(hAPP(U_10445,U_10432),U_10447))
| ~ hBOOL(hAPP(hAPP(c_member(U_10439),U_10432),U_10443)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10439,tc_fun(U_10441,tc_HOL_Obool)),U_10443),U_10445),U_10447)) ) ),
inference(miniscope,[status(thm)],[f_2861_2]) ).
fof(f_2861_4,plain,
( ! [U_10448,U_10446,U_10444,U_10442,U_10440] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10440,tc_fun(U_10442,tc_HOL_Obool)),U_10444),U_10446),U_10448))
| ( ~ hBOOL(hAPP(hAPP(U_10446,sK258(U_10448,U_10446,U_10444,U_10442,U_10440)),U_10448))
& hBOOL(hAPP(hAPP(c_member(U_10440),sK258(U_10448,U_10446,U_10444,U_10442,U_10440)),U_10444)) ) )
& ! [U_10447,U_10445,U_10443,U_10441,U_10439] :
( ! [U_10432] :
( hBOOL(hAPP(hAPP(U_10445,U_10432),U_10447))
| ~ hBOOL(hAPP(hAPP(c_member(U_10439),U_10432),U_10443)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10439,tc_fun(U_10441,tc_HOL_Obool)),U_10443),U_10445),U_10447)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_10433,sK258(U_10448,U_10446,U_10444,U_10442,U_10440))],[f_2861_3]) ).
fof(f_2861_5,plain,
( ! [U_10440,U_10442,U_10446,U_10444,U_10448] :
( ~ hBOOL(hAPP(hAPP(U_10446,sK258(U_10448,U_10446,U_10444,U_10442,U_10440)),U_10448))
| ~ sP817(U_10440,U_10442,U_10446,U_10444,U_10448) )
& ! [U_10440,U_10442,U_10446,U_10444,U_10448] :
( hBOOL(hAPP(hAPP(c_member(U_10440),sK258(U_10448,U_10446,U_10444,U_10442,U_10440)),U_10444))
| ~ sP817(U_10440,U_10442,U_10446,U_10444,U_10448) )
& ! [U_10440,U_10442,U_10446,U_10444,U_10448] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10440,tc_fun(U_10442,tc_HOL_Obool)),U_10444),U_10446),U_10448))
| sP817(U_10440,U_10442,U_10446,U_10444,U_10448) )
& ! [U_10441,U_10445,U_10432,U_10439,U_10443,U_10447] :
( hBOOL(hAPP(hAPP(U_10445,U_10432),U_10447))
| ~ hBOOL(hAPP(hAPP(c_member(U_10439),U_10432),U_10443))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10439,tc_fun(U_10441,tc_HOL_Obool)),U_10443),U_10445),U_10447)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP817])],[f_2861_4]) ).
cnf(f_2861_6,plain,
( hBOOL(hAPP(hAPP(U_10445,U_10432),U_10447))
| ~ hBOOL(hAPP(hAPP(c_member(U_10439),U_10432),U_10443))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10439,tc_fun(U_10441,tc_HOL_Obool)),U_10443),U_10445),U_10447)) ),
inference(clausify,[status(thm)],[f_2861_5]) ).
cnf(f_2861_7,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10440,tc_fun(U_10442,tc_HOL_Obool)),U_10444),U_10446),U_10448))
| sP817(U_10440,U_10442,U_10446,U_10444,U_10448) ),
inference(clausify,[status(thm)],[f_2861_5]) ).
cnf(f_2861_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_10440),sK258(U_10448,U_10446,U_10444,U_10442,U_10440)),U_10444))
| ~ sP817(U_10440,U_10442,U_10446,U_10444,U_10448) ),
inference(clausify,[status(thm)],[f_2861_5]) ).
cnf(f_2861_9,plain,
( ~ hBOOL(hAPP(hAPP(U_10446,sK258(U_10448,U_10446,U_10444,U_10442,U_10440)),U_10448))
| ~ sP817(U_10440,U_10442,U_10446,U_10444,U_10448) ),
inference(clausify,[status(thm)],[f_2861_5]) ).
fof(f_2862_1,plain,
! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ( 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_ca_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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_ca_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF2__iff]) ).
fof(f_2862_2,plain,
! [U_10457,U_10456,U_10455,U_10454,U_10453,U_10452,U_10451] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10451,tc_fun(U_10452,tc_fun(U_10453,tc_HOL_Obool))),U_10454),U_10455),U_10456),U_10457))
| ? [U_10450] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10455,U_10450),U_10456),U_10457))
& hBOOL(hAPP(hAPP(c_member(U_10451),U_10450),U_10454)) ) )
& ( ! [U_10449] :
( hBOOL(hAPP(hAPP(hAPP(U_10455,U_10449),U_10456),U_10457))
| ~ hBOOL(hAPP(hAPP(c_member(U_10451),U_10449),U_10454)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10451,tc_fun(U_10452,tc_fun(U_10453,tc_HOL_Obool))),U_10454),U_10455),U_10456),U_10457)) ) ),
inference(variable_rename,[status(thm)],[f_2862_1]) ).
fof(f_2862_3,plain,
( ! [U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10459,tc_fun(U_10461,tc_fun(U_10463,tc_HOL_Obool))),U_10465),U_10467),U_10469),U_10471))
| ? [U_10450] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10467,U_10450),U_10469),U_10471))
& hBOOL(hAPP(hAPP(c_member(U_10459),U_10450),U_10465)) ) )
& ! [U_10470,U_10468,U_10466,U_10464,U_10462,U_10460,U_10458] :
( ! [U_10449] :
( hBOOL(hAPP(hAPP(hAPP(U_10466,U_10449),U_10468),U_10470))
| ~ hBOOL(hAPP(hAPP(c_member(U_10458),U_10449),U_10464)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10458,tc_fun(U_10460,tc_fun(U_10462,tc_HOL_Obool))),U_10464),U_10466),U_10468),U_10470)) ) ),
inference(miniscope,[status(thm)],[f_2862_2]) ).
fof(f_2862_4,plain,
( ! [U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10459,tc_fun(U_10461,tc_fun(U_10463,tc_HOL_Obool))),U_10465),U_10467),U_10469),U_10471))
| ( ~ hBOOL(hAPP(hAPP(hAPP(U_10467,sK259(U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459)),U_10469),U_10471))
& hBOOL(hAPP(hAPP(c_member(U_10459),sK259(U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459)),U_10465)) ) )
& ! [U_10470,U_10468,U_10466,U_10464,U_10462,U_10460,U_10458] :
( ! [U_10449] :
( hBOOL(hAPP(hAPP(hAPP(U_10466,U_10449),U_10468),U_10470))
| ~ hBOOL(hAPP(hAPP(c_member(U_10458),U_10449),U_10464)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10458,tc_fun(U_10460,tc_fun(U_10462,tc_HOL_Obool))),U_10464),U_10466),U_10468),U_10470)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_10450,sK259(U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459))],[f_2862_3]) ).
fof(f_2862_5,plain,
( ! [U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10467,sK259(U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459)),U_10469),U_10471))
| ~ sP818(U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471) )
& ! [U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471] :
( hBOOL(hAPP(hAPP(c_member(U_10459),sK259(U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459)),U_10465))
| ~ sP818(U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471) )
& ! [U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10459,tc_fun(U_10461,tc_fun(U_10463,tc_HOL_Obool))),U_10465),U_10467),U_10469),U_10471))
| sP818(U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471) )
& ! [U_10460,U_10449,U_10458,U_10462,U_10466,U_10468,U_10464,U_10470] :
( hBOOL(hAPP(hAPP(hAPP(U_10466,U_10449),U_10468),U_10470))
| ~ hBOOL(hAPP(hAPP(c_member(U_10458),U_10449),U_10464))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10458,tc_fun(U_10460,tc_fun(U_10462,tc_HOL_Obool))),U_10464),U_10466),U_10468),U_10470)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP818])],[f_2862_4]) ).
cnf(f_2862_6,plain,
( hBOOL(hAPP(hAPP(hAPP(U_10466,U_10449),U_10468),U_10470))
| ~ hBOOL(hAPP(hAPP(c_member(U_10458),U_10449),U_10464))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10458,tc_fun(U_10460,tc_fun(U_10462,tc_HOL_Obool))),U_10464),U_10466),U_10468),U_10470)) ),
inference(clausify,[status(thm)],[f_2862_5]) ).
cnf(f_2862_7,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10459,tc_fun(U_10461,tc_fun(U_10463,tc_HOL_Obool))),U_10465),U_10467),U_10469),U_10471))
| sP818(U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471) ),
inference(clausify,[status(thm)],[f_2862_5]) ).
cnf(f_2862_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_10459),sK259(U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459)),U_10465))
| ~ sP818(U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471) ),
inference(clausify,[status(thm)],[f_2862_5]) ).
cnf(f_2862_9,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(U_10467,sK259(U_10471,U_10469,U_10467,U_10465,U_10463,U_10461,U_10459)),U_10469),U_10471))
| ~ sP818(U_10467,U_10459,U_10465,U_10461,U_10469,U_10463,U_10471) ),
inference(clausify,[status(thm)],[f_2862_5]) ).
fof(f_2863_1,plain,
! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ( 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_ca_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ 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_ca_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP2__iff]) ).
fof(f_2863_2,plain,
! [U_10480,U_10479,U_10478,U_10477,U_10476,U_10475,U_10474] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10474,tc_fun(U_10475,tc_fun(U_10476,tc_HOL_Obool))),U_10477),U_10478),U_10479),U_10480))
| ! [U_10473] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10478,U_10473),U_10479),U_10480))
| ~ hBOOL(hAPP(hAPP(c_member(U_10474),U_10473),U_10477)) ) )
& ( ? [U_10472] :
( hBOOL(hAPP(hAPP(hAPP(U_10478,U_10472),U_10479),U_10480))
& hBOOL(hAPP(hAPP(c_member(U_10474),U_10472),U_10477)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10474,tc_fun(U_10475,tc_fun(U_10476,tc_HOL_Obool))),U_10477),U_10478),U_10479),U_10480)) ) ),
inference(variable_rename,[status(thm)],[f_2863_1]) ).
fof(f_2863_3,plain,
( ! [U_10494,U_10492,U_10490,U_10488,U_10486,U_10484,U_10482] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10482,tc_fun(U_10484,tc_fun(U_10486,tc_HOL_Obool))),U_10488),U_10490),U_10492),U_10494))
| ! [U_10473] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10490,U_10473),U_10492),U_10494))
| ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10473),U_10488)) ) )
& ! [U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481] :
( ? [U_10472] :
( hBOOL(hAPP(hAPP(hAPP(U_10489,U_10472),U_10491),U_10493))
& hBOOL(hAPP(hAPP(c_member(U_10481),U_10472),U_10487)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10481,tc_fun(U_10483,tc_fun(U_10485,tc_HOL_Obool))),U_10487),U_10489),U_10491),U_10493)) ) ),
inference(miniscope,[status(thm)],[f_2863_2]) ).
fof(f_2863_4,plain,
( ! [U_10494,U_10492,U_10490,U_10488,U_10486,U_10484,U_10482] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10482,tc_fun(U_10484,tc_fun(U_10486,tc_HOL_Obool))),U_10488),U_10490),U_10492),U_10494))
| ! [U_10473] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10490,U_10473),U_10492),U_10494))
| ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10473),U_10488)) ) )
& ! [U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481] :
( ( hBOOL(hAPP(hAPP(hAPP(U_10489,sK260(U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481)),U_10491),U_10493))
& hBOOL(hAPP(hAPP(c_member(U_10481),sK260(U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481)),U_10487)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10481,tc_fun(U_10483,tc_fun(U_10485,tc_HOL_Obool))),U_10487),U_10489),U_10491),U_10493)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_10472,sK260(U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481))],[f_2863_3]) ).
fof(f_2863_5,plain,
( ! [U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493] :
( hBOOL(hAPP(hAPP(hAPP(U_10489,sK260(U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481)),U_10491),U_10493))
| ~ sP819(U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493) )
& ! [U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493] :
( hBOOL(hAPP(hAPP(c_member(U_10481),sK260(U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481)),U_10487))
| ~ sP819(U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493) )
& ! [U_10473,U_10488,U_10482,U_10484,U_10486,U_10492,U_10490,U_10494] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10482,tc_fun(U_10484,tc_fun(U_10486,tc_HOL_Obool))),U_10488),U_10490),U_10492),U_10494))
| ~ hBOOL(hAPP(hAPP(hAPP(U_10490,U_10473),U_10492),U_10494))
| ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10473),U_10488)) )
& ! [U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493] :
( sP819(U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493)
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10481,tc_fun(U_10483,tc_fun(U_10485,tc_HOL_Obool))),U_10487),U_10489),U_10491),U_10493)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP819])],[f_2863_4]) ).
cnf(f_2863_6,plain,
( sP819(U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493)
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10481,tc_fun(U_10483,tc_fun(U_10485,tc_HOL_Obool))),U_10487),U_10489),U_10491),U_10493)) ),
inference(clausify,[status(thm)],[f_2863_5]) ).
cnf(f_2863_7,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10482,tc_fun(U_10484,tc_fun(U_10486,tc_HOL_Obool))),U_10488),U_10490),U_10492),U_10494))
| ~ hBOOL(hAPP(hAPP(hAPP(U_10490,U_10473),U_10492),U_10494))
| ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10473),U_10488)) ),
inference(clausify,[status(thm)],[f_2863_5]) ).
cnf(f_2863_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_10481),sK260(U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481)),U_10487))
| ~ sP819(U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493) ),
inference(clausify,[status(thm)],[f_2863_5]) ).
cnf(f_2863_9,plain,
( hBOOL(hAPP(hAPP(hAPP(U_10489,sK260(U_10493,U_10491,U_10489,U_10487,U_10485,U_10483,U_10481)),U_10491),U_10493))
| ~ sP819(U_10485,U_10483,U_10481,U_10489,U_10491,U_10487,U_10493) ),
inference(clausify,[status(thm)],[f_2863_5]) ).
fof(f_2864_1,plain,
! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).
fof(f_2864_2,plain,
! [U_10500,U_10499,U_10498,U_10497,U_10496,U_10495] :
( hBOOL(hAPP(hAPP(U_10500,U_10496),U_10497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10498,tc_fun(U_10499,tc_HOL_Obool))),U_10495),U_10500))
| ~ hBOOL(hAPP(hAPP(U_10495,U_10496),U_10497)) ),
inference(variable_rename,[status(thm)],[f_2864_1]) ).
fof(f_2864_3,plain,
! [U_10500,U_10498,U_10497,U_10496,U_10495,U_10499] :
( hBOOL(hAPP(hAPP(U_10500,U_10496),U_10497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10498,tc_fun(U_10499,tc_HOL_Obool))),U_10495),U_10500))
| ~ hBOOL(hAPP(hAPP(U_10495,U_10496),U_10497)) ),
inference(definitional_conversion,[status(esa)],[f_2864_2]) ).
cnf(f_2864_4,plain,
( hBOOL(hAPP(hAPP(U_10500,U_10496),U_10497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10498,tc_fun(U_10499,tc_HOL_Obool))),U_10495),U_10500))
| ~ hBOOL(hAPP(hAPP(U_10495,U_10496),U_10497)) ),
inference(clausify,[status(thm)],[f_2864_3]) ).
fof(f_2865_1,plain,
! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).
fof(f_2865_2,plain,
! [U_10506,U_10505,U_10504,U_10503,U_10502,U_10501] :
( hBOOL(hAPP(hAPP(U_10504,U_10505),U_10506))
| ~ hBOOL(hAPP(hAPP(U_10503,U_10505),U_10506))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10501,tc_fun(U_10502,tc_HOL_Obool))),U_10503),U_10504)) ),
inference(variable_rename,[status(thm)],[f_2865_1]) ).
fof(f_2865_3,plain,
! [U_10506,U_10505,U_10504,U_10503] :
( ! [U_10502,U_10501] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10501,tc_fun(U_10502,tc_HOL_Obool))),U_10503),U_10504))
| hBOOL(hAPP(hAPP(U_10504,U_10505),U_10506))
| ~ hBOOL(hAPP(hAPP(U_10503,U_10505),U_10506)) ),
inference(miniscope,[status(thm)],[f_2865_2]) ).
fof(f_2865_4,plain,
! [U_10504,U_10501,U_10502,U_10503,U_10505,U_10506] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10501,tc_fun(U_10502,tc_HOL_Obool))),U_10503),U_10504))
| hBOOL(hAPP(hAPP(U_10504,U_10505),U_10506))
| ~ hBOOL(hAPP(hAPP(U_10503,U_10505),U_10506)) ),
inference(definitional_conversion,[status(esa)],[f_2865_3]) ).
cnf(f_2865_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10501,tc_fun(U_10502,tc_HOL_Obool))),U_10503),U_10504))
| hBOOL(hAPP(hAPP(U_10504,U_10505),U_10506))
| ~ hBOOL(hAPP(hAPP(U_10503,U_10505),U_10506)) ),
inference(clausify,[status(thm)],[f_2865_4]) ).
fof(f_2866_1,plain,
! [V_B_2,T_b,V_A_2] :
( 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))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_less__by__empty]) ).
fof(f_2866_2,plain,
! [U_10509,U_10508,U_10507] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10508,U_10508),tc_HOL_Obool)),U_10507),U_10509))
| U_10507 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10508,U_10508),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2866_1]) ).
fof(f_2866_3,plain,
! [U_10508,U_10507,U_10509] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10508,U_10508),tc_HOL_Obool)),U_10507),U_10509))
| U_10507 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10508,U_10508),tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_2866_2]) ).
cnf(f_2866_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10508,U_10508),tc_HOL_Obool)),U_10507),U_10509))
| U_10507 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10508,U_10508),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2866_3]) ).
fof(f_2867_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_inf2D1]) ).
fof(f_2867_2,plain,
! [U_10515,U_10514,U_10513,U_10512,U_10511,U_10510] :
( hBOOL(hAPP(hAPP(U_10512,U_10514),U_10515))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10510,tc_fun(U_10511,tc_HOL_Obool))),U_10512),U_10513),U_10514),U_10515)) ),
inference(variable_rename,[status(thm)],[f_2867_1]) ).
fof(f_2867_3,plain,
! [U_10515,U_10514,U_10513,U_10512] :
( ! [U_10511,U_10510] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10510,tc_fun(U_10511,tc_HOL_Obool))),U_10512),U_10513),U_10514),U_10515))
| hBOOL(hAPP(hAPP(U_10512,U_10514),U_10515)) ),
inference(miniscope,[status(thm)],[f_2867_2]) ).
fof(f_2867_4,plain,
! [U_10510,U_10511,U_10512,U_10513,U_10514,U_10515] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10510,tc_fun(U_10511,tc_HOL_Obool))),U_10512),U_10513),U_10514),U_10515))
| hBOOL(hAPP(hAPP(U_10512,U_10514),U_10515)) ),
inference(definitional_conversion,[status(esa)],[f_2867_3]) ).
cnf(f_2867_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10510,tc_fun(U_10511,tc_HOL_Obool))),U_10512),U_10513),U_10514),U_10515))
| hBOOL(hAPP(hAPP(U_10512,U_10514),U_10515)) ),
inference(clausify,[status(thm)],[f_2867_4]) ).
fof(f_2868_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_inf2D2]) ).
fof(f_2868_2,plain,
! [U_10521,U_10520,U_10519,U_10518,U_10517,U_10516] :
( hBOOL(hAPP(hAPP(U_10519,U_10520),U_10521))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10516,tc_fun(U_10517,tc_HOL_Obool))),U_10518),U_10519),U_10520),U_10521)) ),
inference(variable_rename,[status(thm)],[f_2868_1]) ).
fof(f_2868_3,plain,
! [U_10521,U_10520,U_10519] :
( ! [U_10518,U_10517,U_10516] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10516,tc_fun(U_10517,tc_HOL_Obool))),U_10518),U_10519),U_10520),U_10521))
| hBOOL(hAPP(hAPP(U_10519,U_10520),U_10521)) ),
inference(miniscope,[status(thm)],[f_2868_2]) ).
fof(f_2868_4,plain,
! [U_10516,U_10517,U_10518,U_10519,U_10520,U_10521] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10516,tc_fun(U_10517,tc_HOL_Obool))),U_10518),U_10519),U_10520),U_10521))
| hBOOL(hAPP(hAPP(U_10519,U_10520),U_10521)) ),
inference(definitional_conversion,[status(esa)],[f_2868_3]) ).
cnf(f_2868_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10516,tc_fun(U_10517,tc_HOL_Obool))),U_10518),U_10519),U_10520),U_10521))
| hBOOL(hAPP(hAPP(U_10519,U_10520),U_10521)) ),
inference(clausify,[status(thm)],[f_2868_4]) ).
fof(f_2869_1,plain,
! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
( 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))
| ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup2I2]) ).
fof(f_2869_2,plain,
! [U_10527,U_10526,U_10525,U_10524,U_10523,U_10522] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10525,tc_fun(U_10526,tc_HOL_Obool))),U_10527),U_10522),U_10523),U_10524))
| ~ hBOOL(hAPP(hAPP(U_10522,U_10523),U_10524)) ),
inference(variable_rename,[status(thm)],[f_2869_1]) ).
fof(f_2869_3,plain,
! [U_10522,U_10523,U_10524,U_10525,U_10526,U_10527] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10525,tc_fun(U_10526,tc_HOL_Obool))),U_10527),U_10522),U_10523),U_10524))
| ~ hBOOL(hAPP(hAPP(U_10522,U_10523),U_10524)) ),
inference(definitional_conversion,[status(esa)],[f_2869_2]) ).
cnf(f_2869_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10525,tc_fun(U_10526,tc_HOL_Obool))),U_10527),U_10522),U_10523),U_10524))
| ~ hBOOL(hAPP(hAPP(U_10522,U_10523),U_10524)) ),
inference(clausify,[status(thm)],[f_2869_3]) ).
fof(f_2870_1,plain,
! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
( 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))
| ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup2I1]) ).
fof(f_2870_2,plain,
! [U_10533,U_10532,U_10531,U_10530,U_10529,U_10528] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10531,tc_fun(U_10532,tc_HOL_Obool))),U_10528),U_10533),U_10529),U_10530))
| ~ hBOOL(hAPP(hAPP(U_10528,U_10529),U_10530)) ),
inference(variable_rename,[status(thm)],[f_2870_1]) ).
fof(f_2870_3,plain,
! [U_10529,U_10528,U_10530,U_10531,U_10532,U_10533] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10531,tc_fun(U_10532,tc_HOL_Obool))),U_10528),U_10533),U_10529),U_10530))
| ~ hBOOL(hAPP(hAPP(U_10528,U_10529),U_10530)) ),
inference(definitional_conversion,[status(esa)],[f_2870_2]) ).
cnf(f_2870_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10531,tc_fun(U_10532,tc_HOL_Obool))),U_10528),U_10533),U_10529),U_10530))
| ~ hBOOL(hAPP(hAPP(U_10528,U_10529),U_10530)) ),
inference(clausify,[status(thm)],[f_2870_3]) ).
fof(f_2871_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_nat__case__0]) ).
fof(f_2871_2,plain,
! [U_10536,U_10535,U_10534] : c_Nat_Onat_Onat__case(U_10534,U_10535,U_10536,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10535,
inference(variable_rename,[status(thm)],[f_2871_1]) ).
fof(f_2871_3,plain,
! [U_10536,U_10534,U_10535] : c_Nat_Onat_Onat__case(U_10534,U_10535,U_10536,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10535,
inference(definitional_conversion,[status(esa)],[f_2871_2]) ).
cnf(f_2871_4,plain,
c_Nat_Onat_Onat__case(U_10534,U_10535,U_10536,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10535,
inference(clausify,[status(thm)],[f_2871_3]) ).
fof(f_2872_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__case__Suc]) ).
fof(f_2872_2,plain,
! [U_10540,U_10539,U_10538,U_10537] : c_Nat_Onat_Onat__case(U_10537,U_10538,U_10539,hAPP(c_Nat_OSuc,U_10540)) = hAPP(U_10539,U_10540),
inference(variable_rename,[status(thm)],[f_2872_1]) ).
fof(f_2872_3,plain,
! [U_10537,U_10538,U_10539,U_10540] : c_Nat_Onat_Onat__case(U_10537,U_10538,U_10539,hAPP(c_Nat_OSuc,U_10540)) = hAPP(U_10539,U_10540),
inference(definitional_conversion,[status(esa)],[f_2872_2]) ).
cnf(f_2872_4,plain,
c_Nat_Onat_Onat__case(U_10537,U_10538,U_10539,hAPP(c_Nat_OSuc,U_10540)) = hAPP(U_10539,U_10540),
inference(clausify,[status(thm)],[f_2872_3]) ).
fof(f_2873_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_posDivAlg__0]) ).
fof(f_2873_2,plain,
! [U_10541] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10541) = 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)),
inference(variable_rename,[status(thm)],[f_2873_1]) ).
fof(f_2873_3,plain,
! [U_10541] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10541) = 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)),
inference(definitional_conversion,[status(esa)],[f_2873_2]) ).
cnf(f_2873_4,plain,
c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10541) = 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)),
inference(clausify,[status(thm)],[f_2873_3]) ).
fof(f_2874_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_max__Suc1]) ).
fof(f_2874_2,plain,
! [U_10543,U_10542] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10542)),U_10543) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10542),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),U_10542)),U_10543),
inference(variable_rename,[status(thm)],[f_2874_1]) ).
fof(f_2874_3,plain,
! [U_10542,U_10543] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10542)),U_10543) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10542),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),U_10542)),U_10543),
inference(definitional_conversion,[status(esa)],[f_2874_2]) ).
cnf(f_2874_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10542)),U_10543) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10542),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),U_10542)),U_10543),
inference(clausify,[status(thm)],[f_2874_3]) ).
fof(f_2875_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_max__Suc2]) ).
fof(f_2875_2,plain,
! [U_10545,U_10544] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10544),hAPP(c_Nat_OSuc,U_10545)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10545),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)),U_10545)),U_10544),
inference(variable_rename,[status(thm)],[f_2875_1]) ).
fof(f_2875_3,plain,
! [U_10544,U_10545] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10544),hAPP(c_Nat_OSuc,U_10545)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10545),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)),U_10545)),U_10544),
inference(definitional_conversion,[status(esa)],[f_2875_2]) ).
cnf(f_2875_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10544),hAPP(c_Nat_OSuc,U_10545)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10545),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)),U_10545)),U_10544),
inference(clausify,[status(thm)],[f_2875_3]) ).
fof(f_2876_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
| ~ 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)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J]) ).
fof(f_2876_2,plain,
! [U_10547,U_10546] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10546)),U_10547))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10546),U_10547)) )
& ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10546),U_10547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10546)),U_10547)) ) ),
inference(variable_rename,[status(thm)],[f_2876_1]) ).
fof(f_2876_3,plain,
( ! [U_10551,U_10549] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10549)),U_10551))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10549),U_10551)) )
& ! [U_10550,U_10548] :
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10548),U_10550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10548)),U_10550)) ) ),
inference(miniscope,[status(thm)],[f_2876_2]) ).
fof(f_2876_4,plain,
( ! [U_10551,U_10549] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10549)),U_10551))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10549),U_10551)) )
& ! [U_10550,U_10548] :
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10548),U_10550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10548)),U_10550)) ) ),
inference(definitional_conversion,[status(esa)],[f_2876_3]) ).
cnf(f_2876_5,plain,
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10548),U_10550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10548)),U_10550)) ),
inference(clausify,[status(thm)],[f_2876_4]) ).
cnf(f_2876_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10549)),U_10551))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10549),U_10551)) ),
inference(clausify,[status(thm)],[f_2876_4]) ).
fof(f_2877_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_diff__Suc]) ).
fof(f_2877_2,plain,
! [U_10553,U_10552] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10552),hAPP(c_Nat_OSuc,U_10553)) = 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),U_10552),U_10553)),
inference(variable_rename,[status(thm)],[f_2877_1]) ).
fof(f_2877_3,plain,
! [U_10553,U_10552] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10552),hAPP(c_Nat_OSuc,U_10553)) = 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),U_10552),U_10553)),
inference(definitional_conversion,[status(esa)],[f_2877_2]) ).
cnf(f_2877_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10552),hAPP(c_Nat_OSuc,U_10553)) = 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),U_10552),U_10553)),
inference(clausify,[status(thm)],[f_2877_3]) ).
fof(f_2878_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_min__Suc2]) ).
fof(f_2878_2,plain,
! [U_10555,U_10554] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10554),hAPP(c_Nat_OSuc,U_10555)) = 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)),U_10555)),U_10554),
inference(variable_rename,[status(thm)],[f_2878_1]) ).
fof(f_2878_3,plain,
! [U_10554,U_10555] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10554),hAPP(c_Nat_OSuc,U_10555)) = 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)),U_10555)),U_10554),
inference(definitional_conversion,[status(esa)],[f_2878_2]) ).
cnf(f_2878_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10554),hAPP(c_Nat_OSuc,U_10555)) = 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)),U_10555)),U_10554),
inference(clausify,[status(thm)],[f_2878_3]) ).
fof(f_2879_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_min__Suc1]) ).
fof(f_2879_2,plain,
! [U_10557,U_10556] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10556)),U_10557) = 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),U_10556)),U_10557),
inference(variable_rename,[status(thm)],[f_2879_1]) ).
fof(f_2879_3,plain,
! [U_10556,U_10557] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10556)),U_10557) = 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),U_10556)),U_10557),
inference(definitional_conversion,[status(esa)],[f_2879_2]) ).
cnf(f_2879_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10556)),U_10557) = 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),U_10556)),U_10557),
inference(clausify,[status(thm)],[f_2879_3]) ).
fof(f_2880_1,plain,
! [V_l,V_k] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod]) ).
fof(f_2880_2,plain,
! [U_10559,U_10558] :
( c_Divides_OposDivAlg(U_10558,U_10559) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10558),U_10559)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10558,U_10559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10558)) ),
inference(variable_rename,[status(thm)],[f_2880_1]) ).
fof(f_2880_3,plain,
! [U_10558,U_10559] :
( c_Divides_OposDivAlg(U_10558,U_10559) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10558),U_10559)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10558,U_10559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10558)) ),
inference(definitional_conversion,[status(esa)],[f_2880_2]) ).
cnf(f_2880_4,plain,
( c_Divides_OposDivAlg(U_10558,U_10559) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10558),U_10559)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10558,U_10559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10558)) ),
inference(clausify,[status(thm)],[f_2880_3]) ).
fof(f_2881_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_nat__case__number__of]) ).
fof(f_2881_2,plain,
! [U_10563,U_10562,U_10561,U_10560] : c_Nat_Onat_Onat__case(U_10560,U_10561,U_10562,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10563)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10560),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10563))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10560,U_10560),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10560,tc_fun(U_10560,U_10560)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10560,tc_fun(U_10560,U_10560)),tc_Int_Oint),c_If(U_10560)),c_Nat__Numeral_Oneg)),U_10561)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10560,tc_Int_Oint),U_10562),c_Int_Onat))),
inference(variable_rename,[status(thm)],[f_2881_1]) ).
fof(f_2881_3,plain,
! [U_10560,U_10561,U_10562,U_10563] : c_Nat_Onat_Onat__case(U_10560,U_10561,U_10562,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10563)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10560),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10563))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10560,U_10560),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10560,tc_fun(U_10560,U_10560)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10560,tc_fun(U_10560,U_10560)),tc_Int_Oint),c_If(U_10560)),c_Nat__Numeral_Oneg)),U_10561)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10560,tc_Int_Oint),U_10562),c_Int_Onat))),
inference(definitional_conversion,[status(esa)],[f_2881_2]) ).
cnf(f_2881_4,plain,
c_Nat_Onat_Onat__case(U_10560,U_10561,U_10562,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10563)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10560),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10563))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10560,U_10560),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10560,tc_fun(U_10560,U_10560)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10560,tc_fun(U_10560,U_10560)),tc_Int_Oint),c_If(U_10560)),c_Nat__Numeral_Oneg)),U_10561)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10560,tc_Int_Oint),U_10562),c_Int_Onat))),
inference(clausify,[status(thm)],[f_2881_3]) ).
fof(f_2882_1,plain,
! [V_a,V_b] :
( ( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
& ( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn]) ).
fof(f_2882_2,plain,
! [U_10565,U_10564] :
( ( ( c_Divides_OposDivAlg(U_10565,U_10564) = hAPP(c_Divides_Oadjust(U_10564),c_Divides_OposDivAlg(U_10565,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)))),U_10564)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10565),U_10564)) )
& ( c_Divides_OposDivAlg(U_10565,U_10564) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10565),U_10564)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10564)) ),
inference(variable_rename,[status(thm)],[f_2882_1]) ).
fof(f_2882_3,plain,
( ! [U_10564,U_10565] :
( c_Divides_OposDivAlg(U_10565,U_10564) = hAPP(c_Divides_Oadjust(U_10564),c_Divides_OposDivAlg(U_10565,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)))),U_10564)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10565),U_10564))
| ~ sP820(U_10564,U_10565) )
& ! [U_10564,U_10565] :
( c_Divides_OposDivAlg(U_10565,U_10564) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10565),U_10564))
| ~ sP820(U_10564,U_10565) )
& ! [U_10564,U_10565] :
( sP820(U_10564,U_10565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10564)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP820])],[f_2882_2]) ).
cnf(f_2882_4,plain,
( sP820(U_10564,U_10565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10564)) ),
inference(clausify,[status(thm)],[f_2882_3]) ).
cnf(f_2882_5,plain,
( c_Divides_OposDivAlg(U_10565,U_10564) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10565),U_10564))
| ~ sP820(U_10564,U_10565) ),
inference(clausify,[status(thm)],[f_2882_3]) ).
cnf(f_2882_6,plain,
( c_Divides_OposDivAlg(U_10565,U_10564) = hAPP(c_Divides_Oadjust(U_10564),c_Divides_OposDivAlg(U_10565,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)))),U_10564)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10565),U_10564))
| ~ sP820(U_10564,U_10565) ),
inference(clausify,[status(thm)],[f_2882_3]) ).
fof(f_2883_1,plain,
! [V_w,V_v] :
( ( ( 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))))
| 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))) )
& ( 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))
| ~ 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))) ) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn__number__of]) ).
fof(f_2883_2,plain,
! [U_10567,U_10566] :
( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),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),U_10566))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566))) )
& ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)) = 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),U_10567))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566))) ) )
| ~ 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),U_10566))) ),
inference(variable_rename,[status(thm)],[f_2883_1]) ).
fof(f_2883_3,plain,
( ! [U_10567,U_10566] :
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),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),U_10566))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)))
| ~ sP821(U_10567,U_10566) )
& ! [U_10567,U_10566] :
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)) = 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),U_10567))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)))
| ~ sP821(U_10567,U_10566) )
& ! [U_10567,U_10566] :
( sP821(U_10567,U_10566)
| ~ 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),U_10566))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP821])],[f_2883_2]) ).
cnf(f_2883_4,plain,
( sP821(U_10567,U_10566)
| ~ 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),U_10566))) ),
inference(clausify,[status(thm)],[f_2883_3]) ).
cnf(f_2883_5,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)) = 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),U_10567))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)))
| ~ sP821(U_10567,U_10566) ),
inference(clausify,[status(thm)],[f_2883_3]) ).
cnf(f_2883_6,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567),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),U_10566))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10567)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10566)))
| ~ sP821(U_10567,U_10566) ),
inference(clausify,[status(thm)],[f_2883_3]) ).
fof(f_2884_1,plain,
! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
| ~ 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)) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_in__rel__def]) ).
fof(f_2884_2,plain,
! [U_10572,U_10571,U_10570,U_10569,U_10568] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10568,U_10569,U_10570),U_10571),U_10572))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10568,U_10569)),hAPP(hAPP(c_Product__Type_OPair(U_10568,U_10569),U_10571),U_10572)),U_10570)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10568,U_10569)),hAPP(hAPP(c_Product__Type_OPair(U_10568,U_10569),U_10571),U_10572)),U_10570))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10568,U_10569,U_10570),U_10571),U_10572)) ) ),
inference(variable_rename,[status(thm)],[f_2884_1]) ).
fof(f_2884_3,plain,
( ! [U_10582,U_10580,U_10578,U_10576,U_10574] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10574,U_10576,U_10578),U_10580),U_10582))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10574,U_10576)),hAPP(hAPP(c_Product__Type_OPair(U_10574,U_10576),U_10580),U_10582)),U_10578)) )
& ! [U_10581,U_10579,U_10577,U_10575,U_10573] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10573,U_10575)),hAPP(hAPP(c_Product__Type_OPair(U_10573,U_10575),U_10579),U_10581)),U_10577))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10573,U_10575,U_10577),U_10579),U_10581)) ) ),
inference(miniscope,[status(thm)],[f_2884_2]) ).
fof(f_2884_4,plain,
( ! [U_10574,U_10576,U_10578,U_10580,U_10582] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10574,U_10576,U_10578),U_10580),U_10582))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10574,U_10576)),hAPP(hAPP(c_Product__Type_OPair(U_10574,U_10576),U_10580),U_10582)),U_10578)) )
& ! [U_10577,U_10575,U_10579,U_10573,U_10581] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10573,U_10575)),hAPP(hAPP(c_Product__Type_OPair(U_10573,U_10575),U_10579),U_10581)),U_10577))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10573,U_10575,U_10577),U_10579),U_10581)) ) ),
inference(definitional_conversion,[status(esa)],[f_2884_3]) ).
cnf(f_2884_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10573,U_10575)),hAPP(hAPP(c_Product__Type_OPair(U_10573,U_10575),U_10579),U_10581)),U_10577))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10573,U_10575,U_10577),U_10579),U_10581)) ),
inference(clausify,[status(thm)],[f_2884_4]) ).
cnf(f_2884_6,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10574,U_10576,U_10578),U_10580),U_10582))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10574,U_10576)),hAPP(hAPP(c_Product__Type_OPair(U_10574,U_10576),U_10580),U_10582)),U_10578)) ),
inference(clausify,[status(thm)],[f_2884_4]) ).
fof(f_2885_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_div__mod__code__numeral__def]) ).
fof(f_2885_2,plain,
! [U_10584,U_10583] : c_Code__Numeral_Odiv__mod__code__numeral(U_10583,U_10584) = 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),U_10583),U_10584)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_10583,U_10584)),
inference(variable_rename,[status(thm)],[f_2885_1]) ).
fof(f_2885_3,plain,
! [U_10584,U_10583] : c_Code__Numeral_Odiv__mod__code__numeral(U_10583,U_10584) = 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),U_10583),U_10584)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_10583,U_10584)),
inference(definitional_conversion,[status(esa)],[f_2885_2]) ).
cnf(f_2885_4,plain,
c_Code__Numeral_Odiv__mod__code__numeral(U_10583,U_10584) = 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),U_10583),U_10584)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_10583,U_10584)),
inference(clausify,[status(thm)],[f_2885_3]) ).
fof(f_2886_1,plain,
! [V_r_2,T_b] :
( ( c_Nitpick_Orefl_H(T_b,V_r_2)
| ? [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)) )
& ( ! [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))
| ~ c_Nitpick_Orefl_H(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def]) ).
fof(f_2886_2,plain,
! [U_10588,U_10587] :
( ( c_Nitpick_Orefl_H(U_10587,U_10588)
| ? [U_10586] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10587,U_10587)),hAPP(hAPP(c_Product__Type_OPair(U_10587,U_10587),U_10586),U_10586)),U_10588)) )
& ( ! [U_10585] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10587,U_10587)),hAPP(hAPP(c_Product__Type_OPair(U_10587,U_10587),U_10585),U_10585)),U_10588))
| ~ c_Nitpick_Orefl_H(U_10587,U_10588) ) ),
inference(variable_rename,[status(thm)],[f_2886_1]) ).
fof(f_2886_3,plain,
( ! [U_10592,U_10590] :
( c_Nitpick_Orefl_H(U_10590,U_10592)
| ? [U_10586] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10590,U_10590)),hAPP(hAPP(c_Product__Type_OPair(U_10590,U_10590),U_10586),U_10586)),U_10592)) )
& ! [U_10591,U_10589] :
( ! [U_10585] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10589,U_10589)),hAPP(hAPP(c_Product__Type_OPair(U_10589,U_10589),U_10585),U_10585)),U_10591))
| ~ c_Nitpick_Orefl_H(U_10589,U_10591) ) ),
inference(miniscope,[status(thm)],[f_2886_2]) ).
fof(f_2886_4,plain,
( ! [U_10592,U_10590] :
( c_Nitpick_Orefl_H(U_10590,U_10592)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10590,U_10590)),hAPP(hAPP(c_Product__Type_OPair(U_10590,U_10590),sK261(U_10592,U_10590)),sK261(U_10592,U_10590))),U_10592)) )
& ! [U_10591,U_10589] :
( ! [U_10585] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10589,U_10589)),hAPP(hAPP(c_Product__Type_OPair(U_10589,U_10589),U_10585),U_10585)),U_10591))
| ~ c_Nitpick_Orefl_H(U_10589,U_10591) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_10586,sK261(U_10592,U_10590))],[f_2886_3]) ).
fof(f_2886_5,plain,
( ! [U_10592,U_10590] :
( c_Nitpick_Orefl_H(U_10590,U_10592)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10590,U_10590)),hAPP(hAPP(c_Product__Type_OPair(U_10590,U_10590),sK261(U_10592,U_10590)),sK261(U_10592,U_10590))),U_10592)) )
& ! [U_10585,U_10591,U_10589] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10589,U_10589)),hAPP(hAPP(c_Product__Type_OPair(U_10589,U_10589),U_10585),U_10585)),U_10591))
| ~ c_Nitpick_Orefl_H(U_10589,U_10591) ) ),
inference(definitional_conversion,[status(esa)],[f_2886_4]) ).
cnf(f_2886_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10589,U_10589)),hAPP(hAPP(c_Product__Type_OPair(U_10589,U_10589),U_10585),U_10585)),U_10591))
| ~ c_Nitpick_Orefl_H(U_10589,U_10591) ),
inference(clausify,[status(thm)],[f_2886_5]) ).
cnf(f_2886_7,plain,
( c_Nitpick_Orefl_H(U_10590,U_10592)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10590,U_10590)),hAPP(hAPP(c_Product__Type_OPair(U_10590,U_10590),sK261(U_10592,U_10590)),sK261(U_10592,U_10590))),U_10592)) ),
inference(clausify,[status(thm)],[f_2886_5]) ).
fof(f_2887_1,plain,
! [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))))))),
inference(fof_nnf,[status(thm)],[fact_adjust__def]) ).
fof(f_2887_2,plain,
! [U_10593] : c_Divides_Oadjust(U_10593) = 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)),U_10593))))),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)),U_10593))))),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))))))),
inference(variable_rename,[status(thm)],[f_2887_1]) ).
fof(f_2887_3,plain,
! [U_10593] : c_Divides_Oadjust(U_10593) = 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)),U_10593))))),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)),U_10593))))),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))))))),
inference(definitional_conversion,[status(esa)],[f_2887_2]) ).
cnf(f_2887_4,plain,
c_Divides_Oadjust(U_10593) = 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)),U_10593))))),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)),U_10593))))),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))))))),
inference(clausify,[status(thm)],[f_2887_3]) ).
fof(f_2888_1,plain,
! [V_m,V_n] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__step]) ).
fof(f_2888_2,plain,
! [U_10595,U_10594] :
( c_Divides_Odivmod__nat(U_10595,U_10594) = 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),U_10595),U_10594)),U_10594))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10595),U_10594),U_10594))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10594),U_10595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10594)) ),
inference(variable_rename,[status(thm)],[f_2888_1]) ).
fof(f_2888_3,plain,
! [U_10594,U_10595] :
( c_Divides_Odivmod__nat(U_10595,U_10594) = 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),U_10595),U_10594)),U_10594))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10595),U_10594),U_10594))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10594),U_10595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10594)) ),
inference(definitional_conversion,[status(esa)],[f_2888_2]) ).
cnf(f_2888_4,plain,
( c_Divides_Odivmod__nat(U_10595,U_10594) = 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),U_10595),U_10594)),U_10594))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10595),U_10594),U_10594))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10594),U_10595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10594)) ),
inference(clausify,[status(thm)],[f_2888_3]) ).
fof(f_2889_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_nat__rec__add__eq__if]) ).
fof(f_2889_2,plain,
! [U_10600,U_10599,U_10598,U_10597,U_10596] : hAPP(c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10599)),U_10600)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10596),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10599))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10596,U_10596),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10596,tc_fun(U_10596,U_10596)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10596,tc_fun(U_10596,U_10596)),tc_Int_Oint),c_If(U_10596)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598),U_10600))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10596,U_10596),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10596,U_10596),tc_Int_Oint),U_10598),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)),U_10600))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10596,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598)),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)),U_10600))))),
inference(variable_rename,[status(thm)],[f_2889_1]) ).
fof(f_2889_3,plain,
! [U_10596,U_10597,U_10598,U_10599,U_10600] : hAPP(c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10599)),U_10600)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10596),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10599))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10596,U_10596),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10596,tc_fun(U_10596,U_10596)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10596,tc_fun(U_10596,U_10596)),tc_Int_Oint),c_If(U_10596)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598),U_10600))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10596,U_10596),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10596,U_10596),tc_Int_Oint),U_10598),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)),U_10600))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10596,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598)),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)),U_10600))))),
inference(definitional_conversion,[status(esa)],[f_2889_2]) ).
cnf(f_2889_4,plain,
hAPP(c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10599)),U_10600)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10596),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10599))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10596,U_10596),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10596,tc_fun(U_10596,U_10596)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10596,tc_fun(U_10596,U_10596)),tc_Int_Oint),c_If(U_10596)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598),U_10600))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10596,U_10596),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10596,U_10596),tc_Int_Oint),U_10598),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)),U_10600))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10596,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10596,U_10597,U_10598)),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)),U_10600))))),
inference(clausify,[status(thm)],[f_2889_3]) ).
fof(f_2890_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_nat__rec__0]) ).
fof(f_2890_2,plain,
! [U_10603,U_10602,U_10601] : hAPP(c_Nat_Onat_Onat__rec(U_10601,U_10602,U_10603),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10602,
inference(variable_rename,[status(thm)],[f_2890_1]) ).
fof(f_2890_3,plain,
! [U_10601,U_10603,U_10602] : hAPP(c_Nat_Onat_Onat__rec(U_10601,U_10602,U_10603),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10602,
inference(definitional_conversion,[status(esa)],[f_2890_2]) ).
cnf(f_2890_4,plain,
hAPP(c_Nat_Onat_Onat__rec(U_10601,U_10602,U_10603),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10602,
inference(clausify,[status(thm)],[f_2890_3]) ).
fof(f_2891_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_nat__rec__Suc]) ).
fof(f_2891_2,plain,
! [U_10607,U_10606,U_10605,U_10604] : hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),hAPP(c_Nat_OSuc,U_10607)) = hAPP(hAPP(U_10606,U_10607),hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),U_10607)),
inference(variable_rename,[status(thm)],[f_2891_1]) ).
fof(f_2891_3,plain,
! [U_10604,U_10606,U_10605,U_10607] : hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),hAPP(c_Nat_OSuc,U_10607)) = hAPP(hAPP(U_10606,U_10607),hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),U_10607)),
inference(definitional_conversion,[status(esa)],[f_2891_2]) ).
cnf(f_2891_4,plain,
hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),hAPP(c_Nat_OSuc,U_10607)) = hAPP(hAPP(U_10606,U_10607),hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),U_10607)),
inference(clausify,[status(thm)],[f_2891_3]) ).
fof(f_2892_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__zero]) ).
fof(f_2892_2,plain,
! [U_10608] : c_Divides_Odivmod__nat(U_10608,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)),U_10608),
inference(variable_rename,[status(thm)],[f_2892_1]) ).
fof(f_2892_3,plain,
! [U_10608] : c_Divides_Odivmod__nat(U_10608,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)),U_10608),
inference(definitional_conversion,[status(esa)],[f_2892_2]) ).
cnf(f_2892_4,plain,
c_Divides_Odivmod__nat(U_10608,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)),U_10608),
inference(clausify,[status(thm)],[f_2892_3]) ).
fof(f_2893_1,plain,
! [V_n,V_m] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__base]) ).
fof(f_2893_2,plain,
! [U_10610,U_10609] :
( c_Divides_Odivmod__nat(U_10609,U_10610) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10609)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10609),U_10610)) ),
inference(variable_rename,[status(thm)],[f_2893_1]) ).
fof(f_2893_3,plain,
! [U_10609,U_10610] :
( c_Divides_Odivmod__nat(U_10609,U_10610) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10609)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10609),U_10610)) ),
inference(definitional_conversion,[status(esa)],[f_2893_2]) ).
cnf(f_2893_4,plain,
( c_Divides_Odivmod__nat(U_10609,U_10610) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10609)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10609),U_10610)) ),
inference(clausify,[status(thm)],[f_2893_3]) ).
fof(f_2894_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__div__mod]) ).
fof(f_2894_2,plain,
! [U_10612,U_10611] : c_Divides_Odivmod__nat(U_10611,U_10612) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10611),U_10612)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10611,U_10612)),
inference(variable_rename,[status(thm)],[f_2894_1]) ).
fof(f_2894_3,plain,
! [U_10611,U_10612] : c_Divides_Odivmod__nat(U_10611,U_10612) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10611),U_10612)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10611,U_10612)),
inference(definitional_conversion,[status(esa)],[f_2894_2]) ).
cnf(f_2894_4,plain,
c_Divides_Odivmod__nat(U_10611,U_10612) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10611),U_10612)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10611,U_10612)),
inference(clausify,[status(thm)],[f_2894_3]) ).
fof(f_2895_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_nat__rec__number__of]) ).
fof(f_2895_2,plain,
! [U_10616,U_10615,U_10614,U_10613] : hAPP(c_Nat_Onat_Onat__rec(U_10613,U_10614,U_10615),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10616)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10613),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10616))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10613,U_10613),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10613,tc_fun(U_10613,U_10613)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10613,tc_fun(U_10613,U_10613)),tc_Int_Oint),c_If(U_10613)),c_Nat__Numeral_Oneg)),U_10614)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10613,U_10613),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10613,U_10613),tc_Int_Oint),U_10615),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10613,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10613,U_10614,U_10615)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2895_1]) ).
fof(f_2895_3,plain,
! [U_10613,U_10614,U_10615,U_10616] : hAPP(c_Nat_Onat_Onat__rec(U_10613,U_10614,U_10615),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10616)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10613),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10616))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10613,U_10613),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10613,tc_fun(U_10613,U_10613)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10613,tc_fun(U_10613,U_10613)),tc_Int_Oint),c_If(U_10613)),c_Nat__Numeral_Oneg)),U_10614)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10613,U_10613),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10613,U_10613),tc_Int_Oint),U_10615),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10613,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10613,U_10614,U_10615)),c_Int_Onat)))),
inference(definitional_conversion,[status(esa)],[f_2895_2]) ).
cnf(f_2895_4,plain,
hAPP(c_Nat_Onat_Onat__rec(U_10613,U_10614,U_10615),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10616)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10613),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10616))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10613,U_10613),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10613,tc_fun(U_10613,U_10613)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10613,tc_fun(U_10613,U_10613)),tc_Int_Oint),c_If(U_10613)),c_Nat__Numeral_Oneg)),U_10614)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10613,U_10613),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10613,U_10613),tc_Int_Oint),U_10615),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10613,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10613,U_10614,U_10615)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2895_3]) ).
fof(f_2896_1,plain,
! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( 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)))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_pair__imageI]) ).
fof(f_2896_2,plain,
! [U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617] :
( hBOOL(hAPP(hAPP(c_member(U_10622),hAPP(hAPP(U_10623,U_10619),U_10620)),hAPP(c_Set_Oimage(tc_prod(U_10617,U_10618),U_10622,hAPP(c_Product__Type_Oprod_Oprod__case(U_10617,U_10618,U_10622),U_10623)),U_10621)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10617,U_10618)),hAPP(hAPP(c_Product__Type_OPair(U_10617,U_10618),U_10619),U_10620)),U_10621)) ),
inference(variable_rename,[status(thm)],[f_2896_1]) ).
fof(f_2896_3,plain,
! [U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623] :
( hBOOL(hAPP(hAPP(c_member(U_10622),hAPP(hAPP(U_10623,U_10619),U_10620)),hAPP(c_Set_Oimage(tc_prod(U_10617,U_10618),U_10622,hAPP(c_Product__Type_Oprod_Oprod__case(U_10617,U_10618,U_10622),U_10623)),U_10621)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10617,U_10618)),hAPP(hAPP(c_Product__Type_OPair(U_10617,U_10618),U_10619),U_10620)),U_10621)) ),
inference(definitional_conversion,[status(esa)],[f_2896_2]) ).
cnf(f_2896_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10622),hAPP(hAPP(U_10623,U_10619),U_10620)),hAPP(c_Set_Oimage(tc_prod(U_10617,U_10618),U_10622,hAPP(c_Product__Type_Oprod_Oprod__case(U_10617,U_10618,U_10622),U_10623)),U_10621)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10617,U_10618)),hAPP(hAPP(c_Product__Type_OPair(U_10617,U_10618),U_10619),U_10620)),U_10621)) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
fof(f_2897_1,plain,
! [V_k_2,T_b] :
( ( ( ( ( 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)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__num]) ).
fof(f_2897_2,plain,
! [U_10625,U_10624] :
( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_10624),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_10624,U_10624)),tc_fun(tc_Int_Oint,U_10624)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10624,U_10624),U_10624),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_10624,U_10624)),tc_fun(tc_Int_Oint,U_10624)),tc_Int_Oint),c_COMBB(tc_fun(U_10624,U_10624),U_10624,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_10624,tc_fun(tc_fun(U_10624,U_10624),U_10624),tc_Int_Oint),c_HOL_OLet(U_10624,U_10624)),c_Int_Oring__1__class_Oof__int(U_10624)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10624,U_10624),tc_fun(U_10624,U_10624)),hAPP(hAPP(c_COMBB(tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_fun(tc_fun(U_10624,U_10624),tc_fun(U_10624,U_10624)),tc_Int_Oint),c_COMBS(U_10624,U_10624,U_10624)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10624,U_10624),tc_fun(U_10624,tc_fun(U_10624,U_10624))),hAPP(hAPP(c_COMBB(tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_fun(tc_fun(U_10624,U_10624),tc_fun(U_10624,tc_fun(U_10624,U_10624))),tc_Int_Oint),c_COMBB(U_10624,tc_fun(U_10624,U_10624),U_10624)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_Int_Oint),c_If(U_10624)),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(U_10624,U_10624,U_10624),c_Groups_Oplus__class_Oplus(U_10624)),c_COMBI(U_10624))))),hAPP(hAPP(c_COMBC(U_10624,U_10624,U_10624),hAPP(hAPP(c_COMBB(U_10624,tc_fun(U_10624,U_10624),U_10624),c_Groups_Oplus__class_Oplus(U_10624)),hAPP(hAPP(c_COMBS(U_10624,U_10624,U_10624),c_Groups_Oplus__class_Oplus(U_10624)),c_COMBI(U_10624)))),c_Groups_Oone__class_Oone(U_10624))))),c_Divides_Odivmod__int(U_10625,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10624),hAPP(c_Int_Oring__1__class_Oof__int(U_10624),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| U_10625 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = c_Groups_Ozero__class_Ozero(U_10624)
| U_10625 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ class_Rings_Oring__1(U_10624) ),
inference(variable_rename,[status(thm)],[f_2897_1]) ).
fof(f_2897_3,plain,
( ! [U_10624,U_10625] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_10624),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_10624,U_10624)),tc_fun(tc_Int_Oint,U_10624)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10624,U_10624),U_10624),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_10624,U_10624)),tc_fun(tc_Int_Oint,U_10624)),tc_Int_Oint),c_COMBB(tc_fun(U_10624,U_10624),U_10624,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_10624,tc_fun(tc_fun(U_10624,U_10624),U_10624),tc_Int_Oint),c_HOL_OLet(U_10624,U_10624)),c_Int_Oring__1__class_Oof__int(U_10624)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10624,U_10624),tc_fun(U_10624,U_10624)),hAPP(hAPP(c_COMBB(tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_fun(tc_fun(U_10624,U_10624),tc_fun(U_10624,U_10624)),tc_Int_Oint),c_COMBS(U_10624,U_10624,U_10624)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10624,U_10624),tc_fun(U_10624,tc_fun(U_10624,U_10624))),hAPP(hAPP(c_COMBB(tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_fun(tc_fun(U_10624,U_10624),tc_fun(U_10624,tc_fun(U_10624,U_10624))),tc_Int_Oint),c_COMBB(U_10624,tc_fun(U_10624,U_10624),U_10624)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_Int_Oint),c_If(U_10624)),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(U_10624,U_10624,U_10624),c_Groups_Oplus__class_Oplus(U_10624)),c_COMBI(U_10624))))),hAPP(hAPP(c_COMBC(U_10624,U_10624,U_10624),hAPP(hAPP(c_COMBB(U_10624,tc_fun(U_10624,U_10624),U_10624),c_Groups_Oplus__class_Oplus(U_10624)),hAPP(hAPP(c_COMBS(U_10624,U_10624,U_10624),c_Groups_Oplus__class_Oplus(U_10624)),c_COMBI(U_10624)))),c_Groups_Oone__class_Oone(U_10624))))),c_Divides_Odivmod__int(U_10625,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP822(U_10624,U_10625) )
& ! [U_10624,U_10625] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10624),hAPP(c_Int_Oring__1__class_Oof__int(U_10624),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP822(U_10624,U_10625) )
& ! [U_10624,U_10625] :
( sP822(U_10624,U_10625)
| U_10625 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP823(U_10624,U_10625) )
& ! [U_10624,U_10625] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = c_Groups_Ozero__class_Ozero(U_10624)
| U_10625 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP823(U_10624,U_10625) )
& ! [U_10624,U_10625] :
( sP823(U_10624,U_10625)
| ~ class_Rings_Oring__1(U_10624) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP822,sP823])],[f_2897_2]) ).
cnf(f_2897_4,plain,
( sP823(U_10624,U_10625)
| ~ class_Rings_Oring__1(U_10624) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
cnf(f_2897_5,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = c_Groups_Ozero__class_Ozero(U_10624)
| U_10625 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP823(U_10624,U_10625) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
cnf(f_2897_6,plain,
( sP822(U_10624,U_10625)
| U_10625 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP823(U_10624,U_10625) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
cnf(f_2897_7,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10624),hAPP(c_Int_Oring__1__class_Oof__int(U_10624),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP822(U_10624,U_10625) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
cnf(f_2897_8,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_10624),U_10625) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_10624),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_10624,U_10624)),tc_fun(tc_Int_Oint,U_10624)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10624,U_10624),U_10624),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_10624,U_10624)),tc_fun(tc_Int_Oint,U_10624)),tc_Int_Oint),c_COMBB(tc_fun(U_10624,U_10624),U_10624,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_10624,tc_fun(tc_fun(U_10624,U_10624),U_10624),tc_Int_Oint),c_HOL_OLet(U_10624,U_10624)),c_Int_Oring__1__class_Oof__int(U_10624)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10624,U_10624),tc_fun(U_10624,U_10624)),hAPP(hAPP(c_COMBB(tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_fun(tc_fun(U_10624,U_10624),tc_fun(U_10624,U_10624)),tc_Int_Oint),c_COMBS(U_10624,U_10624,U_10624)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10624,U_10624),tc_fun(U_10624,tc_fun(U_10624,U_10624))),hAPP(hAPP(c_COMBB(tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_fun(tc_fun(U_10624,U_10624),tc_fun(U_10624,tc_fun(U_10624,U_10624))),tc_Int_Oint),c_COMBB(U_10624,tc_fun(U_10624,U_10624),U_10624)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10624,tc_fun(U_10624,U_10624)),tc_Int_Oint),c_If(U_10624)),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(U_10624,U_10624,U_10624),c_Groups_Oplus__class_Oplus(U_10624)),c_COMBI(U_10624))))),hAPP(hAPP(c_COMBC(U_10624,U_10624,U_10624),hAPP(hAPP(c_COMBB(U_10624,tc_fun(U_10624,U_10624),U_10624),c_Groups_Oplus__class_Oplus(U_10624)),hAPP(hAPP(c_COMBS(U_10624,U_10624,U_10624),c_Groups_Oplus__class_Oplus(U_10624)),c_COMBI(U_10624)))),c_Groups_Oone__class_Oone(U_10624))))),c_Divides_Odivmod__int(U_10625,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP822(U_10624,U_10625) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
fof(f_2898_1,plain,
! [V_n_2,T_b] :
( 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))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code]) ).
fof(f_2898_2,plain,
! [U_10627,U_10626] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10626),U_10627) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10626,hAPP(hAPP(c_COMBC(U_10626,U_10626,U_10626),c_Groups_Oplus__class_Oplus(U_10626)),c_Groups_Oone__class_Oone(U_10626)),U_10627,c_Groups_Ozero__class_Ozero(U_10626))
| ~ class_Rings_Osemiring__1(U_10626) ),
inference(variable_rename,[status(thm)],[f_2898_1]) ).
fof(f_2898_3,plain,
! [U_10627,U_10626] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10626),U_10627) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10626,hAPP(hAPP(c_COMBC(U_10626,U_10626,U_10626),c_Groups_Oplus__class_Oplus(U_10626)),c_Groups_Oone__class_Oone(U_10626)),U_10627,c_Groups_Ozero__class_Ozero(U_10626))
| ~ class_Rings_Osemiring__1(U_10626) ),
inference(definitional_conversion,[status(esa)],[f_2898_2]) ).
cnf(f_2898_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10626),U_10627) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10626,hAPP(hAPP(c_COMBC(U_10626,U_10626,U_10626),c_Groups_Oplus__class_Oplus(U_10626)),c_Groups_Oone__class_Oone(U_10626)),U_10627,c_Groups_Ozero__class_Ozero(U_10626))
| ~ class_Rings_Osemiring__1(U_10626) ),
inference(clausify,[status(thm)],[f_2898_3]) ).
fof(f_2899_1,plain,
! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
( 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)))
| ~ hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_splitI]) ).
fof(f_2899_2,plain,
! [U_10632,U_10631,U_10630,U_10629,U_10628] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10631,U_10632,tc_HOL_Obool),U_10628),hAPP(hAPP(c_Product__Type_OPair(U_10631,U_10632),U_10629),U_10630)))
| ~ hBOOL(hAPP(hAPP(U_10628,U_10629),U_10630)) ),
inference(variable_rename,[status(thm)],[f_2899_1]) ).
fof(f_2899_3,plain,
! [U_10629,U_10630,U_10631,U_10628,U_10632] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10631,U_10632,tc_HOL_Obool),U_10628),hAPP(hAPP(c_Product__Type_OPair(U_10631,U_10632),U_10629),U_10630)))
| ~ hBOOL(hAPP(hAPP(U_10628,U_10629),U_10630)) ),
inference(definitional_conversion,[status(esa)],[f_2899_2]) ).
cnf(f_2899_4,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10631,U_10632,tc_HOL_Obool),U_10628),hAPP(hAPP(c_Product__Type_OPair(U_10631,U_10632),U_10629),U_10630)))
| ~ hBOOL(hAPP(hAPP(U_10628,U_10629),U_10630)) ),
inference(clausify,[status(thm)],[f_2899_3]) ).
fof(f_2900_1,plain,
! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
( 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)))
| ~ hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_prod__caseI]) ).
fof(f_2900_2,plain,
! [U_10637,U_10636,U_10635,U_10634,U_10633] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10636,U_10637,tc_HOL_Obool),U_10633),hAPP(hAPP(c_Product__Type_OPair(U_10636,U_10637),U_10634),U_10635)))
| ~ hBOOL(hAPP(hAPP(U_10633,U_10634),U_10635)) ),
inference(variable_rename,[status(thm)],[f_2900_1]) ).
fof(f_2900_3,plain,
! [U_10634,U_10633,U_10635,U_10636,U_10637] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10636,U_10637,tc_HOL_Obool),U_10633),hAPP(hAPP(c_Product__Type_OPair(U_10636,U_10637),U_10634),U_10635)))
| ~ hBOOL(hAPP(hAPP(U_10633,U_10634),U_10635)) ),
inference(definitional_conversion,[status(esa)],[f_2900_2]) ).
cnf(f_2900_4,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10636,U_10637,tc_HOL_Obool),U_10633),hAPP(hAPP(c_Product__Type_OPair(U_10636,U_10637),U_10634),U_10635)))
| ~ hBOOL(hAPP(hAPP(U_10633,U_10634),U_10635)) ),
inference(clausify,[status(thm)],[f_2900_3]) ).
fof(f_2901_1,plain,
! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
( 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_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) ),
inference(fof_nnf,[status(thm)],[fact_mem__splitI]) ).
fof(f_2901_2,plain,
! [U_10644,U_10643,U_10642,U_10641,U_10640,U_10639,U_10638] :
( hBOOL(hAPP(hAPP(c_member(U_10638),U_10639),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10643,U_10644,tc_fun(U_10638,tc_HOL_Obool)),U_10640),hAPP(hAPP(c_Product__Type_OPair(U_10643,U_10644),U_10641),U_10642))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10638),U_10639),hAPP(hAPP(U_10640,U_10641),U_10642))) ),
inference(variable_rename,[status(thm)],[f_2901_1]) ).
fof(f_2901_3,plain,
! [U_10638,U_10639,U_10640,U_10641,U_10642,U_10643,U_10644] :
( hBOOL(hAPP(hAPP(c_member(U_10638),U_10639),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10643,U_10644,tc_fun(U_10638,tc_HOL_Obool)),U_10640),hAPP(hAPP(c_Product__Type_OPair(U_10643,U_10644),U_10641),U_10642))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10638),U_10639),hAPP(hAPP(U_10640,U_10641),U_10642))) ),
inference(definitional_conversion,[status(esa)],[f_2901_2]) ).
cnf(f_2901_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10638),U_10639),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10643,U_10644,tc_fun(U_10638,tc_HOL_Obool)),U_10640),hAPP(hAPP(c_Product__Type_OPair(U_10643,U_10644),U_10641),U_10642))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10638),U_10639),hAPP(hAPP(U_10640,U_10641),U_10642))) ),
inference(clausify,[status(thm)],[f_2901_3]) ).
fof(f_2902_1,plain,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_splitD]) ).
fof(f_2902_2,plain,
! [U_10649,U_10648,U_10647,U_10646,U_10645] :
( hBOOL(hAPP(hAPP(U_10647,U_10648),U_10649))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10645,U_10646,tc_HOL_Obool),U_10647),hAPP(hAPP(c_Product__Type_OPair(U_10645,U_10646),U_10648),U_10649))) ),
inference(variable_rename,[status(thm)],[f_2902_1]) ).
fof(f_2902_3,plain,
! [U_10649,U_10648,U_10647] :
( ! [U_10646,U_10645] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10645,U_10646,tc_HOL_Obool),U_10647),hAPP(hAPP(c_Product__Type_OPair(U_10645,U_10646),U_10648),U_10649)))
| hBOOL(hAPP(hAPP(U_10647,U_10648),U_10649)) ),
inference(miniscope,[status(thm)],[f_2902_2]) ).
fof(f_2902_4,plain,
! [U_10646,U_10645,U_10647,U_10648,U_10649] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10645,U_10646,tc_HOL_Obool),U_10647),hAPP(hAPP(c_Product__Type_OPair(U_10645,U_10646),U_10648),U_10649)))
| hBOOL(hAPP(hAPP(U_10647,U_10648),U_10649)) ),
inference(definitional_conversion,[status(esa)],[f_2902_3]) ).
cnf(f_2902_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10645,U_10646,tc_HOL_Obool),U_10647),hAPP(hAPP(c_Product__Type_OPair(U_10645,U_10646),U_10648),U_10649)))
| hBOOL(hAPP(hAPP(U_10647,U_10648),U_10649)) ),
inference(clausify,[status(thm)],[f_2902_4]) ).
fof(f_2903_1,plain,
! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2))
| ~ 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_ca_2)) ),
inference(fof_nnf,[status(thm)],[fact_splitD_H]) ).
fof(f_2903_2,plain,
! [U_10656,U_10655,U_10654,U_10653,U_10652,U_10651,U_10650] :
( hBOOL(hAPP(hAPP(hAPP(U_10653,U_10654),U_10655),U_10656))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10650,U_10651,tc_fun(U_10652,tc_HOL_Obool)),U_10653),hAPP(hAPP(c_Product__Type_OPair(U_10650,U_10651),U_10654),U_10655)),U_10656)) ),
inference(variable_rename,[status(thm)],[f_2903_1]) ).
fof(f_2903_3,plain,
! [U_10656,U_10655,U_10654,U_10653] :
( ! [U_10652,U_10651,U_10650] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10650,U_10651,tc_fun(U_10652,tc_HOL_Obool)),U_10653),hAPP(hAPP(c_Product__Type_OPair(U_10650,U_10651),U_10654),U_10655)),U_10656))
| hBOOL(hAPP(hAPP(hAPP(U_10653,U_10654),U_10655),U_10656)) ),
inference(miniscope,[status(thm)],[f_2903_2]) ).
fof(f_2903_4,plain,
! [U_10650,U_10651,U_10652,U_10653,U_10654,U_10655,U_10656] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10650,U_10651,tc_fun(U_10652,tc_HOL_Obool)),U_10653),hAPP(hAPP(c_Product__Type_OPair(U_10650,U_10651),U_10654),U_10655)),U_10656))
| hBOOL(hAPP(hAPP(hAPP(U_10653,U_10654),U_10655),U_10656)) ),
inference(definitional_conversion,[status(esa)],[f_2903_3]) ).
cnf(f_2903_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10650,U_10651,tc_fun(U_10652,tc_HOL_Obool)),U_10653),hAPP(hAPP(c_Product__Type_OPair(U_10650,U_10651),U_10654),U_10655)),U_10656))
| hBOOL(hAPP(hAPP(hAPP(U_10653,U_10654),U_10655),U_10656)) ),
inference(clausify,[status(thm)],[f_2903_4]) ).
fof(f_2904_1,plain,
! [V_i_2,V_inc_2,T_b] :
( 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
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J]) ).
fof(f_2904_2,plain,
! [U_10659,U_10658,U_10657] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10657,U_10658,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_10659) = U_10659
| ~ class_Rings_Osemiring__1(U_10657) ),
inference(variable_rename,[status(thm)],[f_2904_1]) ).
fof(f_2904_3,plain,
! [U_10657,U_10658,U_10659] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10657,U_10658,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_10659) = U_10659
| ~ class_Rings_Osemiring__1(U_10657) ),
inference(definitional_conversion,[status(esa)],[f_2904_2]) ).
cnf(f_2904_4,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10657,U_10658,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_10659) = U_10659
| ~ class_Rings_Osemiring__1(U_10657) ),
inference(clausify,[status(thm)],[f_2904_3]) ).
fof(f_2905_1,plain,
! [V_i_2,V_n_2,V_inc_2,T_b] :
( 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))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J]) ).
fof(f_2905_2,plain,
! [U_10663,U_10662,U_10661,U_10660] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10660,U_10661,hAPP(c_Nat_OSuc,U_10662),U_10663) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10660,U_10661,U_10662,hAPP(U_10661,U_10663))
| ~ class_Rings_Osemiring__1(U_10660) ),
inference(variable_rename,[status(thm)],[f_2905_1]) ).
fof(f_2905_3,plain,
! [U_10662,U_10660,U_10661,U_10663] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10660,U_10661,hAPP(c_Nat_OSuc,U_10662),U_10663) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10660,U_10661,U_10662,hAPP(U_10661,U_10663))
| ~ class_Rings_Osemiring__1(U_10660) ),
inference(definitional_conversion,[status(esa)],[f_2905_2]) ).
cnf(f_2905_4,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10660,U_10661,hAPP(c_Nat_OSuc,U_10662),U_10663) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10660,U_10661,U_10662,hAPP(U_10661,U_10663))
| ~ class_Rings_Osemiring__1(U_10660) ),
inference(clausify,[status(thm)],[f_2905_3]) ).
fof(f_2906_1,plain,
! [T_c,T_b,V_Pa_2] :
( ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
| ? [B_a,B_b] : ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) )
& ( ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)))
| ? [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).
fof(f_2906_2,plain,
! [U_10672,U_10671,U_10670] :
( ( ! [U_10669] : hBOOL(hAPP(U_10670,U_10669))
| ? [U_10668,U_10667] : ~ hBOOL(hAPP(U_10670,hAPP(hAPP(c_Product__Type_OPair(U_10671,U_10672),U_10668),U_10667))) )
& ( ! [U_10666,U_10665] : hBOOL(hAPP(U_10670,hAPP(hAPP(c_Product__Type_OPair(U_10671,U_10672),U_10666),U_10665)))
| ? [U_10664] : ~ hBOOL(hAPP(U_10670,U_10664)) ) ),
inference(variable_rename,[status(thm)],[f_2906_1]) ).
fof(f_2906_3,plain,
( ! [U_10678,U_10676,U_10674] :
( ! [U_10669] : hBOOL(hAPP(U_10674,U_10669))
| ? [U_10668,U_10667] : ~ hBOOL(hAPP(U_10674,hAPP(hAPP(c_Product__Type_OPair(U_10676,U_10678),U_10668),U_10667))) )
& ! [U_10677,U_10675,U_10673] :
( ! [U_10666,U_10665] : hBOOL(hAPP(U_10673,hAPP(hAPP(c_Product__Type_OPair(U_10675,U_10677),U_10666),U_10665)))
| ? [U_10664] : ~ hBOOL(hAPP(U_10673,U_10664)) ) ),
inference(miniscope,[status(thm)],[f_2906_2]) ).
fof(f_2906_4,plain,
( ! [U_10678,U_10676,U_10674] :
( ! [U_10669] : hBOOL(hAPP(U_10674,U_10669))
| ? [U_10668,U_10667] : ~ hBOOL(hAPP(U_10674,hAPP(hAPP(c_Product__Type_OPair(U_10676,U_10678),U_10668),U_10667))) )
& ! [U_10677,U_10675,U_10673] :
( ! [U_10666,U_10665] : hBOOL(hAPP(U_10673,hAPP(hAPP(c_Product__Type_OPair(U_10675,U_10677),U_10666),U_10665)))
| ~ hBOOL(hAPP(U_10673,sK262(U_10677,U_10675,U_10673))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_10664,sK262(U_10677,U_10675,U_10673))],[f_2906_3]) ).
fof(f_2906_5,plain,
( ! [U_10678,U_10676,U_10674] :
( ! [U_10669] : hBOOL(hAPP(U_10674,U_10669))
| ? [U_10667] : ~ hBOOL(hAPP(U_10674,hAPP(hAPP(c_Product__Type_OPair(U_10676,U_10678),sK263(U_10678,U_10676,U_10674)),U_10667))) )
& ! [U_10677,U_10675,U_10673] :
( ! [U_10666,U_10665] : hBOOL(hAPP(U_10673,hAPP(hAPP(c_Product__Type_OPair(U_10675,U_10677),U_10666),U_10665)))
| ~ hBOOL(hAPP(U_10673,sK262(U_10677,U_10675,U_10673))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_10668,sK263(U_10678,U_10676,U_10674))],[f_2906_4]) ).
fof(f_2906_6,plain,
( ! [U_10678,U_10676,U_10674] :
( ! [U_10669] : hBOOL(hAPP(U_10674,U_10669))
| ~ hBOOL(hAPP(U_10674,hAPP(hAPP(c_Product__Type_OPair(U_10676,U_10678),sK263(U_10678,U_10676,U_10674)),sK264(U_10678,U_10676,U_10674)))) )
& ! [U_10677,U_10675,U_10673] :
( ! [U_10666,U_10665] : hBOOL(hAPP(U_10673,hAPP(hAPP(c_Product__Type_OPair(U_10675,U_10677),U_10666),U_10665)))
| ~ hBOOL(hAPP(U_10673,sK262(U_10677,U_10675,U_10673))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_10667,sK264(U_10678,U_10676,U_10674))],[f_2906_5]) ).
fof(f_2906_7,plain,
( ! [U_10669,U_10674,U_10676,U_10678] :
( hBOOL(hAPP(U_10674,U_10669))
| ~ hBOOL(hAPP(U_10674,hAPP(hAPP(c_Product__Type_OPair(U_10676,U_10678),sK263(U_10678,U_10676,U_10674)),sK264(U_10678,U_10676,U_10674)))) )
& ! [U_10675,U_10665,U_10666,U_10673,U_10677] :
( hBOOL(hAPP(U_10673,hAPP(hAPP(c_Product__Type_OPair(U_10675,U_10677),U_10666),U_10665)))
| ~ hBOOL(hAPP(U_10673,sK262(U_10677,U_10675,U_10673))) ) ),
inference(definitional_conversion,[status(esa)],[f_2906_6]) ).
cnf(f_2906_8,plain,
( hBOOL(hAPP(U_10673,hAPP(hAPP(c_Product__Type_OPair(U_10675,U_10677),U_10666),U_10665)))
| ~ hBOOL(hAPP(U_10673,sK262(U_10677,U_10675,U_10673))) ),
inference(clausify,[status(thm)],[f_2906_7]) ).
cnf(f_2906_9,plain,
( hBOOL(hAPP(U_10674,U_10669))
| ~ hBOOL(hAPP(U_10674,hAPP(hAPP(c_Product__Type_OPair(U_10676,U_10678),sK263(U_10678,U_10676,U_10674)),sK264(U_10678,U_10676,U_10674)))) ),
inference(clausify,[status(thm)],[f_2906_7]) ).
fof(f_2907_1,plain,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( ( 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)
| V_b_2 != V_b_H_2
| V_a_2 != V_a_H_2 )
& ( ( V_b_2 = V_b_H_2
& V_a_2 = V_a_H_2 )
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_Pair__eq]) ).
fof(f_2907_2,plain,
! [U_10684,U_10683,U_10682,U_10681,U_10680,U_10679] :
( ( hAPP(hAPP(c_Product__Type_OPair(U_10679,U_10680),U_10681),U_10682) = hAPP(hAPP(c_Product__Type_OPair(U_10679,U_10680),U_10683),U_10684)
| U_10682 != U_10684
| U_10681 != U_10683 )
& ( ( U_10682 = U_10684
& U_10681 = U_10683 )
| hAPP(hAPP(c_Product__Type_OPair(U_10679,U_10680),U_10681),U_10682) != hAPP(hAPP(c_Product__Type_OPair(U_10679,U_10680),U_10683),U_10684) ) ),
inference(variable_rename,[status(thm)],[f_2907_1]) ).
fof(f_2907_3,plain,
( ! [U_10696,U_10694,U_10692,U_10690] :
( ! [U_10688,U_10686] : hAPP(hAPP(c_Product__Type_OPair(U_10686,U_10688),U_10690),U_10692) = hAPP(hAPP(c_Product__Type_OPair(U_10686,U_10688),U_10694),U_10696)
| U_10692 != U_10696
| U_10690 != U_10694 )
& ! [U_10695,U_10693,U_10691,U_10689] :
( ! [U_10687,U_10685] : hAPP(hAPP(c_Product__Type_OPair(U_10685,U_10687),U_10689),U_10691) != hAPP(hAPP(c_Product__Type_OPair(U_10685,U_10687),U_10693),U_10695)
| ( U_10691 = U_10695
& U_10689 = U_10693 ) ) ),
inference(miniscope,[status(thm)],[f_2907_2]) ).
fof(f_2907_4,plain,
( ! [U_10693,U_10691,U_10689,U_10695] :
( U_10691 = U_10695
| ~ sP824(U_10693,U_10691,U_10689,U_10695) )
& ! [U_10693,U_10691,U_10689,U_10695] :
( U_10689 = U_10693
| ~ sP824(U_10693,U_10691,U_10689,U_10695) )
& ! [U_10696,U_10690,U_10692,U_10686,U_10688,U_10694] :
( hAPP(hAPP(c_Product__Type_OPair(U_10686,U_10688),U_10690),U_10692) = hAPP(hAPP(c_Product__Type_OPair(U_10686,U_10688),U_10694),U_10696)
| U_10692 != U_10696
| U_10690 != U_10694 )
& ! [U_10687,U_10693,U_10691,U_10685,U_10689,U_10695] :
( hAPP(hAPP(c_Product__Type_OPair(U_10685,U_10687),U_10689),U_10691) != hAPP(hAPP(c_Product__Type_OPair(U_10685,U_10687),U_10693),U_10695)
| sP824(U_10693,U_10691,U_10689,U_10695) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP824])],[f_2907_3]) ).
cnf(f_2907_5,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_10685,U_10687),U_10689),U_10691) != hAPP(hAPP(c_Product__Type_OPair(U_10685,U_10687),U_10693),U_10695)
| sP824(U_10693,U_10691,U_10689,U_10695) ),
inference(clausify,[status(thm)],[f_2907_4]) ).
cnf(f_2907_6,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_10686,U_10688),U_10690),U_10692) = hAPP(hAPP(c_Product__Type_OPair(U_10686,U_10688),U_10694),U_10696)
| U_10692 != U_10696
| U_10690 != U_10694 ),
inference(clausify,[status(thm)],[f_2907_4]) ).
cnf(f_2907_7,plain,
( U_10689 = U_10693
| ~ sP824(U_10693,U_10691,U_10689,U_10695) ),
inference(clausify,[status(thm)],[f_2907_4]) ).
cnf(f_2907_8,plain,
( U_10691 = U_10695
| ~ sP824(U_10693,U_10691,U_10689,U_10695) ),
inference(clausify,[status(thm)],[f_2907_4]) ).
fof(f_2908_1,plain,
! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
( ( V_b = V_b_H
& V_a = V_a_H )
| 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) ),
inference(fof_nnf,[status(thm)],[fact_Pair__inject]) ).
fof(f_2908_2,plain,
! [U_10702,U_10701,U_10700,U_10699,U_10698,U_10697] :
( ( U_10700 = U_10702
& U_10699 = U_10701 )
| hAPP(hAPP(c_Product__Type_OPair(U_10697,U_10698),U_10699),U_10700) != hAPP(hAPP(c_Product__Type_OPair(U_10697,U_10698),U_10701),U_10702) ),
inference(variable_rename,[status(thm)],[f_2908_1]) ).
fof(f_2908_3,plain,
! [U_10702,U_10701,U_10700,U_10699] :
( ! [U_10698,U_10697] : hAPP(hAPP(c_Product__Type_OPair(U_10697,U_10698),U_10699),U_10700) != hAPP(hAPP(c_Product__Type_OPair(U_10697,U_10698),U_10701),U_10702)
| ( U_10700 = U_10702
& U_10699 = U_10701 ) ),
inference(miniscope,[status(thm)],[f_2908_2]) ).
fof(f_2908_4,plain,
( ! [U_10699,U_10700,U_10701,U_10702] :
( U_10700 = U_10702
| ~ sP825(U_10699,U_10700,U_10701,U_10702) )
& ! [U_10699,U_10700,U_10701,U_10702] :
( U_10699 = U_10701
| ~ sP825(U_10699,U_10700,U_10701,U_10702) )
& ! [U_10699,U_10697,U_10700,U_10701,U_10698,U_10702] :
( hAPP(hAPP(c_Product__Type_OPair(U_10697,U_10698),U_10699),U_10700) != hAPP(hAPP(c_Product__Type_OPair(U_10697,U_10698),U_10701),U_10702)
| sP825(U_10699,U_10700,U_10701,U_10702) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP825])],[f_2908_3]) ).
cnf(f_2908_5,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_10697,U_10698),U_10699),U_10700) != hAPP(hAPP(c_Product__Type_OPair(U_10697,U_10698),U_10701),U_10702)
| sP825(U_10699,U_10700,U_10701,U_10702) ),
inference(clausify,[status(thm)],[f_2908_4]) ).
cnf(f_2908_6,plain,
( U_10699 = U_10701
| ~ sP825(U_10699,U_10700,U_10701,U_10702) ),
inference(clausify,[status(thm)],[f_2908_4]) ).
cnf(f_2908_7,plain,
( U_10700 = U_10702
| ~ sP825(U_10699,U_10700,U_10701,U_10702) ),
inference(clausify,[status(thm)],[f_2908_4]) ).
fof(f_2909_1,plain,
! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2)
| V_p_2 != V_q_2 ),
inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).
fof(f_2909_2,plain,
! [U_10708,U_10707,U_10706,U_10705,U_10704,U_10703] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10705,U_10706,U_10707),U_10708),U_10703) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10705,U_10706,U_10707),U_10708),U_10704)
| U_10703 != U_10704 ),
inference(variable_rename,[status(thm)],[f_2909_1]) ).
fof(f_2909_3,plain,
! [U_10706,U_10704,U_10705,U_10703,U_10707,U_10708] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10705,U_10706,U_10707),U_10708),U_10703) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10705,U_10706,U_10707),U_10708),U_10704)
| U_10703 != U_10704 ),
inference(definitional_conversion,[status(esa)],[f_2909_2]) ).
cnf(f_2909_4,plain,
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10705,U_10706,U_10707),U_10708),U_10703) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10705,U_10706,U_10707),U_10708),U_10704)
| U_10703 != U_10704 ),
inference(clausify,[status(thm)],[f_2909_3]) ).
fof(f_2910_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_divmod__int__mod__div]) ).
fof(f_2910_2,plain,
! [U_10710,U_10709] : c_Divides_Odivmod__int(U_10709,U_10710) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10709),U_10710)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10710)),
inference(variable_rename,[status(thm)],[f_2910_1]) ).
fof(f_2910_3,plain,
! [U_10709,U_10710] : c_Divides_Odivmod__int(U_10709,U_10710) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10709),U_10710)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10710)),
inference(definitional_conversion,[status(esa)],[f_2910_2]) ).
cnf(f_2910_4,plain,
c_Divides_Odivmod__int(U_10709,U_10710) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10709),U_10710)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10710)),
inference(clausify,[status(thm)],[f_2910_3]) ).
fof(f_2911_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_prod_Osimps_I2_J]) ).
fof(f_2911_2,plain,
! [U_10716,U_10715,U_10714,U_10713,U_10712,U_10711] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10711,U_10712,U_10713),U_10714),hAPP(hAPP(c_Product__Type_OPair(U_10711,U_10712),U_10715),U_10716)) = hAPP(hAPP(U_10714,U_10715),U_10716),
inference(variable_rename,[status(thm)],[f_2911_1]) ).
fof(f_2911_3,plain,
! [U_10711,U_10712,U_10713,U_10714,U_10715,U_10716] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10711,U_10712,U_10713),U_10714),hAPP(hAPP(c_Product__Type_OPair(U_10711,U_10712),U_10715),U_10716)) = hAPP(hAPP(U_10714,U_10715),U_10716),
inference(definitional_conversion,[status(esa)],[f_2911_2]) ).
cnf(f_2911_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10711,U_10712,U_10713),U_10714),hAPP(hAPP(c_Product__Type_OPair(U_10711,U_10712),U_10715),U_10716)) = hAPP(hAPP(U_10714,U_10715),U_10716),
inference(clausify,[status(thm)],[f_2911_3]) ).
fof(f_2912_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_split__conv]) ).
fof(f_2912_2,plain,
! [U_10722,U_10721,U_10720,U_10719,U_10718,U_10717] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10717,U_10718,U_10719),U_10720),hAPP(hAPP(c_Product__Type_OPair(U_10717,U_10718),U_10721),U_10722)) = hAPP(hAPP(U_10720,U_10721),U_10722),
inference(variable_rename,[status(thm)],[f_2912_1]) ).
fof(f_2912_3,plain,
! [U_10717,U_10718,U_10719,U_10720,U_10721,U_10722] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10717,U_10718,U_10719),U_10720),hAPP(hAPP(c_Product__Type_OPair(U_10717,U_10718),U_10721),U_10722)) = hAPP(hAPP(U_10720,U_10721),U_10722),
inference(definitional_conversion,[status(esa)],[f_2912_2]) ).
cnf(f_2912_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10717,U_10718,U_10719),U_10720),hAPP(hAPP(c_Product__Type_OPair(U_10717,U_10718),U_10721),U_10722)) = hAPP(hAPP(U_10720,U_10721),U_10722),
inference(clausify,[status(thm)],[f_2912_3]) ).
fof(f_2913_1,plain,
! [V_m_2,V_n_2] :
( ( 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))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( 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)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
& V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__if]) ).
fof(f_2913_2,plain,
! [U_10724,U_10723] :
( ( c_Divides_Odivmod__nat(U_10724,U_10723) = 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),U_10724),U_10723),U_10723))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10724),U_10723))
| U_10723 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Divides_Odivmod__nat(U_10724,U_10723) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10724)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10724),U_10723))
& U_10723 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(variable_rename,[status(thm)],[f_2913_1]) ).
fof(f_2913_3,plain,
( ! [U_10728,U_10726] :
( c_Divides_Odivmod__nat(U_10728,U_10726) = 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),U_10728),U_10726),U_10726))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10728),U_10726))
| U_10726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_10727,U_10725] :
( c_Divides_Odivmod__nat(U_10727,U_10725) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10727)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10727),U_10725))
& U_10725 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(miniscope,[status(thm)],[f_2913_2]) ).
fof(f_2913_4,plain,
( ! [U_10727,U_10725] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10727),U_10725))
| ~ sP826(U_10727,U_10725) )
& ! [U_10727,U_10725] :
( U_10725 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP826(U_10727,U_10725) )
& ! [U_10726,U_10728] :
( c_Divides_Odivmod__nat(U_10728,U_10726) = 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),U_10728),U_10726),U_10726))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10728),U_10726))
| U_10726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_10727,U_10725] :
( c_Divides_Odivmod__nat(U_10727,U_10725) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10727)
| sP826(U_10727,U_10725) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP826])],[f_2913_3]) ).
cnf(f_2913_5,plain,
( c_Divides_Odivmod__nat(U_10727,U_10725) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10727)
| sP826(U_10727,U_10725) ),
inference(clausify,[status(thm)],[f_2913_4]) ).
cnf(f_2913_6,plain,
( c_Divides_Odivmod__nat(U_10728,U_10726) = 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),U_10728),U_10726),U_10726))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10728),U_10726))
| U_10726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2913_4]) ).
cnf(f_2913_7,plain,
( U_10725 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP826(U_10727,U_10725) ),
inference(clausify,[status(thm)],[f_2913_4]) ).
cnf(f_2913_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10727),U_10725))
| ~ sP826(U_10727,U_10725) ),
inference(clausify,[status(thm)],[f_2913_4]) ).
fof(f_2914_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_split__eta]) ).
fof(f_2914_2,plain,
! [U_10732,U_10731,U_10730,U_10729] : hAPP(c_Product__Type_Oprod_Oprod__case(U_10729,U_10730,U_10731),hAPP(hAPP(c_COMBB(tc_fun(U_10730,tc_prod(U_10729,U_10730)),tc_fun(U_10730,U_10731),U_10729),hAPP(c_COMBB(tc_prod(U_10729,U_10730),U_10731,U_10730),U_10732)),c_Product__Type_OPair(U_10729,U_10730))) = U_10732,
inference(variable_rename,[status(thm)],[f_2914_1]) ).
fof(f_2914_3,plain,
! [U_10730,U_10731,U_10729,U_10732] : hAPP(c_Product__Type_Oprod_Oprod__case(U_10729,U_10730,U_10731),hAPP(hAPP(c_COMBB(tc_fun(U_10730,tc_prod(U_10729,U_10730)),tc_fun(U_10730,U_10731),U_10729),hAPP(c_COMBB(tc_prod(U_10729,U_10730),U_10731,U_10730),U_10732)),c_Product__Type_OPair(U_10729,U_10730))) = U_10732,
inference(definitional_conversion,[status(esa)],[f_2914_2]) ).
cnf(f_2914_4,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_10729,U_10730,U_10731),hAPP(hAPP(c_COMBB(tc_fun(U_10730,tc_prod(U_10729,U_10730)),tc_fun(U_10730,U_10731),U_10729),hAPP(c_COMBB(tc_prod(U_10729,U_10730),U_10731,U_10730),U_10732)),c_Product__Type_OPair(U_10729,U_10730))) = U_10732,
inference(clausify,[status(thm)],[f_2914_3]) ).
fof(f_2915_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_split__twice]) ).
fof(f_2915_2,plain,
! [U_10740,U_10739,U_10738,U_10737,U_10736,U_10735,U_10734,U_10733] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10733,U_10734,U_10735),U_10736),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10737,U_10738,tc_prod(U_10733,U_10734)),U_10739),U_10740)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10737,U_10738,U_10735),hAPP(hAPP(c_COMBB(tc_fun(U_10738,tc_prod(U_10733,U_10734)),tc_fun(U_10738,U_10735),U_10737),hAPP(c_COMBB(tc_prod(U_10733,U_10734),U_10735,U_10738),hAPP(c_Product__Type_Oprod_Oprod__case(U_10733,U_10734,U_10735),U_10736))),U_10739)),U_10740),
inference(variable_rename,[status(thm)],[f_2915_1]) ).
fof(f_2915_3,plain,
! [U_10733,U_10734,U_10735,U_10736,U_10737,U_10738,U_10739,U_10740] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10733,U_10734,U_10735),U_10736),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10737,U_10738,tc_prod(U_10733,U_10734)),U_10739),U_10740)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10737,U_10738,U_10735),hAPP(hAPP(c_COMBB(tc_fun(U_10738,tc_prod(U_10733,U_10734)),tc_fun(U_10738,U_10735),U_10737),hAPP(c_COMBB(tc_prod(U_10733,U_10734),U_10735,U_10738),hAPP(c_Product__Type_Oprod_Oprod__case(U_10733,U_10734,U_10735),U_10736))),U_10739)),U_10740),
inference(definitional_conversion,[status(esa)],[f_2915_2]) ).
cnf(f_2915_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10733,U_10734,U_10735),U_10736),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10737,U_10738,tc_prod(U_10733,U_10734)),U_10739),U_10740)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10737,U_10738,U_10735),hAPP(hAPP(c_COMBB(tc_fun(U_10738,tc_prod(U_10733,U_10734)),tc_fun(U_10738,U_10735),U_10737),hAPP(c_COMBB(tc_prod(U_10733,U_10734),U_10735,U_10738),hAPP(c_Product__Type_Oprod_Oprod__case(U_10733,U_10734,U_10735),U_10736))),U_10739)),U_10740),
inference(clausify,[status(thm)],[f_2915_3]) ).
fof(f_2916_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_OFrac__def]) ).
fof(f_2916_2,plain,
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)))),
inference(definitional_conversion,[status(esa)],[f_2916_1]) ).
cnf(f_2916_3,plain,
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)))),
inference(clausify,[status(thm)],[f_2916_2]) ).
fof(f_2917_1,plain,
! [V_b,V_a] :
( ( ( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
& ( c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) )
& ( ( ( ( ( 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)))
| V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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))
| V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
& ( c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__def]) ).
fof(f_2917_2,plain,
! [U_10742,U_10741] :
( ( ( ( c_Divides_Odivmod__int(U_10741,U_10742) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10741),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10742)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10742)) )
& ( c_Divides_Odivmod__int(U_10741,U_10742) = c_Divides_OnegDivAlg(U_10741,U_10742)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10742)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10741)) )
& ( ( ( ( ( c_Divides_Odivmod__int(U_10741,U_10742) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10741),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10742)))
| U_10741 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_10741,U_10742) = 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))
| U_10741 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10742)) )
& ( c_Divides_Odivmod__int(U_10741,U_10742) = c_Divides_OposDivAlg(U_10741,U_10742)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10742)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10741)) ) ),
inference(variable_rename,[status(thm)],[f_2917_1]) ).
fof(f_2917_3,plain,
( ! [U_10746,U_10744] :
( ( ( c_Divides_Odivmod__int(U_10744,U_10746) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10744),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10746)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10746)) )
& ( c_Divides_Odivmod__int(U_10744,U_10746) = c_Divides_OnegDivAlg(U_10744,U_10746)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10746)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10744)) )
& ! [U_10745,U_10743] :
( ( ( ( ( c_Divides_Odivmod__int(U_10743,U_10745) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10743),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10745)))
| U_10743 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_10743,U_10745) = 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))
| U_10743 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10745)) )
& ( c_Divides_Odivmod__int(U_10743,U_10745) = c_Divides_OposDivAlg(U_10743,U_10745)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10745)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10743)) ) ),
inference(miniscope,[status(thm)],[f_2917_2]) ).
fof(f_2917_4,plain,
( ! [U_10744,U_10746] :
( c_Divides_Odivmod__int(U_10744,U_10746) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10744),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10746)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10746))
| ~ sP829(U_10744,U_10746) )
& ! [U_10744,U_10746] :
( c_Divides_Odivmod__int(U_10744,U_10746) = c_Divides_OnegDivAlg(U_10744,U_10746)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10746))
| ~ sP829(U_10744,U_10746) )
& ! [U_10743,U_10745] :
( c_Divides_Odivmod__int(U_10743,U_10745) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10743),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10745)))
| U_10743 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP827(U_10743,U_10745) )
& ! [U_10743,U_10745] :
( c_Divides_Odivmod__int(U_10743,U_10745) = 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))
| U_10743 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP827(U_10743,U_10745) )
& ! [U_10743,U_10745] :
( sP827(U_10743,U_10745)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10745))
| ~ sP828(U_10743,U_10745) )
& ! [U_10743,U_10745] :
( c_Divides_Odivmod__int(U_10743,U_10745) = c_Divides_OposDivAlg(U_10743,U_10745)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10745))
| ~ sP828(U_10743,U_10745) )
& ! [U_10744,U_10746] :
( sP829(U_10744,U_10746)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10744)) )
& ! [U_10743,U_10745] :
( sP828(U_10743,U_10745)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10743)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP827,sP828,sP829])],[f_2917_3]) ).
cnf(f_2917_5,plain,
( sP828(U_10743,U_10745)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10743)) ),
inference(clausify,[status(thm)],[f_2917_4]) ).
cnf(f_2917_6,plain,
( sP829(U_10744,U_10746)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10744)) ),
inference(clausify,[status(thm)],[f_2917_4]) ).
cnf(f_2917_7,plain,
( c_Divides_Odivmod__int(U_10743,U_10745) = c_Divides_OposDivAlg(U_10743,U_10745)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10745))
| ~ sP828(U_10743,U_10745) ),
inference(clausify,[status(thm)],[f_2917_4]) ).
cnf(f_2917_8,plain,
( sP827(U_10743,U_10745)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10745))
| ~ sP828(U_10743,U_10745) ),
inference(clausify,[status(thm)],[f_2917_4]) ).
cnf(f_2917_9,plain,
( c_Divides_Odivmod__int(U_10743,U_10745) = 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))
| U_10743 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP827(U_10743,U_10745) ),
inference(clausify,[status(thm)],[f_2917_4]) ).
cnf(f_2917_10,plain,
( c_Divides_Odivmod__int(U_10743,U_10745) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10743),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10745)))
| U_10743 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP827(U_10743,U_10745) ),
inference(clausify,[status(thm)],[f_2917_4]) ).
cnf(f_2917_11,plain,
( c_Divides_Odivmod__int(U_10744,U_10746) = c_Divides_OnegDivAlg(U_10744,U_10746)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10746))
| ~ sP829(U_10744,U_10746) ),
inference(clausify,[status(thm)],[f_2917_4]) ).
cnf(f_2917_12,plain,
( c_Divides_Odivmod__int(U_10744,U_10746) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10744),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10746)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10746))
| ~ sP829(U_10744,U_10746) ),
inference(clausify,[status(thm)],[f_2917_4]) ).
fof(f_2918_1,plain,
! [V_l_2,V_k_2] :
( ( ( ( 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))))
| V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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)
| V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__pdivmod]) ).
fof(f_2918_2,plain,
! [U_10748,U_10747] :
( ( ( ( c_Divides_Odivmod__int(U_10747,U_10748) = 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,U_10748))),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)),U_10748)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10747))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10748),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10747),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_10747,U_10748)),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),U_10748))))),c_Divides_Opdivmod(U_10747,U_10748))))
| U_10748 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_10747,U_10748) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10747)
| U_10748 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_10747 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_10747,U_10748) = 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))
| U_10747 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2918_1]) ).
fof(f_2918_3,plain,
( ! [U_10752,U_10750] :
( ( ( c_Divides_Odivmod__int(U_10750,U_10752) = 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,U_10752))),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)),U_10752)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10750))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10752),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10750),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_10750,U_10752)),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),U_10752))))),c_Divides_Opdivmod(U_10750,U_10752))))
| U_10752 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_10750,U_10752) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10750)
| U_10752 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_10750 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_10751,U_10749] :
( c_Divides_Odivmod__int(U_10749,U_10751) = 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))
| U_10749 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2918_2]) ).
fof(f_2918_4,plain,
( ! [U_10752,U_10750] :
( c_Divides_Odivmod__int(U_10750,U_10752) = 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,U_10752))),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)),U_10752)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10750))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10752),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10750),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_10750,U_10752)),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),U_10752))))),c_Divides_Opdivmod(U_10750,U_10752))))
| U_10752 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP830(U_10752,U_10750) )
& ! [U_10752,U_10750] :
( c_Divides_Odivmod__int(U_10750,U_10752) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10750)
| U_10752 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP830(U_10752,U_10750) )
& ! [U_10752,U_10750] :
( sP830(U_10752,U_10750)
| U_10750 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_10749,U_10751] :
( c_Divides_Odivmod__int(U_10749,U_10751) = 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))
| U_10749 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP830])],[f_2918_3]) ).
cnf(f_2918_5,plain,
( c_Divides_Odivmod__int(U_10749,U_10751) = 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))
| U_10749 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2918_4]) ).
cnf(f_2918_6,plain,
( sP830(U_10752,U_10750)
| U_10750 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2918_4]) ).
cnf(f_2918_7,plain,
( c_Divides_Odivmod__int(U_10750,U_10752) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10750)
| U_10752 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP830(U_10752,U_10750) ),
inference(clausify,[status(thm)],[f_2918_4]) ).
cnf(f_2918_8,plain,
( c_Divides_Odivmod__int(U_10750,U_10752) = 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,U_10752))),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)),U_10752)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10750))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10752),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10750),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_10750,U_10752)),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),U_10752))))),c_Divides_Opdivmod(U_10750,U_10752))))
| U_10752 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP830(U_10752,U_10750) ),
inference(clausify,[status(thm)],[f_2918_4]) ).
fof(f_2919_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_apsnd__conv]) ).
fof(f_2919_2,plain,
! [U_10758,U_10757,U_10756,U_10755,U_10754,U_10753] : hAPP(c_Product__Type_Oapsnd(U_10753,U_10754,U_10755,U_10756),hAPP(hAPP(c_Product__Type_OPair(U_10755,U_10753),U_10757),U_10758)) = hAPP(hAPP(c_Product__Type_OPair(U_10755,U_10754),U_10757),hAPP(U_10756,U_10758)),
inference(variable_rename,[status(thm)],[f_2919_1]) ).
fof(f_2919_3,plain,
! [U_10755,U_10754,U_10756,U_10753,U_10758,U_10757] : hAPP(c_Product__Type_Oapsnd(U_10753,U_10754,U_10755,U_10756),hAPP(hAPP(c_Product__Type_OPair(U_10755,U_10753),U_10757),U_10758)) = hAPP(hAPP(c_Product__Type_OPair(U_10755,U_10754),U_10757),hAPP(U_10756,U_10758)),
inference(definitional_conversion,[status(esa)],[f_2919_2]) ).
cnf(f_2919_4,plain,
hAPP(c_Product__Type_Oapsnd(U_10753,U_10754,U_10755,U_10756),hAPP(hAPP(c_Product__Type_OPair(U_10755,U_10753),U_10757),U_10758)) = hAPP(hAPP(c_Product__Type_OPair(U_10755,U_10754),U_10757),hAPP(U_10756,U_10758)),
inference(clausify,[status(thm)],[f_2919_3]) ).
fof(f_2920_1,plain,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_negateSnd__def]) ).
fof(f_2920_2,plain,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_2920_1]) ).
cnf(f_2920_3,plain,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_2920_2]) ).
fof(f_2921_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_negateSnd__eq]) ).
fof(f_2921_2,plain,
! [U_10760,U_10759] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10759),U_10760)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10760)),
inference(variable_rename,[status(thm)],[f_2921_1]) ).
fof(f_2921_3,plain,
! [U_10760,U_10759] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10759),U_10760)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10760)),
inference(definitional_conversion,[status(esa)],[f_2921_2]) ).
cnf(f_2921_4,plain,
hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10759),U_10760)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10760)),
inference(clausify,[status(thm)],[f_2921_3]) ).
fof(f_2922_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_pdivmod__def]) ).
fof(f_2922_2,plain,
! [U_10762,U_10761] : c_Divides_Opdivmod(U_10761,U_10762) = 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),U_10761)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10762))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10761),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10762))),
inference(variable_rename,[status(thm)],[f_2922_1]) ).
fof(f_2922_3,plain,
! [U_10761,U_10762] : c_Divides_Opdivmod(U_10761,U_10762) = 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),U_10761)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10762))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10761),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10762))),
inference(definitional_conversion,[status(esa)],[f_2922_2]) ).
cnf(f_2922_4,plain,
c_Divides_Opdivmod(U_10761,U_10762) = 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),U_10761)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10762))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10761),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10762))),
inference(clausify,[status(thm)],[f_2922_3]) ).
fof(f_2923_1,plain,
! [V_k,V_l] :
( ( 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))
| V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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))
| V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg]) ).
fof(f_2923_2,plain,
! [U_10764,U_10763] :
( ( c_Divides_Opdivmod(U_10764,U_10763) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10764),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10763))
| U_10763 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Opdivmod(U_10764,U_10763) = 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),U_10764))
| U_10763 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2923_1]) ).
fof(f_2923_3,plain,
( ! [U_10768,U_10766] :
( c_Divides_Opdivmod(U_10768,U_10766) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10768),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10766))
| U_10766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_10767,U_10765] :
( c_Divides_Opdivmod(U_10767,U_10765) = 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),U_10767))
| U_10765 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2923_2]) ).
fof(f_2923_4,plain,
( ! [U_10766,U_10768] :
( c_Divides_Opdivmod(U_10768,U_10766) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10768),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10766))
| U_10766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_10767,U_10765] :
( c_Divides_Opdivmod(U_10767,U_10765) = 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),U_10767))
| U_10765 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_2923_3]) ).
cnf(f_2923_5,plain,
( c_Divides_Opdivmod(U_10767,U_10765) = 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),U_10767))
| U_10765 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2923_4]) ).
cnf(f_2923_6,plain,
( c_Divides_Opdivmod(U_10768,U_10766) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10768),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10766))
| U_10766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2923_4]) ).
fof(f_2924_1,plain,
! [V_l_2,V_k_2] :
( ( ( ( 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))))
| V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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)
| V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__code]) ).
fof(f_2924_2,plain,
! [U_10770,U_10769] :
( ( ( ( c_Divides_Odivmod__int(U_10769,U_10770) = 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,U_10770))),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,U_10769)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10770))),c_Divides_Opdivmod(U_10769,U_10770)),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),U_10770))))),c_Divides_Opdivmod(U_10769,U_10770))))
| U_10770 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_10769,U_10770) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10769)
| U_10770 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_10769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_10769,U_10770) = 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))
| U_10769 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2924_1]) ).
fof(f_2924_3,plain,
( ! [U_10774,U_10772] :
( ( ( c_Divides_Odivmod__int(U_10772,U_10774) = 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,U_10774))),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,U_10772)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10774))),c_Divides_Opdivmod(U_10772,U_10774)),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),U_10774))))),c_Divides_Opdivmod(U_10772,U_10774))))
| U_10774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_10772,U_10774) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10772)
| U_10774 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_10772 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_10773,U_10771] :
( c_Divides_Odivmod__int(U_10771,U_10773) = 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))
| U_10771 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2924_2]) ).
fof(f_2924_4,plain,
( ! [U_10772,U_10774] :
( c_Divides_Odivmod__int(U_10772,U_10774) = 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,U_10774))),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,U_10772)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10774))),c_Divides_Opdivmod(U_10772,U_10774)),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),U_10774))))),c_Divides_Opdivmod(U_10772,U_10774))))
| U_10774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP831(U_10772,U_10774) )
& ! [U_10772,U_10774] :
( c_Divides_Odivmod__int(U_10772,U_10774) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10772)
| U_10774 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP831(U_10772,U_10774) )
& ! [U_10772,U_10774] :
( sP831(U_10772,U_10774)
| U_10772 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_10771,U_10773] :
( c_Divides_Odivmod__int(U_10771,U_10773) = 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))
| U_10771 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP831])],[f_2924_3]) ).
cnf(f_2924_5,plain,
( c_Divides_Odivmod__int(U_10771,U_10773) = 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))
| U_10771 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2924_4]) ).
cnf(f_2924_6,plain,
( sP831(U_10772,U_10774)
| U_10772 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2924_4]) ).
cnf(f_2924_7,plain,
( c_Divides_Odivmod__int(U_10772,U_10774) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10772)
| U_10774 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP831(U_10772,U_10774) ),
inference(clausify,[status(thm)],[f_2924_4]) ).
cnf(f_2924_8,plain,
( c_Divides_Odivmod__int(U_10772,U_10774) = 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,U_10774))),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,U_10772)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10774))),c_Divides_Opdivmod(U_10772,U_10774)),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),U_10774))))),c_Divides_Opdivmod(U_10772,U_10774))))
| U_10774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP831(U_10772,U_10774) ),
inference(clausify,[status(thm)],[f_2924_4]) ).
fof(f_2925_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oprod__def]) ).
fof(f_2925_2,plain,
! [U_10778,U_10777,U_10776,U_10775] : c_Nitpick_Oprod(U_10775,U_10776,U_10777,U_10778) = hAPP(c_Set_OCollect(tc_prod(U_10775,U_10776)),hAPP(c_Product__Type_Oprod_Oprod__case(U_10775,U_10776,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10775,tc_fun(U_10776,tc_HOL_Obool),tc_fun(U_10776,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10776,tc_HOL_Obool),tc_fun(U_10776,tc_HOL_Obool)),U_10775),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10776)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10775),c_fconj),hAPP(hAPP(c_COMBC(U_10775,tc_fun(U_10775,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10775)),U_10777)))),hAPP(hAPP(c_COMBC(U_10776,tc_fun(U_10776,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10776)),U_10778)))),
inference(variable_rename,[status(thm)],[f_2925_1]) ).
fof(f_2925_3,plain,
! [U_10775,U_10776,U_10777,U_10778] : c_Nitpick_Oprod(U_10775,U_10776,U_10777,U_10778) = hAPP(c_Set_OCollect(tc_prod(U_10775,U_10776)),hAPP(c_Product__Type_Oprod_Oprod__case(U_10775,U_10776,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10775,tc_fun(U_10776,tc_HOL_Obool),tc_fun(U_10776,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10776,tc_HOL_Obool),tc_fun(U_10776,tc_HOL_Obool)),U_10775),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10776)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10775),c_fconj),hAPP(hAPP(c_COMBC(U_10775,tc_fun(U_10775,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10775)),U_10777)))),hAPP(hAPP(c_COMBC(U_10776,tc_fun(U_10776,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10776)),U_10778)))),
inference(definitional_conversion,[status(esa)],[f_2925_2]) ).
cnf(f_2925_4,plain,
c_Nitpick_Oprod(U_10775,U_10776,U_10777,U_10778) = hAPP(c_Set_OCollect(tc_prod(U_10775,U_10776)),hAPP(c_Product__Type_Oprod_Oprod__case(U_10775,U_10776,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10775,tc_fun(U_10776,tc_HOL_Obool),tc_fun(U_10776,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10776,tc_HOL_Obool),tc_fun(U_10776,tc_HOL_Obool)),U_10775),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10776)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10775),c_fconj),hAPP(hAPP(c_COMBC(U_10775,tc_fun(U_10775,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10775)),U_10777)))),hAPP(hAPP(c_COMBC(U_10776,tc_fun(U_10776,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10776)),U_10778)))),
inference(clausify,[status(thm)],[f_2925_3]) ).
fof(f_2926_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_int__ge__less__than2__def]) ).
fof(f_2926_2,plain,
! [U_10779] : c_Int_Oint__ge__less__than2(U_10779) = 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),U_10779)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_2926_1]) ).
fof(f_2926_3,plain,
! [U_10779] : c_Int_Oint__ge__less__than2(U_10779) = 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),U_10779)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(definitional_conversion,[status(esa)],[f_2926_2]) ).
cnf(f_2926_4,plain,
c_Int_Oint__ge__less__than2(U_10779) = 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),U_10779)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_2926_3]) ).
fof(f_2927_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_int__ge__less__than__def]) ).
fof(f_2927_2,plain,
! [U_10780] : c_Int_Oint__ge__less__than(U_10780) = 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),U_10780)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_2927_1]) ).
fof(f_2927_3,plain,
! [U_10780] : c_Int_Oint__ge__less__than(U_10780) = 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),U_10780)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(definitional_conversion,[status(esa)],[f_2927_2]) ).
cnf(f_2927_4,plain,
c_Int_Oint__ge__less__than(U_10780) = 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),U_10780)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_2927_3]) ).
fof(f_2928_1,plain,
! [V_a,V_r,V_q,V_c,V_b] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq]) ).
fof(f_2928_2,plain,
! [U_10785,U_10784,U_10783,U_10782,U_10781] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10781),U_10782),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),U_10785),U_10783)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10784)),U_10782))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10784),U_10782))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10782))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10781,U_10782),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10783),U_10784))) ),
inference(variable_rename,[status(thm)],[f_2928_1]) ).
fof(f_2928_3,plain,
! [U_10781,U_10782,U_10783,U_10784,U_10785] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10781),U_10782),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),U_10785),U_10783)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10784)),U_10782))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10784),U_10782))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10782))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10781,U_10782),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10783),U_10784))) ),
inference(definitional_conversion,[status(esa)],[f_2928_2]) ).
cnf(f_2928_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10781),U_10782),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),U_10785),U_10783)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10784)),U_10782))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10785),U_10784),U_10782))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10782))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10781,U_10782),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10783),U_10784))) ),
inference(clausify,[status(thm)],[f_2928_3]) ).
fof(f_2929_1,plain,
! [V_c,V_r,V_q,V_b,V_a] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq]) ).
fof(f_2929_2,plain,
! [U_10790,U_10789,U_10788,U_10787,U_10786] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10786,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10787),U_10790)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10788),U_10790)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10787),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10788,U_10790))),U_10789))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10787))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10786,U_10787),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10788),U_10789))) ),
inference(variable_rename,[status(thm)],[f_2929_1]) ).
fof(f_2929_3,plain,
! [U_10787,U_10786,U_10788,U_10789,U_10790] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10786,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10787),U_10790)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10788),U_10790)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10787),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10788,U_10790))),U_10789))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10787))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10786,U_10787),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10788),U_10789))) ),
inference(definitional_conversion,[status(esa)],[f_2929_2]) ).
cnf(f_2929_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10786,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10787),U_10790)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10788),U_10790)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10787),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10788,U_10790))),U_10789))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10787))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10786,U_10787),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10788),U_10789))) ),
inference(clausify,[status(thm)],[f_2929_3]) ).
fof(f_2930_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_pair__box_Osize_I2_J]) ).
fof(f_2930_2,plain,
! [U_10794,U_10793,U_10792,U_10791] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_10791,U_10792)),c_Nitpick_Opair__box_OPairBox(U_10791,U_10792,U_10793,U_10794)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_2930_1]) ).
fof(f_2930_3,plain,
! [U_10794,U_10791,U_10793,U_10792] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_10791,U_10792)),c_Nitpick_Opair__box_OPairBox(U_10791,U_10792,U_10793,U_10794)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_2930_2]) ).
cnf(f_2930_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_10791,U_10792)),c_Nitpick_Opair__box_OPairBox(U_10791,U_10792,U_10793,U_10794)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2930_3]) ).
fof(f_2931_1,plain,
! [V_qr_H,V_qr,V_n,V_m] :
( V_qr = V_qr_H
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique]) ).
fof(f_2931_2,plain,
! [U_10798,U_10797,U_10796,U_10795] :
( U_10797 = U_10798
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10795,U_10796),U_10798))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10795,U_10796),U_10797)) ),
inference(variable_rename,[status(thm)],[f_2931_1]) ).
fof(f_2931_3,plain,
! [U_10795,U_10796,U_10797,U_10798] :
( U_10797 = U_10798
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10795,U_10796),U_10798))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10795,U_10796),U_10797)) ),
inference(definitional_conversion,[status(esa)],[f_2931_2]) ).
cnf(f_2931_4,plain,
( U_10797 = U_10798
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10795,U_10796),U_10798))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10795,U_10796),U_10797)) ),
inference(clausify,[status(thm)],[f_2931_3]) ).
fof(f_2932_1,plain,
! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).
fof(f_2932_2,plain,
! [U_10800,U_10799] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10799,U_10800),c_Divides_Odivmod__nat(U_10799,U_10800))),
inference(variable_rename,[status(thm)],[f_2932_1]) ).
fof(f_2932_3,plain,
! [U_10800,U_10799] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10799,U_10800),c_Divides_Odivmod__nat(U_10799,U_10800))),
inference(definitional_conversion,[status(esa)],[f_2932_2]) ).
cnf(f_2932_4,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10799,U_10800),c_Divides_Odivmod__nat(U_10799,U_10800))),
inference(clausify,[status(thm)],[f_2932_3]) ).
fof(f_2933_1,plain,
! [V_qr,V_n,V_m] :
( c_Divides_Odivmod__nat(V_m,V_n) = V_qr
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq]) ).
fof(f_2933_2,plain,
! [U_10803,U_10802,U_10801] :
( c_Divides_Odivmod__nat(U_10801,U_10802) = U_10803
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10801,U_10802),U_10803)) ),
inference(variable_rename,[status(thm)],[f_2933_1]) ).
fof(f_2933_3,plain,
! [U_10801,U_10802,U_10803] :
( c_Divides_Odivmod__nat(U_10801,U_10802) = U_10803
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10801,U_10802),U_10803)) ),
inference(definitional_conversion,[status(esa)],[f_2933_2]) ).
cnf(f_2933_4,plain,
( c_Divides_Odivmod__nat(U_10801,U_10802) = U_10803
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10801,U_10802),U_10803)) ),
inference(clausify,[status(thm)],[f_2933_3]) ).
fof(f_2934_1,plain,
! [V_r,V_q,V_n,V_m] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_mod__eq]) ).
fof(f_2934_2,plain,
! [U_10807,U_10806,U_10805,U_10804] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10804,U_10805) = U_10807
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10804,U_10805),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10806),U_10807))) ),
inference(variable_rename,[status(thm)],[f_2934_1]) ).
fof(f_2934_3,plain,
! [U_10804,U_10805,U_10806,U_10807] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10804,U_10805) = U_10807
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10804,U_10805),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10806),U_10807))) ),
inference(definitional_conversion,[status(esa)],[f_2934_2]) ).
cnf(f_2934_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10804,U_10805) = U_10807
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10804,U_10805),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10806),U_10807))) ),
inference(clausify,[status(thm)],[f_2934_3]) ).
fof(f_2935_1,plain,
! [V_r,V_q,V_n,V_m] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_div__eq]) ).
fof(f_2935_2,plain,
! [U_10811,U_10810,U_10809,U_10808] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10808),U_10809) = U_10810
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10808,U_10809),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10810),U_10811))) ),
inference(variable_rename,[status(thm)],[f_2935_1]) ).
fof(f_2935_3,plain,
! [U_10808,U_10809,U_10810,U_10811] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10808),U_10809) = U_10810
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10808,U_10809),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10810),U_10811))) ),
inference(definitional_conversion,[status(esa)],[f_2935_2]) ).
cnf(f_2935_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10808),U_10809) = U_10810
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10808,U_10809),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10810),U_10811))) ),
inference(clausify,[status(thm)],[f_2935_3]) ).
fof(f_2936_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel]) ).
fof(f_2936_2,plain,
! [U_10813,U_10812] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10812,U_10813),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10812),U_10813)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10812,U_10813)))),
inference(variable_rename,[status(thm)],[f_2936_1]) ).
fof(f_2936_3,plain,
! [U_10812,U_10813] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10812,U_10813),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10812),U_10813)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10812,U_10813)))),
inference(definitional_conversion,[status(esa)],[f_2936_2]) ).
cnf(f_2936_4,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10812,U_10813),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10812),U_10813)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10812,U_10813)))),
inference(clausify,[status(thm)],[f_2936_3]) ).
fof(f_2937_1,plain,
! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
| ~ 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq]) ).
fof(f_2937_2,plain,
! [U_10820,U_10819,U_10818,U_10817,U_10816,U_10815,U_10814] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10814),U_10818),U_10815),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),U_10816),U_10819)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10817),U_10820)),U_10815))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10817),U_10820),U_10815))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10815))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10818,U_10815),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10819),U_10820)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10814,U_10815),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10816),U_10817))) ),
inference(variable_rename,[status(thm)],[f_2937_1]) ).
fof(f_2937_3,plain,
! [U_10814,U_10815,U_10816,U_10817,U_10818,U_10819,U_10820] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10814),U_10818),U_10815),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),U_10816),U_10819)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10817),U_10820)),U_10815))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10817),U_10820),U_10815))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10815))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10818,U_10815),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10819),U_10820)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10814,U_10815),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10816),U_10817))) ),
inference(definitional_conversion,[status(esa)],[f_2937_2]) ).
cnf(f_2937_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10814),U_10818),U_10815),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),U_10816),U_10819)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10817),U_10820)),U_10815))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10817),U_10820),U_10815))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10815))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10818,U_10815),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10819),U_10820)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10814,U_10815),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10816),U_10817))) ),
inference(clausify,[status(thm)],[f_2937_3]) ).
fof(f_2938_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_pair__box_Orecs]) ).
fof(f_2938_2,plain,
! [U_10826,U_10825,U_10824,U_10823,U_10822,U_10821] : c_Nitpick_Opair__box_Opair__box__rec(U_10821,U_10822,U_10823,U_10824,c_Nitpick_Opair__box_OPairBox(U_10821,U_10822,U_10825,U_10826)) = hAPP(hAPP(U_10824,U_10825),U_10826),
inference(variable_rename,[status(thm)],[f_2938_1]) ).
fof(f_2938_3,plain,
! [U_10823,U_10824,U_10821,U_10822,U_10825,U_10826] : c_Nitpick_Opair__box_Opair__box__rec(U_10821,U_10822,U_10823,U_10824,c_Nitpick_Opair__box_OPairBox(U_10821,U_10822,U_10825,U_10826)) = hAPP(hAPP(U_10824,U_10825),U_10826),
inference(definitional_conversion,[status(esa)],[f_2938_2]) ).
cnf(f_2938_4,plain,
c_Nitpick_Opair__box_Opair__box__rec(U_10821,U_10822,U_10823,U_10824,c_Nitpick_Opair__box_OPairBox(U_10821,U_10822,U_10825,U_10826)) = hAPP(hAPP(U_10824,U_10825),U_10826),
inference(clausify,[status(thm)],[f_2938_3]) ).
fof(f_2939_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).
fof(f_2939_2,plain,
! [U_10832,U_10831,U_10830,U_10829,U_10828,U_10827] : c_Nitpick_Opair__box_Opair__box__case(U_10827,U_10828,U_10829,U_10830,c_Nitpick_Opair__box_OPairBox(U_10827,U_10828,U_10831,U_10832)) = hAPP(hAPP(U_10830,U_10831),U_10832),
inference(variable_rename,[status(thm)],[f_2939_1]) ).
fof(f_2939_3,plain,
! [U_10827,U_10828,U_10829,U_10830,U_10831,U_10832] : c_Nitpick_Opair__box_Opair__box__case(U_10827,U_10828,U_10829,U_10830,c_Nitpick_Opair__box_OPairBox(U_10827,U_10828,U_10831,U_10832)) = hAPP(hAPP(U_10830,U_10831),U_10832),
inference(definitional_conversion,[status(esa)],[f_2939_2]) ).
cnf(f_2939_4,plain,
c_Nitpick_Opair__box_Opair__box__case(U_10827,U_10828,U_10829,U_10830,c_Nitpick_Opair__box_OPairBox(U_10827,U_10828,U_10831,U_10832)) = hAPP(hAPP(U_10830,U_10831),U_10832),
inference(clausify,[status(thm)],[f_2939_3]) ).
fof(f_2940_1,plain,
! [V_b_2,V_a_2] :
( ( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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))) )
& ( 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))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ 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))) ) ) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps]) ).
fof(f_2940_2,plain,
! [U_10834,U_10833] :
( ( ( c_Divides_OnegDivAlg(U_10833,U_10834) = hAPP(c_Divides_Oadjust(U_10834),c_Divides_OnegDivAlg(U_10833,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)))),U_10834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),U_10833),U_10834))) )
& ( c_Divides_OnegDivAlg(U_10833,U_10834) = 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),U_10833),U_10834))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ 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),U_10833),U_10834))) ) ) )
| ~ 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),U_10833),U_10834))) ),
inference(variable_rename,[status(thm)],[f_2940_1]) ).
fof(f_2940_3,plain,
( ! [U_10833,U_10834] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP832(U_10833,U_10834) )
& ! [U_10833,U_10834] :
( ~ 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),U_10833),U_10834)))
| ~ sP832(U_10833,U_10834) )
& ! [U_10833,U_10834] :
( c_Divides_OnegDivAlg(U_10833,U_10834) = hAPP(c_Divides_Oadjust(U_10834),c_Divides_OnegDivAlg(U_10833,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)))),U_10834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),U_10833),U_10834)))
| ~ sP833(U_10833,U_10834) )
& ! [U_10833,U_10834] :
( c_Divides_OnegDivAlg(U_10833,U_10834) = 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),U_10833),U_10834))
| sP832(U_10833,U_10834)
| ~ sP833(U_10833,U_10834) )
& ! [U_10833,U_10834] :
( sP833(U_10833,U_10834)
| ~ 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),U_10833),U_10834))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP832,sP833])],[f_2940_2]) ).
cnf(f_2940_4,plain,
( sP833(U_10833,U_10834)
| ~ 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),U_10833),U_10834))) ),
inference(clausify,[status(thm)],[f_2940_3]) ).
cnf(f_2940_5,plain,
( c_Divides_OnegDivAlg(U_10833,U_10834) = 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),U_10833),U_10834))
| sP832(U_10833,U_10834)
| ~ sP833(U_10833,U_10834) ),
inference(clausify,[status(thm)],[f_2940_3]) ).
cnf(f_2940_6,plain,
( c_Divides_OnegDivAlg(U_10833,U_10834) = hAPP(c_Divides_Oadjust(U_10834),c_Divides_OnegDivAlg(U_10833,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)))),U_10834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),U_10833),U_10834)))
| ~ sP833(U_10833,U_10834) ),
inference(clausify,[status(thm)],[f_2940_3]) ).
cnf(f_2940_7,plain,
( ~ 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),U_10833),U_10834)))
| ~ sP832(U_10833,U_10834) ),
inference(clausify,[status(thm)],[f_2940_3]) ).
cnf(f_2940_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP832(U_10833,U_10834) ),
inference(clausify,[status(thm)],[f_2940_3]) ).
fof(f_2941_1,plain,
! [V_a_2,V_b_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_accp__downward]) ).
fof(f_2941_2,plain,
! [U_10838,U_10837,U_10836,U_10835] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10835,U_10836),U_10838))
| ~ hBOOL(hAPP(hAPP(U_10836,U_10838),U_10837))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10835,U_10836),U_10837)) ),
inference(variable_rename,[status(thm)],[f_2941_1]) ).
fof(f_2941_3,plain,
! [U_10837,U_10836,U_10835,U_10838] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10835,U_10836),U_10838))
| ~ hBOOL(hAPP(hAPP(U_10836,U_10838),U_10837))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10835,U_10836),U_10837)) ),
inference(definitional_conversion,[status(esa)],[f_2941_2]) ).
cnf(f_2941_4,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10835,U_10836),U_10838))
| ~ hBOOL(hAPP(hAPP(U_10836,U_10838),U_10837))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10835,U_10836),U_10837)) ),
inference(clausify,[status(thm)],[f_2941_3]) ).
fof(f_2942_1,plain,
! [V_a_2,V_r_2,T_b] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
& hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
| ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_accp_Oequations]) ).
fof(f_2942_2,plain,
! [U_10843,U_10842,U_10841] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10841,U_10842),U_10843))
| ? [U_10840] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10841,U_10842),U_10840))
& hBOOL(hAPP(hAPP(U_10842,U_10840),U_10843)) ) )
& ( ! [U_10839] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10841,U_10842),U_10839))
| ~ hBOOL(hAPP(hAPP(U_10842,U_10839),U_10843)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10841,U_10842),U_10843)) ) ),
inference(variable_rename,[status(thm)],[f_2942_1]) ).
fof(f_2942_3,plain,
( ! [U_10849,U_10847,U_10845] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10845,U_10847),U_10849))
| ? [U_10840] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10845,U_10847),U_10840))
& hBOOL(hAPP(hAPP(U_10847,U_10840),U_10849)) ) )
& ! [U_10848,U_10846,U_10844] :
( ! [U_10839] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10844,U_10846),U_10839))
| ~ hBOOL(hAPP(hAPP(U_10846,U_10839),U_10848)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10844,U_10846),U_10848)) ) ),
inference(miniscope,[status(thm)],[f_2942_2]) ).
fof(f_2942_4,plain,
( ! [U_10849,U_10847,U_10845] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10845,U_10847),U_10849))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10845,U_10847),sK265(U_10849,U_10847,U_10845)))
& hBOOL(hAPP(hAPP(U_10847,sK265(U_10849,U_10847,U_10845)),U_10849)) ) )
& ! [U_10848,U_10846,U_10844] :
( ! [U_10839] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10844,U_10846),U_10839))
| ~ hBOOL(hAPP(hAPP(U_10846,U_10839),U_10848)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10844,U_10846),U_10848)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_10840,sK265(U_10849,U_10847,U_10845))],[f_2942_3]) ).
fof(f_2942_5,plain,
( ! [U_10849,U_10845,U_10847] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10845,U_10847),sK265(U_10849,U_10847,U_10845)))
| ~ sP834(U_10849,U_10845,U_10847) )
& ! [U_10849,U_10845,U_10847] :
( hBOOL(hAPP(hAPP(U_10847,sK265(U_10849,U_10847,U_10845)),U_10849))
| ~ sP834(U_10849,U_10845,U_10847) )
& ! [U_10849,U_10845,U_10847] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10845,U_10847),U_10849))
| sP834(U_10849,U_10845,U_10847) )
& ! [U_10846,U_10839,U_10844,U_10848] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10844,U_10846),U_10839))
| ~ hBOOL(hAPP(hAPP(U_10846,U_10839),U_10848))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10844,U_10846),U_10848)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP834])],[f_2942_4]) ).
cnf(f_2942_6,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10844,U_10846),U_10839))
| ~ hBOOL(hAPP(hAPP(U_10846,U_10839),U_10848))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10844,U_10846),U_10848)) ),
inference(clausify,[status(thm)],[f_2942_5]) ).
cnf(f_2942_7,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10845,U_10847),U_10849))
| sP834(U_10849,U_10845,U_10847) ),
inference(clausify,[status(thm)],[f_2942_5]) ).
cnf(f_2942_8,plain,
( hBOOL(hAPP(hAPP(U_10847,sK265(U_10849,U_10847,U_10845)),U_10849))
| ~ sP834(U_10849,U_10845,U_10847) ),
inference(clausify,[status(thm)],[f_2942_5]) ).
cnf(f_2942_9,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10845,U_10847),sK265(U_10849,U_10847,U_10845)))
| ~ sP834(U_10849,U_10845,U_10847) ),
inference(clausify,[status(thm)],[f_2942_5]) ).
fof(f_2943_1,plain,
! [V_a_2,V_r_2,T_b] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
& hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
| ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_accp_Osimps]) ).
fof(f_2943_2,plain,
! [U_10854,U_10853,U_10852] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10852,U_10853),U_10854))
| ? [U_10851] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10852,U_10853),U_10851))
& hBOOL(hAPP(hAPP(U_10853,U_10851),U_10854)) ) )
& ( ! [U_10850] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10852,U_10853),U_10850))
| ~ hBOOL(hAPP(hAPP(U_10853,U_10850),U_10854)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10852,U_10853),U_10854)) ) ),
inference(variable_rename,[status(thm)],[f_2943_1]) ).
fof(f_2943_3,plain,
( ! [U_10860,U_10858,U_10856] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10856,U_10858),U_10860))
| ? [U_10851] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10856,U_10858),U_10851))
& hBOOL(hAPP(hAPP(U_10858,U_10851),U_10860)) ) )
& ! [U_10859,U_10857,U_10855] :
( ! [U_10850] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10855,U_10857),U_10850))
| ~ hBOOL(hAPP(hAPP(U_10857,U_10850),U_10859)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10855,U_10857),U_10859)) ) ),
inference(miniscope,[status(thm)],[f_2943_2]) ).
fof(f_2943_4,plain,
( ! [U_10860,U_10858,U_10856] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10856,U_10858),U_10860))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10856,U_10858),sK266(U_10860,U_10858,U_10856)))
& hBOOL(hAPP(hAPP(U_10858,sK266(U_10860,U_10858,U_10856)),U_10860)) ) )
& ! [U_10859,U_10857,U_10855] :
( ! [U_10850] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10855,U_10857),U_10850))
| ~ hBOOL(hAPP(hAPP(U_10857,U_10850),U_10859)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10855,U_10857),U_10859)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_10851,sK266(U_10860,U_10858,U_10856))],[f_2943_3]) ).
fof(f_2943_5,plain,
( ! [U_10858,U_10860,U_10856] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10856,U_10858),sK266(U_10860,U_10858,U_10856)))
| ~ sP835(U_10858,U_10860,U_10856) )
& ! [U_10858,U_10860,U_10856] :
( hBOOL(hAPP(hAPP(U_10858,sK266(U_10860,U_10858,U_10856)),U_10860))
| ~ sP835(U_10858,U_10860,U_10856) )
& ! [U_10858,U_10860,U_10856] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10856,U_10858),U_10860))
| sP835(U_10858,U_10860,U_10856) )
& ! [U_10859,U_10857,U_10850,U_10855] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10855,U_10857),U_10850))
| ~ hBOOL(hAPP(hAPP(U_10857,U_10850),U_10859))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10855,U_10857),U_10859)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP835])],[f_2943_4]) ).
cnf(f_2943_6,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10855,U_10857),U_10850))
| ~ hBOOL(hAPP(hAPP(U_10857,U_10850),U_10859))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10855,U_10857),U_10859)) ),
inference(clausify,[status(thm)],[f_2943_5]) ).
cnf(f_2943_7,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_10856,U_10858),U_10860))
| sP835(U_10858,U_10860,U_10856) ),
inference(clausify,[status(thm)],[f_2943_5]) ).
cnf(f_2943_8,plain,
( hBOOL(hAPP(hAPP(U_10858,sK266(U_10860,U_10858,U_10856)),U_10860))
| ~ sP835(U_10858,U_10860,U_10856) ),
inference(clausify,[status(thm)],[f_2943_5]) ).
cnf(f_2943_9,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_10856,U_10858),sK266(U_10860,U_10858,U_10856)))
| ~ sP835(U_10858,U_10860,U_10856) ),
inference(clausify,[status(thm)],[f_2943_5]) ).
fof(f_2944_1,plain,
! [V_R2_2,V_R1_2,T_b] :
( 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)))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_accp__subset]) ).
fof(f_2944_2,plain,
! [U_10863,U_10862,U_10861] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10861,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_10861,U_10863)),c_Wellfounded_Oaccp(U_10861,U_10862)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10861,tc_fun(U_10861,tc_HOL_Obool))),U_10862),U_10863)) ),
inference(variable_rename,[status(thm)],[f_2944_1]) ).
fof(f_2944_3,plain,
! [U_10862,U_10861,U_10863] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10861,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_10861,U_10863)),c_Wellfounded_Oaccp(U_10861,U_10862)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10861,tc_fun(U_10861,tc_HOL_Obool))),U_10862),U_10863)) ),
inference(definitional_conversion,[status(esa)],[f_2944_2]) ).
cnf(f_2944_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10861,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_10861,U_10863)),c_Wellfounded_Oaccp(U_10861,U_10862)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10861,tc_fun(U_10861,tc_HOL_Obool))),U_10862),U_10863)) ),
inference(clausify,[status(thm)],[f_2944_3]) ).
fof(f_2945_1,plain,
! [V_b_2,V_a_2] :
( ( ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
& ( 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)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) ) ) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps]) ).
fof(f_2945_2,plain,
! [U_10865,U_10864] :
( ( ( c_Divides_OposDivAlg(U_10864,U_10865) = hAPP(c_Divides_Oadjust(U_10865),c_Divides_OposDivAlg(U_10864,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)))),U_10865)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10865),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10864),U_10865)) )
& ( c_Divides_OposDivAlg(U_10864,U_10865) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10864)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10865),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10864),U_10865)) ) ) )
| ~ 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),U_10864),U_10865))) ),
inference(variable_rename,[status(thm)],[f_2945_1]) ).
fof(f_2945_3,plain,
( ! [U_10865,U_10864] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10865),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP836(U_10865,U_10864) )
& ! [U_10865,U_10864] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10864),U_10865))
| ~ sP836(U_10865,U_10864) )
& ! [U_10865,U_10864] :
( c_Divides_OposDivAlg(U_10864,U_10865) = hAPP(c_Divides_Oadjust(U_10865),c_Divides_OposDivAlg(U_10864,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)))),U_10865)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10865),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10864),U_10865))
| ~ sP837(U_10865,U_10864) )
& ! [U_10865,U_10864] :
( c_Divides_OposDivAlg(U_10864,U_10865) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10864)
| sP836(U_10865,U_10864)
| ~ sP837(U_10865,U_10864) )
& ! [U_10865,U_10864] :
( sP837(U_10865,U_10864)
| ~ 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),U_10864),U_10865))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP836,sP837])],[f_2945_2]) ).
cnf(f_2945_4,plain,
( sP837(U_10865,U_10864)
| ~ 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),U_10864),U_10865))) ),
inference(clausify,[status(thm)],[f_2945_3]) ).
cnf(f_2945_5,plain,
( c_Divides_OposDivAlg(U_10864,U_10865) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10864)
| sP836(U_10865,U_10864)
| ~ sP837(U_10865,U_10864) ),
inference(clausify,[status(thm)],[f_2945_3]) ).
cnf(f_2945_6,plain,
( c_Divides_OposDivAlg(U_10864,U_10865) = hAPP(c_Divides_Oadjust(U_10865),c_Divides_OposDivAlg(U_10864,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)))),U_10865)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10865),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10864),U_10865))
| ~ sP837(U_10865,U_10864) ),
inference(clausify,[status(thm)],[f_2945_3]) ).
cnf(f_2945_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10864),U_10865))
| ~ sP836(U_10865,U_10864) ),
inference(clausify,[status(thm)],[f_2945_3]) ).
cnf(f_2945_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10865),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP836(U_10865,U_10864) ),
inference(clausify,[status(thm)],[f_2945_3]) ).
fof(f_2946_1,plain,
! [V_b_2,V_a_2] :
( ( ( ( ( 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)))
| V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( 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))
| ( V_b_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& V_a_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_norm__frac_Opsimps]) ).
fof(f_2946_2,plain,
! [U_10867,U_10866] :
( ( ( ( ( c_Nitpick_Onorm__frac(U_10866,U_10867) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10866),U_10867)),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),U_10866))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10867)))
| U_10867 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10866 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_10866,U_10867) = 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))
| ( U_10867 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_10866 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10867),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(U_10866,U_10867) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10866),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10867),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ 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),U_10866),U_10867))) ),
inference(variable_rename,[status(thm)],[f_2946_1]) ).
fof(f_2946_3,plain,
( ! [U_10867,U_10866] :
( U_10867 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP838(U_10867,U_10866) )
& ! [U_10867,U_10866] :
( U_10866 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP838(U_10867,U_10866) )
& ! [U_10867,U_10866] :
( c_Nitpick_Onorm__frac(U_10866,U_10867) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10866),U_10867)),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),U_10866))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10867)))
| U_10867 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10866 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP839(U_10867,U_10866) )
& ! [U_10867,U_10866] :
( c_Nitpick_Onorm__frac(U_10866,U_10867) = 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))
| sP838(U_10867,U_10866)
| ~ sP839(U_10867,U_10866) )
& ! [U_10867,U_10866] :
( sP839(U_10867,U_10866)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP840(U_10867,U_10866) )
& ! [U_10867,U_10866] :
( c_Nitpick_Onorm__frac(U_10866,U_10867) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10866),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP840(U_10867,U_10866) )
& ! [U_10867,U_10866] :
( sP840(U_10867,U_10866)
| ~ 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),U_10866),U_10867))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP838,sP839,sP840])],[f_2946_2]) ).
cnf(f_2946_4,plain,
( sP840(U_10867,U_10866)
| ~ 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),U_10866),U_10867))) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
cnf(f_2946_5,plain,
( c_Nitpick_Onorm__frac(U_10866,U_10867) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10866),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP840(U_10867,U_10866) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
cnf(f_2946_6,plain,
( sP839(U_10867,U_10866)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP840(U_10867,U_10866) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
cnf(f_2946_7,plain,
( c_Nitpick_Onorm__frac(U_10866,U_10867) = 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))
| sP838(U_10867,U_10866)
| ~ sP839(U_10867,U_10866) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
cnf(f_2946_8,plain,
( c_Nitpick_Onorm__frac(U_10866,U_10867) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10866),U_10867)),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),U_10866))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10867)))
| U_10867 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10866 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP839(U_10867,U_10866) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
cnf(f_2946_9,plain,
( U_10866 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP838(U_10867,U_10866) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
cnf(f_2946_10,plain,
( U_10867 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP838(U_10867,U_10866) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
fof(f_2947_1,plain,
! [V_Pa_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
& ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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))) )
& 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))) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct]) ).
fof(f_2947_2,plain,
! [U_10872,U_10871,U_10870] :
( hBOOL(hAPP(hAPP(U_10872,U_10870),U_10871))
| ? [U_10869,U_10868] :
( ~ hBOOL(hAPP(hAPP(U_10872,U_10869),U_10868))
& ( hBOOL(hAPP(hAPP(U_10872,U_10869),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)))),U_10868)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10868),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),U_10869),U_10868))) )
& 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),U_10869),U_10868))) )
| ~ 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),U_10870),U_10871))) ),
inference(variable_rename,[status(thm)],[f_2947_1]) ).
fof(f_2947_3,plain,
! [U_10872,U_10871,U_10870] :
( hBOOL(hAPP(hAPP(U_10872,U_10870),U_10871))
| ? [U_10868] :
( ~ hBOOL(hAPP(hAPP(U_10872,sK267(U_10872,U_10871,U_10870)),U_10868))
& ( hBOOL(hAPP(hAPP(U_10872,sK267(U_10872,U_10871,U_10870)),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)))),U_10868)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10868),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),sK267(U_10872,U_10871,U_10870)),U_10868))) )
& 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),sK267(U_10872,U_10871,U_10870)),U_10868))) )
| ~ 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),U_10870),U_10871))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_10869,sK267(U_10872,U_10871,U_10870))],[f_2947_2]) ).
fof(f_2947_4,plain,
! [U_10872,U_10871,U_10870] :
( hBOOL(hAPP(hAPP(U_10872,U_10870),U_10871))
| ( ~ hBOOL(hAPP(hAPP(U_10872,sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870)))
& ( hBOOL(hAPP(hAPP(U_10872,sK267(U_10872,U_10871,U_10870)),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)))),sK268(U_10872,U_10871,U_10870))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK268(U_10872,U_10871,U_10870)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870)))) )
& 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),sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870)))) )
| ~ 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),U_10870),U_10871))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_10868,sK268(U_10872,U_10871,U_10870))],[f_2947_3]) ).
fof(f_2947_5,plain,
( ! [U_10871,U_10870,U_10872] :
( ~ hBOOL(hAPP(hAPP(U_10872,sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870)))
| ~ sP841(U_10871,U_10870,U_10872) )
& ! [U_10871,U_10870,U_10872] :
( hBOOL(hAPP(hAPP(U_10872,sK267(U_10872,U_10871,U_10870)),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)))),sK268(U_10872,U_10871,U_10870))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK268(U_10872,U_10871,U_10870)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870))))
| ~ sP841(U_10871,U_10870,U_10872) )
& ! [U_10871,U_10870,U_10872] :
( 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),sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870))))
| ~ sP841(U_10871,U_10870,U_10872) )
& ! [U_10871,U_10870,U_10872] :
( hBOOL(hAPP(hAPP(U_10872,U_10870),U_10871))
| sP841(U_10871,U_10870,U_10872)
| ~ 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),U_10870),U_10871))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP841])],[f_2947_4]) ).
cnf(f_2947_6,plain,
( hBOOL(hAPP(hAPP(U_10872,U_10870),U_10871))
| sP841(U_10871,U_10870,U_10872)
| ~ 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),U_10870),U_10871))) ),
inference(clausify,[status(thm)],[f_2947_5]) ).
cnf(f_2947_7,plain,
( 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),sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870))))
| ~ sP841(U_10871,U_10870,U_10872) ),
inference(clausify,[status(thm)],[f_2947_5]) ).
cnf(f_2947_8,plain,
( hBOOL(hAPP(hAPP(U_10872,sK267(U_10872,U_10871,U_10870)),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)))),sK268(U_10872,U_10871,U_10870))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK268(U_10872,U_10871,U_10870)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| 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),sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870))))
| ~ sP841(U_10871,U_10870,U_10872) ),
inference(clausify,[status(thm)],[f_2947_5]) ).
cnf(f_2947_9,plain,
( ~ hBOOL(hAPP(hAPP(U_10872,sK267(U_10872,U_10871,U_10870)),sK268(U_10872,U_10871,U_10870)))
| ~ sP841(U_10871,U_10870,U_10872) ),
inference(clausify,[status(thm)],[f_2947_5]) ).
fof(f_2948_1,plain,
! [V_Pa_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
& ( 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)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
& 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))) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct]) ).
fof(f_2948_2,plain,
! [U_10877,U_10876,U_10875] :
( hBOOL(hAPP(hAPP(U_10877,U_10875),U_10876))
| ? [U_10874,U_10873] :
( ~ hBOOL(hAPP(hAPP(U_10877,U_10874),U_10873))
& ( hBOOL(hAPP(hAPP(U_10877,U_10874),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)))),U_10873)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10873),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10874),U_10873)) )
& 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),U_10874),U_10873))) )
| ~ 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),U_10875),U_10876))) ),
inference(variable_rename,[status(thm)],[f_2948_1]) ).
fof(f_2948_3,plain,
! [U_10877,U_10876,U_10875] :
( hBOOL(hAPP(hAPP(U_10877,U_10875),U_10876))
| ? [U_10873] :
( ~ hBOOL(hAPP(hAPP(U_10877,sK269(U_10877,U_10876,U_10875)),U_10873))
& ( hBOOL(hAPP(hAPP(U_10877,sK269(U_10877,U_10876,U_10875)),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)))),U_10873)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10873),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK269(U_10877,U_10876,U_10875)),U_10873)) )
& 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),sK269(U_10877,U_10876,U_10875)),U_10873))) )
| ~ 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),U_10875),U_10876))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_10874,sK269(U_10877,U_10876,U_10875))],[f_2948_2]) ).
fof(f_2948_4,plain,
! [U_10877,U_10876,U_10875] :
( hBOOL(hAPP(hAPP(U_10877,U_10875),U_10876))
| ( ~ hBOOL(hAPP(hAPP(U_10877,sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875)))
& ( hBOOL(hAPP(hAPP(U_10877,sK269(U_10877,U_10876,U_10875)),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)))),sK270(U_10877,U_10876,U_10875))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK270(U_10877,U_10876,U_10875)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875))) )
& 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),sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875)))) )
| ~ 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),U_10875),U_10876))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_10873,sK270(U_10877,U_10876,U_10875))],[f_2948_3]) ).
fof(f_2948_5,plain,
( ! [U_10877,U_10875,U_10876] :
( ~ hBOOL(hAPP(hAPP(U_10877,sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875)))
| ~ sP842(U_10877,U_10875,U_10876) )
& ! [U_10877,U_10875,U_10876] :
( hBOOL(hAPP(hAPP(U_10877,sK269(U_10877,U_10876,U_10875)),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)))),sK270(U_10877,U_10876,U_10875))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK270(U_10877,U_10876,U_10875)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875)))
| ~ sP842(U_10877,U_10875,U_10876) )
& ! [U_10877,U_10875,U_10876] :
( 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),sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875))))
| ~ sP842(U_10877,U_10875,U_10876) )
& ! [U_10877,U_10875,U_10876] :
( hBOOL(hAPP(hAPP(U_10877,U_10875),U_10876))
| sP842(U_10877,U_10875,U_10876)
| ~ 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),U_10875),U_10876))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP842])],[f_2948_4]) ).
cnf(f_2948_6,plain,
( hBOOL(hAPP(hAPP(U_10877,U_10875),U_10876))
| sP842(U_10877,U_10875,U_10876)
| ~ 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),U_10875),U_10876))) ),
inference(clausify,[status(thm)],[f_2948_5]) ).
cnf(f_2948_7,plain,
( 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),sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875))))
| ~ sP842(U_10877,U_10875,U_10876) ),
inference(clausify,[status(thm)],[f_2948_5]) ).
cnf(f_2948_8,plain,
( hBOOL(hAPP(hAPP(U_10877,sK269(U_10877,U_10876,U_10875)),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)))),sK270(U_10877,U_10876,U_10875))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK270(U_10877,U_10876,U_10875)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875)))
| ~ sP842(U_10877,U_10875,U_10876) ),
inference(clausify,[status(thm)],[f_2948_5]) ).
cnf(f_2948_9,plain,
( ~ hBOOL(hAPP(hAPP(U_10877,sK269(U_10877,U_10876,U_10875)),sK270(U_10877,U_10876,U_10875)))
| ~ sP842(U_10877,U_10875,U_10876) ),
inference(clausify,[status(thm)],[f_2948_5]) ).
fof(f_2949_1,plain,
! [V_y_2,V_x_2] :
( ( ( 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))
| V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps]) ).
fof(f_2949_2,plain,
! [U_10879,U_10878] :
( ( ( c_Nitpick_Onat__gcd(U_10878,U_10879) = c_Nitpick_Onat__gcd(U_10879,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10878,U_10879))
| U_10879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(U_10878,U_10879) = U_10878
| U_10879 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ 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),U_10878),U_10879))) ),
inference(variable_rename,[status(thm)],[f_2949_1]) ).
fof(f_2949_3,plain,
( ! [U_10878,U_10879] :
( c_Nitpick_Onat__gcd(U_10878,U_10879) = c_Nitpick_Onat__gcd(U_10879,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10878,U_10879))
| U_10879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP843(U_10878,U_10879) )
& ! [U_10878,U_10879] :
( c_Nitpick_Onat__gcd(U_10878,U_10879) = U_10878
| U_10879 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP843(U_10878,U_10879) )
& ! [U_10878,U_10879] :
( sP843(U_10878,U_10879)
| ~ 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),U_10878),U_10879))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP843])],[f_2949_2]) ).
cnf(f_2949_4,plain,
( sP843(U_10878,U_10879)
| ~ 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),U_10878),U_10879))) ),
inference(clausify,[status(thm)],[f_2949_3]) ).
cnf(f_2949_5,plain,
( c_Nitpick_Onat__gcd(U_10878,U_10879) = U_10878
| U_10879 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP843(U_10878,U_10879) ),
inference(clausify,[status(thm)],[f_2949_3]) ).
cnf(f_2949_6,plain,
( c_Nitpick_Onat__gcd(U_10878,U_10879) = c_Nitpick_Onat__gcd(U_10879,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10878,U_10879))
| U_10879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP843(U_10878,U_10879) ),
inference(clausify,[status(thm)],[f_2949_3]) ).
fof(f_2950_1,plain,
! [V_c,V_r,V_q,V_b,V_a] :
( 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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_zmult2__lemma]) ).
fof(f_2950_2,plain,
! [U_10884,U_10883,U_10882,U_10881,U_10880] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10880,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10881),U_10884)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10882),U_10884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10881),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10882,U_10884))),U_10883))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10884))
| U_10881 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10880,U_10881),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10882),U_10883))) ),
inference(variable_rename,[status(thm)],[f_2950_1]) ).
fof(f_2950_3,plain,
! [U_10882,U_10880,U_10881,U_10883,U_10884] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10880,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10881),U_10884)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10882),U_10884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10881),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10882,U_10884))),U_10883))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10884))
| U_10881 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10880,U_10881),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10882),U_10883))) ),
inference(definitional_conversion,[status(esa)],[f_2950_2]) ).
cnf(f_2950_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10880,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10881),U_10884)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10882),U_10884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10881),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10882,U_10884))),U_10883))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10884))
| U_10881 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10880,U_10881),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10882),U_10883))) ),
inference(clausify,[status(thm)],[f_2950_3]) ).
fof(f_2951_1,plain,
! [V_b] :
( 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))))
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__0]) ).
fof(f_2951_2,plain,
! [U_10885] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10885),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))))
| U_10885 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2951_1]) ).
fof(f_2951_3,plain,
! [U_10885] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10885),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))))
| U_10885 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2951_2]) ).
cnf(f_2951_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10885),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))))
| U_10885 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2951_3]) ).
fof(f_2952_1,plain,
! [V_r,V_q,V_a] :
( V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_self__remainder]) ).
fof(f_2952_2,plain,
! [U_10888,U_10887,U_10886] :
( U_10888 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10886 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10886,U_10886),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10887),U_10888))) ),
inference(variable_rename,[status(thm)],[f_2952_1]) ).
fof(f_2952_3,plain,
! [U_10886,U_10887,U_10888] :
( U_10888 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10886 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10886,U_10886),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10887),U_10888))) ),
inference(definitional_conversion,[status(esa)],[f_2952_2]) ).
cnf(f_2952_4,plain,
( U_10888 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10886 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10886,U_10886),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10887),U_10888))) ),
inference(clausify,[status(thm)],[f_2952_3]) ).
fof(f_2953_1,plain,
! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
( V_q = V_q_H
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient]) ).
fof(f_2953_2,plain,
! [U_10894,U_10893,U_10892,U_10891,U_10890,U_10889] :
( U_10891 = U_10893
| U_10890 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10889,U_10890),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10893),U_10894)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10889,U_10890),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10891),U_10892))) ),
inference(variable_rename,[status(thm)],[f_2953_1]) ).
fof(f_2953_3,plain,
! [U_10890,U_10889,U_10891,U_10892,U_10893,U_10894] :
( U_10891 = U_10893
| U_10890 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10889,U_10890),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10893),U_10894)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10889,U_10890),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10891),U_10892))) ),
inference(definitional_conversion,[status(esa)],[f_2953_2]) ).
cnf(f_2953_4,plain,
( U_10891 = U_10893
| U_10890 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10889,U_10890),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10893),U_10894)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10889,U_10890),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10891),U_10892))) ),
inference(clausify,[status(thm)],[f_2953_3]) ).
fof(f_2954_1,plain,
! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
( V_r = V_r_H
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_unique__remainder]) ).
fof(f_2954_2,plain,
! [U_10900,U_10899,U_10898,U_10897,U_10896,U_10895] :
( U_10898 = U_10900
| U_10896 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10895,U_10896),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10899),U_10900)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10895,U_10896),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10897),U_10898))) ),
inference(variable_rename,[status(thm)],[f_2954_1]) ).
fof(f_2954_3,plain,
! [U_10897,U_10895,U_10896,U_10898,U_10899,U_10900] :
( U_10898 = U_10900
| U_10896 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10895,U_10896),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10899),U_10900)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10895,U_10896),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10897),U_10898))) ),
inference(definitional_conversion,[status(esa)],[f_2954_2]) ).
cnf(f_2954_4,plain,
( U_10898 = U_10900
| U_10896 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10895,U_10896),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10899),U_10900)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10895,U_10896),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10897),U_10898))) ),
inference(clausify,[status(thm)],[f_2954_3]) ).
fof(f_2955_1,plain,
! [V_qr,V_b,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr)))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg]) ).
fof(f_2955_2,plain,
! [U_10903,U_10902,U_10901] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10901,U_10902),hAPP(c_Divides_OnegateSnd,U_10903)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10901),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10902)),U_10903)) ),
inference(variable_rename,[status(thm)],[f_2955_1]) ).
fof(f_2955_3,plain,
! [U_10903,U_10902,U_10901] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10901,U_10902),hAPP(c_Divides_OnegateSnd,U_10903)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10901),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10902)),U_10903)) ),
inference(definitional_conversion,[status(esa)],[f_2955_2]) ).
cnf(f_2955_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10901,U_10902),hAPP(c_Divides_OnegateSnd,U_10903)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10901),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10902)),U_10903)) ),
inference(clausify,[status(thm)],[f_2955_3]) ).
fof(f_2956_1,plain,
! [V_a,V_b] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b)))
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__correct]) ).
fof(f_2956_2,plain,
! [U_10905,U_10904] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10905,U_10904),c_Divides_Odivmod__int(U_10905,U_10904)))
| U_10904 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2956_1]) ).
fof(f_2956_3,plain,
! [U_10904,U_10905] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10905,U_10904),c_Divides_Odivmod__int(U_10905,U_10904)))
| U_10904 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2956_2]) ).
cnf(f_2956_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10905,U_10904),c_Divides_Odivmod__int(U_10905,U_10904)))
| U_10904 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2956_3]) ).
fof(f_2957_1,plain,
! [V_r,V_q,V_a] :
( V_q = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_self__quotient]) ).
fof(f_2957_2,plain,
! [U_10908,U_10907,U_10906] :
( U_10907 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_10906 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10906,U_10906),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10907),U_10908))) ),
inference(variable_rename,[status(thm)],[f_2957_1]) ).
fof(f_2957_3,plain,
! [U_10906,U_10907,U_10908] :
( U_10907 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_10906 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10906,U_10906),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10907),U_10908))) ),
inference(definitional_conversion,[status(esa)],[f_2957_2]) ).
cnf(f_2957_4,plain,
( U_10907 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_10906 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10906,U_10906),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10907),U_10908))) ),
inference(clausify,[status(thm)],[f_2957_3]) ).
fof(f_2958_1,plain,
! [V_r,V_q,V_b,V_a] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod]) ).
fof(f_2958_2,plain,
! [U_10912,U_10911,U_10910,U_10909] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10909,U_10910) = U_10912
| U_10910 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10909,U_10910),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10911),U_10912))) ),
inference(variable_rename,[status(thm)],[f_2958_1]) ).
fof(f_2958_3,plain,
! [U_10910,U_10909,U_10911,U_10912] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10909,U_10910) = U_10912
| U_10910 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10909,U_10910),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10911),U_10912))) ),
inference(definitional_conversion,[status(esa)],[f_2958_2]) ).
cnf(f_2958_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10909,U_10910) = U_10912
| U_10910 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10909,U_10910),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10911),U_10912))) ),
inference(clausify,[status(thm)],[f_2958_3]) ).
fof(f_2959_1,plain,
! [V_r,V_q,V_b,V_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div]) ).
fof(f_2959_2,plain,
! [U_10916,U_10915,U_10914,U_10913] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10913),U_10914) = U_10915
| U_10914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10913,U_10914),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10915),U_10916))) ),
inference(variable_rename,[status(thm)],[f_2959_1]) ).
fof(f_2959_3,plain,
! [U_10914,U_10913,U_10915,U_10916] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10913),U_10914) = U_10915
| U_10914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10913,U_10914),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10915),U_10916))) ),
inference(definitional_conversion,[status(esa)],[f_2959_2]) ).
cnf(f_2959_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10913),U_10914) = U_10915
| U_10914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10913,U_10914),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10915),U_10916))) ),
inference(clausify,[status(thm)],[f_2959_3]) ).
fof(f_2960_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct]) ).
fof(f_2960_2,plain,
! [U_10918,U_10917] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10917,U_10918),c_Divides_OnegDivAlg(U_10917,U_10918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10917),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2960_1]) ).
fof(f_2960_3,plain,
! [U_10917,U_10918] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10917,U_10918),c_Divides_OnegDivAlg(U_10917,U_10918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10917),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2960_2]) ).
cnf(f_2960_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10917,U_10918),c_Divides_OnegDivAlg(U_10917,U_10918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10917),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2960_3]) ).
fof(f_2961_1,plain,
! [V_a,V_b] :
( 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))))
| V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod]) ).
fof(f_2961_2,plain,
! [U_10920,U_10919] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10920,U_10919),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10920),U_10919)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10920,U_10919))))
| U_10919 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2961_1]) ).
fof(f_2961_3,plain,
! [U_10919,U_10920] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10920,U_10919),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10920),U_10919)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10920,U_10919))))
| U_10919 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2961_2]) ).
cnf(f_2961_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10920,U_10919),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10920),U_10919)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10920,U_10919))))
| U_10919 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2961_3]) ).
fof(f_2962_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct]) ).
fof(f_2962_2,plain,
! [U_10922,U_10921] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10921,U_10922),c_Divides_OposDivAlg(U_10921,U_10922)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10921)) ),
inference(variable_rename,[status(thm)],[f_2962_1]) ).
fof(f_2962_3,plain,
! [U_10921,U_10922] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10921,U_10922),c_Divides_OposDivAlg(U_10921,U_10922)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10921)) ),
inference(definitional_conversion,[status(esa)],[f_2962_2]) ).
cnf(f_2962_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10921,U_10922),c_Divides_OposDivAlg(U_10921,U_10922)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10921)) ),
inference(clausify,[status(thm)],[f_2962_3]) ).
fof(f_2963_1,plain,
! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
( 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))))
| V_c = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_zadd1__lemma]) ).
fof(f_2963_2,plain,
! [U_10929,U_10928,U_10927,U_10926,U_10925,U_10924,U_10923] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10923),U_10927),U_10924),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),U_10925),U_10928)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10926),U_10929)),U_10924))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10926),U_10929),U_10924))))
| U_10924 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10927,U_10924),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10928),U_10929)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10923,U_10924),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10925),U_10926))) ),
inference(variable_rename,[status(thm)],[f_2963_1]) ).
fof(f_2963_3,plain,
! [U_10923,U_10924,U_10925,U_10926,U_10927,U_10928,U_10929] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10923),U_10927),U_10924),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),U_10925),U_10928)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10926),U_10929)),U_10924))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10926),U_10929),U_10924))))
| U_10924 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10927,U_10924),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10928),U_10929)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10923,U_10924),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10925),U_10926))) ),
inference(definitional_conversion,[status(esa)],[f_2963_2]) ).
cnf(f_2963_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10923),U_10927),U_10924),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),U_10925),U_10928)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10926),U_10929)),U_10924))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10926),U_10929),U_10924))))
| U_10924 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10927,U_10924),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10928),U_10929)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10923,U_10924),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10925),U_10926))) ),
inference(clausify,[status(thm)],[f_2963_3]) ).
fof(f_2964_1,plain,
! [V_r_2,V_q_2,V_b_2,V_a_2] :
( 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)))))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_zminus1__lemma]) ).
fof(f_2964_2,plain,
! [U_10933,U_10932,U_10931,U_10930] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10930),U_10931),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_10933),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10932)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10932)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_10933),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),U_10931),U_10933)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10930,U_10931),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10932),U_10933))) ),
inference(variable_rename,[status(thm)],[f_2964_1]) ).
fof(f_2964_3,plain,
! [U_10931,U_10930,U_10932,U_10933] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10930),U_10931),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_10933),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10932)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10932)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_10933),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),U_10931),U_10933)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10930,U_10931),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10932),U_10933))) ),
inference(definitional_conversion,[status(esa)],[f_2964_2]) ).
cnf(f_2964_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10930),U_10931),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_10933),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10932)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10932)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_10933),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),U_10931),U_10933)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10930,U_10931),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10932),U_10933))) ),
inference(clausify,[status(thm)],[f_2964_3]) ).
fof(f_2965_1,plain,
! [V_r,V_q,V_b,V_a] :
( 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)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
| 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) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__relI]) ).
fof(f_2965_2,plain,
! [U_10937,U_10936,U_10935,U_10934] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10934,U_10935),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10936),U_10937)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10937),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10935),U_10937)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10935)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10937),U_10935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10937)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10935)) )
| U_10934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10935),U_10936)),U_10937) ),
inference(variable_rename,[status(thm)],[f_2965_1]) ).
fof(f_2965_3,plain,
( ! [U_10935,U_10937] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10937),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10935),U_10937))
| ~ sP845(U_10935,U_10937) )
& ! [U_10935,U_10937] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10935))
| ~ sP845(U_10935,U_10937) )
& ! [U_10935,U_10937] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10937),U_10935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10937))
| ~ sP844(U_10935,U_10937) )
& ! [U_10935,U_10937] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10935))
| ~ sP844(U_10935,U_10937) )
& ! [U_10934,U_10935,U_10936,U_10937] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10934,U_10935),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10936),U_10937)))
| sP845(U_10935,U_10937)
| sP844(U_10935,U_10937)
| U_10934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10935),U_10936)),U_10937) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP844,sP845])],[f_2965_2]) ).
cnf(f_2965_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10934,U_10935),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10936),U_10937)))
| sP845(U_10935,U_10937)
| sP844(U_10935,U_10937)
| U_10934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10935),U_10936)),U_10937) ),
inference(clausify,[status(thm)],[f_2965_3]) ).
cnf(f_2965_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10935))
| ~ sP844(U_10935,U_10937) ),
inference(clausify,[status(thm)],[f_2965_3]) ).
cnf(f_2965_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10937),U_10935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10937))
| ~ sP844(U_10935,U_10937) ),
inference(clausify,[status(thm)],[f_2965_3]) ).
cnf(f_2965_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10935))
| ~ sP845(U_10935,U_10937) ),
inference(clausify,[status(thm)],[f_2965_3]) ).
cnf(f_2965_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10937),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10935),U_10937))
| ~ sP845(U_10935,U_10937) ),
inference(clausify,[status(thm)],[f_2965_3]) ).
fof(f_2966_1,plain,
! [V_a,V_r,V_q,V_c,V_b] :
( 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))))
| V_c = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_zmult1__lemma]) ).
fof(f_2966_2,plain,
! [U_10942,U_10941,U_10940,U_10939,U_10938] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10938),U_10939),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),U_10942),U_10940)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10941)),U_10939))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10941),U_10939))))
| U_10939 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10938,U_10939),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10940),U_10941))) ),
inference(variable_rename,[status(thm)],[f_2966_1]) ).
fof(f_2966_3,plain,
! [U_10938,U_10939,U_10941,U_10942,U_10940] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10938),U_10939),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),U_10942),U_10940)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10941)),U_10939))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10941),U_10939))))
| U_10939 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10938,U_10939),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10940),U_10941))) ),
inference(definitional_conversion,[status(esa)],[f_2966_2]) ).
cnf(f_2966_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10938),U_10939),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),U_10942),U_10940)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10941)),U_10939))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10942),U_10941),U_10939))))
| U_10939 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_10938,U_10939),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10940),U_10941))) ),
inference(clausify,[status(thm)],[f_2966_3]) ).
fof(f_2967_1,plain,
! [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))))))),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__def]) ).
fof(f_2967_2,plain,
! [U_10944,U_10943] : c_Divides_Odivmod__int__rel(U_10943,U_10944) = 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,U_10943))),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),U_10944)))))),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)),U_10944))),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)),U_10944))))),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)),U_10944)))),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),U_10944))),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))))))),
inference(variable_rename,[status(thm)],[f_2967_1]) ).
fof(f_2967_3,plain,
! [U_10943,U_10944] : c_Divides_Odivmod__int__rel(U_10943,U_10944) = 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,U_10943))),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),U_10944)))))),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)),U_10944))),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)),U_10944))))),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)),U_10944)))),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),U_10944))),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))))))),
inference(definitional_conversion,[status(esa)],[f_2967_2]) ).
cnf(f_2967_4,plain,
c_Divides_Odivmod__int__rel(U_10943,U_10944) = 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,U_10943))),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),U_10944)))))),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)),U_10944))),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)),U_10944))))),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)),U_10944)))),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),U_10944))),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))))))),
inference(clausify,[status(thm)],[f_2967_3]) ).
fof(f_2968_1,plain,
! [V_f_2,V_A_2,T_b] :
( 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))
| ? [B_x] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J]) ).
fof(f_2968_2,plain,
! [U_10948,U_10947,U_10946] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10946,tc_Int_Oint),U_10948),U_10947) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10946,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10946),c_Int_Onat),U_10948)),U_10947))
| ? [U_10945] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10948,U_10945))
& hBOOL(hAPP(hAPP(c_member(U_10946),U_10945),U_10947)) ) ),
inference(variable_rename,[status(thm)],[f_2968_1]) ).
fof(f_2968_3,plain,
! [U_10948,U_10947,U_10946] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10946,tc_Int_Oint),U_10948),U_10947) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10946,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10946),c_Int_Onat),U_10948)),U_10947))
| ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10948,sK271(U_10948,U_10947,U_10946)))
& hBOOL(hAPP(hAPP(c_member(U_10946),sK271(U_10948,U_10947,U_10946)),U_10947)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_10945,sK271(U_10948,U_10947,U_10946))],[f_2968_2]) ).
fof(f_2968_4,plain,
( ! [U_10946,U_10947,U_10948] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10948,sK271(U_10948,U_10947,U_10946)))
| ~ sP846(U_10946,U_10947,U_10948) )
& ! [U_10946,U_10947,U_10948] :
( hBOOL(hAPP(hAPP(c_member(U_10946),sK271(U_10948,U_10947,U_10946)),U_10947))
| ~ sP846(U_10946,U_10947,U_10948) )
& ! [U_10946,U_10947,U_10948] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10946,tc_Int_Oint),U_10948),U_10947) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10946,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10946),c_Int_Onat),U_10948)),U_10947))
| sP846(U_10946,U_10947,U_10948) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP846])],[f_2968_3]) ).
cnf(f_2968_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10946,tc_Int_Oint),U_10948),U_10947) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10946,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10946),c_Int_Onat),U_10948)),U_10947))
| sP846(U_10946,U_10947,U_10948) ),
inference(clausify,[status(thm)],[f_2968_4]) ).
cnf(f_2968_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10946),sK271(U_10948,U_10947,U_10946)),U_10947))
| ~ sP846(U_10946,U_10947,U_10948) ),
inference(clausify,[status(thm)],[f_2968_4]) ).
cnf(f_2968_7,plain,
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10948,sK271(U_10948,U_10947,U_10946)))
| ~ sP846(U_10946,U_10947,U_10948) ),
inference(clausify,[status(thm)],[f_2968_4]) ).
fof(f_2969_1,plain,
! [V_w] :
( 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)))))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of]) ).
fof(f_2969_2,plain,
! [U_10949] :
( 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),U_10949)) = 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),U_10949)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10949)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2969_1]) ).
fof(f_2969_3,plain,
! [U_10949] :
( 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),U_10949)) = 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),U_10949)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10949)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2969_2]) ).
cnf(f_2969_4,plain,
( 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),U_10949)) = 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),U_10949)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10949)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2969_3]) ).
fof(f_2970_1,plain,
! [V_f_2,V_y_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_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
| ~ 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))) )
& ( 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)))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__measure]) ).
fof(f_2970_2,plain,
! [U_10953,U_10952,U_10951,U_10950] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10950,U_10950)),hAPP(hAPP(c_Product__Type_OPair(U_10950,U_10950),U_10951),U_10952)),hAPP(c_Wellfounded_Omeasure(U_10950),U_10953)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_10953,U_10951)),hAPP(U_10953,U_10952))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_10953,U_10951)),hAPP(U_10953,U_10952)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10950,U_10950)),hAPP(hAPP(c_Product__Type_OPair(U_10950,U_10950),U_10951),U_10952)),hAPP(c_Wellfounded_Omeasure(U_10950),U_10953))) ) ),
inference(variable_rename,[status(thm)],[f_2970_1]) ).
fof(f_2970_3,plain,
( ! [U_10961,U_10959,U_10957] :
( ! [U_10955] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10955,U_10955)),hAPP(hAPP(c_Product__Type_OPair(U_10955,U_10955),U_10957),U_10959)),hAPP(c_Wellfounded_Omeasure(U_10955),U_10961)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_10961,U_10957)),hAPP(U_10961,U_10959))) )
& ! [U_10960,U_10958,U_10956] :
( ! [U_10954] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10954,U_10954)),hAPP(hAPP(c_Product__Type_OPair(U_10954,U_10954),U_10956),U_10958)),hAPP(c_Wellfounded_Omeasure(U_10954),U_10960)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_10960,U_10956)),hAPP(U_10960,U_10958))) ) ),
inference(miniscope,[status(thm)],[f_2970_2]) ).
fof(f_2970_4,plain,
( ! [U_10955,U_10957,U_10959,U_10961] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10955,U_10955)),hAPP(hAPP(c_Product__Type_OPair(U_10955,U_10955),U_10957),U_10959)),hAPP(c_Wellfounded_Omeasure(U_10955),U_10961)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_10961,U_10957)),hAPP(U_10961,U_10959))) )
& ! [U_10960,U_10956,U_10954,U_10958] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10954,U_10954)),hAPP(hAPP(c_Product__Type_OPair(U_10954,U_10954),U_10956),U_10958)),hAPP(c_Wellfounded_Omeasure(U_10954),U_10960)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_10960,U_10956)),hAPP(U_10960,U_10958))) ) ),
inference(definitional_conversion,[status(esa)],[f_2970_3]) ).
cnf(f_2970_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10954,U_10954)),hAPP(hAPP(c_Product__Type_OPair(U_10954,U_10954),U_10956),U_10958)),hAPP(c_Wellfounded_Omeasure(U_10954),U_10960)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_10960,U_10956)),hAPP(U_10960,U_10958))) ),
inference(clausify,[status(thm)],[f_2970_4]) ).
cnf(f_2970_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10955,U_10955)),hAPP(hAPP(c_Product__Type_OPair(U_10955,U_10955),U_10957),U_10959)),hAPP(c_Wellfounded_Omeasure(U_10955),U_10961)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_10961,U_10957)),hAPP(U_10961,U_10959))) ),
inference(clausify,[status(thm)],[f_2970_4]) ).
fof(f_2971_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_snd__apsnd]) ).
fof(f_2971_2,plain,
! [U_10966,U_10965,U_10964,U_10963,U_10962] : hAPP(c_Product__Type_Osnd(U_10962,U_10963),hAPP(c_Product__Type_Oapsnd(U_10964,U_10963,U_10962,U_10965),U_10966)) = hAPP(U_10965,hAPP(c_Product__Type_Osnd(U_10962,U_10964),U_10966)),
inference(variable_rename,[status(thm)],[f_2971_1]) ).
fof(f_2971_3,plain,
! [U_10962,U_10963,U_10964,U_10965,U_10966] : hAPP(c_Product__Type_Osnd(U_10962,U_10963),hAPP(c_Product__Type_Oapsnd(U_10964,U_10963,U_10962,U_10965),U_10966)) = hAPP(U_10965,hAPP(c_Product__Type_Osnd(U_10962,U_10964),U_10966)),
inference(definitional_conversion,[status(esa)],[f_2971_2]) ).
cnf(f_2971_4,plain,
hAPP(c_Product__Type_Osnd(U_10962,U_10963),hAPP(c_Product__Type_Oapsnd(U_10964,U_10963,U_10962,U_10965),U_10966)) = hAPP(U_10965,hAPP(c_Product__Type_Osnd(U_10962,U_10964),U_10966)),
inference(clausify,[status(thm)],[f_2971_3]) ).
fof(f_2972_1,plain,
! [V_g_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),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
| 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)) )
& ( 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))
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv]) ).
fof(f_2972_2,plain,
! [U_10972,U_10971,U_10970,U_10969,U_10968,U_10967] :
( ( hAPP(c_Product__Type_Oapsnd(U_10967,U_10968,U_10969,U_10970),U_10971) = hAPP(c_Product__Type_Oapsnd(U_10967,U_10968,U_10969,U_10972),U_10971)
| hAPP(U_10970,hAPP(c_Product__Type_Osnd(U_10969,U_10967),U_10971)) != hAPP(U_10972,hAPP(c_Product__Type_Osnd(U_10969,U_10967),U_10971)) )
& ( hAPP(U_10970,hAPP(c_Product__Type_Osnd(U_10969,U_10967),U_10971)) = hAPP(U_10972,hAPP(c_Product__Type_Osnd(U_10969,U_10967),U_10971))
| hAPP(c_Product__Type_Oapsnd(U_10967,U_10968,U_10969,U_10970),U_10971) != hAPP(c_Product__Type_Oapsnd(U_10967,U_10968,U_10969,U_10972),U_10971) ) ),
inference(variable_rename,[status(thm)],[f_2972_1]) ).
fof(f_2972_3,plain,
( ! [U_10984,U_10982,U_10980,U_10978,U_10976,U_10974] :
( hAPP(c_Product__Type_Oapsnd(U_10974,U_10976,U_10978,U_10980),U_10982) = hAPP(c_Product__Type_Oapsnd(U_10974,U_10976,U_10978,U_10984),U_10982)
| hAPP(U_10980,hAPP(c_Product__Type_Osnd(U_10978,U_10974),U_10982)) != hAPP(U_10984,hAPP(c_Product__Type_Osnd(U_10978,U_10974),U_10982)) )
& ! [U_10983,U_10981,U_10979,U_10977,U_10975,U_10973] :
( hAPP(U_10979,hAPP(c_Product__Type_Osnd(U_10977,U_10973),U_10981)) = hAPP(U_10983,hAPP(c_Product__Type_Osnd(U_10977,U_10973),U_10981))
| hAPP(c_Product__Type_Oapsnd(U_10973,U_10975,U_10977,U_10979),U_10981) != hAPP(c_Product__Type_Oapsnd(U_10973,U_10975,U_10977,U_10983),U_10981) ) ),
inference(miniscope,[status(thm)],[f_2972_2]) ).
fof(f_2972_4,plain,
( ! [U_10974,U_10976,U_10978,U_10980,U_10982,U_10984] :
( hAPP(c_Product__Type_Oapsnd(U_10974,U_10976,U_10978,U_10980),U_10982) = hAPP(c_Product__Type_Oapsnd(U_10974,U_10976,U_10978,U_10984),U_10982)
| hAPP(U_10980,hAPP(c_Product__Type_Osnd(U_10978,U_10974),U_10982)) != hAPP(U_10984,hAPP(c_Product__Type_Osnd(U_10978,U_10974),U_10982)) )
& ! [U_10979,U_10973,U_10975,U_10977,U_10983,U_10981] :
( hAPP(U_10979,hAPP(c_Product__Type_Osnd(U_10977,U_10973),U_10981)) = hAPP(U_10983,hAPP(c_Product__Type_Osnd(U_10977,U_10973),U_10981))
| hAPP(c_Product__Type_Oapsnd(U_10973,U_10975,U_10977,U_10979),U_10981) != hAPP(c_Product__Type_Oapsnd(U_10973,U_10975,U_10977,U_10983),U_10981) ) ),
inference(definitional_conversion,[status(esa)],[f_2972_3]) ).
cnf(f_2972_5,plain,
( hAPP(U_10979,hAPP(c_Product__Type_Osnd(U_10977,U_10973),U_10981)) = hAPP(U_10983,hAPP(c_Product__Type_Osnd(U_10977,U_10973),U_10981))
| hAPP(c_Product__Type_Oapsnd(U_10973,U_10975,U_10977,U_10979),U_10981) != hAPP(c_Product__Type_Oapsnd(U_10973,U_10975,U_10977,U_10983),U_10981) ),
inference(clausify,[status(thm)],[f_2972_4]) ).
cnf(f_2972_6,plain,
( hAPP(c_Product__Type_Oapsnd(U_10974,U_10976,U_10978,U_10980),U_10982) = hAPP(c_Product__Type_Oapsnd(U_10974,U_10976,U_10978,U_10984),U_10982)
| hAPP(U_10980,hAPP(c_Product__Type_Osnd(U_10978,U_10974),U_10982)) != hAPP(U_10984,hAPP(c_Product__Type_Osnd(U_10978,U_10974),U_10982)) ),
inference(clausify,[status(thm)],[f_2972_4]) ).
fof(f_2973_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_snd__conv]) ).
fof(f_2973_2,plain,
! [U_10988,U_10987,U_10986,U_10985] : hAPP(c_Product__Type_Osnd(U_10985,U_10986),hAPP(hAPP(c_Product__Type_OPair(U_10985,U_10986),U_10987),U_10988)) = U_10988,
inference(variable_rename,[status(thm)],[f_2973_1]) ).
fof(f_2973_3,plain,
! [U_10985,U_10986,U_10988,U_10987] : hAPP(c_Product__Type_Osnd(U_10985,U_10986),hAPP(hAPP(c_Product__Type_OPair(U_10985,U_10986),U_10987),U_10988)) = U_10988,
inference(definitional_conversion,[status(esa)],[f_2973_2]) ).
cnf(f_2973_4,plain,
hAPP(c_Product__Type_Osnd(U_10985,U_10986),hAPP(hAPP(c_Product__Type_OPair(U_10985,U_10986),U_10987),U_10988)) = U_10988,
inference(clausify,[status(thm)],[f_2973_3]) ).
fof(f_2974_1,plain,
! [V_a,V_y,V_x,T_a,T_b] :
( V_y = V_a
| 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 ),
inference(fof_nnf,[status(thm)],[fact_snd__eqD]) ).
fof(f_2974_2,plain,
! [U_10993,U_10992,U_10991,U_10990,U_10989] :
( U_10992 = U_10993
| hAPP(c_Product__Type_Osnd(U_10989,U_10990),hAPP(hAPP(c_Product__Type_OPair(U_10989,U_10990),U_10991),U_10992)) != U_10993 ),
inference(variable_rename,[status(thm)],[f_2974_1]) ).
fof(f_2974_3,plain,
! [U_10993,U_10992] :
( ! [U_10991,U_10990,U_10989] : hAPP(c_Product__Type_Osnd(U_10989,U_10990),hAPP(hAPP(c_Product__Type_OPair(U_10989,U_10990),U_10991),U_10992)) != U_10993
| U_10992 = U_10993 ),
inference(miniscope,[status(thm)],[f_2974_2]) ).
fof(f_2974_4,plain,
! [U_10989,U_10990,U_10991,U_10992,U_10993] :
( hAPP(c_Product__Type_Osnd(U_10989,U_10990),hAPP(hAPP(c_Product__Type_OPair(U_10989,U_10990),U_10991),U_10992)) != U_10993
| U_10992 = U_10993 ),
inference(definitional_conversion,[status(esa)],[f_2974_3]) ).
cnf(f_2974_5,plain,
( hAPP(c_Product__Type_Osnd(U_10989,U_10990),hAPP(hAPP(c_Product__Type_OPair(U_10989,U_10990),U_10991),U_10992)) != U_10993
| U_10992 = U_10993 ),
inference(clausify,[status(thm)],[f_2974_4]) ).
fof(f_2975_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_snd__def]) ).
fof(f_2975_2,plain,
! [U_10996,U_10995,U_10994] : hAPP(c_Product__Type_Osnd(U_10994,U_10995),U_10996) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10994,U_10995,U_10995),hAPP(c_COMBK(tc_fun(U_10995,U_10995),U_10994),c_COMBI(U_10995))),U_10996),
inference(variable_rename,[status(thm)],[f_2975_1]) ).
fof(f_2975_3,plain,
! [U_10996,U_10994,U_10995] : hAPP(c_Product__Type_Osnd(U_10994,U_10995),U_10996) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10994,U_10995,U_10995),hAPP(c_COMBK(tc_fun(U_10995,U_10995),U_10994),c_COMBI(U_10995))),U_10996),
inference(definitional_conversion,[status(esa)],[f_2975_2]) ).
cnf(f_2975_4,plain,
hAPP(c_Product__Type_Osnd(U_10994,U_10995),U_10996) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10994,U_10995,U_10995),hAPP(c_COMBK(tc_fun(U_10995,U_10995),U_10994),c_COMBI(U_10995))),U_10996),
inference(clausify,[status(thm)],[f_2975_3]) ).
fof(f_2976_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mod__int__def]) ).
fof(f_2976_2,plain,
! [U_10998,U_10997] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10997,U_10998) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_10997,U_10998)),
inference(variable_rename,[status(thm)],[f_2976_1]) ).
fof(f_2976_3,plain,
! [U_10997,U_10998] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10997,U_10998) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_10997,U_10998)),
inference(definitional_conversion,[status(esa)],[f_2976_2]) ).
cnf(f_2976_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10997,U_10998) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_10997,U_10998)),
inference(clausify,[status(thm)],[f_2976_3]) ).
fof(f_2977_1,plain,
! [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_OnegDivAlg(V_a,V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_mod__neg__pos]) ).
fof(f_2977_2,plain,
! [U_11000,U_10999] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10999,U_11000) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_10999,U_11000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10999),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2977_1]) ).
fof(f_2977_3,plain,
! [U_10999,U_11000] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10999,U_11000) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_10999,U_11000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10999),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2977_2]) ).
cnf(f_2977_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10999,U_11000) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_10999,U_11000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10999),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2977_3]) ).
fof(f_2978_1,plain,
! [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_OposDivAlg(V_a,V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_mod__pos__pos]) ).
fof(f_2978_2,plain,
! [U_11002,U_11001] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11001,U_11002) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11001,U_11002))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11002))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11001)) ),
inference(variable_rename,[status(thm)],[f_2978_1]) ).
fof(f_2978_3,plain,
! [U_11002,U_11001] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11001,U_11002) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11001,U_11002))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11002))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11001)) ),
inference(definitional_conversion,[status(esa)],[f_2978_2]) ).
cnf(f_2978_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11001,U_11002) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11001,U_11002))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11002))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11001)) ),
inference(clausify,[status(thm)],[f_2978_3]) ).
fof(f_2979_1,plain,
! [V_w] :
( 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of]) ).
fof(f_2979_2,plain,
! [U_11003] :
( 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),U_11003)) = 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),U_11003)))
| ~ 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),U_11003))) ),
inference(variable_rename,[status(thm)],[f_2979_1]) ).
fof(f_2979_3,plain,
! [U_11003] :
( 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),U_11003)) = 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),U_11003)))
| ~ 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),U_11003))) ),
inference(definitional_conversion,[status(esa)],[f_2979_2]) ).
cnf(f_2979_4,plain,
( 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),U_11003)) = 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),U_11003)))
| ~ 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),U_11003))) ),
inference(clausify,[status(thm)],[f_2979_3]) ).
fof(f_2980_1,plain,
! [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),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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_mod__pos__neg]) ).
fof(f_2980_2,plain,
! [U_11005,U_11004] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11004,U_11005) = 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),U_11004),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11005))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11005),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11004)) ),
inference(variable_rename,[status(thm)],[f_2980_1]) ).
fof(f_2980_3,plain,
! [U_11004,U_11005] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11004,U_11005) = 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),U_11004),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11005))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11005),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11004)) ),
inference(definitional_conversion,[status(esa)],[f_2980_2]) ).
cnf(f_2980_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11004,U_11005) = 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),U_11004),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11005))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11005),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11004)) ),
inference(clausify,[status(thm)],[f_2980_3]) ).
fof(f_2981_1,plain,
! [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),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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_mod__neg__neg]) ).
fof(f_2981_2,plain,
! [U_11007,U_11006] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11006,U_11007) = 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),U_11006),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11007))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11006),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2981_1]) ).
fof(f_2981_3,plain,
! [U_11006,U_11007] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11006,U_11007) = 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),U_11006),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11007))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11006),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2981_2]) ).
cnf(f_2981_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11006,U_11007) = 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),U_11006),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11007))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11006),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2981_3]) ).
fof(f_2982_1,plain,
! [V_f_2,V_A_2,T_b] :
( 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))
| ? [B_x] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J]) ).
fof(f_2982_2,plain,
! [U_11011,U_11010,U_11009] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11009,tc_Int_Oint),U_11011),U_11010) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11009,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11009),c_Int_Onat),U_11011)),U_11010))
| ? [U_11008] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11011,U_11008))
& hBOOL(hAPP(hAPP(c_member(U_11009),U_11008),U_11010)) ) ),
inference(variable_rename,[status(thm)],[f_2982_1]) ).
fof(f_2982_3,plain,
! [U_11011,U_11010,U_11009] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11009,tc_Int_Oint),U_11011),U_11010) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11009,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11009),c_Int_Onat),U_11011)),U_11010))
| ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11011,sK272(U_11011,U_11010,U_11009)))
& hBOOL(hAPP(hAPP(c_member(U_11009),sK272(U_11011,U_11010,U_11009)),U_11010)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_11008,sK272(U_11011,U_11010,U_11009))],[f_2982_2]) ).
fof(f_2982_4,plain,
( ! [U_11009,U_11010,U_11011] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11011,sK272(U_11011,U_11010,U_11009)))
| ~ sP847(U_11009,U_11010,U_11011) )
& ! [U_11009,U_11010,U_11011] :
( hBOOL(hAPP(hAPP(c_member(U_11009),sK272(U_11011,U_11010,U_11009)),U_11010))
| ~ sP847(U_11009,U_11010,U_11011) )
& ! [U_11009,U_11010,U_11011] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11009,tc_Int_Oint),U_11011),U_11010) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11009,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11009),c_Int_Onat),U_11011)),U_11010))
| sP847(U_11009,U_11010,U_11011) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP847])],[f_2982_3]) ).
cnf(f_2982_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11009,tc_Int_Oint),U_11011),U_11010) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11009,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11009),c_Int_Onat),U_11011)),U_11010))
| sP847(U_11009,U_11010,U_11011) ),
inference(clausify,[status(thm)],[f_2982_4]) ).
cnf(f_2982_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11009),sK272(U_11011,U_11010,U_11009)),U_11010))
| ~ sP847(U_11009,U_11010,U_11011) ),
inference(clausify,[status(thm)],[f_2982_4]) ).
cnf(f_2982_7,plain,
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11011,sK272(U_11011,U_11010,U_11009)))
| ~ sP847(U_11009,U_11010,U_11011) ),
inference(clausify,[status(thm)],[f_2982_4]) ).
fof(f_2983_1,plain,
! [V_Pa_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
& ( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& 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))) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_norm__frac_Opinduct]) ).
fof(f_2983_2,plain,
! [U_11016,U_11015,U_11014] :
( hBOOL(hAPP(hAPP(U_11016,U_11014),U_11015))
| ? [U_11013,U_11012] :
( ~ hBOOL(hAPP(hAPP(U_11016,U_11013),U_11012))
& ( hBOOL(hAPP(hAPP(U_11016,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11013)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11012)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11012),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& 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),U_11013),U_11012))) )
| ~ 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),U_11014),U_11015))) ),
inference(variable_rename,[status(thm)],[f_2983_1]) ).
fof(f_2983_3,plain,
! [U_11016,U_11015,U_11014] :
( hBOOL(hAPP(hAPP(U_11016,U_11014),U_11015))
| ? [U_11012] :
( ~ hBOOL(hAPP(hAPP(U_11016,sK273(U_11016,U_11015,U_11014)),U_11012))
& ( hBOOL(hAPP(hAPP(U_11016,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK273(U_11016,U_11015,U_11014))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11012)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11012),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& 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),sK273(U_11016,U_11015,U_11014)),U_11012))) )
| ~ 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),U_11014),U_11015))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_11013,sK273(U_11016,U_11015,U_11014))],[f_2983_2]) ).
fof(f_2983_4,plain,
! [U_11016,U_11015,U_11014] :
( hBOOL(hAPP(hAPP(U_11016,U_11014),U_11015))
| ( ~ hBOOL(hAPP(hAPP(U_11016,sK273(U_11016,U_11015,U_11014)),sK274(U_11016,U_11015,U_11014)))
& ( hBOOL(hAPP(hAPP(U_11016,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK273(U_11016,U_11015,U_11014))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK274(U_11016,U_11015,U_11014))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK274(U_11016,U_11015,U_11014)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& 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),sK273(U_11016,U_11015,U_11014)),sK274(U_11016,U_11015,U_11014)))) )
| ~ 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),U_11014),U_11015))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_11012,sK274(U_11016,U_11015,U_11014))],[f_2983_3]) ).
fof(f_2983_5,plain,
( ! [U_11014,U_11015,U_11016] :
( ~ hBOOL(hAPP(hAPP(U_11016,sK273(U_11016,U_11015,U_11014)),sK274(U_11016,U_11015,U_11014)))
| ~ sP848(U_11014,U_11015,U_11016) )
& ! [U_11014,U_11015,U_11016] :
( hBOOL(hAPP(hAPP(U_11016,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK273(U_11016,U_11015,U_11014))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK274(U_11016,U_11015,U_11014))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK274(U_11016,U_11015,U_11014)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP848(U_11014,U_11015,U_11016) )
& ! [U_11014,U_11015,U_11016] :
( 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),sK273(U_11016,U_11015,U_11014)),sK274(U_11016,U_11015,U_11014))))
| ~ sP848(U_11014,U_11015,U_11016) )
& ! [U_11014,U_11015,U_11016] :
( hBOOL(hAPP(hAPP(U_11016,U_11014),U_11015))
| sP848(U_11014,U_11015,U_11016)
| ~ 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),U_11014),U_11015))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP848])],[f_2983_4]) ).
cnf(f_2983_6,plain,
( hBOOL(hAPP(hAPP(U_11016,U_11014),U_11015))
| sP848(U_11014,U_11015,U_11016)
| ~ 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),U_11014),U_11015))) ),
inference(clausify,[status(thm)],[f_2983_5]) ).
cnf(f_2983_7,plain,
( 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),sK273(U_11016,U_11015,U_11014)),sK274(U_11016,U_11015,U_11014))))
| ~ sP848(U_11014,U_11015,U_11016) ),
inference(clausify,[status(thm)],[f_2983_5]) ).
cnf(f_2983_8,plain,
( hBOOL(hAPP(hAPP(U_11016,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK273(U_11016,U_11015,U_11014))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK274(U_11016,U_11015,U_11014))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK274(U_11016,U_11015,U_11014)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP848(U_11014,U_11015,U_11016) ),
inference(clausify,[status(thm)],[f_2983_5]) ).
cnf(f_2983_9,plain,
( ~ hBOOL(hAPP(hAPP(U_11016,sK273(U_11016,U_11015,U_11014)),sK274(U_11016,U_11015,U_11014)))
| ~ sP848(U_11014,U_11015,U_11016) ),
inference(clausify,[status(thm)],[f_2983_5]) ).
fof(f_2984_1,plain,
! [V_w] :
( 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)))))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of]) ).
fof(f_2984_2,plain,
! [U_11017] :
( 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),U_11017)) = 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),U_11017)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2984_1]) ).
fof(f_2984_3,plain,
! [U_11017] :
( 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),U_11017)) = 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),U_11017)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2984_2]) ).
cnf(f_2984_4,plain,
( 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),U_11017)) = 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),U_11017)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2984_3]) ).
fof(f_2985_1,plain,
! [T_c,T_b,V_t_2,V_s_2] :
( ( V_s_2 = V_t_2
| hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) != hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
| hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) != hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) )
& ( ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
& hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) )
| V_s_2 != V_t_2 ) ),
inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq]) ).
fof(f_2985_2,plain,
! [U_11021,U_11020,U_11019,U_11018] :
( ( U_11018 = U_11019
| hAPP(c_Product__Type_Osnd(U_11020,U_11021),U_11018) != hAPP(c_Product__Type_Osnd(U_11020,U_11021),U_11019)
| hAPP(c_Product__Type_Ofst(U_11020,U_11021),U_11018) != hAPP(c_Product__Type_Ofst(U_11020,U_11021),U_11019) )
& ( ( hAPP(c_Product__Type_Osnd(U_11020,U_11021),U_11018) = hAPP(c_Product__Type_Osnd(U_11020,U_11021),U_11019)
& hAPP(c_Product__Type_Ofst(U_11020,U_11021),U_11018) = hAPP(c_Product__Type_Ofst(U_11020,U_11021),U_11019) )
| U_11018 != U_11019 ) ),
inference(variable_rename,[status(thm)],[f_2985_1]) ).
fof(f_2985_3,plain,
( ! [U_11029,U_11027,U_11025,U_11023] :
( U_11023 = U_11025
| hAPP(c_Product__Type_Osnd(U_11027,U_11029),U_11023) != hAPP(c_Product__Type_Osnd(U_11027,U_11029),U_11025)
| hAPP(c_Product__Type_Ofst(U_11027,U_11029),U_11023) != hAPP(c_Product__Type_Ofst(U_11027,U_11029),U_11025) )
& ! [U_11028,U_11026,U_11024,U_11022] :
( ( hAPP(c_Product__Type_Osnd(U_11026,U_11028),U_11022) = hAPP(c_Product__Type_Osnd(U_11026,U_11028),U_11024)
& hAPP(c_Product__Type_Ofst(U_11026,U_11028),U_11022) = hAPP(c_Product__Type_Ofst(U_11026,U_11028),U_11024) )
| U_11022 != U_11024 ) ),
inference(miniscope,[status(thm)],[f_2985_2]) ).
fof(f_2985_4,plain,
( ! [U_11024,U_11026,U_11022,U_11028] :
( hAPP(c_Product__Type_Osnd(U_11026,U_11028),U_11022) = hAPP(c_Product__Type_Osnd(U_11026,U_11028),U_11024)
| ~ sP849(U_11024,U_11026,U_11022,U_11028) )
& ! [U_11024,U_11026,U_11022,U_11028] :
( hAPP(c_Product__Type_Ofst(U_11026,U_11028),U_11022) = hAPP(c_Product__Type_Ofst(U_11026,U_11028),U_11024)
| ~ sP849(U_11024,U_11026,U_11022,U_11028) )
& ! [U_11023,U_11025,U_11027,U_11029] :
( U_11023 = U_11025
| hAPP(c_Product__Type_Osnd(U_11027,U_11029),U_11023) != hAPP(c_Product__Type_Osnd(U_11027,U_11029),U_11025)
| hAPP(c_Product__Type_Ofst(U_11027,U_11029),U_11023) != hAPP(c_Product__Type_Ofst(U_11027,U_11029),U_11025) )
& ! [U_11024,U_11026,U_11022,U_11028] :
( sP849(U_11024,U_11026,U_11022,U_11028)
| U_11022 != U_11024 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP849])],[f_2985_3]) ).
cnf(f_2985_5,plain,
( sP849(U_11024,U_11026,U_11022,U_11028)
| U_11022 != U_11024 ),
inference(clausify,[status(thm)],[f_2985_4]) ).
cnf(f_2985_6,plain,
( U_11023 = U_11025
| hAPP(c_Product__Type_Osnd(U_11027,U_11029),U_11023) != hAPP(c_Product__Type_Osnd(U_11027,U_11029),U_11025)
| hAPP(c_Product__Type_Ofst(U_11027,U_11029),U_11023) != hAPP(c_Product__Type_Ofst(U_11027,U_11029),U_11025) ),
inference(clausify,[status(thm)],[f_2985_4]) ).
cnf(f_2985_7,plain,
( hAPP(c_Product__Type_Ofst(U_11026,U_11028),U_11022) = hAPP(c_Product__Type_Ofst(U_11026,U_11028),U_11024)
| ~ sP849(U_11024,U_11026,U_11022,U_11028) ),
inference(clausify,[status(thm)],[f_2985_4]) ).
cnf(f_2985_8,plain,
( hAPP(c_Product__Type_Osnd(U_11026,U_11028),U_11022) = hAPP(c_Product__Type_Osnd(U_11026,U_11028),U_11024)
| ~ sP849(U_11024,U_11026,U_11022,U_11028) ),
inference(clausify,[status(thm)],[f_2985_4]) ).
fof(f_2986_1,plain,
! [V_q,V_p,T_b,T_a] :
( V_p = V_q
| hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) != hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
| hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) != hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) ),
inference(fof_nnf,[status(thm)],[fact_prod__eqI]) ).
fof(f_2986_2,plain,
! [U_11033,U_11032,U_11031,U_11030] :
( U_11032 = U_11033
| hAPP(c_Product__Type_Osnd(U_11030,U_11031),U_11032) != hAPP(c_Product__Type_Osnd(U_11030,U_11031),U_11033)
| hAPP(c_Product__Type_Ofst(U_11030,U_11031),U_11032) != hAPP(c_Product__Type_Ofst(U_11030,U_11031),U_11033) ),
inference(variable_rename,[status(thm)],[f_2986_1]) ).
fof(f_2986_3,plain,
! [U_11030,U_11031,U_11032,U_11033] :
( U_11032 = U_11033
| hAPP(c_Product__Type_Osnd(U_11030,U_11031),U_11032) != hAPP(c_Product__Type_Osnd(U_11030,U_11031),U_11033)
| hAPP(c_Product__Type_Ofst(U_11030,U_11031),U_11032) != hAPP(c_Product__Type_Ofst(U_11030,U_11031),U_11033) ),
inference(definitional_conversion,[status(esa)],[f_2986_2]) ).
cnf(f_2986_4,plain,
( U_11032 = U_11033
| hAPP(c_Product__Type_Osnd(U_11030,U_11031),U_11032) != hAPP(c_Product__Type_Osnd(U_11030,U_11031),U_11033)
| hAPP(c_Product__Type_Ofst(U_11030,U_11031),U_11032) != hAPP(c_Product__Type_Ofst(U_11030,U_11031),U_11033) ),
inference(clausify,[status(thm)],[f_2986_3]) ).
fof(f_2987_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_fst__def]) ).
fof(f_2987_2,plain,
! [U_11036,U_11035,U_11034] : hAPP(c_Product__Type_Ofst(U_11034,U_11035),U_11036) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11034,U_11035,U_11034),c_COMBK(U_11034,U_11035)),U_11036),
inference(variable_rename,[status(thm)],[f_2987_1]) ).
fof(f_2987_3,plain,
! [U_11034,U_11035,U_11036] : hAPP(c_Product__Type_Ofst(U_11034,U_11035),U_11036) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11034,U_11035,U_11034),c_COMBK(U_11034,U_11035)),U_11036),
inference(definitional_conversion,[status(esa)],[f_2987_2]) ).
cnf(f_2987_4,plain,
hAPP(c_Product__Type_Ofst(U_11034,U_11035),U_11036) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11034,U_11035,U_11034),c_COMBK(U_11034,U_11035)),U_11036),
inference(clausify,[status(thm)],[f_2987_3]) ).
fof(f_2988_1,plain,
! [V_a,V_y,V_x,T_b,T_a] :
( V_x = V_a
| 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 ),
inference(fof_nnf,[status(thm)],[fact_fst__eqD]) ).
fof(f_2988_2,plain,
! [U_11041,U_11040,U_11039,U_11038,U_11037] :
( U_11039 = U_11041
| hAPP(c_Product__Type_Ofst(U_11037,U_11038),hAPP(hAPP(c_Product__Type_OPair(U_11037,U_11038),U_11039),U_11040)) != U_11041 ),
inference(variable_rename,[status(thm)],[f_2988_1]) ).
fof(f_2988_3,plain,
! [U_11041,U_11040,U_11039] :
( ! [U_11038,U_11037] : hAPP(c_Product__Type_Ofst(U_11037,U_11038),hAPP(hAPP(c_Product__Type_OPair(U_11037,U_11038),U_11039),U_11040)) != U_11041
| U_11039 = U_11041 ),
inference(miniscope,[status(thm)],[f_2988_2]) ).
fof(f_2988_4,plain,
! [U_11037,U_11038,U_11039,U_11040,U_11041] :
( hAPP(c_Product__Type_Ofst(U_11037,U_11038),hAPP(hAPP(c_Product__Type_OPair(U_11037,U_11038),U_11039),U_11040)) != U_11041
| U_11039 = U_11041 ),
inference(definitional_conversion,[status(esa)],[f_2988_3]) ).
cnf(f_2988_5,plain,
( hAPP(c_Product__Type_Ofst(U_11037,U_11038),hAPP(hAPP(c_Product__Type_OPair(U_11037,U_11038),U_11039),U_11040)) != U_11041
| U_11039 = U_11041 ),
inference(clausify,[status(thm)],[f_2988_4]) ).
fof(f_2989_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_fst__conv]) ).
fof(f_2989_2,plain,
! [U_11045,U_11044,U_11043,U_11042] : hAPP(c_Product__Type_Ofst(U_11042,U_11043),hAPP(hAPP(c_Product__Type_OPair(U_11042,U_11043),U_11044),U_11045)) = U_11044,
inference(variable_rename,[status(thm)],[f_2989_1]) ).
fof(f_2989_3,plain,
! [U_11042,U_11043,U_11044,U_11045] : hAPP(c_Product__Type_Ofst(U_11042,U_11043),hAPP(hAPP(c_Product__Type_OPair(U_11042,U_11043),U_11044),U_11045)) = U_11044,
inference(definitional_conversion,[status(esa)],[f_2989_2]) ).
cnf(f_2989_4,plain,
hAPP(c_Product__Type_Ofst(U_11042,U_11043),hAPP(hAPP(c_Product__Type_OPair(U_11042,U_11043),U_11044),U_11045)) = U_11044,
inference(clausify,[status(thm)],[f_2989_3]) ).
fof(f_2990_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_fst__apsnd]) ).
fof(f_2990_2,plain,
! [U_11050,U_11049,U_11048,U_11047,U_11046] : hAPP(c_Product__Type_Ofst(U_11046,U_11047),hAPP(c_Product__Type_Oapsnd(U_11048,U_11047,U_11046,U_11049),U_11050)) = hAPP(c_Product__Type_Ofst(U_11046,U_11048),U_11050),
inference(variable_rename,[status(thm)],[f_2990_1]) ).
fof(f_2990_3,plain,
! [U_11046,U_11047,U_11048,U_11049,U_11050] : hAPP(c_Product__Type_Ofst(U_11046,U_11047),hAPP(c_Product__Type_Oapsnd(U_11048,U_11047,U_11046,U_11049),U_11050)) = hAPP(c_Product__Type_Ofst(U_11046,U_11048),U_11050),
inference(definitional_conversion,[status(esa)],[f_2990_2]) ).
cnf(f_2990_4,plain,
hAPP(c_Product__Type_Ofst(U_11046,U_11047),hAPP(c_Product__Type_Oapsnd(U_11048,U_11047,U_11046,U_11049),U_11050)) = hAPP(c_Product__Type_Ofst(U_11046,U_11048),U_11050),
inference(clausify,[status(thm)],[f_2990_3]) ).
fof(f_2991_1,plain,
! [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,
inference(fof_nnf,[status(thm)],[fact_pair__collapse]) ).
fof(f_2991_2,plain,
! [U_11053,U_11052,U_11051] : hAPP(hAPP(c_Product__Type_OPair(U_11051,U_11052),hAPP(c_Product__Type_Ofst(U_11051,U_11052),U_11053)),hAPP(c_Product__Type_Osnd(U_11051,U_11052),U_11053)) = U_11053,
inference(variable_rename,[status(thm)],[f_2991_1]) ).
fof(f_2991_3,plain,
! [U_11051,U_11052,U_11053] : hAPP(hAPP(c_Product__Type_OPair(U_11051,U_11052),hAPP(c_Product__Type_Ofst(U_11051,U_11052),U_11053)),hAPP(c_Product__Type_Osnd(U_11051,U_11052),U_11053)) = U_11053,
inference(definitional_conversion,[status(esa)],[f_2991_2]) ).
cnf(f_2991_4,plain,
hAPP(hAPP(c_Product__Type_OPair(U_11051,U_11052),hAPP(c_Product__Type_Ofst(U_11051,U_11052),U_11053)),hAPP(c_Product__Type_Osnd(U_11051,U_11052),U_11053)) = U_11053,
inference(clausify,[status(thm)],[f_2991_3]) ).
fof(f_2992_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_surjective__pairing]) ).
fof(f_2992_2,plain,
! [U_11056,U_11055,U_11054] : U_11054 = hAPP(hAPP(c_Product__Type_OPair(U_11055,U_11056),hAPP(c_Product__Type_Ofst(U_11055,U_11056),U_11054)),hAPP(c_Product__Type_Osnd(U_11055,U_11056),U_11054)),
inference(variable_rename,[status(thm)],[f_2992_1]) ).
fof(f_2992_3,plain,
! [U_11054,U_11055,U_11056] : U_11054 = hAPP(hAPP(c_Product__Type_OPair(U_11055,U_11056),hAPP(c_Product__Type_Ofst(U_11055,U_11056),U_11054)),hAPP(c_Product__Type_Osnd(U_11055,U_11056),U_11054)),
inference(definitional_conversion,[status(esa)],[f_2992_2]) ).
cnf(f_2992_4,plain,
U_11054 = hAPP(hAPP(c_Product__Type_OPair(U_11055,U_11056),hAPP(c_Product__Type_Ofst(U_11055,U_11056),U_11054)),hAPP(c_Product__Type_Osnd(U_11055,U_11056),U_11054)),
inference(clausify,[status(thm)],[f_2992_3]) ).
fof(f_2993_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_prod__case__beta]) ).
fof(f_2993_2,plain,
! [U_11061,U_11060,U_11059,U_11058,U_11057] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11057,U_11058,U_11059),U_11060),U_11061) = hAPP(hAPP(U_11060,hAPP(c_Product__Type_Ofst(U_11057,U_11058),U_11061)),hAPP(c_Product__Type_Osnd(U_11057,U_11058),U_11061)),
inference(variable_rename,[status(thm)],[f_2993_1]) ).
fof(f_2993_3,plain,
! [U_11057,U_11058,U_11059,U_11060,U_11061] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11057,U_11058,U_11059),U_11060),U_11061) = hAPP(hAPP(U_11060,hAPP(c_Product__Type_Ofst(U_11057,U_11058),U_11061)),hAPP(c_Product__Type_Osnd(U_11057,U_11058),U_11061)),
inference(definitional_conversion,[status(esa)],[f_2993_2]) ).
cnf(f_2993_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11057,U_11058,U_11059),U_11060),U_11061) = hAPP(hAPP(U_11060,hAPP(c_Product__Type_Ofst(U_11057,U_11058),U_11061)),hAPP(c_Product__Type_Osnd(U_11057,U_11058),U_11061)),
inference(clausify,[status(thm)],[f_2993_3]) ).
fof(f_2994_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_div__int__def]) ).
fof(f_2994_2,plain,
! [U_11063,U_11062] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11062),U_11063) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11062,U_11063)),
inference(variable_rename,[status(thm)],[f_2994_1]) ).
fof(f_2994_3,plain,
! [U_11062,U_11063] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11062),U_11063) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11062,U_11063)),
inference(definitional_conversion,[status(esa)],[f_2994_2]) ).
cnf(f_2994_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11062),U_11063) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11062,U_11063)),
inference(clausify,[status(thm)],[f_2994_3]) ).
fof(f_2995_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_mod__nat__def]) ).
fof(f_2995_2,plain,
! [U_11065,U_11064] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11064,U_11065) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11064,U_11065)),
inference(variable_rename,[status(thm)],[f_2995_1]) ).
fof(f_2995_3,plain,
! [U_11064,U_11065] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11064,U_11065) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11064,U_11065)),
inference(definitional_conversion,[status(esa)],[f_2995_2]) ).
cnf(f_2995_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11064,U_11065) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11064,U_11065)),
inference(clausify,[status(thm)],[f_2995_3]) ).
fof(f_2996_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_split__comp__eq]) ).
fof(f_2996_2,plain,
! [U_11071,U_11070,U_11069,U_11068,U_11067,U_11066] : hAPP(hAPP(c_COMBS(tc_prod(U_11066,U_11067),U_11067,U_11068),hAPP(hAPP(c_COMBB(U_11069,tc_fun(U_11067,U_11068),tc_prod(U_11066,U_11067)),U_11070),hAPP(hAPP(c_COMBB(U_11066,U_11069,tc_prod(U_11066,U_11067)),U_11071),c_Product__Type_Ofst(U_11066,U_11067)))),c_Product__Type_Osnd(U_11066,U_11067)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11066,U_11067,U_11068),hAPP(hAPP(c_COMBB(U_11069,tc_fun(U_11067,U_11068),U_11066),U_11070),U_11071)),
inference(variable_rename,[status(thm)],[f_2996_1]) ).
fof(f_2996_3,plain,
! [U_11066,U_11067,U_11068,U_11069,U_11070,U_11071] : hAPP(hAPP(c_COMBS(tc_prod(U_11066,U_11067),U_11067,U_11068),hAPP(hAPP(c_COMBB(U_11069,tc_fun(U_11067,U_11068),tc_prod(U_11066,U_11067)),U_11070),hAPP(hAPP(c_COMBB(U_11066,U_11069,tc_prod(U_11066,U_11067)),U_11071),c_Product__Type_Ofst(U_11066,U_11067)))),c_Product__Type_Osnd(U_11066,U_11067)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11066,U_11067,U_11068),hAPP(hAPP(c_COMBB(U_11069,tc_fun(U_11067,U_11068),U_11066),U_11070),U_11071)),
inference(definitional_conversion,[status(esa)],[f_2996_2]) ).
cnf(f_2996_4,plain,
hAPP(hAPP(c_COMBS(tc_prod(U_11066,U_11067),U_11067,U_11068),hAPP(hAPP(c_COMBB(U_11069,tc_fun(U_11067,U_11068),tc_prod(U_11066,U_11067)),U_11070),hAPP(hAPP(c_COMBB(U_11066,U_11069,tc_prod(U_11066,U_11067)),U_11071),c_Product__Type_Ofst(U_11066,U_11067)))),c_Product__Type_Osnd(U_11066,U_11067)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11066,U_11067,U_11068),hAPP(hAPP(c_COMBB(U_11069,tc_fun(U_11067,U_11068),U_11066),U_11070),U_11071)),
inference(clausify,[status(thm)],[f_2996_3]) ).
fof(f_2997_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_split__beta]) ).
fof(f_2997_2,plain,
! [U_11076,U_11075,U_11074,U_11073,U_11072] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11072,U_11073,U_11074),U_11075),U_11076) = hAPP(hAPP(U_11075,hAPP(c_Product__Type_Ofst(U_11072,U_11073),U_11076)),hAPP(c_Product__Type_Osnd(U_11072,U_11073),U_11076)),
inference(variable_rename,[status(thm)],[f_2997_1]) ).
fof(f_2997_3,plain,
! [U_11072,U_11073,U_11074,U_11075,U_11076] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11072,U_11073,U_11074),U_11075),U_11076) = hAPP(hAPP(U_11075,hAPP(c_Product__Type_Ofst(U_11072,U_11073),U_11076)),hAPP(c_Product__Type_Osnd(U_11072,U_11073),U_11076)),
inference(definitional_conversion,[status(esa)],[f_2997_2]) ).
cnf(f_2997_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11072,U_11073,U_11074),U_11075),U_11076) = hAPP(hAPP(U_11075,hAPP(c_Product__Type_Ofst(U_11072,U_11073),U_11076)),hAPP(c_Product__Type_Osnd(U_11072,U_11073),U_11076)),
inference(clausify,[status(thm)],[f_2997_3]) ).
fof(f_2998_1,plain,
! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_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)),
inference(fof_nnf,[status(thm)],[fact_split__def]) ).
fof(f_2998_2,plain,
! [U_11081,U_11080,U_11079,U_11078,U_11077] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11077,U_11078,U_11079),U_11080),U_11081) = hAPP(hAPP(U_11080,hAPP(c_Product__Type_Ofst(U_11077,U_11078),U_11081)),hAPP(c_Product__Type_Osnd(U_11077,U_11078),U_11081)),
inference(variable_rename,[status(thm)],[f_2998_1]) ).
fof(f_2998_3,plain,
! [U_11077,U_11078,U_11079,U_11080,U_11081] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11077,U_11078,U_11079),U_11080),U_11081) = hAPP(hAPP(U_11080,hAPP(c_Product__Type_Ofst(U_11077,U_11078),U_11081)),hAPP(c_Product__Type_Osnd(U_11077,U_11078),U_11081)),
inference(definitional_conversion,[status(esa)],[f_2998_2]) ).
cnf(f_2998_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11077,U_11078,U_11079),U_11080),U_11081) = hAPP(hAPP(U_11080,hAPP(c_Product__Type_Ofst(U_11077,U_11078),U_11081)),hAPP(c_Product__Type_Osnd(U_11077,U_11078),U_11081)),
inference(clausify,[status(thm)],[f_2998_3]) ).
fof(f_2999_1,plain,
! [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_OnegDivAlg(V_a,V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__pos]) ).
fof(f_2999_2,plain,
! [U_11083,U_11082] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11082),U_11083) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11082,U_11083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11082),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2999_1]) ).
fof(f_2999_3,plain,
! [U_11082,U_11083] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11082),U_11083) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11082,U_11083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11082),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2999_2]) ).
cnf(f_2999_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11082),U_11083) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11082,U_11083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11082),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2999_3]) ).
fof(f_3000_1,plain,
! [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_OposDivAlg(V_a,V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__pos]) ).
fof(f_3000_2,plain,
! [U_11085,U_11084] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11084),U_11085) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11084,U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11084)) ),
inference(variable_rename,[status(thm)],[f_3000_1]) ).
fof(f_3000_3,plain,
! [U_11084,U_11085] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11084),U_11085) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11084,U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11084)) ),
inference(definitional_conversion,[status(esa)],[f_3000_2]) ).
cnf(f_3000_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11084),U_11085) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11084,U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11084)) ),
inference(clausify,[status(thm)],[f_3000_3]) ).
fof(f_3001_1,plain,
! [V_w] :
( 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of]) ).
fof(f_3001_2,plain,
! [U_11086] :
( 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),U_11086)) = 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),U_11086)))
| ~ 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),U_11086))) ),
inference(variable_rename,[status(thm)],[f_3001_1]) ).
fof(f_3001_3,plain,
! [U_11086] :
( 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),U_11086)) = 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),U_11086)))
| ~ 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),U_11086))) ),
inference(definitional_conversion,[status(esa)],[f_3001_2]) ).
cnf(f_3001_4,plain,
( 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),U_11086)) = 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),U_11086)))
| ~ 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),U_11086))) ),
inference(clausify,[status(thm)],[f_3001_3]) ).
fof(f_3002_1,plain,
! [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),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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__neg]) ).
fof(f_3002_2,plain,
! [U_11088,U_11087] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11087),U_11088) = 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),U_11087),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11088))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11088),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11087)) ),
inference(variable_rename,[status(thm)],[f_3002_1]) ).
fof(f_3002_3,plain,
! [U_11087,U_11088] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11087),U_11088) = 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),U_11087),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11088))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11088),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11087)) ),
inference(definitional_conversion,[status(esa)],[f_3002_2]) ).
cnf(f_3002_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11087),U_11088) = 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),U_11087),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11088))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11088),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11087)) ),
inference(clausify,[status(thm)],[f_3002_3]) ).
fof(f_3003_1,plain,
! [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),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))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__neg]) ).
fof(f_3003_2,plain,
! [U_11090,U_11089] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11089),U_11090) = 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),U_11089),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11090))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11090),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11089),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3003_1]) ).
fof(f_3003_3,plain,
! [U_11090,U_11089] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11089),U_11090) = 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),U_11089),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11090))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11090),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11089),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_3003_2]) ).
cnf(f_3003_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11089),U_11090) = 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),U_11089),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11090))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11090),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11089),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3003_3]) ).
fof(f_3004_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_prod__size__simp]) ).
fof(f_3004_2,plain,
! [U_11095,U_11094,U_11093,U_11092,U_11091] : c_Product__Type_Oprod_Oprod__size(U_11091,U_11092,U_11093,U_11094,U_11095) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_11093,hAPP(c_Product__Type_Ofst(U_11091,U_11092),U_11095))),hAPP(U_11094,hAPP(c_Product__Type_Osnd(U_11091,U_11092),U_11095)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_3004_1]) ).
fof(f_3004_3,plain,
! [U_11091,U_11092,U_11093,U_11094,U_11095] : c_Product__Type_Oprod_Oprod__size(U_11091,U_11092,U_11093,U_11094,U_11095) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_11093,hAPP(c_Product__Type_Ofst(U_11091,U_11092),U_11095))),hAPP(U_11094,hAPP(c_Product__Type_Osnd(U_11091,U_11092),U_11095)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_3004_2]) ).
cnf(f_3004_4,plain,
c_Product__Type_Oprod_Oprod__size(U_11091,U_11092,U_11093,U_11094,U_11095) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_11093,hAPP(c_Product__Type_Ofst(U_11091,U_11092),U_11095))),hAPP(U_11094,hAPP(c_Product__Type_Osnd(U_11091,U_11092),U_11095)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_3004_3]) ).
fof(f_3005_1,plain,
! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
( 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))))
| ~ hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_exI__realizer]) ).
fof(f_3005_2,plain,
! [U_11100,U_11099,U_11098,U_11097,U_11096] :
( hBOOL(hAPP(hAPP(U_11096,hAPP(c_Product__Type_Osnd(U_11099,U_11100),hAPP(hAPP(c_Product__Type_OPair(U_11099,U_11100),U_11098),U_11097))),hAPP(c_Product__Type_Ofst(U_11099,U_11100),hAPP(hAPP(c_Product__Type_OPair(U_11099,U_11100),U_11098),U_11097))))
| ~ hBOOL(hAPP(hAPP(U_11096,U_11097),U_11098)) ),
inference(variable_rename,[status(thm)],[f_3005_1]) ).
fof(f_3005_3,plain,
! [U_11096,U_11097,U_11098,U_11099,U_11100] :
( hBOOL(hAPP(hAPP(U_11096,hAPP(c_Product__Type_Osnd(U_11099,U_11100),hAPP(hAPP(c_Product__Type_OPair(U_11099,U_11100),U_11098),U_11097))),hAPP(c_Product__Type_Ofst(U_11099,U_11100),hAPP(hAPP(c_Product__Type_OPair(U_11099,U_11100),U_11098),U_11097))))
| ~ hBOOL(hAPP(hAPP(U_11096,U_11097),U_11098)) ),
inference(definitional_conversion,[status(esa)],[f_3005_2]) ).
cnf(f_3005_4,plain,
( hBOOL(hAPP(hAPP(U_11096,hAPP(c_Product__Type_Osnd(U_11099,U_11100),hAPP(hAPP(c_Product__Type_OPair(U_11099,U_11100),U_11098),U_11097))),hAPP(c_Product__Type_Ofst(U_11099,U_11100),hAPP(hAPP(c_Product__Type_OPair(U_11099,U_11100),U_11098),U_11097))))
| ~ hBOOL(hAPP(hAPP(U_11096,U_11097),U_11098)) ),
inference(clausify,[status(thm)],[f_3005_3]) ).
fof(f_3006_1,plain,
! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
( ( 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))))
& 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)))) )
| ~ hBOOL(hAPP(V_Qa_2,V_q_2))
| ~ hBOOL(hAPP(V_Pa_2,V_p_2)) ),
inference(fof_nnf,[status(thm)],[fact_conjI__realizer]) ).
fof(f_3006_2,plain,
! [U_11106,U_11105,U_11104,U_11103,U_11102,U_11101] :
( ( hBOOL(hAPP(U_11103,hAPP(c_Product__Type_Osnd(U_11105,U_11106),hAPP(hAPP(c_Product__Type_OPair(U_11105,U_11106),U_11102),U_11104))))
& hBOOL(hAPP(U_11101,hAPP(c_Product__Type_Ofst(U_11105,U_11106),hAPP(hAPP(c_Product__Type_OPair(U_11105,U_11106),U_11102),U_11104)))) )
| ~ hBOOL(hAPP(U_11103,U_11104))
| ~ hBOOL(hAPP(U_11101,U_11102)) ),
inference(variable_rename,[status(thm)],[f_3006_1]) ).
fof(f_3006_3,plain,
( ! [U_11102,U_11101,U_11103,U_11104,U_11105,U_11106] :
( hBOOL(hAPP(U_11103,hAPP(c_Product__Type_Osnd(U_11105,U_11106),hAPP(hAPP(c_Product__Type_OPair(U_11105,U_11106),U_11102),U_11104))))
| ~ sP850(U_11102,U_11101,U_11103,U_11104,U_11105,U_11106) )
& ! [U_11102,U_11101,U_11103,U_11104,U_11105,U_11106] :
( hBOOL(hAPP(U_11101,hAPP(c_Product__Type_Ofst(U_11105,U_11106),hAPP(hAPP(c_Product__Type_OPair(U_11105,U_11106),U_11102),U_11104))))
| ~ sP850(U_11102,U_11101,U_11103,U_11104,U_11105,U_11106) )
& ! [U_11102,U_11101,U_11103,U_11104,U_11105,U_11106] :
( sP850(U_11102,U_11101,U_11103,U_11104,U_11105,U_11106)
| ~ hBOOL(hAPP(U_11103,U_11104))
| ~ hBOOL(hAPP(U_11101,U_11102)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP850])],[f_3006_2]) ).
cnf(f_3006_4,plain,
( sP850(U_11102,U_11101,U_11103,U_11104,U_11105,U_11106)
| ~ hBOOL(hAPP(U_11103,U_11104))
| ~ hBOOL(hAPP(U_11101,U_11102)) ),
inference(clausify,[status(thm)],[f_3006_3]) ).
cnf(f_3006_5,plain,
( hBOOL(hAPP(U_11101,hAPP(c_Product__Type_Ofst(U_11105,U_11106),hAPP(hAPP(c_Product__Type_OPair(U_11105,U_11106),U_11102),U_11104))))
| ~ sP850(U_11102,U_11101,U_11103,U_11104,U_11105,U_11106) ),
inference(clausify,[status(thm)],[f_3006_3]) ).
cnf(f_3006_6,plain,
( hBOOL(hAPP(U_11103,hAPP(c_Product__Type_Osnd(U_11105,U_11106),hAPP(hAPP(c_Product__Type_OPair(U_11105,U_11106),U_11102),U_11104))))
| ~ sP850(U_11102,U_11101,U_11103,U_11104,U_11105,U_11106) ),
inference(clausify,[status(thm)],[f_3006_3]) ).
fof(f_3007_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_div__nat__def]) ).
fof(f_3007_2,plain,
! [U_11108,U_11107] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11107),U_11108) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11107,U_11108)),
inference(variable_rename,[status(thm)],[f_3007_1]) ).
fof(f_3007_3,plain,
! [U_11107,U_11108] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11107),U_11108) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11107,U_11108)),
inference(definitional_conversion,[status(esa)],[f_3007_2]) ).
cnf(f_3007_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11107),U_11108) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11107,U_11108)),
inference(clausify,[status(thm)],[f_3007_3]) ).
fof(f_3008_1,plain,
! [V_qr_2,V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
| ( ( ( ( ~ 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)))
| ~ 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))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
| ( ( ~ 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))
| ~ 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))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) )
& V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_n_2 = c_Groups_Ozero__class_Ozero(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(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)) )
& ( ( ( ( ( ( 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)))
& 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))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
& ( ( 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))
& 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))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) )
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n_2 != c_Groups_Ozero__class_Ozero(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(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)) )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__def]) ).
fof(f_3008_2,plain,
! [U_11111,U_11110,U_11109] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11109,U_11110),U_11111))
| ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11111)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11110),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11111))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11110)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11111)),U_11110))
| ~ 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),U_11111))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11110)) ) )
& U_11110 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11111) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_11110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| U_11109 != 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),U_11111)),U_11110)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11111)) )
& ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11111)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11110),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11111))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11110)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11111)),U_11110))
& 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),U_11111))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11110)) ) )
| U_11110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11111) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11110 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& U_11109 = 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),U_11111)),U_11110)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11111)) )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11109,U_11110),U_11111)) ) ),
inference(variable_rename,[status(thm)],[f_3008_1]) ).
fof(f_3008_3,plain,
( ! [U_11117,U_11115,U_11113] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11113,U_11115),U_11117))
| ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11115),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11115)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)),U_11115))
| ~ 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),U_11117))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11115)) ) )
& U_11115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11117) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_11115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| U_11113 != 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),U_11117)),U_11115)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)) )
& ! [U_11116,U_11114,U_11112] :
( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11114),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11114)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)),U_11114))
& 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),U_11116))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11114)) ) )
| U_11114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11116) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& U_11112 = 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),U_11116)),U_11114)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)) )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11112,U_11114),U_11116)) ) ),
inference(miniscope,[status(thm)],[f_3008_2]) ).
fof(f_3008_4,plain,
( ! [U_11115,U_11117] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11115),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)))
| ~ sP857(U_11115,U_11117) )
& ! [U_11115,U_11117] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11115))
| ~ sP857(U_11115,U_11117) )
& ! [U_11115,U_11117] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)),U_11115))
| ~ 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),U_11117)))
| ~ sP856(U_11115,U_11117) )
& ! [U_11115,U_11117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11115))
| ~ sP856(U_11115,U_11117) )
& ! [U_11115,U_11117] :
( sP857(U_11115,U_11117)
| sP856(U_11115,U_11117)
| ~ sP858(U_11115,U_11117) )
& ! [U_11115,U_11117] :
( U_11115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP858(U_11115,U_11117) )
& ! [U_11115,U_11117] :
( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11117) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP855(U_11115,U_11117) )
& ! [U_11115,U_11117] :
( U_11115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP855(U_11115,U_11117) )
& ! [U_11114,U_11116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP852(U_11114,U_11116) )
& ! [U_11114,U_11116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11114),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)))
| ~ sP852(U_11114,U_11116) )
& ! [U_11114,U_11116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)),U_11114))
| ~ sP851(U_11114,U_11116) )
& ! [U_11114,U_11116] :
( 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),U_11116)))
| ~ sP851(U_11114,U_11116) )
& ! [U_11114,U_11116] :
( sP852(U_11114,U_11116)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11114))
| ~ sP853(U_11114,U_11116) )
& ! [U_11114,U_11116] :
( sP851(U_11114,U_11116)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11114))
| ~ sP853(U_11114,U_11116) )
& ! [U_11114,U_11112,U_11116] :
( sP853(U_11114,U_11116)
| U_11114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP854(U_11114,U_11112,U_11116) )
& ! [U_11114,U_11112,U_11116] :
( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11116) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP854(U_11114,U_11112,U_11116) )
& ! [U_11114,U_11112,U_11116] :
( U_11112 = 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),U_11116)),U_11114)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116))
| ~ sP854(U_11114,U_11112,U_11116) )
& ! [U_11115,U_11117,U_11113] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11113,U_11115),U_11117))
| sP858(U_11115,U_11117)
| sP855(U_11115,U_11117)
| U_11113 != 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),U_11117)),U_11115)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)) )
& ! [U_11114,U_11112,U_11116] :
( sP854(U_11114,U_11112,U_11116)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11112,U_11114),U_11116)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP851,sP852,sP853,sP854,sP855,sP856,sP857,sP858])],[f_3008_3]) ).
cnf(f_3008_5,plain,
( sP854(U_11114,U_11112,U_11116)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11112,U_11114),U_11116)) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_6,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11113,U_11115),U_11117))
| sP858(U_11115,U_11117)
| sP855(U_11115,U_11117)
| U_11113 != 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),U_11117)),U_11115)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_7,plain,
( U_11112 = 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),U_11116)),U_11114)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116))
| ~ sP854(U_11114,U_11112,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_8,plain,
( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11116) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP854(U_11114,U_11112,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_9,plain,
( sP853(U_11114,U_11116)
| U_11114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP854(U_11114,U_11112,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_10,plain,
( sP851(U_11114,U_11116)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11114))
| ~ sP853(U_11114,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_11,plain,
( sP852(U_11114,U_11116)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11114))
| ~ sP853(U_11114,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_12,plain,
( 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),U_11116)))
| ~ sP851(U_11114,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)),U_11114))
| ~ sP851(U_11114,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_14,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11114),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)))
| ~ sP852(U_11114,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11116)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP852(U_11114,U_11116) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_16,plain,
( U_11115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP855(U_11115,U_11117) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_17,plain,
( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11117) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP855(U_11115,U_11117) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_18,plain,
( U_11115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP858(U_11115,U_11117) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_19,plain,
( sP857(U_11115,U_11117)
| sP856(U_11115,U_11117)
| ~ sP858(U_11115,U_11117) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_20,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11115))
| ~ sP856(U_11115,U_11117) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_21,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)),U_11115))
| ~ 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),U_11117)))
| ~ sP856(U_11115,U_11117) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_22,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11115))
| ~ sP857(U_11115,U_11117) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
cnf(f_3008_23,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11115),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11117)))
| ~ sP857(U_11115,U_11117) ),
inference(clausify,[status(thm)],[f_3008_4]) ).
fof(f_3009_1,plain,
! [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)))))),
inference(fof_nnf,[status(thm)],[fact_nat__def]) ).
fof(f_3009_2,plain,
! [U_11118] : hAPP(c_Int_Onat,U_11118) = 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,U_11118)),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)))))),
inference(variable_rename,[status(thm)],[f_3009_1]) ).
fof(f_3009_3,plain,
! [U_11118] : hAPP(c_Int_Onat,U_11118) = 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,U_11118)),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)))))),
inference(definitional_conversion,[status(esa)],[f_3009_2]) ).
cnf(f_3009_4,plain,
hAPP(c_Int_Onat,U_11118) = 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,U_11118)),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)))))),
inference(clausify,[status(thm)],[f_3009_3]) ).
fof(f_3010_1,plain,
! [V_B_2,V_k_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_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)))
| ? [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))) ),
inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset]) ).
fof(f_3010_2,plain,
! [U_11123,U_11122,U_11121,U_11120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11120,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11121)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11123)))
| ? [U_11119] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11120,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11119)),U_11121)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,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),U_11119),U_11122))),U_11123))) ),
inference(variable_rename,[status(thm)],[f_3010_1]) ).
fof(f_3010_3,plain,
! [U_11123,U_11122,U_11121,U_11120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11120,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11121)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11120,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK275(U_11123,U_11122,U_11121,U_11120))),U_11121)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,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),sK275(U_11123,U_11122,U_11121,U_11120)),U_11122))),U_11123))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_11119,sK275(U_11123,U_11122,U_11121,U_11120))],[f_3010_2]) ).
fof(f_3010_4,plain,
! [U_11121,U_11123,U_11120,U_11122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11120,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11121)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11120,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK275(U_11123,U_11122,U_11121,U_11120))),U_11121)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,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),sK275(U_11123,U_11122,U_11121,U_11120)),U_11122))),U_11123))) ),
inference(definitional_conversion,[status(esa)],[f_3010_3]) ).
cnf(f_3010_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11120,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11121)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11120,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK275(U_11123,U_11122,U_11121,U_11120))),U_11121)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11120,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),sK275(U_11123,U_11122,U_11121,U_11120)),U_11122))),U_11123))) ),
inference(clausify,[status(thm)],[f_3010_4]) ).
fof(f_3011_1,plain,
! [V_Pa_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
| ? [B_x,B_y] :
( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y))
& ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y)))
| B_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& 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))) )
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opinduct]) ).
fof(f_3011_2,plain,
! [U_11128,U_11127,U_11126] :
( hBOOL(hAPP(hAPP(U_11128,U_11126),U_11127))
| ? [U_11125,U_11124] :
( ~ hBOOL(hAPP(hAPP(U_11128,U_11125),U_11124))
& ( hBOOL(hAPP(hAPP(U_11128,U_11124),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11125,U_11124)))
| U_11124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& 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),U_11125),U_11124))) )
| ~ 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),U_11126),U_11127))) ),
inference(variable_rename,[status(thm)],[f_3011_1]) ).
fof(f_3011_3,plain,
! [U_11128,U_11127,U_11126] :
( hBOOL(hAPP(hAPP(U_11128,U_11126),U_11127))
| ? [U_11124] :
( ~ hBOOL(hAPP(hAPP(U_11128,sK276(U_11128,U_11127,U_11126)),U_11124))
& ( hBOOL(hAPP(hAPP(U_11128,U_11124),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK276(U_11128,U_11127,U_11126),U_11124)))
| U_11124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& 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),sK276(U_11128,U_11127,U_11126)),U_11124))) )
| ~ 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),U_11126),U_11127))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_11125,sK276(U_11128,U_11127,U_11126))],[f_3011_2]) ).
fof(f_3011_4,plain,
! [U_11128,U_11127,U_11126] :
( hBOOL(hAPP(hAPP(U_11128,U_11126),U_11127))
| ( ~ hBOOL(hAPP(hAPP(U_11128,sK276(U_11128,U_11127,U_11126)),sK277(U_11128,U_11127,U_11126)))
& ( hBOOL(hAPP(hAPP(U_11128,sK277(U_11128,U_11127,U_11126)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK276(U_11128,U_11127,U_11126),sK277(U_11128,U_11127,U_11126))))
| sK277(U_11128,U_11127,U_11126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& 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),sK276(U_11128,U_11127,U_11126)),sK277(U_11128,U_11127,U_11126)))) )
| ~ 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),U_11126),U_11127))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_11124,sK277(U_11128,U_11127,U_11126))],[f_3011_3]) ).
fof(f_3011_5,plain,
( ! [U_11127,U_11126,U_11128] :
( ~ hBOOL(hAPP(hAPP(U_11128,sK276(U_11128,U_11127,U_11126)),sK277(U_11128,U_11127,U_11126)))
| ~ sP859(U_11127,U_11126,U_11128) )
& ! [U_11127,U_11126,U_11128] :
( hBOOL(hAPP(hAPP(U_11128,sK277(U_11128,U_11127,U_11126)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK276(U_11128,U_11127,U_11126),sK277(U_11128,U_11127,U_11126))))
| sK277(U_11128,U_11127,U_11126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP859(U_11127,U_11126,U_11128) )
& ! [U_11127,U_11126,U_11128] :
( 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),sK276(U_11128,U_11127,U_11126)),sK277(U_11128,U_11127,U_11126))))
| ~ sP859(U_11127,U_11126,U_11128) )
& ! [U_11127,U_11126,U_11128] :
( hBOOL(hAPP(hAPP(U_11128,U_11126),U_11127))
| sP859(U_11127,U_11126,U_11128)
| ~ 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),U_11126),U_11127))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP859])],[f_3011_4]) ).
cnf(f_3011_6,plain,
( hBOOL(hAPP(hAPP(U_11128,U_11126),U_11127))
| sP859(U_11127,U_11126,U_11128)
| ~ 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),U_11126),U_11127))) ),
inference(clausify,[status(thm)],[f_3011_5]) ).
cnf(f_3011_7,plain,
( 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),sK276(U_11128,U_11127,U_11126)),sK277(U_11128,U_11127,U_11126))))
| ~ sP859(U_11127,U_11126,U_11128) ),
inference(clausify,[status(thm)],[f_3011_5]) ).
cnf(f_3011_8,plain,
( hBOOL(hAPP(hAPP(U_11128,sK277(U_11128,U_11127,U_11126)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK276(U_11128,U_11127,U_11126),sK277(U_11128,U_11127,U_11126))))
| sK277(U_11128,U_11127,U_11126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP859(U_11127,U_11126,U_11128) ),
inference(clausify,[status(thm)],[f_3011_5]) ).
cnf(f_3011_9,plain,
( ~ hBOOL(hAPP(hAPP(U_11128,sK276(U_11128,U_11127,U_11126)),sK277(U_11128,U_11127,U_11126)))
| ~ sP859(U_11127,U_11126,U_11128) ),
inference(clausify,[status(thm)],[f_3011_5]) ).
fof(f_3012_1,plain,
! [V_y_2,V_x_2] :
( ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Int_ORep__Integ,V_x_2) != hAPP(c_Int_ORep__Integ,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject]) ).
fof(f_3012_2,plain,
! [U_11130,U_11129] :
( ( hAPP(c_Int_ORep__Integ,U_11129) = hAPP(c_Int_ORep__Integ,U_11130)
| U_11129 != U_11130 )
& ( U_11129 = U_11130
| hAPP(c_Int_ORep__Integ,U_11129) != hAPP(c_Int_ORep__Integ,U_11130) ) ),
inference(variable_rename,[status(thm)],[f_3012_1]) ).
fof(f_3012_3,plain,
( ! [U_11134,U_11132] :
( hAPP(c_Int_ORep__Integ,U_11132) = hAPP(c_Int_ORep__Integ,U_11134)
| U_11132 != U_11134 )
& ! [U_11133,U_11131] :
( U_11131 = U_11133
| hAPP(c_Int_ORep__Integ,U_11131) != hAPP(c_Int_ORep__Integ,U_11133) ) ),
inference(miniscope,[status(thm)],[f_3012_2]) ).
fof(f_3012_4,plain,
( ! [U_11134,U_11132] :
( hAPP(c_Int_ORep__Integ,U_11132) = hAPP(c_Int_ORep__Integ,U_11134)
| U_11132 != U_11134 )
& ! [U_11133,U_11131] :
( U_11131 = U_11133
| hAPP(c_Int_ORep__Integ,U_11131) != hAPP(c_Int_ORep__Integ,U_11133) ) ),
inference(definitional_conversion,[status(esa)],[f_3012_3]) ).
cnf(f_3012_5,plain,
( U_11131 = U_11133
| hAPP(c_Int_ORep__Integ,U_11131) != hAPP(c_Int_ORep__Integ,U_11133) ),
inference(clausify,[status(thm)],[f_3012_4]) ).
cnf(f_3012_6,plain,
( hAPP(c_Int_ORep__Integ,U_11132) = hAPP(c_Int_ORep__Integ,U_11134)
| U_11132 != U_11134 ),
inference(clausify,[status(thm)],[f_3012_4]) ).
fof(f_3013_1,plain,
! [V_s,V_k] :
( 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))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_range]) ).
fof(f_3013_2,plain,
! [U_11136,U_11135] :
( 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(U_11135),U_11136))),U_11135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_11135)) ),
inference(variable_rename,[status(thm)],[f_3013_1]) ).
fof(f_3013_3,plain,
! [U_11135,U_11136] :
( 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(U_11135),U_11136))),U_11135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_11135)) ),
inference(definitional_conversion,[status(esa)],[f_3013_2]) ).
cnf(f_3013_4,plain,
( 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(U_11135),U_11136))),U_11135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_11135)) ),
inference(clausify,[status(thm)],[f_3013_3]) ).
fof(f_3014_1,plain,
! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
( 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))
| ? [B_x] :
( 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
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__multicount]) ).
fof(f_3014_2,plain,
! [U_11143,U_11142,U_11141,U_11140,U_11139,U_11138] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11138,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_Nat_Onat,U_11138),c_Finite__Set_Ocard(U_11140)),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_fun(U_11140,tc_HOL_Obool),U_11138),c_Set_OCollect(U_11140)),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_fun(U_11140,tc_HOL_Obool),U_11138),hAPP(c_COMBS(U_11140,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11140),c_fconj),hAPP(hAPP(c_COMBC(U_11140,tc_fun(U_11140,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11140)),U_11141)))),U_11142)))),U_11139) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11143),hAPP(c_Finite__Set_Ocard(U_11140),U_11141))
| ? [U_11137] :
( hAPP(c_Finite__Set_Ocard(U_11138),hAPP(c_Set_OCollect(U_11138),hAPP(hAPP(c_COMBS(U_11138,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11138),c_fconj),hAPP(hAPP(c_COMBC(U_11138,tc_fun(U_11138,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11138)),U_11139))),hAPP(hAPP(c_COMBC(U_11138,U_11140,tc_HOL_Obool),U_11142),U_11137)))) != U_11143
& hBOOL(hAPP(hAPP(c_member(U_11140),U_11137),U_11141)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11140),U_11141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11138),U_11139)) ),
inference(variable_rename,[status(thm)],[f_3014_1]) ).
fof(f_3014_3,plain,
! [U_11143,U_11142,U_11141,U_11140,U_11139,U_11138] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11138,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_Nat_Onat,U_11138),c_Finite__Set_Ocard(U_11140)),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_fun(U_11140,tc_HOL_Obool),U_11138),c_Set_OCollect(U_11140)),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_fun(U_11140,tc_HOL_Obool),U_11138),hAPP(c_COMBS(U_11140,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11140),c_fconj),hAPP(hAPP(c_COMBC(U_11140,tc_fun(U_11140,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11140)),U_11141)))),U_11142)))),U_11139) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11143),hAPP(c_Finite__Set_Ocard(U_11140),U_11141))
| ( hAPP(c_Finite__Set_Ocard(U_11138),hAPP(c_Set_OCollect(U_11138),hAPP(hAPP(c_COMBS(U_11138,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11138),c_fconj),hAPP(hAPP(c_COMBC(U_11138,tc_fun(U_11138,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11138)),U_11139))),hAPP(hAPP(c_COMBC(U_11138,U_11140,tc_HOL_Obool),U_11142),sK278(U_11143,U_11142,U_11141,U_11140,U_11139,U_11138))))) != U_11143
& hBOOL(hAPP(hAPP(c_member(U_11140),sK278(U_11143,U_11142,U_11141,U_11140,U_11139,U_11138)),U_11141)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11140),U_11141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11138),U_11139)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_11137,sK278(U_11143,U_11142,U_11141,U_11140,U_11139,U_11138))],[f_3014_2]) ).
fof(f_3014_4,plain,
( ! [U_11138,U_11139,U_11140,U_11141,U_11142,U_11143] :
( hAPP(c_Finite__Set_Ocard(U_11138),hAPP(c_Set_OCollect(U_11138),hAPP(hAPP(c_COMBS(U_11138,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11138),c_fconj),hAPP(hAPP(c_COMBC(U_11138,tc_fun(U_11138,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11138)),U_11139))),hAPP(hAPP(c_COMBC(U_11138,U_11140,tc_HOL_Obool),U_11142),sK278(U_11143,U_11142,U_11141,U_11140,U_11139,U_11138))))) != U_11143
| ~ sP860(U_11138,U_11139,U_11140,U_11141,U_11142,U_11143) )
& ! [U_11138,U_11139,U_11140,U_11141,U_11142,U_11143] :
( hBOOL(hAPP(hAPP(c_member(U_11140),sK278(U_11143,U_11142,U_11141,U_11140,U_11139,U_11138)),U_11141))
| ~ sP860(U_11138,U_11139,U_11140,U_11141,U_11142,U_11143) )
& ! [U_11138,U_11139,U_11140,U_11141,U_11142,U_11143] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11138,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_Nat_Onat,U_11138),c_Finite__Set_Ocard(U_11140)),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_fun(U_11140,tc_HOL_Obool),U_11138),c_Set_OCollect(U_11140)),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_fun(U_11140,tc_HOL_Obool),U_11138),hAPP(c_COMBS(U_11140,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11140),c_fconj),hAPP(hAPP(c_COMBC(U_11140,tc_fun(U_11140,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11140)),U_11141)))),U_11142)))),U_11139) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11143),hAPP(c_Finite__Set_Ocard(U_11140),U_11141))
| sP860(U_11138,U_11139,U_11140,U_11141,U_11142,U_11143)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11140),U_11141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11138),U_11139)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP860])],[f_3014_3]) ).
cnf(f_3014_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11138,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_Nat_Onat,U_11138),c_Finite__Set_Ocard(U_11140)),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_fun(U_11140,tc_HOL_Obool),U_11138),c_Set_OCollect(U_11140)),hAPP(hAPP(c_COMBB(tc_fun(U_11140,tc_HOL_Obool),tc_fun(U_11140,tc_HOL_Obool),U_11138),hAPP(c_COMBS(U_11140,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11140),c_fconj),hAPP(hAPP(c_COMBC(U_11140,tc_fun(U_11140,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11140)),U_11141)))),U_11142)))),U_11139) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11143),hAPP(c_Finite__Set_Ocard(U_11140),U_11141))
| sP860(U_11138,U_11139,U_11140,U_11141,U_11142,U_11143)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11140),U_11141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11138),U_11139)) ),
inference(clausify,[status(thm)],[f_3014_4]) ).
cnf(f_3014_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11140),sK278(U_11143,U_11142,U_11141,U_11140,U_11139,U_11138)),U_11141))
| ~ sP860(U_11138,U_11139,U_11140,U_11141,U_11142,U_11143) ),
inference(clausify,[status(thm)],[f_3014_4]) ).
cnf(f_3014_7,plain,
( hAPP(c_Finite__Set_Ocard(U_11138),hAPP(c_Set_OCollect(U_11138),hAPP(hAPP(c_COMBS(U_11138,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11138),c_fconj),hAPP(hAPP(c_COMBC(U_11138,tc_fun(U_11138,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11138)),U_11139))),hAPP(hAPP(c_COMBC(U_11138,U_11140,tc_HOL_Obool),U_11142),sK278(U_11143,U_11142,U_11141,U_11140,U_11139,U_11138))))) != U_11143
| ~ sP860(U_11138,U_11139,U_11140,U_11141,U_11142,U_11143) ),
inference(clausify,[status(thm)],[f_3014_4]) ).
fof(f_3015_1,plain,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( 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)))
| ~ 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))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_mlex__leq]) ).
fof(f_3015_2,plain,
! [U_11148,U_11147,U_11146,U_11145,U_11144] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11147,U_11147)),hAPP(hAPP(c_Product__Type_OPair(U_11147,U_11147),U_11145),U_11146)),c_Wellfounded_Omlex__prod(U_11147,U_11144,U_11148)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11147,U_11147)),hAPP(hAPP(c_Product__Type_OPair(U_11147,U_11147),U_11145),U_11146)),U_11148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11144,U_11145)),hAPP(U_11144,U_11146))) ),
inference(variable_rename,[status(thm)],[f_3015_1]) ).
fof(f_3015_3,plain,
! [U_11144,U_11145,U_11147,U_11146,U_11148] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11147,U_11147)),hAPP(hAPP(c_Product__Type_OPair(U_11147,U_11147),U_11145),U_11146)),c_Wellfounded_Omlex__prod(U_11147,U_11144,U_11148)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11147,U_11147)),hAPP(hAPP(c_Product__Type_OPair(U_11147,U_11147),U_11145),U_11146)),U_11148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11144,U_11145)),hAPP(U_11144,U_11146))) ),
inference(definitional_conversion,[status(esa)],[f_3015_2]) ).
cnf(f_3015_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11147,U_11147)),hAPP(hAPP(c_Product__Type_OPair(U_11147,U_11147),U_11145),U_11146)),c_Wellfounded_Omlex__prod(U_11147,U_11144,U_11148)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11147,U_11147)),hAPP(hAPP(c_Product__Type_OPair(U_11147,U_11147),U_11145),U_11146)),U_11148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11144,U_11145)),hAPP(U_11144,U_11146))) ),
inference(clausify,[status(thm)],[f_3015_3]) ).
fof(f_3016_1,plain,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_mlex__less]) ).
fof(f_3016_2,plain,
! [U_11153,U_11152,U_11151,U_11150,U_11149] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11152,U_11152)),hAPP(hAPP(c_Product__Type_OPair(U_11152,U_11152),U_11150),U_11151)),c_Wellfounded_Omlex__prod(U_11152,U_11149,U_11153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11149,U_11150)),hAPP(U_11149,U_11151))) ),
inference(variable_rename,[status(thm)],[f_3016_1]) ).
fof(f_3016_3,plain,
! [U_11150,U_11149,U_11151,U_11152,U_11153] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11152,U_11152)),hAPP(hAPP(c_Product__Type_OPair(U_11152,U_11152),U_11150),U_11151)),c_Wellfounded_Omlex__prod(U_11152,U_11149,U_11153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11149,U_11150)),hAPP(U_11149,U_11151))) ),
inference(definitional_conversion,[status(esa)],[f_3016_2]) ).
cnf(f_3016_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11152,U_11152)),hAPP(hAPP(c_Product__Type_OPair(U_11152,U_11152),U_11150),U_11151)),c_Wellfounded_Omlex__prod(U_11152,U_11149,U_11153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11149,U_11150)),hAPP(U_11149,U_11151))) ),
inference(clausify,[status(thm)],[f_3016_3]) ).
fof(f_3017_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_finite__psubset__def]) ).
fof(f_3017_2,plain,
! [U_11154] : c_Wellfounded_Ofinite__psubset(U_11154) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11154,tc_HOL_Obool)),c_COMBS(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11154,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_11154,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_11154)))),
inference(variable_rename,[status(thm)],[f_3017_1]) ).
fof(f_3017_3,plain,
! [U_11154] : c_Wellfounded_Ofinite__psubset(U_11154) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11154,tc_HOL_Obool)),c_COMBS(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11154,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_11154,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_11154)))),
inference(definitional_conversion,[status(esa)],[f_3017_2]) ).
cnf(f_3017_4,plain,
c_Wellfounded_Ofinite__psubset(U_11154) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11154,tc_HOL_Obool)),c_COMBS(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11154,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11154,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_11154,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_11154)))),
inference(clausify,[status(thm)],[f_3017_3]) ).
fof(f_3018_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)))))))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib]) ).
fof(f_3018_2,plain,
! [U_11157,U_11156,U_11155] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11155),c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),U_11156)),c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),U_11157)) = c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),hAPP(c_Set_OCollect(U_11155),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool,U_11155),c_HOL_OEx(U_11155)),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_HOL_Obool),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool,U_11155),c_HOL_OEx(U_11155))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),tc_fun(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),U_11155),c_COMBS(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11155,tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBS(U_11155,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11155),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11155),c_fconj))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_fun(U_11155,U_11155)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool)),tc_fun(tc_fun(U_11155,tc_fun(U_11155,U_11155)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),U_11155),c_COMBB(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool),U_11155)),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_fun(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBB(U_11155,tc_HOL_Obool,U_11155)),c_fequal))),c_Orderings_Oord__class_Omax(U_11155)))))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11155)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11155),c_fconj),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11155)),U_11156)))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11155)),U_11157)))))))
| U_11157 = c_Orderings_Obot__class_Obot(tc_fun(U_11155,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11155),U_11157))
| U_11156 = c_Orderings_Obot__class_Obot(tc_fun(U_11155,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11155),U_11156))
| ~ class_Orderings_Olinorder(U_11155) ),
inference(variable_rename,[status(thm)],[f_3018_1]) ).
fof(f_3018_3,plain,
! [U_11155,U_11156,U_11157] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11155),c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),U_11156)),c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),U_11157)) = c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),hAPP(c_Set_OCollect(U_11155),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool,U_11155),c_HOL_OEx(U_11155)),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_HOL_Obool),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool,U_11155),c_HOL_OEx(U_11155))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),tc_fun(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),U_11155),c_COMBS(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11155,tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBS(U_11155,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11155),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11155),c_fconj))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_fun(U_11155,U_11155)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool)),tc_fun(tc_fun(U_11155,tc_fun(U_11155,U_11155)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),U_11155),c_COMBB(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool),U_11155)),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_fun(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBB(U_11155,tc_HOL_Obool,U_11155)),c_fequal))),c_Orderings_Oord__class_Omax(U_11155)))))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11155)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11155),c_fconj),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11155)),U_11156)))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11155)),U_11157)))))))
| U_11157 = c_Orderings_Obot__class_Obot(tc_fun(U_11155,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11155),U_11157))
| U_11156 = c_Orderings_Obot__class_Obot(tc_fun(U_11155,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11155),U_11156))
| ~ class_Orderings_Olinorder(U_11155) ),
inference(definitional_conversion,[status(esa)],[f_3018_2]) ).
cnf(f_3018_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11155),c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),U_11156)),c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),U_11157)) = c_Big__Operators_Olattice_OInf__fin(U_11155,c_Orderings_Oord__class_Omin(U_11155),hAPP(c_Set_OCollect(U_11155),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool,U_11155),c_HOL_OEx(U_11155)),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_HOL_Obool),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool,U_11155),c_HOL_OEx(U_11155))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),tc_fun(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),U_11155),c_COMBS(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11155,tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool))),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBS(U_11155,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool)),tc_fun(U_11155,tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11155),hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11155),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11155),c_fconj))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_fun(U_11155,U_11155)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool)),tc_fun(tc_fun(U_11155,tc_fun(U_11155,U_11155)),tc_fun(U_11155,tc_fun(U_11155,tc_HOL_Obool))),U_11155),c_COMBB(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool),U_11155)),hAPP(hAPP(c_COMBB(tc_fun(U_11155,tc_HOL_Obool),tc_fun(tc_fun(U_11155,U_11155),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBB(U_11155,tc_HOL_Obool,U_11155)),c_fequal))),c_Orderings_Oord__class_Omax(U_11155)))))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11155,tc_HOL_Obool),tc_fun(U_11155,tc_HOL_Obool)),U_11155),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11155)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11155),c_fconj),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11155)),U_11156)))),hAPP(hAPP(c_COMBC(U_11155,tc_fun(U_11155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11155)),U_11157)))))))
| U_11157 = c_Orderings_Obot__class_Obot(tc_fun(U_11155,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11155),U_11157))
| U_11156 = c_Orderings_Obot__class_Obot(tc_fun(U_11155,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11155),U_11156))
| ~ class_Orderings_Olinorder(U_11155) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
fof(f_3019_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib]) ).
fof(f_3019_2,plain,
! [U_11160,U_11159,U_11158] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11158),U_11160),c_Big__Operators_Olattice_OInf__fin(U_11158,c_Orderings_Oord__class_Omin(U_11158),U_11159)) = c_Big__Operators_Olattice_OInf__fin(U_11158,c_Orderings_Oord__class_Omin(U_11158),hAPP(c_Set_OCollect(U_11158),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_HOL_Obool,U_11158),c_HOL_OEx(U_11158)),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_HOL_Obool)),U_11158),c_COMBS(U_11158,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11158),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11158),c_fconj)),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,U_11158),tc_fun(U_11158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_fun(tc_fun(U_11158,U_11158),tc_fun(U_11158,tc_HOL_Obool)),U_11158),c_COMBB(U_11158,tc_HOL_Obool,U_11158)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_11158),U_11160))))),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11158)),U_11159)))))
| U_11159 = c_Orderings_Obot__class_Obot(tc_fun(U_11158,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11158),U_11159))
| ~ class_Orderings_Olinorder(U_11158) ),
inference(variable_rename,[status(thm)],[f_3019_1]) ).
fof(f_3019_3,plain,
! [U_11159,U_11158,U_11160] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11158),U_11160),c_Big__Operators_Olattice_OInf__fin(U_11158,c_Orderings_Oord__class_Omin(U_11158),U_11159)) = c_Big__Operators_Olattice_OInf__fin(U_11158,c_Orderings_Oord__class_Omin(U_11158),hAPP(c_Set_OCollect(U_11158),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_HOL_Obool,U_11158),c_HOL_OEx(U_11158)),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_HOL_Obool)),U_11158),c_COMBS(U_11158,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11158),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11158),c_fconj)),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,U_11158),tc_fun(U_11158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_fun(tc_fun(U_11158,U_11158),tc_fun(U_11158,tc_HOL_Obool)),U_11158),c_COMBB(U_11158,tc_HOL_Obool,U_11158)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_11158),U_11160))))),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11158)),U_11159)))))
| U_11159 = c_Orderings_Obot__class_Obot(tc_fun(U_11158,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11158),U_11159))
| ~ class_Orderings_Olinorder(U_11158) ),
inference(definitional_conversion,[status(esa)],[f_3019_2]) ).
cnf(f_3019_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11158),U_11160),c_Big__Operators_Olattice_OInf__fin(U_11158,c_Orderings_Oord__class_Omin(U_11158),U_11159)) = c_Big__Operators_Olattice_OInf__fin(U_11158,c_Orderings_Oord__class_Omin(U_11158),hAPP(c_Set_OCollect(U_11158),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_HOL_Obool,U_11158),c_HOL_OEx(U_11158)),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_HOL_Obool)),U_11158),c_COMBS(U_11158,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_fun(U_11158,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11158),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11158),c_fconj)),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,U_11158),tc_fun(U_11158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11158,tc_HOL_Obool),tc_fun(tc_fun(U_11158,U_11158),tc_fun(U_11158,tc_HOL_Obool)),U_11158),c_COMBB(U_11158,tc_HOL_Obool,U_11158)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_11158),U_11160))))),hAPP(hAPP(c_COMBC(U_11158,tc_fun(U_11158,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11158)),U_11159)))))
| U_11159 = c_Orderings_Obot__class_Obot(tc_fun(U_11158,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11158),U_11159))
| ~ class_Orderings_Olinorder(U_11158) ),
inference(clausify,[status(thm)],[f_3019_3]) ).
fof(f_3020_1,plain,
! [V_Qa_2,T_c,V_Pa_2,T_b] :
( ( ( 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)))))
| ? [B_y] :
( ~ 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))))
& hBOOL(hAPP(V_Pa_2,B_y)) ) )
& ( ! [B_y] :
( 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))))
| ~ hBOOL(hAPP(V_Pa_2,B_y)) )
| ~ 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))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).
fof(f_3020_2,plain,
! [U_11166,U_11165,U_11164,U_11163] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_HOL_Obool,U_11165),c_HOL_OEx(U_11163)),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_fun(U_11163,tc_HOL_Obool),U_11165),hAPP(c_COMBS(U_11163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11163),c_fconj),U_11164))),U_11166)))))
| ? [U_11162] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBC(U_11165,U_11163,tc_HOL_Obool),U_11166),U_11162))))
& hBOOL(hAPP(U_11164,U_11162)) ) )
& ( ! [U_11161] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBC(U_11165,U_11163,tc_HOL_Obool),U_11166),U_11161))))
| ~ hBOOL(hAPP(U_11164,U_11161)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_HOL_Obool,U_11165),c_HOL_OEx(U_11163)),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_fun(U_11163,tc_HOL_Obool),U_11165),hAPP(c_COMBS(U_11163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11163),c_fconj),U_11164))),U_11166))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11163),hAPP(c_Set_OCollect(U_11163),U_11164))) ),
inference(variable_rename,[status(thm)],[f_3020_1]) ).
fof(f_3020_3,plain,
! [U_11166,U_11165,U_11164,U_11163] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_HOL_Obool,U_11165),c_HOL_OEx(U_11163)),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_fun(U_11163,tc_HOL_Obool),U_11165),hAPP(c_COMBS(U_11163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11163),c_fconj),U_11164))),U_11166)))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBC(U_11165,U_11163,tc_HOL_Obool),U_11166),sK279(U_11166,U_11165,U_11164,U_11163)))))
& hBOOL(hAPP(U_11164,sK279(U_11166,U_11165,U_11164,U_11163))) ) )
& ( ! [U_11161] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBC(U_11165,U_11163,tc_HOL_Obool),U_11166),U_11161))))
| ~ hBOOL(hAPP(U_11164,U_11161)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_HOL_Obool,U_11165),c_HOL_OEx(U_11163)),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_fun(U_11163,tc_HOL_Obool),U_11165),hAPP(c_COMBS(U_11163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11163),c_fconj),U_11164))),U_11166))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11163),hAPP(c_Set_OCollect(U_11163),U_11164))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_11162,sK279(U_11166,U_11165,U_11164,U_11163))],[f_3020_2]) ).
fof(f_3020_4,plain,
( ! [U_11163,U_11164,U_11165,U_11166] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBC(U_11165,U_11163,tc_HOL_Obool),U_11166),sK279(U_11166,U_11165,U_11164,U_11163)))))
| ~ sP861(U_11163,U_11164,U_11165,U_11166) )
& ! [U_11163,U_11164,U_11165,U_11166] :
( hBOOL(hAPP(U_11164,sK279(U_11166,U_11165,U_11164,U_11163)))
| ~ sP861(U_11163,U_11164,U_11165,U_11166) )
& ! [U_11161,U_11163,U_11164,U_11165,U_11166] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_HOL_Obool,U_11165),c_HOL_OEx(U_11163)),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_fun(U_11163,tc_HOL_Obool),U_11165),hAPP(c_COMBS(U_11163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11163),c_fconj),U_11164))),U_11166)))))
| sP861(U_11163,U_11164,U_11165,U_11166)
| ~ sP862(U_11161,U_11163,U_11164,U_11165,U_11166) )
& ! [U_11161,U_11163,U_11164,U_11165,U_11166] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBC(U_11165,U_11163,tc_HOL_Obool),U_11166),U_11161))))
| ~ hBOOL(hAPP(U_11164,U_11161))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_HOL_Obool,U_11165),c_HOL_OEx(U_11163)),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_fun(U_11163,tc_HOL_Obool),U_11165),hAPP(c_COMBS(U_11163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11163),c_fconj),U_11164))),U_11166)))))
| ~ sP862(U_11161,U_11163,U_11164,U_11165,U_11166) )
& ! [U_11161,U_11163,U_11164,U_11165,U_11166] :
( sP862(U_11161,U_11163,U_11164,U_11165,U_11166)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11163),hAPP(c_Set_OCollect(U_11163),U_11164))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP861,sP862])],[f_3020_3]) ).
cnf(f_3020_5,plain,
( sP862(U_11161,U_11163,U_11164,U_11165,U_11166)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11163),hAPP(c_Set_OCollect(U_11163),U_11164))) ),
inference(clausify,[status(thm)],[f_3020_4]) ).
cnf(f_3020_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBC(U_11165,U_11163,tc_HOL_Obool),U_11166),U_11161))))
| ~ hBOOL(hAPP(U_11164,U_11161))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_HOL_Obool,U_11165),c_HOL_OEx(U_11163)),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_fun(U_11163,tc_HOL_Obool),U_11165),hAPP(c_COMBS(U_11163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11163),c_fconj),U_11164))),U_11166)))))
| ~ sP862(U_11161,U_11163,U_11164,U_11165,U_11166) ),
inference(clausify,[status(thm)],[f_3020_4]) ).
cnf(f_3020_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_HOL_Obool,U_11165),c_HOL_OEx(U_11163)),hAPP(hAPP(c_COMBB(tc_fun(U_11163,tc_HOL_Obool),tc_fun(U_11163,tc_HOL_Obool),U_11165),hAPP(c_COMBS(U_11163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11163),c_fconj),U_11164))),U_11166)))))
| sP861(U_11163,U_11164,U_11165,U_11166)
| ~ sP862(U_11161,U_11163,U_11164,U_11165,U_11166) ),
inference(clausify,[status(thm)],[f_3020_4]) ).
cnf(f_3020_8,plain,
( hBOOL(hAPP(U_11164,sK279(U_11166,U_11165,U_11164,U_11163)))
| ~ sP861(U_11163,U_11164,U_11165,U_11166) ),
inference(clausify,[status(thm)],[f_3020_4]) ).
cnf(f_3020_9,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),hAPP(c_Set_OCollect(U_11165),hAPP(hAPP(c_COMBC(U_11165,U_11163,tc_HOL_Obool),U_11166),sK279(U_11166,U_11165,U_11164,U_11163)))))
| ~ sP861(U_11163,U_11164,U_11165,U_11166) ),
inference(clausify,[status(thm)],[f_3020_4]) ).
fof(f_3021_1,plain,
! [V_f_2,T_c,V_Pa_2,T_b] :
( 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)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).
fof(f_3021_2,plain,
! [U_11170,U_11169,U_11168,U_11167] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11169),hAPP(c_Set_OCollect(U_11169),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_HOL_Obool),tc_HOL_Obool,U_11169),c_HOL_OEx(U_11167)),hAPP(hAPP(c_COMBC(U_11169,tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_HOL_Obool)),U_11169),c_COMBS(U_11167,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11169),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11167),c_fconj)),hAPP(hAPP(c_COMBC(U_11169,tc_fun(U_11167,U_11169),tc_fun(U_11167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11169,tc_HOL_Obool),tc_fun(tc_fun(U_11167,U_11169),tc_fun(U_11167,tc_HOL_Obool)),U_11169),c_COMBB(U_11169,tc_HOL_Obool,U_11167)),c_fequal)),U_11170)))),U_11168)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11167),hAPP(c_Set_OCollect(U_11167),U_11168))) ),
inference(variable_rename,[status(thm)],[f_3021_1]) ).
fof(f_3021_3,plain,
! [U_11169,U_11168,U_11170,U_11167] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11169),hAPP(c_Set_OCollect(U_11169),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_HOL_Obool),tc_HOL_Obool,U_11169),c_HOL_OEx(U_11167)),hAPP(hAPP(c_COMBC(U_11169,tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_HOL_Obool)),U_11169),c_COMBS(U_11167,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11169),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11167),c_fconj)),hAPP(hAPP(c_COMBC(U_11169,tc_fun(U_11167,U_11169),tc_fun(U_11167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11169,tc_HOL_Obool),tc_fun(tc_fun(U_11167,U_11169),tc_fun(U_11167,tc_HOL_Obool)),U_11169),c_COMBB(U_11169,tc_HOL_Obool,U_11167)),c_fequal)),U_11170)))),U_11168)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11167),hAPP(c_Set_OCollect(U_11167),U_11168))) ),
inference(definitional_conversion,[status(esa)],[f_3021_2]) ).
cnf(f_3021_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11169),hAPP(c_Set_OCollect(U_11169),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_HOL_Obool),tc_HOL_Obool,U_11169),c_HOL_OEx(U_11167)),hAPP(hAPP(c_COMBC(U_11169,tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_HOL_Obool)),U_11169),c_COMBS(U_11167,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11167,tc_HOL_Obool),tc_fun(U_11167,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11169),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11167),c_fconj)),hAPP(hAPP(c_COMBC(U_11169,tc_fun(U_11167,U_11169),tc_fun(U_11167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11169,tc_HOL_Obool),tc_fun(tc_fun(U_11167,U_11169),tc_fun(U_11167,tc_HOL_Obool)),U_11169),c_COMBB(U_11169,tc_HOL_Obool,U_11167)),c_fequal)),U_11170)))),U_11168)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11167),hAPP(c_Set_OCollect(U_11167),U_11168))) ),
inference(clausify,[status(thm)],[f_3021_3]) ).
fof(f_3022_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_Pow__Compl]) ).
fof(f_3022_2,plain,
! [U_11172,U_11171] : hAPP(c_Set_OPow(U_11171),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11171,tc_HOL_Obool)),U_11172)) = hAPP(c_Set_OCollect(tc_fun(U_11171,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_11171,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),c_COMBS(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),c_COMBB(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_11171,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_11171,tc_HOL_Obool)),U_11172)),c_Set_OPow(U_11171))))),
inference(variable_rename,[status(thm)],[f_3022_1]) ).
fof(f_3022_3,plain,
! [U_11171,U_11172] : hAPP(c_Set_OPow(U_11171),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11171,tc_HOL_Obool)),U_11172)) = hAPP(c_Set_OCollect(tc_fun(U_11171,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_11171,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),c_COMBS(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),c_COMBB(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_11171,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_11171,tc_HOL_Obool)),U_11172)),c_Set_OPow(U_11171))))),
inference(definitional_conversion,[status(esa)],[f_3022_2]) ).
cnf(f_3022_4,plain,
hAPP(c_Set_OPow(U_11171),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11171,tc_HOL_Obool)),U_11172)) = hAPP(c_Set_OCollect(tc_fun(U_11171,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_11171,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),c_COMBS(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_11171,tc_HOL_Obool),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_fun(U_11171,tc_HOL_Obool)),tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11171,tc_HOL_Obool)),c_COMBB(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_11171,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11171,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11171,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_11171,tc_HOL_Obool)),U_11172)),c_Set_OPow(U_11171))))),
inference(clausify,[status(thm)],[f_3022_3]) ).
fof(f_3023_1,plain,
! [V_k_2,V_N_2,T_b] :
( 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)))))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ~ class_Groups_Olinordered__ab__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__Max__commute]) ).
fof(f_3023_2,plain,
! [U_11175,U_11174,U_11173] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11173),U_11175),c_Big__Operators_Olinorder__class_OMax(U_11173,U_11174)) = c_Big__Operators_Olinorder__class_OMax(U_11173,hAPP(c_Set_OCollect(U_11173),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_HOL_Obool,U_11173),c_HOL_OEx(U_11173)),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_HOL_Obool)),U_11173),c_COMBS(U_11173,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11173),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11173),c_fconj)),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,U_11173),tc_fun(U_11173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_fun(tc_fun(U_11173,U_11173),tc_fun(U_11173,tc_HOL_Obool)),U_11173),c_COMBB(U_11173,tc_HOL_Obool,U_11173)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_11173),U_11175))))),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11173)),U_11174)))))
| U_11174 = c_Orderings_Obot__class_Obot(tc_fun(U_11173,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11173),U_11174))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_11173) ),
inference(variable_rename,[status(thm)],[f_3023_1]) ).
fof(f_3023_3,plain,
! [U_11173,U_11174,U_11175] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11173),U_11175),c_Big__Operators_Olinorder__class_OMax(U_11173,U_11174)) = c_Big__Operators_Olinorder__class_OMax(U_11173,hAPP(c_Set_OCollect(U_11173),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_HOL_Obool,U_11173),c_HOL_OEx(U_11173)),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_HOL_Obool)),U_11173),c_COMBS(U_11173,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11173),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11173),c_fconj)),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,U_11173),tc_fun(U_11173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_fun(tc_fun(U_11173,U_11173),tc_fun(U_11173,tc_HOL_Obool)),U_11173),c_COMBB(U_11173,tc_HOL_Obool,U_11173)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_11173),U_11175))))),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11173)),U_11174)))))
| U_11174 = c_Orderings_Obot__class_Obot(tc_fun(U_11173,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11173),U_11174))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_11173) ),
inference(definitional_conversion,[status(esa)],[f_3023_2]) ).
cnf(f_3023_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11173),U_11175),c_Big__Operators_Olinorder__class_OMax(U_11173,U_11174)) = c_Big__Operators_Olinorder__class_OMax(U_11173,hAPP(c_Set_OCollect(U_11173),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_HOL_Obool,U_11173),c_HOL_OEx(U_11173)),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_HOL_Obool)),U_11173),c_COMBS(U_11173,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_fun(U_11173,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11173),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11173),c_fconj)),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,U_11173),tc_fun(U_11173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11173,tc_HOL_Obool),tc_fun(tc_fun(U_11173,U_11173),tc_fun(U_11173,tc_HOL_Obool)),U_11173),c_COMBB(U_11173,tc_HOL_Obool,U_11173)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_11173),U_11175))))),hAPP(hAPP(c_COMBC(U_11173,tc_fun(U_11173,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11173)),U_11174)))))
| U_11174 = c_Orderings_Obot__class_Obot(tc_fun(U_11173,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11173),U_11174))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_11173) ),
inference(clausify,[status(thm)],[f_3023_3]) ).
fof(f_3024_1,plain,
! [V_k_2,V_N_2,T_b] :
( 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)))))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ~ class_Groups_Olinordered__ab__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__Min__commute]) ).
fof(f_3024_2,plain,
! [U_11178,U_11177,U_11176] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11176),U_11178),c_Big__Operators_Olinorder__class_OMin(U_11176,U_11177)) = c_Big__Operators_Olinorder__class_OMin(U_11176,hAPP(c_Set_OCollect(U_11176),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_HOL_Obool,U_11176),c_HOL_OEx(U_11176)),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_HOL_Obool)),U_11176),c_COMBS(U_11176,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11176),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11176),c_fconj)),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,U_11176),tc_fun(U_11176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_fun(tc_fun(U_11176,U_11176),tc_fun(U_11176,tc_HOL_Obool)),U_11176),c_COMBB(U_11176,tc_HOL_Obool,U_11176)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_11176),U_11178))))),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11176)),U_11177)))))
| U_11177 = c_Orderings_Obot__class_Obot(tc_fun(U_11176,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11176),U_11177))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_11176) ),
inference(variable_rename,[status(thm)],[f_3024_1]) ).
fof(f_3024_3,plain,
! [U_11176,U_11177,U_11178] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11176),U_11178),c_Big__Operators_Olinorder__class_OMin(U_11176,U_11177)) = c_Big__Operators_Olinorder__class_OMin(U_11176,hAPP(c_Set_OCollect(U_11176),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_HOL_Obool,U_11176),c_HOL_OEx(U_11176)),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_HOL_Obool)),U_11176),c_COMBS(U_11176,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11176),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11176),c_fconj)),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,U_11176),tc_fun(U_11176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_fun(tc_fun(U_11176,U_11176),tc_fun(U_11176,tc_HOL_Obool)),U_11176),c_COMBB(U_11176,tc_HOL_Obool,U_11176)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_11176),U_11178))))),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11176)),U_11177)))))
| U_11177 = c_Orderings_Obot__class_Obot(tc_fun(U_11176,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11176),U_11177))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_11176) ),
inference(definitional_conversion,[status(esa)],[f_3024_2]) ).
cnf(f_3024_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11176),U_11178),c_Big__Operators_Olinorder__class_OMin(U_11176,U_11177)) = c_Big__Operators_Olinorder__class_OMin(U_11176,hAPP(c_Set_OCollect(U_11176),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_HOL_Obool,U_11176),c_HOL_OEx(U_11176)),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_HOL_Obool)),U_11176),c_COMBS(U_11176,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11176),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11176),c_fconj)),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,U_11176),tc_fun(U_11176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_fun(tc_fun(U_11176,U_11176),tc_fun(U_11176,tc_HOL_Obool)),U_11176),c_COMBB(U_11176,tc_HOL_Obool,U_11176)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_11176),U_11178))))),hAPP(hAPP(c_COMBC(U_11176,tc_fun(U_11176,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11176)),U_11177)))))
| U_11177 = c_Orderings_Obot__class_Obot(tc_fun(U_11176,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11176),U_11177))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_11176) ),
inference(clausify,[status(thm)],[f_3024_3]) ).
fof(f_3025_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib]) ).
fof(f_3025_2,plain,
! [U_11181,U_11180,U_11179] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11179),U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11179,U_11180)) = c_Big__Operators_Olattice__class_OInf__fin(U_11179,hAPP(c_Set_OCollect(U_11179),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_HOL_Obool,U_11179),c_HOL_OEx(U_11179)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_HOL_Obool)),U_11179),c_COMBS(U_11179,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11179),c_fconj)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,U_11179),tc_fun(U_11179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_fun(tc_fun(U_11179,U_11179),tc_fun(U_11179,tc_HOL_Obool)),U_11179),c_COMBB(U_11179,tc_HOL_Obool,U_11179)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11179),U_11181))))),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11179)),U_11180)))))
| U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11179,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11179),U_11180))
| ~ class_Lattices_Odistrib__lattice(U_11179) ),
inference(variable_rename,[status(thm)],[f_3025_1]) ).
fof(f_3025_3,plain,
! [U_11179,U_11180,U_11181] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11179),U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11179,U_11180)) = c_Big__Operators_Olattice__class_OInf__fin(U_11179,hAPP(c_Set_OCollect(U_11179),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_HOL_Obool,U_11179),c_HOL_OEx(U_11179)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_HOL_Obool)),U_11179),c_COMBS(U_11179,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11179),c_fconj)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,U_11179),tc_fun(U_11179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_fun(tc_fun(U_11179,U_11179),tc_fun(U_11179,tc_HOL_Obool)),U_11179),c_COMBB(U_11179,tc_HOL_Obool,U_11179)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11179),U_11181))))),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11179)),U_11180)))))
| U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11179,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11179),U_11180))
| ~ class_Lattices_Odistrib__lattice(U_11179) ),
inference(definitional_conversion,[status(esa)],[f_3025_2]) ).
cnf(f_3025_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11179),U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11179,U_11180)) = c_Big__Operators_Olattice__class_OInf__fin(U_11179,hAPP(c_Set_OCollect(U_11179),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_HOL_Obool,U_11179),c_HOL_OEx(U_11179)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_HOL_Obool)),U_11179),c_COMBS(U_11179,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_fun(U_11179,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11179),c_fconj)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,U_11179),tc_fun(U_11179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11179,tc_HOL_Obool),tc_fun(tc_fun(U_11179,U_11179),tc_fun(U_11179,tc_HOL_Obool)),U_11179),c_COMBB(U_11179,tc_HOL_Obool,U_11179)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11179),U_11181))))),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11179)),U_11180)))))
| U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11179,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11179),U_11180))
| ~ class_Lattices_Odistrib__lattice(U_11179) ),
inference(clausify,[status(thm)],[f_3025_3]) ).
fof(f_3026_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)))))))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib]) ).
fof(f_3026_2,plain,
! [U_11184,U_11183,U_11182] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11182),c_Big__Operators_Olattice__class_OInf__fin(U_11182,U_11183)),c_Big__Operators_Olattice__class_OInf__fin(U_11182,U_11184)) = c_Big__Operators_Olattice__class_OInf__fin(U_11182,hAPP(c_Set_OCollect(U_11182),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool,U_11182),c_HOL_OEx(U_11182)),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_HOL_Obool),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool,U_11182),c_HOL_OEx(U_11182))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),tc_fun(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),U_11182),c_COMBS(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11182,tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBS(U_11182,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11182),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11182),c_fconj))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_fun(U_11182,U_11182)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool)),tc_fun(tc_fun(U_11182,tc_fun(U_11182,U_11182)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),U_11182),c_COMBB(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool),U_11182)),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_fun(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBB(U_11182,tc_HOL_Obool,U_11182)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_11182)))))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11182)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11182),c_fconj),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11182)),U_11183)))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11182)),U_11184)))))))
| U_11184 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11182),U_11184))
| U_11183 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11182),U_11183))
| ~ class_Lattices_Odistrib__lattice(U_11182) ),
inference(variable_rename,[status(thm)],[f_3026_1]) ).
fof(f_3026_3,plain,
! [U_11182,U_11183,U_11184] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11182),c_Big__Operators_Olattice__class_OInf__fin(U_11182,U_11183)),c_Big__Operators_Olattice__class_OInf__fin(U_11182,U_11184)) = c_Big__Operators_Olattice__class_OInf__fin(U_11182,hAPP(c_Set_OCollect(U_11182),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool,U_11182),c_HOL_OEx(U_11182)),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_HOL_Obool),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool,U_11182),c_HOL_OEx(U_11182))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),tc_fun(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),U_11182),c_COMBS(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11182,tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBS(U_11182,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11182),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11182),c_fconj))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_fun(U_11182,U_11182)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool)),tc_fun(tc_fun(U_11182,tc_fun(U_11182,U_11182)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),U_11182),c_COMBB(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool),U_11182)),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_fun(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBB(U_11182,tc_HOL_Obool,U_11182)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_11182)))))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11182)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11182),c_fconj),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11182)),U_11183)))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11182)),U_11184)))))))
| U_11184 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11182),U_11184))
| U_11183 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11182),U_11183))
| ~ class_Lattices_Odistrib__lattice(U_11182) ),
inference(definitional_conversion,[status(esa)],[f_3026_2]) ).
cnf(f_3026_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11182),c_Big__Operators_Olattice__class_OInf__fin(U_11182,U_11183)),c_Big__Operators_Olattice__class_OInf__fin(U_11182,U_11184)) = c_Big__Operators_Olattice__class_OInf__fin(U_11182,hAPP(c_Set_OCollect(U_11182),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool,U_11182),c_HOL_OEx(U_11182)),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_HOL_Obool),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool,U_11182),c_HOL_OEx(U_11182))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),tc_fun(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),U_11182),c_COMBS(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11182,tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool))),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBS(U_11182,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool)),tc_fun(U_11182,tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11182),hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11182),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11182),c_fconj))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_fun(U_11182,U_11182)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool)),tc_fun(tc_fun(U_11182,tc_fun(U_11182,U_11182)),tc_fun(U_11182,tc_fun(U_11182,tc_HOL_Obool))),U_11182),c_COMBB(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool),U_11182)),hAPP(hAPP(c_COMBB(tc_fun(U_11182,tc_HOL_Obool),tc_fun(tc_fun(U_11182,U_11182),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBB(U_11182,tc_HOL_Obool,U_11182)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_11182)))))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11182,tc_HOL_Obool),tc_fun(U_11182,tc_HOL_Obool)),U_11182),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11182)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11182),c_fconj),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11182)),U_11183)))),hAPP(hAPP(c_COMBC(U_11182,tc_fun(U_11182,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11182)),U_11184)))))))
| U_11184 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11182),U_11184))
| U_11183 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11182),U_11183))
| ~ class_Lattices_Odistrib__lattice(U_11182) ),
inference(clausify,[status(thm)],[f_3026_3]) ).
fof(f_3027_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib]) ).
fof(f_3027_2,plain,
! [U_11187,U_11186,U_11185] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11185),U_11187),c_Big__Operators_Olattice__class_OSup__fin(U_11185,U_11186)) = c_Big__Operators_Olattice__class_OSup__fin(U_11185,hAPP(c_Set_OCollect(U_11185),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_HOL_Obool,U_11185),c_HOL_OEx(U_11185)),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_HOL_Obool)),U_11185),c_COMBS(U_11185,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11185),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11185),c_fconj)),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,U_11185),tc_fun(U_11185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(tc_fun(U_11185,U_11185),tc_fun(U_11185,tc_HOL_Obool)),U_11185),c_COMBB(U_11185,tc_HOL_Obool,U_11185)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11185),U_11187))))),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11185)),U_11186)))))
| U_11186 = c_Orderings_Obot__class_Obot(tc_fun(U_11185,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11185),U_11186))
| ~ class_Lattices_Odistrib__lattice(U_11185) ),
inference(variable_rename,[status(thm)],[f_3027_1]) ).
fof(f_3027_3,plain,
! [U_11185,U_11187,U_11186] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11185),U_11187),c_Big__Operators_Olattice__class_OSup__fin(U_11185,U_11186)) = c_Big__Operators_Olattice__class_OSup__fin(U_11185,hAPP(c_Set_OCollect(U_11185),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_HOL_Obool,U_11185),c_HOL_OEx(U_11185)),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_HOL_Obool)),U_11185),c_COMBS(U_11185,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11185),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11185),c_fconj)),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,U_11185),tc_fun(U_11185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(tc_fun(U_11185,U_11185),tc_fun(U_11185,tc_HOL_Obool)),U_11185),c_COMBB(U_11185,tc_HOL_Obool,U_11185)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11185),U_11187))))),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11185)),U_11186)))))
| U_11186 = c_Orderings_Obot__class_Obot(tc_fun(U_11185,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11185),U_11186))
| ~ class_Lattices_Odistrib__lattice(U_11185) ),
inference(definitional_conversion,[status(esa)],[f_3027_2]) ).
cnf(f_3027_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11185),U_11187),c_Big__Operators_Olattice__class_OSup__fin(U_11185,U_11186)) = c_Big__Operators_Olattice__class_OSup__fin(U_11185,hAPP(c_Set_OCollect(U_11185),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_HOL_Obool,U_11185),c_HOL_OEx(U_11185)),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_HOL_Obool)),U_11185),c_COMBS(U_11185,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(U_11185,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11185),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11185),c_fconj)),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,U_11185),tc_fun(U_11185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(tc_fun(U_11185,U_11185),tc_fun(U_11185,tc_HOL_Obool)),U_11185),c_COMBB(U_11185,tc_HOL_Obool,U_11185)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11185),U_11187))))),hAPP(hAPP(c_COMBC(U_11185,tc_fun(U_11185,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11185)),U_11186)))))
| U_11186 = c_Orderings_Obot__class_Obot(tc_fun(U_11185,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11185),U_11186))
| ~ class_Lattices_Odistrib__lattice(U_11185) ),
inference(clausify,[status(thm)],[f_3027_3]) ).
fof(f_3028_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)))))))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib]) ).
fof(f_3028_2,plain,
! [U_11190,U_11189,U_11188] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),c_Big__Operators_Olattice__class_OSup__fin(U_11188,U_11189)),c_Big__Operators_Olattice__class_OSup__fin(U_11188,U_11190)) = c_Big__Operators_Olattice__class_OSup__fin(U_11188,hAPP(c_Set_OCollect(U_11188),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool,U_11188),c_HOL_OEx(U_11188)),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_HOL_Obool),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool,U_11188),c_HOL_OEx(U_11188))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),tc_fun(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),U_11188),c_COMBS(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11188,tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBS(U_11188,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11188),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11188),c_fconj))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_fun(U_11188,U_11188)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool)),tc_fun(tc_fun(U_11188,tc_fun(U_11188,U_11188)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),U_11188),c_COMBB(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool),U_11188)),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_fun(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBB(U_11188,tc_HOL_Obool,U_11188)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_11188)))))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11188)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11188),c_fconj),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11188)),U_11189)))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11188)),U_11190)))))))
| U_11190 = c_Orderings_Obot__class_Obot(tc_fun(U_11188,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11188),U_11190))
| U_11189 = c_Orderings_Obot__class_Obot(tc_fun(U_11188,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11188),U_11189))
| ~ class_Lattices_Odistrib__lattice(U_11188) ),
inference(variable_rename,[status(thm)],[f_3028_1]) ).
fof(f_3028_3,plain,
! [U_11188,U_11189,U_11190] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),c_Big__Operators_Olattice__class_OSup__fin(U_11188,U_11189)),c_Big__Operators_Olattice__class_OSup__fin(U_11188,U_11190)) = c_Big__Operators_Olattice__class_OSup__fin(U_11188,hAPP(c_Set_OCollect(U_11188),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool,U_11188),c_HOL_OEx(U_11188)),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_HOL_Obool),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool,U_11188),c_HOL_OEx(U_11188))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),tc_fun(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),U_11188),c_COMBS(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11188,tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBS(U_11188,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11188),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11188),c_fconj))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_fun(U_11188,U_11188)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool)),tc_fun(tc_fun(U_11188,tc_fun(U_11188,U_11188)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),U_11188),c_COMBB(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool),U_11188)),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_fun(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBB(U_11188,tc_HOL_Obool,U_11188)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_11188)))))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11188)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11188),c_fconj),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11188)),U_11189)))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11188)),U_11190)))))))
| U_11190 = c_Orderings_Obot__class_Obot(tc_fun(U_11188,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11188),U_11190))
| U_11189 = c_Orderings_Obot__class_Obot(tc_fun(U_11188,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11188),U_11189))
| ~ class_Lattices_Odistrib__lattice(U_11188) ),
inference(definitional_conversion,[status(esa)],[f_3028_2]) ).
cnf(f_3028_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),c_Big__Operators_Olattice__class_OSup__fin(U_11188,U_11189)),c_Big__Operators_Olattice__class_OSup__fin(U_11188,U_11190)) = c_Big__Operators_Olattice__class_OSup__fin(U_11188,hAPP(c_Set_OCollect(U_11188),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool,U_11188),c_HOL_OEx(U_11188)),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_HOL_Obool),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool,U_11188),c_HOL_OEx(U_11188))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),tc_fun(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),U_11188),c_COMBS(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11188,tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool))),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBS(U_11188,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool)),tc_fun(U_11188,tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11188),hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11188),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11188),c_fconj))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_fun(U_11188,U_11188)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool)),tc_fun(tc_fun(U_11188,tc_fun(U_11188,U_11188)),tc_fun(U_11188,tc_fun(U_11188,tc_HOL_Obool))),U_11188),c_COMBB(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool),U_11188)),hAPP(hAPP(c_COMBB(tc_fun(U_11188,tc_HOL_Obool),tc_fun(tc_fun(U_11188,U_11188),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBB(U_11188,tc_HOL_Obool,U_11188)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_11188)))))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11188,tc_HOL_Obool),tc_fun(U_11188,tc_HOL_Obool)),U_11188),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11188)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11188),c_fconj),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11188)),U_11189)))),hAPP(hAPP(c_COMBC(U_11188,tc_fun(U_11188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11188)),U_11190)))))))
| U_11190 = c_Orderings_Obot__class_Obot(tc_fun(U_11188,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11188),U_11190))
| U_11189 = c_Orderings_Obot__class_Obot(tc_fun(U_11188,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11188),U_11189))
| ~ class_Lattices_Odistrib__lattice(U_11188) ),
inference(clausify,[status(thm)],[f_3028_3]) ).
fof(f_3029_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( 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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__finite__psubset]) ).
fof(f_3029_2,plain,
! [U_11193,U_11192,U_11191] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11191,tc_HOL_Obool),tc_fun(U_11191,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11191,tc_HOL_Obool),tc_fun(U_11191,tc_HOL_Obool)),U_11192),U_11193)),c_Wellfounded_Ofinite__psubset(U_11191)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11191),U_11193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11191,tc_HOL_Obool)),U_11192),U_11193)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11191),U_11193))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11191,tc_HOL_Obool)),U_11192),U_11193)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11191,tc_HOL_Obool),tc_fun(U_11191,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11191,tc_HOL_Obool),tc_fun(U_11191,tc_HOL_Obool)),U_11192),U_11193)),c_Wellfounded_Ofinite__psubset(U_11191))) ) ),
inference(variable_rename,[status(thm)],[f_3029_1]) ).
fof(f_3029_3,plain,
( ! [U_11199,U_11197,U_11195] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11195,tc_HOL_Obool),tc_fun(U_11195,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11195,tc_HOL_Obool),tc_fun(U_11195,tc_HOL_Obool)),U_11197),U_11199)),c_Wellfounded_Ofinite__psubset(U_11195)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11195),U_11199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11195,tc_HOL_Obool)),U_11197),U_11199)) )
& ! [U_11198,U_11196,U_11194] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11194),U_11198))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11194,tc_HOL_Obool)),U_11196),U_11198)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11194,tc_HOL_Obool),tc_fun(U_11194,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11194,tc_HOL_Obool),tc_fun(U_11194,tc_HOL_Obool)),U_11196),U_11198)),c_Wellfounded_Ofinite__psubset(U_11194))) ) ),
inference(miniscope,[status(thm)],[f_3029_2]) ).
fof(f_3029_4,plain,
( ! [U_11194,U_11198,U_11196] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11194),U_11198))
| ~ sP863(U_11194,U_11198,U_11196) )
& ! [U_11194,U_11198,U_11196] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11194,tc_HOL_Obool)),U_11196),U_11198))
| ~ sP863(U_11194,U_11198,U_11196) )
& ! [U_11197,U_11199,U_11195] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11195,tc_HOL_Obool),tc_fun(U_11195,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11195,tc_HOL_Obool),tc_fun(U_11195,tc_HOL_Obool)),U_11197),U_11199)),c_Wellfounded_Ofinite__psubset(U_11195)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11195),U_11199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11195,tc_HOL_Obool)),U_11197),U_11199)) )
& ! [U_11194,U_11198,U_11196] :
( sP863(U_11194,U_11198,U_11196)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11194,tc_HOL_Obool),tc_fun(U_11194,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11194,tc_HOL_Obool),tc_fun(U_11194,tc_HOL_Obool)),U_11196),U_11198)),c_Wellfounded_Ofinite__psubset(U_11194))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP863])],[f_3029_3]) ).
cnf(f_3029_5,plain,
( sP863(U_11194,U_11198,U_11196)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11194,tc_HOL_Obool),tc_fun(U_11194,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11194,tc_HOL_Obool),tc_fun(U_11194,tc_HOL_Obool)),U_11196),U_11198)),c_Wellfounded_Ofinite__psubset(U_11194))) ),
inference(clausify,[status(thm)],[f_3029_4]) ).
cnf(f_3029_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11195,tc_HOL_Obool),tc_fun(U_11195,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11195,tc_HOL_Obool),tc_fun(U_11195,tc_HOL_Obool)),U_11197),U_11199)),c_Wellfounded_Ofinite__psubset(U_11195)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11195),U_11199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11195,tc_HOL_Obool)),U_11197),U_11199)) ),
inference(clausify,[status(thm)],[f_3029_4]) ).
cnf(f_3029_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11194,tc_HOL_Obool)),U_11196),U_11198))
| ~ sP863(U_11194,U_11198,U_11196) ),
inference(clausify,[status(thm)],[f_3029_4]) ).
cnf(f_3029_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11194),U_11198))
| ~ sP863(U_11194,U_11198,U_11196) ),
inference(clausify,[status(thm)],[f_3029_4]) ).
fof(f_3030_1,plain,
! [V_B_2,V_A_2,T_b] :
( 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)))))))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib]) ).
fof(f_3030_2,plain,
! [U_11202,U_11201,U_11200] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11200),c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),U_11201)),c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),U_11202)) = c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),hAPP(c_Set_OCollect(U_11200),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool,U_11200),c_HOL_OEx(U_11200)),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_HOL_Obool),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool,U_11200),c_HOL_OEx(U_11200))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),tc_fun(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),U_11200),c_COMBS(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11200,tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBS(U_11200,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11200),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11200),c_fconj))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_fun(U_11200,U_11200)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool)),tc_fun(tc_fun(U_11200,tc_fun(U_11200,U_11200)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),U_11200),c_COMBB(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool),U_11200)),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_fun(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBB(U_11200,tc_HOL_Obool,U_11200)),c_fequal))),c_Orderings_Oord__class_Omin(U_11200)))))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11200)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11200),c_fconj),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11200)),U_11201)))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11200)),U_11202)))))))
| U_11202 = c_Orderings_Obot__class_Obot(tc_fun(U_11200,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11200),U_11202))
| U_11201 = c_Orderings_Obot__class_Obot(tc_fun(U_11200,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11200),U_11201))
| ~ class_Orderings_Olinorder(U_11200) ),
inference(variable_rename,[status(thm)],[f_3030_1]) ).
fof(f_3030_3,plain,
! [U_11200,U_11201,U_11202] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11200),c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),U_11201)),c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),U_11202)) = c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),hAPP(c_Set_OCollect(U_11200),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool,U_11200),c_HOL_OEx(U_11200)),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_HOL_Obool),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool,U_11200),c_HOL_OEx(U_11200))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),tc_fun(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),U_11200),c_COMBS(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11200,tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBS(U_11200,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11200),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11200),c_fconj))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_fun(U_11200,U_11200)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool)),tc_fun(tc_fun(U_11200,tc_fun(U_11200,U_11200)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),U_11200),c_COMBB(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool),U_11200)),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_fun(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBB(U_11200,tc_HOL_Obool,U_11200)),c_fequal))),c_Orderings_Oord__class_Omin(U_11200)))))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11200)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11200),c_fconj),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11200)),U_11201)))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11200)),U_11202)))))))
| U_11202 = c_Orderings_Obot__class_Obot(tc_fun(U_11200,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11200),U_11202))
| U_11201 = c_Orderings_Obot__class_Obot(tc_fun(U_11200,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11200),U_11201))
| ~ class_Orderings_Olinorder(U_11200) ),
inference(definitional_conversion,[status(esa)],[f_3030_2]) ).
cnf(f_3030_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11200),c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),U_11201)),c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),U_11202)) = c_Big__Operators_Olattice_OSup__fin(U_11200,c_Orderings_Oord__class_Omax(U_11200),hAPP(c_Set_OCollect(U_11200),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool,U_11200),c_HOL_OEx(U_11200)),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_HOL_Obool),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool,U_11200),c_HOL_OEx(U_11200))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),tc_fun(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),U_11200),c_COMBS(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11200,tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool))),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBS(U_11200,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool)),tc_fun(U_11200,tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11200),hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11200),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11200),c_fconj))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_fun(U_11200,U_11200)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool)),tc_fun(tc_fun(U_11200,tc_fun(U_11200,U_11200)),tc_fun(U_11200,tc_fun(U_11200,tc_HOL_Obool))),U_11200),c_COMBB(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool),U_11200)),hAPP(hAPP(c_COMBB(tc_fun(U_11200,tc_HOL_Obool),tc_fun(tc_fun(U_11200,U_11200),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBB(U_11200,tc_HOL_Obool,U_11200)),c_fequal))),c_Orderings_Oord__class_Omin(U_11200)))))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11200,tc_HOL_Obool),tc_fun(U_11200,tc_HOL_Obool)),U_11200),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11200)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11200),c_fconj),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11200)),U_11201)))),hAPP(hAPP(c_COMBC(U_11200,tc_fun(U_11200,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11200)),U_11202)))))))
| U_11202 = c_Orderings_Obot__class_Obot(tc_fun(U_11200,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11200),U_11202))
| U_11201 = c_Orderings_Obot__class_Obot(tc_fun(U_11200,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11200),U_11201))
| ~ class_Orderings_Olinorder(U_11200) ),
inference(clausify,[status(thm)],[f_3030_3]) ).
fof(f_3031_1,plain,
! [V_x_2,V_A_2,T_b] :
( 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)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib]) ).
fof(f_3031_2,plain,
! [U_11205,U_11204,U_11203] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11203),U_11205),c_Big__Operators_Olattice_OSup__fin(U_11203,c_Orderings_Oord__class_Omax(U_11203),U_11204)) = c_Big__Operators_Olattice_OSup__fin(U_11203,c_Orderings_Oord__class_Omax(U_11203),hAPP(c_Set_OCollect(U_11203),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_HOL_Obool,U_11203),c_HOL_OEx(U_11203)),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_HOL_Obool)),U_11203),c_COMBS(U_11203,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11203),c_fconj)),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,U_11203),tc_fun(U_11203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_fun(tc_fun(U_11203,U_11203),tc_fun(U_11203,tc_HOL_Obool)),U_11203),c_COMBB(U_11203,tc_HOL_Obool,U_11203)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_11203),U_11205))))),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11203)),U_11204)))))
| U_11204 = c_Orderings_Obot__class_Obot(tc_fun(U_11203,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11203),U_11204))
| ~ class_Orderings_Olinorder(U_11203) ),
inference(variable_rename,[status(thm)],[f_3031_1]) ).
fof(f_3031_3,plain,
! [U_11203,U_11204,U_11205] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11203),U_11205),c_Big__Operators_Olattice_OSup__fin(U_11203,c_Orderings_Oord__class_Omax(U_11203),U_11204)) = c_Big__Operators_Olattice_OSup__fin(U_11203,c_Orderings_Oord__class_Omax(U_11203),hAPP(c_Set_OCollect(U_11203),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_HOL_Obool,U_11203),c_HOL_OEx(U_11203)),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_HOL_Obool)),U_11203),c_COMBS(U_11203,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11203),c_fconj)),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,U_11203),tc_fun(U_11203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_fun(tc_fun(U_11203,U_11203),tc_fun(U_11203,tc_HOL_Obool)),U_11203),c_COMBB(U_11203,tc_HOL_Obool,U_11203)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_11203),U_11205))))),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11203)),U_11204)))))
| U_11204 = c_Orderings_Obot__class_Obot(tc_fun(U_11203,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11203),U_11204))
| ~ class_Orderings_Olinorder(U_11203) ),
inference(definitional_conversion,[status(esa)],[f_3031_2]) ).
cnf(f_3031_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11203),U_11205),c_Big__Operators_Olattice_OSup__fin(U_11203,c_Orderings_Oord__class_Omax(U_11203),U_11204)) = c_Big__Operators_Olattice_OSup__fin(U_11203,c_Orderings_Oord__class_Omax(U_11203),hAPP(c_Set_OCollect(U_11203),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_HOL_Obool,U_11203),c_HOL_OEx(U_11203)),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_HOL_Obool)),U_11203),c_COMBS(U_11203,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_fun(U_11203,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11203),c_fconj)),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,U_11203),tc_fun(U_11203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11203,tc_HOL_Obool),tc_fun(tc_fun(U_11203,U_11203),tc_fun(U_11203,tc_HOL_Obool)),U_11203),c_COMBB(U_11203,tc_HOL_Obool,U_11203)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_11203),U_11205))))),hAPP(hAPP(c_COMBC(U_11203,tc_fun(U_11203,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11203)),U_11204)))))
| U_11204 = c_Orderings_Obot__class_Obot(tc_fun(U_11203,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11203),U_11204))
| ~ class_Orderings_Olinorder(U_11203) ),
inference(clausify,[status(thm)],[f_3031_3]) ).
fof(f_3032_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_nat_Osize_I4_J]) ).
fof(f_3032_2,plain,
! [U_11206] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11206)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_3032_1]) ).
fof(f_3032_3,plain,
! [U_11206] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11206)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_3032_2]) ).
cnf(f_3032_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11206)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_3032_3]) ).
fof(f_3033_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_prod_Orecs]) ).
fof(f_3033_2,plain,
! [U_11212,U_11211,U_11210,U_11209,U_11208,U_11207] : c_Product__Type_Oprod_Oprod__rec(U_11207,U_11208,U_11209,U_11210,hAPP(hAPP(c_Product__Type_OPair(U_11207,U_11208),U_11211),U_11212)) = hAPP(hAPP(U_11210,U_11211),U_11212),
inference(variable_rename,[status(thm)],[f_3033_1]) ).
fof(f_3033_3,plain,
! [U_11208,U_11207,U_11209,U_11210,U_11211,U_11212] : c_Product__Type_Oprod_Oprod__rec(U_11207,U_11208,U_11209,U_11210,hAPP(hAPP(c_Product__Type_OPair(U_11207,U_11208),U_11211),U_11212)) = hAPP(hAPP(U_11210,U_11211),U_11212),
inference(definitional_conversion,[status(esa)],[f_3033_2]) ).
cnf(f_3033_4,plain,
c_Product__Type_Oprod_Oprod__rec(U_11207,U_11208,U_11209,U_11210,hAPP(hAPP(c_Product__Type_OPair(U_11207,U_11208),U_11211),U_11212)) = hAPP(hAPP(U_11210,U_11211),U_11212),
inference(clausify,[status(thm)],[f_3033_3]) ).
fof(f_3034_1,plain,
! [V_B_2,V_k_2,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))),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)
| ? [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) ),
inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq]) ).
fof(f_3034_2,plain,
! [U_11217,U_11216,U_11215,U_11214] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11215) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11217)
| ? [U_11213] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11213)),U_11215) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,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),U_11213),U_11216))),U_11217) ),
inference(variable_rename,[status(thm)],[f_3034_1]) ).
fof(f_3034_3,plain,
! [U_11217,U_11216,U_11215,U_11214] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11215) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11217)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK280(U_11217,U_11216,U_11215,U_11214))),U_11215) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,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),sK280(U_11217,U_11216,U_11215,U_11214)),U_11216))),U_11217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_11213,sK280(U_11217,U_11216,U_11215,U_11214))],[f_3034_2]) ).
fof(f_3034_4,plain,
! [U_11214,U_11215,U_11216,U_11217] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11215) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11217)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK280(U_11217,U_11216,U_11215,U_11214))),U_11215) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,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),sK280(U_11217,U_11216,U_11215,U_11214)),U_11216))),U_11217) ),
inference(definitional_conversion,[status(esa)],[f_3034_3]) ).
cnf(f_3034_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11215) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11217)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK280(U_11217,U_11216,U_11215,U_11214))),U_11215) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11214,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),sK280(U_11217,U_11216,U_11215,U_11214)),U_11216))),U_11217) ),
inference(clausify,[status(thm)],[f_3034_4]) ).
fof(f_3035_1,plain,
! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_nat__size]) ).
fof(f_3035_2,plain,
! [U_11218] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11218) = U_11218,
inference(variable_rename,[status(thm)],[f_3035_1]) ).
fof(f_3035_3,plain,
! [U_11218] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11218) = U_11218,
inference(definitional_conversion,[status(esa)],[f_3035_2]) ).
cnf(f_3035_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11218) = U_11218,
inference(clausify,[status(thm)],[f_3035_3]) ).
fof(f_3036_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_nat_Osize_I3_J]) ).
fof(f_3036_2,plain,
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),
inference(definitional_conversion,[status(esa)],[f_3036_1]) ).
cnf(f_3036_3,plain,
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),
inference(clausify,[status(thm)],[f_3036_2]) ).
fof(f_3037_1,plain,
! [V_C_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_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))
| ? [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)) ),
inference(fof_nnf,[status(thm)],[fact_UN__finite__subset]) ).
fof(f_3037_2,plain,
! [U_11222,U_11221,U_11220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11220,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11221)),U_11222))
| ? [U_11219] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11220,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11219)),U_11221)),U_11222)) ),
inference(variable_rename,[status(thm)],[f_3037_1]) ).
fof(f_3037_3,plain,
! [U_11222,U_11221,U_11220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11220,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11221)),U_11222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11220,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK281(U_11222,U_11221,U_11220))),U_11221)),U_11222)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_11219,sK281(U_11222,U_11221,U_11220))],[f_3037_2]) ).
fof(f_3037_4,plain,
! [U_11220,U_11221,U_11222] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11220,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11221)),U_11222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11220,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK281(U_11222,U_11221,U_11220))),U_11221)),U_11222)) ),
inference(definitional_conversion,[status(esa)],[f_3037_3]) ).
cnf(f_3037_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11220,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11221)),U_11222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11220,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK281(U_11222,U_11221,U_11220))),U_11221)),U_11222)) ),
inference(clausify,[status(thm)],[f_3037_4]) ).
fof(f_3038_1,plain,
! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
( 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)
| ? [B_x] :
( 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)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__multicount__gen]) ).
fof(f_3038_2,plain,
! [U_11229,U_11228,U_11227,U_11226,U_11225,U_11224] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11224,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_Nat_Onat,U_11224),c_Finite__Set_Ocard(U_11226)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool),U_11224),c_Set_OCollect(U_11226)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool),U_11224),hAPP(c_COMBS(U_11226,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11226),c_fconj),hAPP(hAPP(c_COMBC(U_11226,tc_fun(U_11226,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11226)),U_11227)))),U_11228)))),U_11225) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11226,tc_Nat_Onat),U_11229),U_11227)
| ? [U_11223] :
( hAPP(c_Finite__Set_Ocard(U_11224),hAPP(c_Set_OCollect(U_11224),hAPP(hAPP(c_COMBS(U_11224,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11224),c_fconj),hAPP(hAPP(c_COMBC(U_11224,tc_fun(U_11224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11224)),U_11225))),hAPP(hAPP(c_COMBC(U_11224,U_11226,tc_HOL_Obool),U_11228),U_11223)))) != hAPP(U_11229,U_11223)
& hBOOL(hAPP(hAPP(c_member(U_11226),U_11223),U_11227)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11226),U_11227))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11224),U_11225)) ),
inference(variable_rename,[status(thm)],[f_3038_1]) ).
fof(f_3038_3,plain,
! [U_11229,U_11228,U_11227,U_11226,U_11225,U_11224] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11224,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_Nat_Onat,U_11224),c_Finite__Set_Ocard(U_11226)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool),U_11224),c_Set_OCollect(U_11226)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool),U_11224),hAPP(c_COMBS(U_11226,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11226),c_fconj),hAPP(hAPP(c_COMBC(U_11226,tc_fun(U_11226,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11226)),U_11227)))),U_11228)))),U_11225) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11226,tc_Nat_Onat),U_11229),U_11227)
| ( hAPP(c_Finite__Set_Ocard(U_11224),hAPP(c_Set_OCollect(U_11224),hAPP(hAPP(c_COMBS(U_11224,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11224),c_fconj),hAPP(hAPP(c_COMBC(U_11224,tc_fun(U_11224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11224)),U_11225))),hAPP(hAPP(c_COMBC(U_11224,U_11226,tc_HOL_Obool),U_11228),sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224))))) != hAPP(U_11229,sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224))
& hBOOL(hAPP(hAPP(c_member(U_11226),sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224)),U_11227)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11226),U_11227))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11224),U_11225)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_11223,sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224))],[f_3038_2]) ).
fof(f_3038_4,plain,
( ! [U_11224,U_11225,U_11226,U_11227,U_11228,U_11229] :
( hAPP(c_Finite__Set_Ocard(U_11224),hAPP(c_Set_OCollect(U_11224),hAPP(hAPP(c_COMBS(U_11224,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11224),c_fconj),hAPP(hAPP(c_COMBC(U_11224,tc_fun(U_11224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11224)),U_11225))),hAPP(hAPP(c_COMBC(U_11224,U_11226,tc_HOL_Obool),U_11228),sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224))))) != hAPP(U_11229,sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224))
| ~ sP864(U_11224,U_11225,U_11226,U_11227,U_11228,U_11229) )
& ! [U_11224,U_11225,U_11226,U_11227,U_11228,U_11229] :
( hBOOL(hAPP(hAPP(c_member(U_11226),sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224)),U_11227))
| ~ sP864(U_11224,U_11225,U_11226,U_11227,U_11228,U_11229) )
& ! [U_11224,U_11225,U_11226,U_11227,U_11228,U_11229] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11224,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_Nat_Onat,U_11224),c_Finite__Set_Ocard(U_11226)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool),U_11224),c_Set_OCollect(U_11226)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool),U_11224),hAPP(c_COMBS(U_11226,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11226),c_fconj),hAPP(hAPP(c_COMBC(U_11226,tc_fun(U_11226,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11226)),U_11227)))),U_11228)))),U_11225) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11226,tc_Nat_Onat),U_11229),U_11227)
| sP864(U_11224,U_11225,U_11226,U_11227,U_11228,U_11229)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11226),U_11227))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11224),U_11225)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP864])],[f_3038_3]) ).
cnf(f_3038_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11224,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_Nat_Onat,U_11224),c_Finite__Set_Ocard(U_11226)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool),U_11224),c_Set_OCollect(U_11226)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool),U_11224),hAPP(c_COMBS(U_11226,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11226),c_fconj),hAPP(hAPP(c_COMBC(U_11226,tc_fun(U_11226,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11226)),U_11227)))),U_11228)))),U_11225) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11226,tc_Nat_Onat),U_11229),U_11227)
| sP864(U_11224,U_11225,U_11226,U_11227,U_11228,U_11229)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11226),U_11227))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11224),U_11225)) ),
inference(clausify,[status(thm)],[f_3038_4]) ).
cnf(f_3038_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11226),sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224)),U_11227))
| ~ sP864(U_11224,U_11225,U_11226,U_11227,U_11228,U_11229) ),
inference(clausify,[status(thm)],[f_3038_4]) ).
cnf(f_3038_7,plain,
( hAPP(c_Finite__Set_Ocard(U_11224),hAPP(c_Set_OCollect(U_11224),hAPP(hAPP(c_COMBS(U_11224,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11224),c_fconj),hAPP(hAPP(c_COMBC(U_11224,tc_fun(U_11224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11224)),U_11225))),hAPP(hAPP(c_COMBC(U_11224,U_11226,tc_HOL_Obool),U_11228),sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224))))) != hAPP(U_11229,sK282(U_11229,U_11228,U_11227,U_11226,U_11225,U_11224))
| ~ sP864(U_11224,U_11225,U_11226,U_11227,U_11228,U_11229) ),
inference(clausify,[status(thm)],[f_3038_4]) ).
fof(f_3039_1,plain,
! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( ( 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)))
| ( ( ~ 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))
| V_a_2 != V_a_H_2 )
& ~ 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)) ) )
& ( ( 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))
& V_a_2 = V_a_H_2 )
| 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))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__lex__prod]) ).
fof(f_3039_2,plain,
! [U_11237,U_11236,U_11235,U_11234,U_11233,U_11232,U_11231,U_11230] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11230,U_11231),tc_prod(U_11230,U_11231))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11230,U_11231),tc_prod(U_11230,U_11231)),hAPP(hAPP(c_Product__Type_OPair(U_11230,U_11231),U_11232),U_11233)),hAPP(hAPP(c_Product__Type_OPair(U_11230,U_11231),U_11234),U_11235))),c_Wellfounded_Olex__prod(U_11230,U_11231,U_11236,U_11237)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11231,U_11231)),hAPP(hAPP(c_Product__Type_OPair(U_11231,U_11231),U_11233),U_11235)),U_11237))
| U_11232 != U_11234 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11230,U_11230)),hAPP(hAPP(c_Product__Type_OPair(U_11230,U_11230),U_11232),U_11234)),U_11236)) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11231,U_11231)),hAPP(hAPP(c_Product__Type_OPair(U_11231,U_11231),U_11233),U_11235)),U_11237))
& U_11232 = U_11234 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11230,U_11230)),hAPP(hAPP(c_Product__Type_OPair(U_11230,U_11230),U_11232),U_11234)),U_11236))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11230,U_11231),tc_prod(U_11230,U_11231))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11230,U_11231),tc_prod(U_11230,U_11231)),hAPP(hAPP(c_Product__Type_OPair(U_11230,U_11231),U_11232),U_11233)),hAPP(hAPP(c_Product__Type_OPair(U_11230,U_11231),U_11234),U_11235))),c_Wellfounded_Olex__prod(U_11230,U_11231,U_11236,U_11237))) ) ),
inference(variable_rename,[status(thm)],[f_3039_1]) ).
fof(f_3039_3,plain,
( ! [U_11253,U_11251,U_11249,U_11247,U_11245,U_11243,U_11241,U_11239] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11239,U_11241),tc_prod(U_11239,U_11241))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11239,U_11241),tc_prod(U_11239,U_11241)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11241),U_11243),U_11245)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11241),U_11247),U_11249))),c_Wellfounded_Olex__prod(U_11239,U_11241,U_11251,U_11253)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11241,U_11241)),hAPP(hAPP(c_Product__Type_OPair(U_11241,U_11241),U_11245),U_11249)),U_11253))
| U_11243 != U_11247 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11239,U_11239)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11239),U_11243),U_11247)),U_11251)) ) )
& ! [U_11252,U_11250,U_11248,U_11246,U_11244,U_11242,U_11240,U_11238] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11240,U_11240)),hAPP(hAPP(c_Product__Type_OPair(U_11240,U_11240),U_11244),U_11248)),U_11252))
& U_11242 = U_11246 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11238,U_11238)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11238),U_11242),U_11246)),U_11250))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11238,U_11240),tc_prod(U_11238,U_11240))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11238,U_11240),tc_prod(U_11238,U_11240)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11240),U_11242),U_11244)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11240),U_11246),U_11248))),c_Wellfounded_Olex__prod(U_11238,U_11240,U_11250,U_11252))) ) ),
inference(miniscope,[status(thm)],[f_3039_2]) ).
fof(f_3039_4,plain,
( ! [U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11241,U_11241)),hAPP(hAPP(c_Product__Type_OPair(U_11241,U_11241),U_11245),U_11249)),U_11253))
| U_11243 != U_11247
| ~ sP866(U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253) )
& ! [U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11239,U_11239)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11239),U_11243),U_11247)),U_11251))
| ~ sP866(U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253) )
& ! [U_11240,U_11242,U_11244,U_11246,U_11248,U_11252] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11240,U_11240)),hAPP(hAPP(c_Product__Type_OPair(U_11240,U_11240),U_11244),U_11248)),U_11252))
| ~ sP865(U_11240,U_11242,U_11244,U_11246,U_11248,U_11252) )
& ! [U_11240,U_11242,U_11244,U_11246,U_11248,U_11252] :
( U_11242 = U_11246
| ~ sP865(U_11240,U_11242,U_11244,U_11246,U_11248,U_11252) )
& ! [U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11239,U_11241),tc_prod(U_11239,U_11241))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11239,U_11241),tc_prod(U_11239,U_11241)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11241),U_11243),U_11245)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11241),U_11247),U_11249))),c_Wellfounded_Olex__prod(U_11239,U_11241,U_11251,U_11253)))
| sP866(U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253) )
& ! [U_11238,U_11240,U_11242,U_11244,U_11246,U_11248,U_11252,U_11250] :
( sP865(U_11240,U_11242,U_11244,U_11246,U_11248,U_11252)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11238,U_11238)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11238),U_11242),U_11246)),U_11250))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11238,U_11240),tc_prod(U_11238,U_11240))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11238,U_11240),tc_prod(U_11238,U_11240)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11240),U_11242),U_11244)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11240),U_11246),U_11248))),c_Wellfounded_Olex__prod(U_11238,U_11240,U_11250,U_11252))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP865,sP866])],[f_3039_3]) ).
cnf(f_3039_5,plain,
( sP865(U_11240,U_11242,U_11244,U_11246,U_11248,U_11252)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11238,U_11238)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11238),U_11242),U_11246)),U_11250))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11238,U_11240),tc_prod(U_11238,U_11240))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11238,U_11240),tc_prod(U_11238,U_11240)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11240),U_11242),U_11244)),hAPP(hAPP(c_Product__Type_OPair(U_11238,U_11240),U_11246),U_11248))),c_Wellfounded_Olex__prod(U_11238,U_11240,U_11250,U_11252))) ),
inference(clausify,[status(thm)],[f_3039_4]) ).
cnf(f_3039_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11239,U_11241),tc_prod(U_11239,U_11241))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11239,U_11241),tc_prod(U_11239,U_11241)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11241),U_11243),U_11245)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11241),U_11247),U_11249))),c_Wellfounded_Olex__prod(U_11239,U_11241,U_11251,U_11253)))
| sP866(U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253) ),
inference(clausify,[status(thm)],[f_3039_4]) ).
cnf(f_3039_7,plain,
( U_11242 = U_11246
| ~ sP865(U_11240,U_11242,U_11244,U_11246,U_11248,U_11252) ),
inference(clausify,[status(thm)],[f_3039_4]) ).
cnf(f_3039_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11240,U_11240)),hAPP(hAPP(c_Product__Type_OPair(U_11240,U_11240),U_11244),U_11248)),U_11252))
| ~ sP865(U_11240,U_11242,U_11244,U_11246,U_11248,U_11252) ),
inference(clausify,[status(thm)],[f_3039_4]) ).
cnf(f_3039_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11239,U_11239)),hAPP(hAPP(c_Product__Type_OPair(U_11239,U_11239),U_11243),U_11247)),U_11251))
| ~ sP866(U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253) ),
inference(clausify,[status(thm)],[f_3039_4]) ).
cnf(f_3039_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11241,U_11241)),hAPP(hAPP(c_Product__Type_OPair(U_11241,U_11241),U_11245),U_11249)),U_11253))
| U_11243 != U_11247
| ~ sP866(U_11239,U_11241,U_11243,U_11245,U_11247,U_11249,U_11251,U_11253) ),
inference(clausify,[status(thm)],[f_3039_4]) ).
fof(f_3040_1,plain,
! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
( 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)))
| ~ 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)))
| ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).
fof(f_3040_2,plain,
! [U_11260,U_11259,U_11258,U_11257,U_11256,U_11255,U_11254] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11260,U_11256),tc_prod(U_11260,U_11256))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11260,U_11256),tc_prod(U_11260,U_11256)),hAPP(hAPP(c_Product__Type_OPair(U_11260,U_11256),U_11255),U_11257)),hAPP(hAPP(c_Product__Type_OPair(U_11260,U_11256),U_11255),U_11258))),c_Recdef_Osame__fst(U_11260,U_11256,U_11254,U_11259)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11256,U_11256)),hAPP(hAPP(c_Product__Type_OPair(U_11256,U_11256),U_11257),U_11258)),hAPP(U_11259,U_11255)))
| ~ hBOOL(hAPP(U_11254,U_11255)) ),
inference(variable_rename,[status(thm)],[f_3040_1]) ).
fof(f_3040_3,plain,
! [U_11256,U_11254,U_11255,U_11257,U_11258,U_11259,U_11260] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11260,U_11256),tc_prod(U_11260,U_11256))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11260,U_11256),tc_prod(U_11260,U_11256)),hAPP(hAPP(c_Product__Type_OPair(U_11260,U_11256),U_11255),U_11257)),hAPP(hAPP(c_Product__Type_OPair(U_11260,U_11256),U_11255),U_11258))),c_Recdef_Osame__fst(U_11260,U_11256,U_11254,U_11259)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11256,U_11256)),hAPP(hAPP(c_Product__Type_OPair(U_11256,U_11256),U_11257),U_11258)),hAPP(U_11259,U_11255)))
| ~ hBOOL(hAPP(U_11254,U_11255)) ),
inference(definitional_conversion,[status(esa)],[f_3040_2]) ).
cnf(f_3040_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11260,U_11256),tc_prod(U_11260,U_11256))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11260,U_11256),tc_prod(U_11260,U_11256)),hAPP(hAPP(c_Product__Type_OPair(U_11260,U_11256),U_11255),U_11257)),hAPP(hAPP(c_Product__Type_OPair(U_11260,U_11256),U_11255),U_11258))),c_Recdef_Osame__fst(U_11260,U_11256,U_11254,U_11259)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11256,U_11256)),hAPP(hAPP(c_Product__Type_OPair(U_11256,U_11256),U_11257),U_11258)),hAPP(U_11259,U_11255)))
| ~ hBOOL(hAPP(U_11254,U_11255)) ),
inference(clausify,[status(thm)],[f_3040_3]) ).
fof(f_3041_1,plain,
! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
( hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
| 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)
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__0]) ).
fof(f_3041_2,plain,
! [U_11266,U_11265,U_11264,U_11263,U_11262] :
( hAPP(U_11265,U_11266) = c_Groups_Ozero__class_Ozero(U_11262)
| ~ hBOOL(hAPP(hAPP(c_member(U_11263),U_11266),U_11264))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11263,U_11262),U_11265),U_11264) != c_Groups_Ozero__class_Ozero(U_11262)
| ? [U_11261] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11262),c_Groups_Ozero__class_Ozero(U_11262)),hAPP(U_11265,U_11261)))
& hBOOL(hAPP(hAPP(c_member(U_11263),U_11261),U_11264)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11263),U_11264))
| ~ class_Groups_Oordered__ab__group__add(U_11262) ),
inference(variable_rename,[status(thm)],[f_3041_1]) ).
fof(f_3041_3,plain,
! [U_11266,U_11265,U_11264,U_11263,U_11262] :
( hAPP(U_11265,U_11266) = c_Groups_Ozero__class_Ozero(U_11262)
| ~ hBOOL(hAPP(hAPP(c_member(U_11263),U_11266),U_11264))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11263,U_11262),U_11265),U_11264) != c_Groups_Ozero__class_Ozero(U_11262)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11262),c_Groups_Ozero__class_Ozero(U_11262)),hAPP(U_11265,sK283(U_11266,U_11265,U_11264,U_11263,U_11262))))
& hBOOL(hAPP(hAPP(c_member(U_11263),sK283(U_11266,U_11265,U_11264,U_11263,U_11262)),U_11264)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11263),U_11264))
| ~ class_Groups_Oordered__ab__group__add(U_11262) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_11261,sK283(U_11266,U_11265,U_11264,U_11263,U_11262))],[f_3041_2]) ).
fof(f_3041_4,plain,
( ! [U_11262,U_11263,U_11264,U_11265,U_11266] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11262),c_Groups_Ozero__class_Ozero(U_11262)),hAPP(U_11265,sK283(U_11266,U_11265,U_11264,U_11263,U_11262))))
| ~ sP867(U_11262,U_11263,U_11264,U_11265,U_11266) )
& ! [U_11262,U_11263,U_11264,U_11265,U_11266] :
( hBOOL(hAPP(hAPP(c_member(U_11263),sK283(U_11266,U_11265,U_11264,U_11263,U_11262)),U_11264))
| ~ sP867(U_11262,U_11263,U_11264,U_11265,U_11266) )
& ! [U_11262,U_11263,U_11264,U_11265,U_11266] :
( hAPP(U_11265,U_11266) = c_Groups_Ozero__class_Ozero(U_11262)
| ~ hBOOL(hAPP(hAPP(c_member(U_11263),U_11266),U_11264))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11263,U_11262),U_11265),U_11264) != c_Groups_Ozero__class_Ozero(U_11262)
| sP867(U_11262,U_11263,U_11264,U_11265,U_11266)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11263),U_11264))
| ~ class_Groups_Oordered__ab__group__add(U_11262) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP867])],[f_3041_3]) ).
cnf(f_3041_5,plain,
( hAPP(U_11265,U_11266) = c_Groups_Ozero__class_Ozero(U_11262)
| ~ hBOOL(hAPP(hAPP(c_member(U_11263),U_11266),U_11264))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11263,U_11262),U_11265),U_11264) != c_Groups_Ozero__class_Ozero(U_11262)
| sP867(U_11262,U_11263,U_11264,U_11265,U_11266)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11263),U_11264))
| ~ class_Groups_Oordered__ab__group__add(U_11262) ),
inference(clausify,[status(thm)],[f_3041_4]) ).
cnf(f_3041_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11263),sK283(U_11266,U_11265,U_11264,U_11263,U_11262)),U_11264))
| ~ sP867(U_11262,U_11263,U_11264,U_11265,U_11266) ),
inference(clausify,[status(thm)],[f_3041_4]) ).
cnf(f_3041_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11262),c_Groups_Ozero__class_Ozero(U_11262)),hAPP(U_11265,sK283(U_11266,U_11265,U_11264,U_11263,U_11262))))
| ~ sP867(U_11262,U_11263,U_11264,U_11265,U_11266) ),
inference(clausify,[status(thm)],[f_3041_4]) ).
fof(f_3042_1,plain,
! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) != V_B_2
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__leq__bound]) ).
fof(f_3042_2,plain,
! [U_11273,U_11272,U_11271,U_11270,U_11269,U_11268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11268),hAPP(U_11271,U_11273)),U_11272))
| ~ hBOOL(hAPP(hAPP(c_member(U_11269),U_11273),U_11270))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11269,U_11268),U_11271),U_11270) != U_11272
| ? [U_11267] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11268),c_Groups_Ozero__class_Ozero(U_11268)),hAPP(U_11271,U_11267)))
& hBOOL(hAPP(hAPP(c_member(U_11269),U_11267),U_11270)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11269),U_11270))
| ~ class_Groups_Oordered__ab__group__add(U_11268) ),
inference(variable_rename,[status(thm)],[f_3042_1]) ).
fof(f_3042_3,plain,
! [U_11273,U_11272,U_11271,U_11270,U_11269,U_11268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11268),hAPP(U_11271,U_11273)),U_11272))
| ~ hBOOL(hAPP(hAPP(c_member(U_11269),U_11273),U_11270))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11269,U_11268),U_11271),U_11270) != U_11272
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11268),c_Groups_Ozero__class_Ozero(U_11268)),hAPP(U_11271,sK284(U_11273,U_11272,U_11271,U_11270,U_11269,U_11268))))
& hBOOL(hAPP(hAPP(c_member(U_11269),sK284(U_11273,U_11272,U_11271,U_11270,U_11269,U_11268)),U_11270)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11269),U_11270))
| ~ class_Groups_Oordered__ab__group__add(U_11268) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_11267,sK284(U_11273,U_11272,U_11271,U_11270,U_11269,U_11268))],[f_3042_2]) ).
fof(f_3042_4,plain,
( ! [U_11269,U_11270,U_11268,U_11271,U_11272,U_11273] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11268),c_Groups_Ozero__class_Ozero(U_11268)),hAPP(U_11271,sK284(U_11273,U_11272,U_11271,U_11270,U_11269,U_11268))))
| ~ sP868(U_11269,U_11270,U_11268,U_11271,U_11272,U_11273) )
& ! [U_11269,U_11270,U_11268,U_11271,U_11272,U_11273] :
( hBOOL(hAPP(hAPP(c_member(U_11269),sK284(U_11273,U_11272,U_11271,U_11270,U_11269,U_11268)),U_11270))
| ~ sP868(U_11269,U_11270,U_11268,U_11271,U_11272,U_11273) )
& ! [U_11269,U_11270,U_11268,U_11271,U_11272,U_11273] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11268),hAPP(U_11271,U_11273)),U_11272))
| ~ hBOOL(hAPP(hAPP(c_member(U_11269),U_11273),U_11270))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11269,U_11268),U_11271),U_11270) != U_11272
| sP868(U_11269,U_11270,U_11268,U_11271,U_11272,U_11273)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11269),U_11270))
| ~ class_Groups_Oordered__ab__group__add(U_11268) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP868])],[f_3042_3]) ).
cnf(f_3042_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11268),hAPP(U_11271,U_11273)),U_11272))
| ~ hBOOL(hAPP(hAPP(c_member(U_11269),U_11273),U_11270))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11269,U_11268),U_11271),U_11270) != U_11272
| sP868(U_11269,U_11270,U_11268,U_11271,U_11272,U_11273)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11269),U_11270))
| ~ class_Groups_Oordered__ab__group__add(U_11268) ),
inference(clausify,[status(thm)],[f_3042_4]) ).
cnf(f_3042_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11269),sK284(U_11273,U_11272,U_11271,U_11270,U_11269,U_11268)),U_11270))
| ~ sP868(U_11269,U_11270,U_11268,U_11271,U_11272,U_11273) ),
inference(clausify,[status(thm)],[f_3042_4]) ).
cnf(f_3042_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11268),c_Groups_Ozero__class_Ozero(U_11268)),hAPP(U_11271,sK284(U_11273,U_11272,U_11271,U_11270,U_11269,U_11268))))
| ~ sP868(U_11269,U_11270,U_11268,U_11271,U_11272,U_11273) ),
inference(clausify,[status(thm)],[f_3042_4]) ).
fof(f_3043_1,plain,
! [V_n_2,V_Pa_2,V_Qa_2] :
( 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))
| ? [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))) ),
inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib]) ).
fof(f_3043_2,plain,
! [U_11277,U_11276,U_11275] :
( 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),U_11276),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11275),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))) = 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)),U_11276)),U_11275)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))
| ? [U_11274] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11275,U_11274)),hAPP(U_11276,U_11274))) ),
inference(variable_rename,[status(thm)],[f_3043_1]) ).
fof(f_3043_3,plain,
! [U_11277,U_11276,U_11275] :
( 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),U_11276),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11275),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))) = 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)),U_11276)),U_11275)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11275,sK285(U_11277,U_11276,U_11275))),hAPP(U_11276,sK285(U_11277,U_11276,U_11275)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_11274,sK285(U_11277,U_11276,U_11275))],[f_3043_2]) ).
fof(f_3043_4,plain,
! [U_11277,U_11275,U_11276] :
( 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),U_11276),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11275),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))) = 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)),U_11276)),U_11275)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11275,sK285(U_11277,U_11276,U_11275))),hAPP(U_11276,sK285(U_11277,U_11276,U_11275)))) ),
inference(definitional_conversion,[status(esa)],[f_3043_3]) ).
cnf(f_3043_5,plain,
( 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),U_11276),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11275),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))) = 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)),U_11276)),U_11275)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11275,sK285(U_11277,U_11276,U_11275))),hAPP(U_11276,sK285(U_11277,U_11276,U_11275)))) ),
inference(clausify,[status(thm)],[f_3043_4]) ).
fof(f_3044_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_apfst__apsnd]) ).
fof(f_3044_2,plain,
! [U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278] : hAPP(c_Product__Type_Oapfst(U_11278,U_11279,U_11280,U_11281),hAPP(c_Product__Type_Oapsnd(U_11282,U_11280,U_11278,U_11283),U_11284)) = hAPP(hAPP(c_Product__Type_OPair(U_11279,U_11280),hAPP(U_11281,hAPP(c_Product__Type_Ofst(U_11278,U_11282),U_11284))),hAPP(U_11283,hAPP(c_Product__Type_Osnd(U_11278,U_11282),U_11284))),
inference(variable_rename,[status(thm)],[f_3044_1]) ).
fof(f_3044_3,plain,
! [U_11278,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284] : hAPP(c_Product__Type_Oapfst(U_11278,U_11279,U_11280,U_11281),hAPP(c_Product__Type_Oapsnd(U_11282,U_11280,U_11278,U_11283),U_11284)) = hAPP(hAPP(c_Product__Type_OPair(U_11279,U_11280),hAPP(U_11281,hAPP(c_Product__Type_Ofst(U_11278,U_11282),U_11284))),hAPP(U_11283,hAPP(c_Product__Type_Osnd(U_11278,U_11282),U_11284))),
inference(definitional_conversion,[status(esa)],[f_3044_2]) ).
cnf(f_3044_4,plain,
hAPP(c_Product__Type_Oapfst(U_11278,U_11279,U_11280,U_11281),hAPP(c_Product__Type_Oapsnd(U_11282,U_11280,U_11278,U_11283),U_11284)) = hAPP(hAPP(c_Product__Type_OPair(U_11279,U_11280),hAPP(U_11281,hAPP(c_Product__Type_Ofst(U_11278,U_11282),U_11284))),hAPP(U_11283,hAPP(c_Product__Type_Osnd(U_11278,U_11282),U_11284))),
inference(clausify,[status(thm)],[f_3044_3]) ).
fof(f_3045_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_apsnd__apfst]) ).
fof(f_3045_2,plain,
! [U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285] : hAPP(c_Product__Type_Oapsnd(U_11285,U_11286,U_11287,U_11288),hAPP(c_Product__Type_Oapfst(U_11289,U_11287,U_11285,U_11290),U_11291)) = hAPP(hAPP(c_Product__Type_OPair(U_11287,U_11286),hAPP(U_11290,hAPP(c_Product__Type_Ofst(U_11289,U_11285),U_11291))),hAPP(U_11288,hAPP(c_Product__Type_Osnd(U_11289,U_11285),U_11291))),
inference(variable_rename,[status(thm)],[f_3045_1]) ).
fof(f_3045_3,plain,
! [U_11285,U_11286,U_11287,U_11288,U_11289,U_11290,U_11291] : hAPP(c_Product__Type_Oapsnd(U_11285,U_11286,U_11287,U_11288),hAPP(c_Product__Type_Oapfst(U_11289,U_11287,U_11285,U_11290),U_11291)) = hAPP(hAPP(c_Product__Type_OPair(U_11287,U_11286),hAPP(U_11290,hAPP(c_Product__Type_Ofst(U_11289,U_11285),U_11291))),hAPP(U_11288,hAPP(c_Product__Type_Osnd(U_11289,U_11285),U_11291))),
inference(definitional_conversion,[status(esa)],[f_3045_2]) ).
cnf(f_3045_4,plain,
hAPP(c_Product__Type_Oapsnd(U_11285,U_11286,U_11287,U_11288),hAPP(c_Product__Type_Oapfst(U_11289,U_11287,U_11285,U_11290),U_11291)) = hAPP(hAPP(c_Product__Type_OPair(U_11287,U_11286),hAPP(U_11290,hAPP(c_Product__Type_Ofst(U_11289,U_11285),U_11291))),hAPP(U_11288,hAPP(c_Product__Type_Osnd(U_11289,U_11285),U_11291))),
inference(clausify,[status(thm)],[f_3045_3]) ).
fof(f_3046_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_fst__apfst]) ).
fof(f_3046_2,plain,
! [U_11296,U_11295,U_11294,U_11293,U_11292] : hAPP(c_Product__Type_Ofst(U_11292,U_11293),hAPP(c_Product__Type_Oapfst(U_11294,U_11292,U_11293,U_11295),U_11296)) = hAPP(U_11295,hAPP(c_Product__Type_Ofst(U_11294,U_11293),U_11296)),
inference(variable_rename,[status(thm)],[f_3046_1]) ).
fof(f_3046_3,plain,
! [U_11292,U_11293,U_11294,U_11295,U_11296] : hAPP(c_Product__Type_Ofst(U_11292,U_11293),hAPP(c_Product__Type_Oapfst(U_11294,U_11292,U_11293,U_11295),U_11296)) = hAPP(U_11295,hAPP(c_Product__Type_Ofst(U_11294,U_11293),U_11296)),
inference(definitional_conversion,[status(esa)],[f_3046_2]) ).
cnf(f_3046_4,plain,
hAPP(c_Product__Type_Ofst(U_11292,U_11293),hAPP(c_Product__Type_Oapfst(U_11294,U_11292,U_11293,U_11295),U_11296)) = hAPP(U_11295,hAPP(c_Product__Type_Ofst(U_11294,U_11293),U_11296)),
inference(clausify,[status(thm)],[f_3046_3]) ).
fof(f_3047_1,plain,
! [V_g_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),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
| 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)) )
& ( 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))
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv]) ).
fof(f_3047_2,plain,
! [U_11302,U_11301,U_11300,U_11299,U_11298,U_11297] :
( ( hAPP(c_Product__Type_Oapfst(U_11297,U_11298,U_11299,U_11300),U_11301) = hAPP(c_Product__Type_Oapfst(U_11297,U_11298,U_11299,U_11302),U_11301)
| hAPP(U_11300,hAPP(c_Product__Type_Ofst(U_11297,U_11299),U_11301)) != hAPP(U_11302,hAPP(c_Product__Type_Ofst(U_11297,U_11299),U_11301)) )
& ( hAPP(U_11300,hAPP(c_Product__Type_Ofst(U_11297,U_11299),U_11301)) = hAPP(U_11302,hAPP(c_Product__Type_Ofst(U_11297,U_11299),U_11301))
| hAPP(c_Product__Type_Oapfst(U_11297,U_11298,U_11299,U_11300),U_11301) != hAPP(c_Product__Type_Oapfst(U_11297,U_11298,U_11299,U_11302),U_11301) ) ),
inference(variable_rename,[status(thm)],[f_3047_1]) ).
fof(f_3047_3,plain,
( ! [U_11314,U_11312,U_11310,U_11308,U_11306,U_11304] :
( hAPP(c_Product__Type_Oapfst(U_11304,U_11306,U_11308,U_11310),U_11312) = hAPP(c_Product__Type_Oapfst(U_11304,U_11306,U_11308,U_11314),U_11312)
| hAPP(U_11310,hAPP(c_Product__Type_Ofst(U_11304,U_11308),U_11312)) != hAPP(U_11314,hAPP(c_Product__Type_Ofst(U_11304,U_11308),U_11312)) )
& ! [U_11313,U_11311,U_11309,U_11307,U_11305,U_11303] :
( hAPP(U_11309,hAPP(c_Product__Type_Ofst(U_11303,U_11307),U_11311)) = hAPP(U_11313,hAPP(c_Product__Type_Ofst(U_11303,U_11307),U_11311))
| hAPP(c_Product__Type_Oapfst(U_11303,U_11305,U_11307,U_11309),U_11311) != hAPP(c_Product__Type_Oapfst(U_11303,U_11305,U_11307,U_11313),U_11311) ) ),
inference(miniscope,[status(thm)],[f_3047_2]) ).
fof(f_3047_4,plain,
( ! [U_11304,U_11306,U_11308,U_11310,U_11312,U_11314] :
( hAPP(c_Product__Type_Oapfst(U_11304,U_11306,U_11308,U_11310),U_11312) = hAPP(c_Product__Type_Oapfst(U_11304,U_11306,U_11308,U_11314),U_11312)
| hAPP(U_11310,hAPP(c_Product__Type_Ofst(U_11304,U_11308),U_11312)) != hAPP(U_11314,hAPP(c_Product__Type_Ofst(U_11304,U_11308),U_11312)) )
& ! [U_11309,U_11303,U_11305,U_11307,U_11313,U_11311] :
( hAPP(U_11309,hAPP(c_Product__Type_Ofst(U_11303,U_11307),U_11311)) = hAPP(U_11313,hAPP(c_Product__Type_Ofst(U_11303,U_11307),U_11311))
| hAPP(c_Product__Type_Oapfst(U_11303,U_11305,U_11307,U_11309),U_11311) != hAPP(c_Product__Type_Oapfst(U_11303,U_11305,U_11307,U_11313),U_11311) ) ),
inference(definitional_conversion,[status(esa)],[f_3047_3]) ).
cnf(f_3047_5,plain,
( hAPP(U_11309,hAPP(c_Product__Type_Ofst(U_11303,U_11307),U_11311)) = hAPP(U_11313,hAPP(c_Product__Type_Ofst(U_11303,U_11307),U_11311))
| hAPP(c_Product__Type_Oapfst(U_11303,U_11305,U_11307,U_11309),U_11311) != hAPP(c_Product__Type_Oapfst(U_11303,U_11305,U_11307,U_11313),U_11311) ),
inference(clausify,[status(thm)],[f_3047_4]) ).
cnf(f_3047_6,plain,
( hAPP(c_Product__Type_Oapfst(U_11304,U_11306,U_11308,U_11310),U_11312) = hAPP(c_Product__Type_Oapfst(U_11304,U_11306,U_11308,U_11314),U_11312)
| hAPP(U_11310,hAPP(c_Product__Type_Ofst(U_11304,U_11308),U_11312)) != hAPP(U_11314,hAPP(c_Product__Type_Ofst(U_11304,U_11308),U_11312)) ),
inference(clausify,[status(thm)],[f_3047_4]) ).
fof(f_3048_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_apfst__conv]) ).
fof(f_3048_2,plain,
! [U_11320,U_11319,U_11318,U_11317,U_11316,U_11315] : hAPP(c_Product__Type_Oapfst(U_11315,U_11316,U_11317,U_11318),hAPP(hAPP(c_Product__Type_OPair(U_11315,U_11317),U_11319),U_11320)) = hAPP(hAPP(c_Product__Type_OPair(U_11316,U_11317),hAPP(U_11318,U_11319)),U_11320),
inference(variable_rename,[status(thm)],[f_3048_1]) ).
fof(f_3048_3,plain,
! [U_11317,U_11316,U_11315,U_11318,U_11319,U_11320] : hAPP(c_Product__Type_Oapfst(U_11315,U_11316,U_11317,U_11318),hAPP(hAPP(c_Product__Type_OPair(U_11315,U_11317),U_11319),U_11320)) = hAPP(hAPP(c_Product__Type_OPair(U_11316,U_11317),hAPP(U_11318,U_11319)),U_11320),
inference(definitional_conversion,[status(esa)],[f_3048_2]) ).
cnf(f_3048_4,plain,
hAPP(c_Product__Type_Oapfst(U_11315,U_11316,U_11317,U_11318),hAPP(hAPP(c_Product__Type_OPair(U_11315,U_11317),U_11319),U_11320)) = hAPP(hAPP(c_Product__Type_OPair(U_11316,U_11317),hAPP(U_11318,U_11319)),U_11320),
inference(clausify,[status(thm)],[f_3048_3]) ).
fof(f_3049_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_snd__apfst]) ).
fof(f_3049_2,plain,
! [U_11325,U_11324,U_11323,U_11322,U_11321] : hAPP(c_Product__Type_Osnd(U_11321,U_11322),hAPP(c_Product__Type_Oapfst(U_11323,U_11321,U_11322,U_11324),U_11325)) = hAPP(c_Product__Type_Osnd(U_11323,U_11322),U_11325),
inference(variable_rename,[status(thm)],[f_3049_1]) ).
fof(f_3049_3,plain,
! [U_11322,U_11321,U_11323,U_11324,U_11325] : hAPP(c_Product__Type_Osnd(U_11321,U_11322),hAPP(c_Product__Type_Oapfst(U_11323,U_11321,U_11322,U_11324),U_11325)) = hAPP(c_Product__Type_Osnd(U_11323,U_11322),U_11325),
inference(definitional_conversion,[status(esa)],[f_3049_2]) ).
cnf(f_3049_4,plain,
hAPP(c_Product__Type_Osnd(U_11321,U_11322),hAPP(c_Product__Type_Oapfst(U_11323,U_11321,U_11322,U_11324),U_11325)) = hAPP(c_Product__Type_Osnd(U_11323,U_11322),U_11325),
inference(clausify,[status(thm)],[f_3049_3]) ).
fof(f_3050_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_apsnd__apfst__commute]) ).
fof(f_3050_2,plain,
! [U_11332,U_11331,U_11330,U_11329,U_11328,U_11327,U_11326] : hAPP(c_Product__Type_Oapsnd(U_11326,U_11327,U_11328,U_11329),hAPP(c_Product__Type_Oapfst(U_11330,U_11328,U_11326,U_11331),U_11332)) = hAPP(c_Product__Type_Oapfst(U_11330,U_11328,U_11327,U_11331),hAPP(c_Product__Type_Oapsnd(U_11326,U_11327,U_11330,U_11329),U_11332)),
inference(variable_rename,[status(thm)],[f_3050_1]) ).
fof(f_3050_3,plain,
! [U_11326,U_11327,U_11328,U_11329,U_11330,U_11331,U_11332] : hAPP(c_Product__Type_Oapsnd(U_11326,U_11327,U_11328,U_11329),hAPP(c_Product__Type_Oapfst(U_11330,U_11328,U_11326,U_11331),U_11332)) = hAPP(c_Product__Type_Oapfst(U_11330,U_11328,U_11327,U_11331),hAPP(c_Product__Type_Oapsnd(U_11326,U_11327,U_11330,U_11329),U_11332)),
inference(definitional_conversion,[status(esa)],[f_3050_2]) ).
cnf(f_3050_4,plain,
hAPP(c_Product__Type_Oapsnd(U_11326,U_11327,U_11328,U_11329),hAPP(c_Product__Type_Oapfst(U_11330,U_11328,U_11326,U_11331),U_11332)) = hAPP(c_Product__Type_Oapfst(U_11330,U_11328,U_11327,U_11331),hAPP(c_Product__Type_Oapsnd(U_11326,U_11327,U_11330,U_11329),U_11332)),
inference(clausify,[status(thm)],[f_3050_3]) ).
fof(f_3051_1,plain,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__lessI2]) ).
fof(f_3051_2,plain,
! [U_11336,U_11335,U_11334,U_11333] :
( 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),U_11333),U_11335)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11334),U_11336))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11335),U_11336))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11333),U_11334)) ),
inference(variable_rename,[status(thm)],[f_3051_1]) ).
fof(f_3051_3,plain,
! [U_11333,U_11334,U_11335,U_11336] :
( 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),U_11333),U_11335)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11334),U_11336))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11335),U_11336))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11333),U_11334)) ),
inference(definitional_conversion,[status(esa)],[f_3051_2]) ).
cnf(f_3051_4,plain,
( 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),U_11333),U_11335)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11334),U_11336))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11335),U_11336))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11333),U_11334)) ),
inference(clausify,[status(thm)],[f_3051_3]) ).
fof(f_3052_1,plain,
! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
( 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)))
| ~ 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)))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_max__ext__additive]) ).
fof(f_3052_2,plain,
! [U_11342,U_11341,U_11340,U_11339,U_11338,U_11337] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11337,tc_HOL_Obool)),U_11338),U_11341)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11337,tc_HOL_Obool)),U_11339),U_11342))),c_Wellfounded_Omax__ext(U_11337,U_11340)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),U_11341),U_11342)),c_Wellfounded_Omax__ext(U_11337,U_11340)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),U_11338),U_11339)),c_Wellfounded_Omax__ext(U_11337,U_11340))) ),
inference(variable_rename,[status(thm)],[f_3052_1]) ).
fof(f_3052_3,plain,
! [U_11337,U_11338,U_11339,U_11340,U_11341,U_11342] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11337,tc_HOL_Obool)),U_11338),U_11341)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11337,tc_HOL_Obool)),U_11339),U_11342))),c_Wellfounded_Omax__ext(U_11337,U_11340)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),U_11341),U_11342)),c_Wellfounded_Omax__ext(U_11337,U_11340)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),U_11338),U_11339)),c_Wellfounded_Omax__ext(U_11337,U_11340))) ),
inference(definitional_conversion,[status(esa)],[f_3052_2]) ).
cnf(f_3052_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11337,tc_HOL_Obool)),U_11338),U_11341)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11337,tc_HOL_Obool)),U_11339),U_11342))),c_Wellfounded_Omax__ext(U_11337,U_11340)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),U_11341),U_11342)),c_Wellfounded_Omax__ext(U_11337,U_11340)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11337,tc_HOL_Obool),tc_fun(U_11337,tc_HOL_Obool)),U_11338),U_11339)),c_Wellfounded_Omax__ext(U_11337,U_11340))) ),
inference(clausify,[status(thm)],[f_3052_3]) ).
fof(f_3053_1,plain,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
( 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)
| ? [B_x] :
( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| V_A_2 != V_B_2
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J]) ).
fof(f_3053_2,plain,
! [U_11348,U_11347,U_11346,U_11345,U_11344] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11344),U_11347),U_11345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11344),U_11348),U_11346)
| ? [U_11343] :
( hAPP(U_11347,U_11343) != hAPP(U_11348,U_11343)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11343)) )
| ~ c_Nat__Transfer_Onat__set(U_11346)
| U_11345 != U_11346
| ~ class_Groups_Ocomm__monoid__mult(U_11344)
| ~ class_Groups_Ocomm__monoid__add(U_11344) ),
inference(variable_rename,[status(thm)],[f_3053_1]) ).
fof(f_3053_3,plain,
! [U_11348,U_11347,U_11346,U_11345,U_11344] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11344),U_11347),U_11345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11344),U_11348),U_11346)
| ( hAPP(U_11347,sK286(U_11348,U_11347,U_11346,U_11345,U_11344)) != hAPP(U_11348,sK286(U_11348,U_11347,U_11346,U_11345,U_11344))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK286(U_11348,U_11347,U_11346,U_11345,U_11344))) )
| ~ c_Nat__Transfer_Onat__set(U_11346)
| U_11345 != U_11346
| ~ class_Groups_Ocomm__monoid__mult(U_11344)
| ~ class_Groups_Ocomm__monoid__add(U_11344) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_11343,sK286(U_11348,U_11347,U_11346,U_11345,U_11344))],[f_3053_2]) ).
fof(f_3053_4,plain,
( ! [U_11344,U_11345,U_11346,U_11347,U_11348] :
( hAPP(U_11347,sK286(U_11348,U_11347,U_11346,U_11345,U_11344)) != hAPP(U_11348,sK286(U_11348,U_11347,U_11346,U_11345,U_11344))
| ~ sP869(U_11344,U_11345,U_11346,U_11347,U_11348) )
& ! [U_11344,U_11345,U_11346,U_11347,U_11348] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK286(U_11348,U_11347,U_11346,U_11345,U_11344)))
| ~ sP869(U_11344,U_11345,U_11346,U_11347,U_11348) )
& ! [U_11344,U_11345,U_11346,U_11347,U_11348] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11344),U_11347),U_11345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11344),U_11348),U_11346)
| sP869(U_11344,U_11345,U_11346,U_11347,U_11348)
| ~ c_Nat__Transfer_Onat__set(U_11346)
| U_11345 != U_11346
| ~ class_Groups_Ocomm__monoid__mult(U_11344)
| ~ class_Groups_Ocomm__monoid__add(U_11344) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP869])],[f_3053_3]) ).
cnf(f_3053_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11344),U_11347),U_11345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11344),U_11348),U_11346)
| sP869(U_11344,U_11345,U_11346,U_11347,U_11348)
| ~ c_Nat__Transfer_Onat__set(U_11346)
| U_11345 != U_11346
| ~ class_Groups_Ocomm__monoid__mult(U_11344)
| ~ class_Groups_Ocomm__monoid__add(U_11344) ),
inference(clausify,[status(thm)],[f_3053_4]) ).
cnf(f_3053_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK286(U_11348,U_11347,U_11346,U_11345,U_11344)))
| ~ sP869(U_11344,U_11345,U_11346,U_11347,U_11348) ),
inference(clausify,[status(thm)],[f_3053_4]) ).
cnf(f_3053_7,plain,
( hAPP(U_11347,sK286(U_11348,U_11347,U_11346,U_11345,U_11344)) != hAPP(U_11348,sK286(U_11348,U_11347,U_11346,U_11345,U_11344))
| ~ sP869(U_11344,U_11345,U_11346,U_11347,U_11348) ),
inference(clausify,[status(thm)],[f_3053_4]) ).
fof(f_3054_1,plain,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__lessI1]) ).
fof(f_3054_2,plain,
! [U_11352,U_11351,U_11350,U_11349] :
( 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),U_11349),U_11351)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11350),U_11352))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11349),U_11350)) ),
inference(variable_rename,[status(thm)],[f_3054_1]) ).
fof(f_3054_3,plain,
! [U_11352,U_11350,U_11351,U_11349] :
( 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),U_11349),U_11351)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11350),U_11352))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11349),U_11350)) ),
inference(definitional_conversion,[status(esa)],[f_3054_2]) ).
cnf(f_3054_4,plain,
( 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),U_11349),U_11351)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11350),U_11352))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11349),U_11350)) ),
inference(clausify,[status(thm)],[f_3054_3]) ).
fof(f_3055_1,plain,
! [V_xa_2,V_x_2,V_R_2,T_b] :
( ( 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)
| ~ 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))) )
& ( 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)))
| ~ 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) ) ),
inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq]) ).
fof(f_3055_2,plain,
! [U_11356,U_11355,U_11354,U_11353] :
( ( c_Wellfounded_Omax__extp(U_11353,hAPP(hAPP(c_COMBC(U_11353,tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_fun(U_11353,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11353,tc_fun(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_fun(U_11353,tc_HOL_Obool)),U_11353),c_COMBC(U_11353,tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11353,tc_prod(U_11353,U_11353)),tc_fun(U_11353,tc_fun(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_HOL_Obool)),U_11353),hAPP(c_COMBB(tc_prod(U_11353,U_11353),tc_fun(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_HOL_Obool),U_11353),c_member(tc_prod(U_11353,U_11353)))),c_Product__Type_OPair(U_11353,U_11353)))),U_11354),U_11355,U_11356)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11353,tc_HOL_Obool),tc_fun(U_11353,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11353,tc_HOL_Obool),tc_fun(U_11353,tc_HOL_Obool)),U_11355),U_11356)),c_Wellfounded_Omax__ext(U_11353,U_11354))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11353,tc_HOL_Obool),tc_fun(U_11353,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11353,tc_HOL_Obool),tc_fun(U_11353,tc_HOL_Obool)),U_11355),U_11356)),c_Wellfounded_Omax__ext(U_11353,U_11354)))
| ~ c_Wellfounded_Omax__extp(U_11353,hAPP(hAPP(c_COMBC(U_11353,tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_fun(U_11353,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11353,tc_fun(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_fun(U_11353,tc_HOL_Obool)),U_11353),c_COMBC(U_11353,tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11353,tc_prod(U_11353,U_11353)),tc_fun(U_11353,tc_fun(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_HOL_Obool)),U_11353),hAPP(c_COMBB(tc_prod(U_11353,U_11353),tc_fun(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool),tc_HOL_Obool),U_11353),c_member(tc_prod(U_11353,U_11353)))),c_Product__Type_OPair(U_11353,U_11353)))),U_11354),U_11355,U_11356) ) ),
inference(variable_rename,[status(thm)],[f_3055_1]) ).
fof(f_3055_3,plain,
( ! [U_11364,U_11362,U_11360,U_11358] :
( c_Wellfounded_Omax__extp(U_11358,hAPP(hAPP(c_COMBC(U_11358,tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11358,tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),U_11358),c_COMBC(U_11358,tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11358,tc_prod(U_11358,U_11358)),tc_fun(U_11358,tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),U_11358),hAPP(c_COMBB(tc_prod(U_11358,U_11358),tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool),U_11358),c_member(tc_prod(U_11358,U_11358)))),c_Product__Type_OPair(U_11358,U_11358)))),U_11360),U_11362,U_11364)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11358,tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11358,tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),U_11362),U_11364)),c_Wellfounded_Omax__ext(U_11358,U_11360))) )
& ! [U_11363,U_11361,U_11359,U_11357] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11357,tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11357,tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),U_11361),U_11363)),c_Wellfounded_Omax__ext(U_11357,U_11359)))
| ~ c_Wellfounded_Omax__extp(U_11357,hAPP(hAPP(c_COMBC(U_11357,tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11357,tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),U_11357),c_COMBC(U_11357,tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11357,tc_prod(U_11357,U_11357)),tc_fun(U_11357,tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),U_11357),hAPP(c_COMBB(tc_prod(U_11357,U_11357),tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool),U_11357),c_member(tc_prod(U_11357,U_11357)))),c_Product__Type_OPair(U_11357,U_11357)))),U_11359),U_11361,U_11363) ) ),
inference(miniscope,[status(thm)],[f_3055_2]) ).
fof(f_3055_4,plain,
( ! [U_11360,U_11358,U_11362,U_11364] :
( c_Wellfounded_Omax__extp(U_11358,hAPP(hAPP(c_COMBC(U_11358,tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11358,tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),U_11358),c_COMBC(U_11358,tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11358,tc_prod(U_11358,U_11358)),tc_fun(U_11358,tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),U_11358),hAPP(c_COMBB(tc_prod(U_11358,U_11358),tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool),U_11358),c_member(tc_prod(U_11358,U_11358)))),c_Product__Type_OPair(U_11358,U_11358)))),U_11360),U_11362,U_11364)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11358,tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11358,tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),U_11362),U_11364)),c_Wellfounded_Omax__ext(U_11358,U_11360))) )
& ! [U_11359,U_11357,U_11361,U_11363] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11357,tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11357,tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),U_11361),U_11363)),c_Wellfounded_Omax__ext(U_11357,U_11359)))
| ~ c_Wellfounded_Omax__extp(U_11357,hAPP(hAPP(c_COMBC(U_11357,tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11357,tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),U_11357),c_COMBC(U_11357,tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11357,tc_prod(U_11357,U_11357)),tc_fun(U_11357,tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),U_11357),hAPP(c_COMBB(tc_prod(U_11357,U_11357),tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool),U_11357),c_member(tc_prod(U_11357,U_11357)))),c_Product__Type_OPair(U_11357,U_11357)))),U_11359),U_11361,U_11363) ) ),
inference(definitional_conversion,[status(esa)],[f_3055_3]) ).
cnf(f_3055_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11357,tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11357,tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),U_11361),U_11363)),c_Wellfounded_Omax__ext(U_11357,U_11359)))
| ~ c_Wellfounded_Omax__extp(U_11357,hAPP(hAPP(c_COMBC(U_11357,tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11357,tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_fun(U_11357,tc_HOL_Obool)),U_11357),c_COMBC(U_11357,tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11357,tc_prod(U_11357,U_11357)),tc_fun(U_11357,tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool)),U_11357),hAPP(c_COMBB(tc_prod(U_11357,U_11357),tc_fun(tc_fun(tc_prod(U_11357,U_11357),tc_HOL_Obool),tc_HOL_Obool),U_11357),c_member(tc_prod(U_11357,U_11357)))),c_Product__Type_OPair(U_11357,U_11357)))),U_11359),U_11361,U_11363) ),
inference(clausify,[status(thm)],[f_3055_4]) ).
cnf(f_3055_6,plain,
( c_Wellfounded_Omax__extp(U_11358,hAPP(hAPP(c_COMBC(U_11358,tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11358,tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),U_11358),c_COMBC(U_11358,tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11358,tc_prod(U_11358,U_11358)),tc_fun(U_11358,tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool)),U_11358),hAPP(c_COMBB(tc_prod(U_11358,U_11358),tc_fun(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool),tc_HOL_Obool),U_11358),c_member(tc_prod(U_11358,U_11358)))),c_Product__Type_OPair(U_11358,U_11358)))),U_11360),U_11362,U_11364)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11358,tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11358,tc_HOL_Obool),tc_fun(U_11358,tc_HOL_Obool)),U_11362),U_11364)),c_Wellfounded_Omax__ext(U_11358,U_11360))) ),
inference(clausify,[status(thm)],[f_3055_4]) ).
fof(f_3056_1,plain,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__leqI2]) ).
fof(f_3056_2,plain,
! [U_11368,U_11367,U_11366,U_11365] :
( 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),U_11365),U_11367)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11366),U_11368))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11367),U_11368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11365),U_11366)) ),
inference(variable_rename,[status(thm)],[f_3056_1]) ).
fof(f_3056_3,plain,
! [U_11365,U_11367,U_11366,U_11368] :
( 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),U_11365),U_11367)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11366),U_11368))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11367),U_11368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11365),U_11366)) ),
inference(definitional_conversion,[status(esa)],[f_3056_2]) ).
cnf(f_3056_4,plain,
( 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),U_11365),U_11367)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11366),U_11368))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11367),U_11368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11365),U_11366)) ),
inference(clausify,[status(thm)],[f_3056_3]) ).
fof(f_3057_1,plain,
! [V_X_2,V_x_2,V_Y_2,V_y_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)),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))
| ~ 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))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) ),
inference(fof_nnf,[status(thm)],[fact_smax__insertI]) ).
fof(f_3057_2,plain,
! [U_11372,U_11371,U_11370,U_11369] :
( 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)),U_11371),U_11372)),U_11370)),c_FunDef_Omax__strict))
| ~ 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)),U_11372),U_11370)),c_FunDef_Omax__strict))
| ~ 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)),U_11371),U_11369)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11369),U_11370)) ),
inference(variable_rename,[status(thm)],[f_3057_1]) ).
fof(f_3057_3,plain,
! [U_11370,U_11369,U_11371,U_11372] :
( 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)),U_11371),U_11372)),U_11370)),c_FunDef_Omax__strict))
| ~ 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)),U_11372),U_11370)),c_FunDef_Omax__strict))
| ~ 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)),U_11371),U_11369)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11369),U_11370)) ),
inference(definitional_conversion,[status(esa)],[f_3057_2]) ).
cnf(f_3057_4,plain,
( 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)),U_11371),U_11372)),U_11370)),c_FunDef_Omax__strict))
| ~ 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)),U_11372),U_11370)),c_FunDef_Omax__strict))
| ~ 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)),U_11371),U_11369)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11369),U_11370)) ),
inference(clausify,[status(thm)],[f_3057_3]) ).
fof(f_3058_1,plain,
! [V_Y_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)),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))
| V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) ),
inference(fof_nnf,[status(thm)],[fact_smax__emptyI]) ).
fof(f_3058_2,plain,
! [U_11373] :
( 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))),U_11373)),c_FunDef_Omax__strict))
| U_11373 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11373)) ),
inference(variable_rename,[status(thm)],[f_3058_1]) ).
fof(f_3058_3,plain,
! [U_11373] :
( 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))),U_11373)),c_FunDef_Omax__strict))
| U_11373 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11373)) ),
inference(definitional_conversion,[status(esa)],[f_3058_2]) ).
cnf(f_3058_4,plain,
( 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))),U_11373)),c_FunDef_Omax__strict))
| U_11373 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11373)) ),
inference(clausify,[status(thm)],[f_3058_3]) ).
fof(f_3059_1,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(fof_nnf,[status(thm)],[fact_max__strict__def]) ).
fof(f_3059_2,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(definitional_conversion,[status(esa)],[f_3059_1]) ).
cnf(f_3059_3,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_3059_2]) ).
fof(f_3060_1,plain,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__leqI1]) ).
fof(f_3060_2,plain,
! [U_11377,U_11376,U_11375,U_11374] :
( 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),U_11374),U_11376)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11375),U_11377))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11374),U_11375)) ),
inference(variable_rename,[status(thm)],[f_3060_1]) ).
fof(f_3060_3,plain,
! [U_11375,U_11374,U_11376,U_11377] :
( 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),U_11374),U_11376)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11375),U_11377))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11374),U_11375)) ),
inference(definitional_conversion,[status(esa)],[f_3060_2]) ).
cnf(f_3060_4,plain,
( 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),U_11374),U_11376)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11375),U_11377))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11374),U_11375)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
fof(f_3061_1,plain,
! [V_YS_2,V_y_2,V_XS_2,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_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))
| ~ 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))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) ),
inference(fof_nnf,[status(thm)],[fact_wmin__insertI]) ).
fof(f_3061_2,plain,
! [U_11381,U_11380,U_11379,U_11378] :
( 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)),U_11379),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11380),U_11381))),c_FunDef_Omin__weak))
| ~ 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)),U_11379),U_11381)),c_FunDef_Omin__weak))
| ~ 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)),U_11378),U_11380)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11378),U_11379)) ),
inference(variable_rename,[status(thm)],[f_3061_1]) ).
fof(f_3061_3,plain,
! [U_11378,U_11379,U_11380,U_11381] :
( 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)),U_11379),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11380),U_11381))),c_FunDef_Omin__weak))
| ~ 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)),U_11379),U_11381)),c_FunDef_Omin__weak))
| ~ 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)),U_11378),U_11380)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11378),U_11379)) ),
inference(definitional_conversion,[status(esa)],[f_3061_2]) ).
cnf(f_3061_4,plain,
( 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)),U_11379),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11380),U_11381))),c_FunDef_Omin__weak))
| ~ 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)),U_11379),U_11381)),c_FunDef_Omin__weak))
| ~ 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)),U_11378),U_11380)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11378),U_11379)) ),
inference(clausify,[status(thm)],[f_3061_3]) ).
fof(f_3062_1,plain,
! [V_XS_2,V_x_2,V_YS_2,V_y_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)),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))
| ~ 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))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) ),
inference(fof_nnf,[status(thm)],[fact_wmax__insertI]) ).
fof(f_3062_2,plain,
! [U_11385,U_11384,U_11383,U_11382] :
( 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)),U_11384),U_11385)),U_11383)),c_FunDef_Omax__weak))
| ~ 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)),U_11385),U_11383)),c_FunDef_Omax__weak))
| ~ 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)),U_11384),U_11382)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11382),U_11383)) ),
inference(variable_rename,[status(thm)],[f_3062_1]) ).
fof(f_3062_3,plain,
! [U_11384,U_11383,U_11382,U_11385] :
( 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)),U_11384),U_11385)),U_11383)),c_FunDef_Omax__weak))
| ~ 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)),U_11385),U_11383)),c_FunDef_Omax__weak))
| ~ 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)),U_11384),U_11382)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11382),U_11383)) ),
inference(definitional_conversion,[status(esa)],[f_3062_2]) ).
cnf(f_3062_4,plain,
( 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)),U_11384),U_11385)),U_11383)),c_FunDef_Omax__weak))
| ~ 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)),U_11385),U_11383)),c_FunDef_Omax__weak))
| ~ 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)),U_11384),U_11382)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11382),U_11383)) ),
inference(clausify,[status(thm)],[f_3062_3]) ).
fof(f_3063_1,plain,
! [V_YS_2,V_y_2,V_XS_2,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_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))
| ~ 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))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) ),
inference(fof_nnf,[status(thm)],[fact_smin__insertI]) ).
fof(f_3063_2,plain,
! [U_11389,U_11388,U_11387,U_11386] :
( 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)),U_11387),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11388),U_11389))),c_FunDef_Omin__strict))
| ~ 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)),U_11387),U_11389)),c_FunDef_Omin__strict))
| ~ 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)),U_11386),U_11388)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11386),U_11387)) ),
inference(variable_rename,[status(thm)],[f_3063_1]) ).
fof(f_3063_3,plain,
! [U_11388,U_11387,U_11386,U_11389] :
( 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)),U_11387),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11388),U_11389))),c_FunDef_Omin__strict))
| ~ 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)),U_11387),U_11389)),c_FunDef_Omin__strict))
| ~ 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)),U_11386),U_11388)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11386),U_11387)) ),
inference(definitional_conversion,[status(esa)],[f_3063_2]) ).
cnf(f_3063_4,plain,
( 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)),U_11387),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11388),U_11389))),c_FunDef_Omin__strict))
| ~ 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)),U_11387),U_11389)),c_FunDef_Omin__strict))
| ~ 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)),U_11386),U_11388)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11386),U_11387)) ),
inference(clausify,[status(thm)],[f_3063_3]) ).
fof(f_3064_1,plain,
! [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)),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) ),
inference(fof_nnf,[status(thm)],[fact_wmax__emptyI]) ).
fof(f_3064_2,plain,
! [U_11390] :
( 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))),U_11390)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11390)) ),
inference(variable_rename,[status(thm)],[f_3064_1]) ).
fof(f_3064_3,plain,
! [U_11390] :
( 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))),U_11390)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11390)) ),
inference(definitional_conversion,[status(esa)],[f_3064_2]) ).
cnf(f_3064_4,plain,
( 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))),U_11390)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11390)) ),
inference(clausify,[status(thm)],[f_3064_3]) ).
fof(f_3065_1,plain,
! [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__strict))
| V_X_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_smin__emptyI]) ).
fof(f_3065_2,plain,
! [U_11391] :
( 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)),U_11391),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
| U_11391 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3065_1]) ).
fof(f_3065_3,plain,
! [U_11391] :
( 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)),U_11391),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
| U_11391 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_3065_2]) ).
cnf(f_3065_4,plain,
( 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)),U_11391),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
| U_11391 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3065_3]) ).
fof(f_3066_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_wmin__emptyI]) ).
fof(f_3066_2,plain,
! [U_11392] : 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)),U_11392),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
inference(variable_rename,[status(thm)],[f_3066_1]) ).
fof(f_3066_3,plain,
! [U_11392] : 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)),U_11392),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
inference(definitional_conversion,[status(esa)],[f_3066_2]) ).
cnf(f_3066_4,plain,
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)),U_11392),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
inference(clausify,[status(thm)],[f_3066_3]) ).
fof(f_3067_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_max__weak__def]) ).
fof(f_3067_2,plain,
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)))),
inference(definitional_conversion,[status(esa)],[f_3067_1]) ).
cnf(f_3067_3,plain,
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)))),
inference(clausify,[status(thm)],[f_3067_2]) ).
fof(f_3068_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_min__weak__def]) ).
fof(f_3068_2,plain,
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)))),
inference(definitional_conversion,[status(esa)],[f_3068_1]) ).
cnf(f_3068_3,plain,
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)))),
inference(clausify,[status(thm)],[f_3068_2]) ).
fof(f_3069_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_min__rpair__set]) ).
fof(f_3069_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_3069_1]) ).
cnf(f_3069_3,plain,
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)),
inference(clausify,[status(thm)],[f_3069_2]) ).
fof(f_3070_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_max__rpair__set]) ).
fof(f_3070_2,plain,
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)),
inference(definitional_conversion,[status(esa)],[f_3070_1]) ).
cnf(f_3070_3,plain,
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)),
inference(clausify,[status(thm)],[f_3070_2]) ).
fof(f_3071_1,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(fof_nnf,[status(thm)],[fact_min__strict__def]) ).
fof(f_3071_2,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(definitional_conversion,[status(esa)],[f_3071_1]) ).
cnf(f_3071_3,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_3071_2]) ).
fof(f_3072_1,plain,
! [V_y_2,V_x_2] :
( ( 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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__than__iff]) ).
fof(f_3072_2,plain,
! [U_11394,U_11393] :
( ( 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),U_11393),U_11394)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11393),U_11394)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11393),U_11394))
| ~ 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),U_11393),U_11394)),c_Wellfounded_Oless__than)) ) ),
inference(variable_rename,[status(thm)],[f_3072_1]) ).
fof(f_3072_3,plain,
( ! [U_11398,U_11396] :
( 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),U_11396),U_11398)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11396),U_11398)) )
& ! [U_11397,U_11395] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11395),U_11397))
| ~ 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),U_11395),U_11397)),c_Wellfounded_Oless__than)) ) ),
inference(miniscope,[status(thm)],[f_3072_2]) ).
fof(f_3072_4,plain,
( ! [U_11396,U_11398] :
( 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),U_11396),U_11398)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11396),U_11398)) )
& ! [U_11397,U_11395] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11395),U_11397))
| ~ 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),U_11395),U_11397)),c_Wellfounded_Oless__than)) ) ),
inference(definitional_conversion,[status(esa)],[f_3072_3]) ).
cnf(f_3072_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11395),U_11397))
| ~ 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),U_11395),U_11397)),c_Wellfounded_Oless__than)) ),
inference(clausify,[status(thm)],[f_3072_4]) ).
cnf(f_3072_6,plain,
( 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),U_11396),U_11398)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11396),U_11398)) ),
inference(clausify,[status(thm)],[f_3072_4]) ).
fof(f_3073_1,plain,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( ( 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))
| 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) )
& ( 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)
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_intrel__iff]) ).
fof(f_3073_2,plain,
! [U_11402,U_11401,U_11400,U_11399] :
( ( 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),U_11399),U_11400)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11401),U_11402))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11399),U_11402) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11401),U_11400) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11399),U_11402) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11401),U_11400)
| ~ 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),U_11399),U_11400)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11401),U_11402))),c_Int_Ointrel)) ) ),
inference(variable_rename,[status(thm)],[f_3073_1]) ).
fof(f_3073_3,plain,
( ! [U_11410,U_11408,U_11406,U_11404] :
( 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),U_11404),U_11406)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11408),U_11410))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11404),U_11410) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11408),U_11406) )
& ! [U_11409,U_11407,U_11405,U_11403] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11403),U_11409) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11407),U_11405)
| ~ 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),U_11403),U_11405)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11407),U_11409))),c_Int_Ointrel)) ) ),
inference(miniscope,[status(thm)],[f_3073_2]) ).
fof(f_3073_4,plain,
( ! [U_11404,U_11406,U_11408,U_11410] :
( 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),U_11404),U_11406)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11408),U_11410))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11404),U_11410) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11408),U_11406) )
& ! [U_11405,U_11409,U_11403,U_11407] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11403),U_11409) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11407),U_11405)
| ~ 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),U_11403),U_11405)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11407),U_11409))),c_Int_Ointrel)) ) ),
inference(definitional_conversion,[status(esa)],[f_3073_3]) ).
cnf(f_3073_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11403),U_11409) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11407),U_11405)
| ~ 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),U_11403),U_11405)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11407),U_11409))),c_Int_Ointrel)) ),
inference(clausify,[status(thm)],[f_3073_4]) ).
cnf(f_3073_6,plain,
( 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),U_11404),U_11406)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11408),U_11410))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11404),U_11410) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11408),U_11406) ),
inference(clausify,[status(thm)],[f_3073_4]) ).
fof(f_3074_1,plain,
! [V_f_2,T_c,V_Pa_2,T_b] :
( c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2))
| ~ c_FunDef_Oreduction__pair(T_b,V_Pa_2) ),
inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).
fof(f_3074_2,plain,
! [U_11414,U_11413,U_11412,U_11411] :
( c_FunDef_Oreduction__pair(U_11413,hAPP(hAPP(c_FunDef_Orp__inv__image(U_11411,U_11413),U_11412),U_11414))
| ~ c_FunDef_Oreduction__pair(U_11411,U_11412) ),
inference(variable_rename,[status(thm)],[f_3074_1]) ).
fof(f_3074_3,plain,
! [U_11411,U_11413,U_11412,U_11414] :
( c_FunDef_Oreduction__pair(U_11413,hAPP(hAPP(c_FunDef_Orp__inv__image(U_11411,U_11413),U_11412),U_11414))
| ~ c_FunDef_Oreduction__pair(U_11411,U_11412) ),
inference(definitional_conversion,[status(esa)],[f_3074_2]) ).
cnf(f_3074_4,plain,
( c_FunDef_Oreduction__pair(U_11413,hAPP(hAPP(c_FunDef_Orp__inv__image(U_11411,U_11413),U_11412),U_11414))
| ~ c_FunDef_Oreduction__pair(U_11411,U_11412) ),
inference(clausify,[status(thm)],[f_3074_3]) ).
fof(f_3075_1,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_pair__less__def]) ).
fof(f_3075_2,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(definitional_conversion,[status(esa)],[f_3075_1]) ).
cnf(f_3075_3,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_3075_2]) ).
fof(f_3076_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_mlex__prod__def]) ).
fof(f_3076_2,plain,
! [U_11417,U_11416,U_11415] : c_Wellfounded_Omlex__prod(U_11415,U_11416,U_11417) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_11415),U_11415),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_11415,c_Wellfounded_Oless__than,U_11417)),hAPP(hAPP(c_COMBS(U_11415,U_11415,tc_prod(tc_Nat_Onat,U_11415)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11415,tc_prod(tc_Nat_Onat,U_11415)),U_11415),c_Product__Type_OPair(tc_Nat_Onat,U_11415)),U_11416)),c_COMBI(U_11415))),
inference(variable_rename,[status(thm)],[f_3076_1]) ).
fof(f_3076_3,plain,
! [U_11415,U_11416,U_11417] : c_Wellfounded_Omlex__prod(U_11415,U_11416,U_11417) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_11415),U_11415),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_11415,c_Wellfounded_Oless__than,U_11417)),hAPP(hAPP(c_COMBS(U_11415,U_11415,tc_prod(tc_Nat_Onat,U_11415)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11415,tc_prod(tc_Nat_Onat,U_11415)),U_11415),c_Product__Type_OPair(tc_Nat_Onat,U_11415)),U_11416)),c_COMBI(U_11415))),
inference(definitional_conversion,[status(esa)],[f_3076_2]) ).
cnf(f_3076_4,plain,
c_Wellfounded_Omlex__prod(U_11415,U_11416,U_11417) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_11415),U_11415),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_11415,c_Wellfounded_Oless__than,U_11417)),hAPP(hAPP(c_COMBS(U_11415,U_11415,tc_prod(tc_Nat_Onat,U_11415)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11415,tc_prod(tc_Nat_Onat,U_11415)),U_11415),c_Product__Type_OPair(tc_Nat_Onat,U_11415)),U_11416)),c_COMBI(U_11415))),
inference(clausify,[status(thm)],[f_3076_3]) ).
fof(f_3077_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_rp__inv__image__def]) ).
fof(f_3077_2,plain,
! [U_11419,U_11418] : c_FunDef_Orp__inv__image(U_11418,U_11419) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),c_COMBS(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(U_11419,U_11418)),c_Product__Type_OPair(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),c_Relation_Oinv__image(U_11418,U_11419))))),c_Relation_Oinv__image(U_11418,U_11419))),
inference(variable_rename,[status(thm)],[f_3077_1]) ).
fof(f_3077_3,plain,
! [U_11418,U_11419] : c_FunDef_Orp__inv__image(U_11418,U_11419) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),c_COMBS(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(U_11419,U_11418)),c_Product__Type_OPair(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),c_Relation_Oinv__image(U_11418,U_11419))))),c_Relation_Oinv__image(U_11418,U_11419))),
inference(definitional_conversion,[status(esa)],[f_3077_2]) ).
cnf(f_3077_4,plain,
c_FunDef_Orp__inv__image(U_11418,U_11419) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),c_COMBS(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)),tc_fun(tc_fun(U_11419,U_11418),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),tc_fun(tc_prod(U_11418,U_11418),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool))),tc_fun(U_11419,U_11418)),c_Product__Type_OPair(tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool),tc_fun(tc_prod(U_11419,U_11419),tc_HOL_Obool)))),c_Relation_Oinv__image(U_11418,U_11419))))),c_Relation_Oinv__image(U_11418,U_11419))),
inference(clausify,[status(thm)],[f_3077_3]) ).
fof(f_3078_1,plain,
! [V_y_2,V_x_2] :
( ( 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))))
| ~ 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)) )
& ( 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))
| 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_equiv__intrel__iff]) ).
fof(f_3078_2,plain,
! [U_11421,U_11420] :
( ( 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)),U_11420),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)),U_11421),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ 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)),U_11420),U_11421)),c_Int_Ointrel)) )
& ( 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)),U_11420),U_11421)),c_Int_Ointrel))
| 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)),U_11420),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)),U_11421),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_3078_1]) ).
fof(f_3078_3,plain,
( ! [U_11425,U_11423] :
( 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)),U_11423),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)),U_11425),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ 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)),U_11423),U_11425)),c_Int_Ointrel)) )
& ! [U_11424,U_11422] :
( 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)),U_11422),U_11424)),c_Int_Ointrel))
| 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)),U_11422),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)),U_11424),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_3078_2]) ).
fof(f_3078_4,plain,
( ! [U_11423,U_11425] :
( 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)),U_11423),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)),U_11425),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ 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)),U_11423),U_11425)),c_Int_Ointrel)) )
& ! [U_11422,U_11424] :
( 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)),U_11422),U_11424)),c_Int_Ointrel))
| 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)),U_11422),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)),U_11424),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa)],[f_3078_3]) ).
cnf(f_3078_5,plain,
( 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)),U_11422),U_11424)),c_Int_Ointrel))
| 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)),U_11422),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)),U_11424),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3078_4]) ).
cnf(f_3078_6,plain,
( 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)),U_11423),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)),U_11425),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ 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)),U_11423),U_11425)),c_Int_Ointrel)) ),
inference(clausify,[status(thm)],[f_3078_4]) ).
fof(f_3079_1,plain,
! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_measure__def]) ).
fof(f_3079_2,plain,
! [U_11426] : c_Wellfounded_Omeasure(U_11426) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_11426),c_Wellfounded_Oless__than),
inference(variable_rename,[status(thm)],[f_3079_1]) ).
fof(f_3079_3,plain,
! [U_11426] : c_Wellfounded_Omeasure(U_11426) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_11426),c_Wellfounded_Oless__than),
inference(definitional_conversion,[status(esa)],[f_3079_2]) ).
cnf(f_3079_4,plain,
c_Wellfounded_Omeasure(U_11426) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_11426),c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_3079_3]) ).
fof(f_3080_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Image__singleton]) ).
fof(f_3080_2,plain,
! [U_11430,U_11429,U_11428,U_11427] : hAPP(c_Relation_OImage(U_11427,U_11428,U_11429),hAPP(hAPP(c_Set_Oinsert(U_11427),U_11430),c_Orderings_Obot__class_Obot(tc_fun(U_11427,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_11428),hAPP(hAPP(c_COMBC(U_11428,tc_fun(tc_prod(U_11427,U_11428),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_11427,U_11428),tc_fun(tc_fun(tc_prod(U_11427,U_11428),tc_HOL_Obool),tc_HOL_Obool),U_11428),c_member(tc_prod(U_11427,U_11428))),hAPP(c_Product__Type_OPair(U_11427,U_11428),U_11430))),U_11429)),
inference(variable_rename,[status(thm)],[f_3080_1]) ).
fof(f_3080_3,plain,
! [U_11427,U_11428,U_11429,U_11430] : hAPP(c_Relation_OImage(U_11427,U_11428,U_11429),hAPP(hAPP(c_Set_Oinsert(U_11427),U_11430),c_Orderings_Obot__class_Obot(tc_fun(U_11427,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_11428),hAPP(hAPP(c_COMBC(U_11428,tc_fun(tc_prod(U_11427,U_11428),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_11427,U_11428),tc_fun(tc_fun(tc_prod(U_11427,U_11428),tc_HOL_Obool),tc_HOL_Obool),U_11428),c_member(tc_prod(U_11427,U_11428))),hAPP(c_Product__Type_OPair(U_11427,U_11428),U_11430))),U_11429)),
inference(definitional_conversion,[status(esa)],[f_3080_2]) ).
cnf(f_3080_4,plain,
hAPP(c_Relation_OImage(U_11427,U_11428,U_11429),hAPP(hAPP(c_Set_Oinsert(U_11427),U_11430),c_Orderings_Obot__class_Obot(tc_fun(U_11427,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_11428),hAPP(hAPP(c_COMBC(U_11428,tc_fun(tc_prod(U_11427,U_11428),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_11427,U_11428),tc_fun(tc_fun(tc_prod(U_11427,U_11428),tc_HOL_Obool),tc_HOL_Obool),U_11428),c_member(tc_prod(U_11427,U_11428))),hAPP(c_Product__Type_OPair(U_11427,U_11428),U_11430))),U_11429)),
inference(clausify,[status(thm)],[f_3080_3]) ).
fof(f_3081_1,plain,
! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
( ( 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))))))
| ~ 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)) )
& ( 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))
| ~ 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)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff]) ).
fof(f_3081_2,plain,
! [U_11435,U_11434,U_11433,U_11432,U_11431] :
( ( hBOOL(hAPP(hAPP(c_member(U_11431),U_11432),hAPP(c_Relation_OImage(U_11433,U_11431,U_11434),hAPP(hAPP(c_Set_Oinsert(U_11433),U_11435),c_Orderings_Obot__class_Obot(tc_fun(U_11433,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11433,U_11431)),hAPP(hAPP(c_Product__Type_OPair(U_11433,U_11431),U_11435),U_11432)),U_11434)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11433,U_11431)),hAPP(hAPP(c_Product__Type_OPair(U_11433,U_11431),U_11435),U_11432)),U_11434))
| ~ hBOOL(hAPP(hAPP(c_member(U_11431),U_11432),hAPP(c_Relation_OImage(U_11433,U_11431,U_11434),hAPP(hAPP(c_Set_Oinsert(U_11433),U_11435),c_Orderings_Obot__class_Obot(tc_fun(U_11433,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[f_3081_1]) ).
fof(f_3081_3,plain,
( ! [U_11445,U_11443,U_11441,U_11439,U_11437] :
( hBOOL(hAPP(hAPP(c_member(U_11437),U_11439),hAPP(c_Relation_OImage(U_11441,U_11437,U_11443),hAPP(hAPP(c_Set_Oinsert(U_11441),U_11445),c_Orderings_Obot__class_Obot(tc_fun(U_11441,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11441,U_11437)),hAPP(hAPP(c_Product__Type_OPair(U_11441,U_11437),U_11445),U_11439)),U_11443)) )
& ! [U_11444,U_11442,U_11440,U_11438,U_11436] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11440,U_11436)),hAPP(hAPP(c_Product__Type_OPair(U_11440,U_11436),U_11444),U_11438)),U_11442))
| ~ hBOOL(hAPP(hAPP(c_member(U_11436),U_11438),hAPP(c_Relation_OImage(U_11440,U_11436,U_11442),hAPP(hAPP(c_Set_Oinsert(U_11440),U_11444),c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool)))))) ) ),
inference(miniscope,[status(thm)],[f_3081_2]) ).
fof(f_3081_4,plain,
( ! [U_11437,U_11439,U_11441,U_11443,U_11445] :
( hBOOL(hAPP(hAPP(c_member(U_11437),U_11439),hAPP(c_Relation_OImage(U_11441,U_11437,U_11443),hAPP(hAPP(c_Set_Oinsert(U_11441),U_11445),c_Orderings_Obot__class_Obot(tc_fun(U_11441,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11441,U_11437)),hAPP(hAPP(c_Product__Type_OPair(U_11441,U_11437),U_11445),U_11439)),U_11443)) )
& ! [U_11438,U_11442,U_11436,U_11440,U_11444] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11440,U_11436)),hAPP(hAPP(c_Product__Type_OPair(U_11440,U_11436),U_11444),U_11438)),U_11442))
| ~ hBOOL(hAPP(hAPP(c_member(U_11436),U_11438),hAPP(c_Relation_OImage(U_11440,U_11436,U_11442),hAPP(hAPP(c_Set_Oinsert(U_11440),U_11444),c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool)))))) ) ),
inference(definitional_conversion,[status(esa)],[f_3081_3]) ).
cnf(f_3081_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11440,U_11436)),hAPP(hAPP(c_Product__Type_OPair(U_11440,U_11436),U_11444),U_11438)),U_11442))
| ~ hBOOL(hAPP(hAPP(c_member(U_11436),U_11438),hAPP(c_Relation_OImage(U_11440,U_11436,U_11442),hAPP(hAPP(c_Set_Oinsert(U_11440),U_11444),c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool)))))) ),
inference(clausify,[status(thm)],[f_3081_4]) ).
cnf(f_3081_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11437),U_11439),hAPP(c_Relation_OImage(U_11441,U_11437,U_11443),hAPP(hAPP(c_Set_Oinsert(U_11441),U_11445),c_Orderings_Obot__class_Obot(tc_fun(U_11441,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11441,U_11437)),hAPP(hAPP(c_Product__Type_OPair(U_11441,U_11437),U_11445),U_11439)),U_11443)) ),
inference(clausify,[status(thm)],[f_3081_4]) ).
fof(f_3082_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_inv__image__def]) ).
fof(f_3082_2,plain,
! [U_11449,U_11448,U_11447,U_11446] : hAPP(hAPP(c_Relation_Oinv__image(U_11446,U_11447),U_11448),U_11449) = hAPP(c_Set_OCollect(tc_prod(U_11447,U_11447)),hAPP(c_Product__Type_Oprod_Oprod__case(U_11447,U_11447,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11447,tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_fun(U_11447,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11447,tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_fun(U_11447,tc_HOL_Obool)),U_11447),c_COMBC(U_11447,tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11447,tc_prod(U_11446,U_11446)),tc_fun(U_11447,tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),U_11447),hAPP(c_COMBB(tc_prod(U_11446,U_11446),tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool),U_11447),c_member(tc_prod(U_11446,U_11446)))),hAPP(hAPP(c_COMBC(U_11447,tc_fun(U_11447,U_11446),tc_fun(U_11447,tc_prod(U_11446,U_11446))),hAPP(hAPP(c_COMBB(tc_fun(U_11446,tc_prod(U_11446,U_11446)),tc_fun(tc_fun(U_11447,U_11446),tc_fun(U_11447,tc_prod(U_11446,U_11446))),U_11447),c_COMBB(U_11446,tc_prod(U_11446,U_11446),U_11447)),hAPP(hAPP(c_COMBB(U_11446,tc_fun(U_11446,tc_prod(U_11446,U_11446)),U_11447),c_Product__Type_OPair(U_11446,U_11446)),U_11449))),U_11449)))),U_11448))),
inference(variable_rename,[status(thm)],[f_3082_1]) ).
fof(f_3082_3,plain,
! [U_11446,U_11447,U_11448,U_11449] : hAPP(hAPP(c_Relation_Oinv__image(U_11446,U_11447),U_11448),U_11449) = hAPP(c_Set_OCollect(tc_prod(U_11447,U_11447)),hAPP(c_Product__Type_Oprod_Oprod__case(U_11447,U_11447,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11447,tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_fun(U_11447,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11447,tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_fun(U_11447,tc_HOL_Obool)),U_11447),c_COMBC(U_11447,tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11447,tc_prod(U_11446,U_11446)),tc_fun(U_11447,tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),U_11447),hAPP(c_COMBB(tc_prod(U_11446,U_11446),tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool),U_11447),c_member(tc_prod(U_11446,U_11446)))),hAPP(hAPP(c_COMBC(U_11447,tc_fun(U_11447,U_11446),tc_fun(U_11447,tc_prod(U_11446,U_11446))),hAPP(hAPP(c_COMBB(tc_fun(U_11446,tc_prod(U_11446,U_11446)),tc_fun(tc_fun(U_11447,U_11446),tc_fun(U_11447,tc_prod(U_11446,U_11446))),U_11447),c_COMBB(U_11446,tc_prod(U_11446,U_11446),U_11447)),hAPP(hAPP(c_COMBB(U_11446,tc_fun(U_11446,tc_prod(U_11446,U_11446)),U_11447),c_Product__Type_OPair(U_11446,U_11446)),U_11449))),U_11449)))),U_11448))),
inference(definitional_conversion,[status(esa)],[f_3082_2]) ).
cnf(f_3082_4,plain,
hAPP(hAPP(c_Relation_Oinv__image(U_11446,U_11447),U_11448),U_11449) = hAPP(c_Set_OCollect(tc_prod(U_11447,U_11447)),hAPP(c_Product__Type_Oprod_Oprod__case(U_11447,U_11447,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11447,tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_fun(U_11447,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11447,tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_fun(U_11447,tc_HOL_Obool)),U_11447),c_COMBC(U_11447,tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11447,tc_prod(U_11446,U_11446)),tc_fun(U_11447,tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool)),U_11447),hAPP(c_COMBB(tc_prod(U_11446,U_11446),tc_fun(tc_fun(tc_prod(U_11446,U_11446),tc_HOL_Obool),tc_HOL_Obool),U_11447),c_member(tc_prod(U_11446,U_11446)))),hAPP(hAPP(c_COMBC(U_11447,tc_fun(U_11447,U_11446),tc_fun(U_11447,tc_prod(U_11446,U_11446))),hAPP(hAPP(c_COMBB(tc_fun(U_11446,tc_prod(U_11446,U_11446)),tc_fun(tc_fun(U_11447,U_11446),tc_fun(U_11447,tc_prod(U_11446,U_11446))),U_11447),c_COMBB(U_11446,tc_prod(U_11446,U_11446),U_11447)),hAPP(hAPP(c_COMBB(U_11446,tc_fun(U_11446,tc_prod(U_11446,U_11446)),U_11447),c_Product__Type_OPair(U_11446,U_11446)),U_11449))),U_11449)))),U_11448))),
inference(clausify,[status(thm)],[f_3082_3]) ).
fof(f_3083_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Image__empty]) ).
fof(f_3083_2,plain,
! [U_11452,U_11451,U_11450] : hAPP(c_Relation_OImage(U_11450,U_11451,U_11452),c_Orderings_Obot__class_Obot(tc_fun(U_11450,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11451,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3083_1]) ).
fof(f_3083_3,plain,
! [U_11450,U_11451,U_11452] : hAPP(c_Relation_OImage(U_11450,U_11451,U_11452),c_Orderings_Obot__class_Obot(tc_fun(U_11450,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11451,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_3083_2]) ).
cnf(f_3083_4,plain,
hAPP(c_Relation_OImage(U_11450,U_11451,U_11452),c_Orderings_Obot__class_Obot(tc_fun(U_11450,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11451,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3083_3]) ).
fof(f_3084_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Image__Un]) ).
fof(f_3084_2,plain,
! [U_11457,U_11456,U_11455,U_11454,U_11453] : hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11453,tc_HOL_Obool)),U_11456),U_11457)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11454,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),U_11456)),hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),U_11457)),
inference(variable_rename,[status(thm)],[f_3084_1]) ).
fof(f_3084_3,plain,
! [U_11453,U_11454,U_11455,U_11456,U_11457] : hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11453,tc_HOL_Obool)),U_11456),U_11457)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11454,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),U_11456)),hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),U_11457)),
inference(definitional_conversion,[status(esa)],[f_3084_2]) ).
cnf(f_3084_4,plain,
hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11453,tc_HOL_Obool)),U_11456),U_11457)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11454,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),U_11456)),hAPP(c_Relation_OImage(U_11453,U_11454,U_11455),U_11457)),
inference(clausify,[status(thm)],[f_3084_3]) ).
fof(f_3085_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Image__UN]) ).
fof(f_3085_2,plain,
! [U_11463,U_11462,U_11461,U_11460,U_11459,U_11458] : hAPP(c_Relation_OImage(U_11458,U_11459,U_11460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11461,tc_fun(U_11458,tc_HOL_Obool)),U_11462),U_11463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11461,tc_fun(U_11459,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_COMBB(tc_fun(U_11458,tc_HOL_Obool),tc_fun(U_11459,tc_HOL_Obool),U_11461),c_Relation_OImage(U_11458,U_11459,U_11460)),U_11463)),
inference(variable_rename,[status(thm)],[f_3085_1]) ).
fof(f_3085_3,plain,
! [U_11458,U_11459,U_11460,U_11461,U_11462,U_11463] : hAPP(c_Relation_OImage(U_11458,U_11459,U_11460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11461,tc_fun(U_11458,tc_HOL_Obool)),U_11462),U_11463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11461,tc_fun(U_11459,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_COMBB(tc_fun(U_11458,tc_HOL_Obool),tc_fun(U_11459,tc_HOL_Obool),U_11461),c_Relation_OImage(U_11458,U_11459,U_11460)),U_11463)),
inference(definitional_conversion,[status(esa)],[f_3085_2]) ).
cnf(f_3085_4,plain,
hAPP(c_Relation_OImage(U_11458,U_11459,U_11460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11461,tc_fun(U_11458,tc_HOL_Obool)),U_11462),U_11463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11461,tc_fun(U_11459,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_COMBB(tc_fun(U_11458,tc_HOL_Obool),tc_fun(U_11459,tc_HOL_Obool),U_11461),c_Relation_OImage(U_11458,U_11459,U_11460)),U_11463)),
inference(clausify,[status(thm)],[f_3085_3]) ).
fof(f_3086_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Image__Int__subset]) ).
fof(f_3086_2,plain,
! [U_11468,U_11467,U_11466,U_11465,U_11464] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11464,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11465,tc_HOL_Obool)),U_11467),U_11468))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11464,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),U_11467)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),U_11468)))),
inference(variable_rename,[status(thm)],[f_3086_1]) ).
fof(f_3086_3,plain,
! [U_11464,U_11465,U_11466,U_11467,U_11468] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11464,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11465,tc_HOL_Obool)),U_11467),U_11468))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11464,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),U_11467)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),U_11468)))),
inference(definitional_conversion,[status(esa)],[f_3086_2]) ).
cnf(f_3086_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11464,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11465,tc_HOL_Obool)),U_11467),U_11468))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11464,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),U_11467)),hAPP(c_Relation_OImage(U_11465,U_11464,U_11466),U_11468)))),
inference(clausify,[status(thm)],[f_3086_3]) ).
fof(f_3087_1,plain,
! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
| ~ 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)) ),
inference(fof_nnf,[status(thm)],[fact_Image__mono]) ).
fof(f_3087_2,plain,
! [U_11474,U_11473,U_11472,U_11471,U_11470,U_11469] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11470,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11469,U_11470,U_11471),U_11473)),hAPP(c_Relation_OImage(U_11469,U_11470,U_11472),U_11474)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11469,tc_HOL_Obool)),U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11469,U_11470),tc_HOL_Obool)),U_11471),U_11472)) ),
inference(variable_rename,[status(thm)],[f_3087_1]) ).
fof(f_3087_3,plain,
! [U_11469,U_11470,U_11471,U_11472,U_11473,U_11474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11470,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11469,U_11470,U_11471),U_11473)),hAPP(c_Relation_OImage(U_11469,U_11470,U_11472),U_11474)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11469,tc_HOL_Obool)),U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11469,U_11470),tc_HOL_Obool)),U_11471),U_11472)) ),
inference(definitional_conversion,[status(esa)],[f_3087_2]) ).
cnf(f_3087_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11470,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11469,U_11470,U_11471),U_11473)),hAPP(c_Relation_OImage(U_11469,U_11470,U_11472),U_11474)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11469,tc_HOL_Obool)),U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11469,U_11470),tc_HOL_Obool)),U_11471),U_11472)) ),
inference(clausify,[status(thm)],[f_3087_3]) ).
fof(f_3088_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Un__Image]) ).
fof(f_3088_2,plain,
! [U_11479,U_11478,U_11477,U_11476,U_11475] : hAPP(c_Relation_OImage(U_11475,U_11476,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11475,U_11476),tc_HOL_Obool)),U_11477),U_11478)),U_11479) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11475,U_11476,U_11477),U_11479)),hAPP(c_Relation_OImage(U_11475,U_11476,U_11478),U_11479)),
inference(variable_rename,[status(thm)],[f_3088_1]) ).
fof(f_3088_3,plain,
! [U_11475,U_11476,U_11477,U_11478,U_11479] : hAPP(c_Relation_OImage(U_11475,U_11476,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11475,U_11476),tc_HOL_Obool)),U_11477),U_11478)),U_11479) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11475,U_11476,U_11477),U_11479)),hAPP(c_Relation_OImage(U_11475,U_11476,U_11478),U_11479)),
inference(definitional_conversion,[status(esa)],[f_3088_2]) ).
cnf(f_3088_4,plain,
hAPP(c_Relation_OImage(U_11475,U_11476,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11475,U_11476),tc_HOL_Obool)),U_11477),U_11478)),U_11479) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11475,U_11476,U_11477),U_11479)),hAPP(c_Relation_OImage(U_11475,U_11476,U_11478),U_11479)),
inference(clausify,[status(thm)],[f_3088_3]) ).
fof(f_3089_1,plain,
! [V_f_2,V_r_2,T_c,V_y_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_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
| ~ 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)) )
& ( 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))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__inv__image]) ).
fof(f_3089_2,plain,
! [U_11485,U_11484,U_11483,U_11482,U_11481,U_11480] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11480,U_11480)),hAPP(hAPP(c_Product__Type_OPair(U_11480,U_11480),U_11481),U_11482)),hAPP(hAPP(c_Relation_Oinv__image(U_11483,U_11480),U_11484),U_11485)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11483,U_11483)),hAPP(hAPP(c_Product__Type_OPair(U_11483,U_11483),hAPP(U_11485,U_11481)),hAPP(U_11485,U_11482))),U_11484)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11483,U_11483)),hAPP(hAPP(c_Product__Type_OPair(U_11483,U_11483),hAPP(U_11485,U_11481)),hAPP(U_11485,U_11482))),U_11484))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11480,U_11480)),hAPP(hAPP(c_Product__Type_OPair(U_11480,U_11480),U_11481),U_11482)),hAPP(hAPP(c_Relation_Oinv__image(U_11483,U_11480),U_11484),U_11485))) ) ),
inference(variable_rename,[status(thm)],[f_3089_1]) ).
fof(f_3089_3,plain,
( ! [U_11497,U_11495,U_11493,U_11491,U_11489] :
( ! [U_11487] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11487,U_11487)),hAPP(hAPP(c_Product__Type_OPair(U_11487,U_11487),U_11489),U_11491)),hAPP(hAPP(c_Relation_Oinv__image(U_11493,U_11487),U_11495),U_11497)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11493,U_11493)),hAPP(hAPP(c_Product__Type_OPair(U_11493,U_11493),hAPP(U_11497,U_11489)),hAPP(U_11497,U_11491))),U_11495)) )
& ! [U_11496,U_11494,U_11492,U_11490,U_11488] :
( ! [U_11486] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11486,U_11486)),hAPP(hAPP(c_Product__Type_OPair(U_11486,U_11486),U_11488),U_11490)),hAPP(hAPP(c_Relation_Oinv__image(U_11492,U_11486),U_11494),U_11496)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11492,U_11492)),hAPP(hAPP(c_Product__Type_OPair(U_11492,U_11492),hAPP(U_11496,U_11488)),hAPP(U_11496,U_11490))),U_11494)) ) ),
inference(miniscope,[status(thm)],[f_3089_2]) ).
fof(f_3089_4,plain,
( ! [U_11487,U_11489,U_11491,U_11493,U_11495,U_11497] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11487,U_11487)),hAPP(hAPP(c_Product__Type_OPair(U_11487,U_11487),U_11489),U_11491)),hAPP(hAPP(c_Relation_Oinv__image(U_11493,U_11487),U_11495),U_11497)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11493,U_11493)),hAPP(hAPP(c_Product__Type_OPair(U_11493,U_11493),hAPP(U_11497,U_11489)),hAPP(U_11497,U_11491))),U_11495)) )
& ! [U_11490,U_11488,U_11492,U_11486,U_11494,U_11496] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11486,U_11486)),hAPP(hAPP(c_Product__Type_OPair(U_11486,U_11486),U_11488),U_11490)),hAPP(hAPP(c_Relation_Oinv__image(U_11492,U_11486),U_11494),U_11496)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11492,U_11492)),hAPP(hAPP(c_Product__Type_OPair(U_11492,U_11492),hAPP(U_11496,U_11488)),hAPP(U_11496,U_11490))),U_11494)) ) ),
inference(definitional_conversion,[status(esa)],[f_3089_3]) ).
cnf(f_3089_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11486,U_11486)),hAPP(hAPP(c_Product__Type_OPair(U_11486,U_11486),U_11488),U_11490)),hAPP(hAPP(c_Relation_Oinv__image(U_11492,U_11486),U_11494),U_11496)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11492,U_11492)),hAPP(hAPP(c_Product__Type_OPair(U_11492,U_11492),hAPP(U_11496,U_11488)),hAPP(U_11496,U_11490))),U_11494)) ),
inference(clausify,[status(thm)],[f_3089_4]) ).
cnf(f_3089_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11487,U_11487)),hAPP(hAPP(c_Product__Type_OPair(U_11487,U_11487),U_11489),U_11491)),hAPP(hAPP(c_Relation_Oinv__image(U_11493,U_11487),U_11495),U_11497)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11493,U_11493)),hAPP(hAPP(c_Product__Type_OPair(U_11493,U_11493),hAPP(U_11497,U_11489)),hAPP(U_11497,U_11491))),U_11495)) ),
inference(clausify,[status(thm)],[f_3089_4]) ).
fof(f_3090_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_Image__INT__subset]) ).
fof(f_3090_2,plain,
! [U_11503,U_11502,U_11501,U_11500,U_11499,U_11498] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11498,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11499,U_11498,U_11500),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11501,tc_fun(U_11499,tc_HOL_Obool)),U_11502),U_11503))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11501,tc_fun(U_11498,tc_HOL_Obool)),U_11502),hAPP(hAPP(c_COMBB(tc_fun(U_11499,tc_HOL_Obool),tc_fun(U_11498,tc_HOL_Obool),U_11501),c_Relation_OImage(U_11499,U_11498,U_11500)),U_11503)))),
inference(variable_rename,[status(thm)],[f_3090_1]) ).
fof(f_3090_3,plain,
! [U_11498,U_11499,U_11500,U_11501,U_11502,U_11503] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11498,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11499,U_11498,U_11500),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11501,tc_fun(U_11499,tc_HOL_Obool)),U_11502),U_11503))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11501,tc_fun(U_11498,tc_HOL_Obool)),U_11502),hAPP(hAPP(c_COMBB(tc_fun(U_11499,tc_HOL_Obool),tc_fun(U_11498,tc_HOL_Obool),U_11501),c_Relation_OImage(U_11499,U_11498,U_11500)),U_11503)))),
inference(definitional_conversion,[status(esa)],[f_3090_2]) ).
cnf(f_3090_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11498,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11499,U_11498,U_11500),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11501,tc_fun(U_11499,tc_HOL_Obool)),U_11502),U_11503))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11501,tc_fun(U_11498,tc_HOL_Obool)),U_11502),hAPP(hAPP(c_COMBB(tc_fun(U_11499,tc_HOL_Obool),tc_fun(U_11498,tc_HOL_Obool),U_11501),c_Relation_OImage(U_11499,U_11498,U_11500)),U_11503)))),
inference(clausify,[status(thm)],[f_3090_3]) ).
fof(f_3091_1,plain,
! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))
| ~ 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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__ImageI]) ).
fof(f_3091_2,plain,
! [U_11509,U_11508,U_11507,U_11506,U_11505,U_11504] :
( hBOOL(hAPP(hAPP(c_member(U_11507),U_11508),hAPP(c_Relation_OImage(U_11504,U_11507,U_11509),U_11506)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11504,U_11507)),hAPP(hAPP(c_Product__Type_OPair(U_11504,U_11507),U_11505),U_11508)),U_11509))
| ~ hBOOL(hAPP(hAPP(c_member(U_11504),U_11505),U_11506)) ),
inference(variable_rename,[status(thm)],[f_3091_1]) ).
fof(f_3091_3,plain,
! [U_11504,U_11505,U_11506,U_11507,U_11508,U_11509] :
( hBOOL(hAPP(hAPP(c_member(U_11507),U_11508),hAPP(c_Relation_OImage(U_11504,U_11507,U_11509),U_11506)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11504,U_11507)),hAPP(hAPP(c_Product__Type_OPair(U_11504,U_11507),U_11505),U_11508)),U_11509))
| ~ hBOOL(hAPP(hAPP(c_member(U_11504),U_11505),U_11506)) ),
inference(definitional_conversion,[status(esa)],[f_3091_2]) ).
cnf(f_3091_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11507),U_11508),hAPP(c_Relation_OImage(U_11504,U_11507,U_11509),U_11506)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11504,U_11507)),hAPP(hAPP(c_Product__Type_OPair(U_11504,U_11507),U_11505),U_11508)),U_11509))
| ~ hBOOL(hAPP(hAPP(c_member(U_11504),U_11505),U_11506)) ),
inference(clausify,[status(thm)],[f_3091_3]) ).
fof(f_3092_1,plain,
! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
| ! [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))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [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))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Image__iff]) ).
fof(f_3092_2,plain,
! [U_11516,U_11515,U_11514,U_11513,U_11512] :
( ( hBOOL(hAPP(hAPP(c_member(U_11512),U_11513),hAPP(c_Relation_OImage(U_11514,U_11512,U_11515),U_11516)))
| ! [U_11511] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11514,U_11512)),hAPP(hAPP(c_Product__Type_OPair(U_11514,U_11512),U_11511),U_11513)),U_11515))
| ~ hBOOL(hAPP(hAPP(c_member(U_11514),U_11511),U_11516)) ) )
& ( ? [U_11510] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11514,U_11512)),hAPP(hAPP(c_Product__Type_OPair(U_11514,U_11512),U_11510),U_11513)),U_11515))
& hBOOL(hAPP(hAPP(c_member(U_11514),U_11510),U_11516)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11512),U_11513),hAPP(c_Relation_OImage(U_11514,U_11512,U_11515),U_11516))) ) ),
inference(variable_rename,[status(thm)],[f_3092_1]) ).
fof(f_3092_3,plain,
( ! [U_11526,U_11524,U_11522,U_11520,U_11518] :
( hBOOL(hAPP(hAPP(c_member(U_11518),U_11520),hAPP(c_Relation_OImage(U_11522,U_11518,U_11524),U_11526)))
| ! [U_11511] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11522,U_11518)),hAPP(hAPP(c_Product__Type_OPair(U_11522,U_11518),U_11511),U_11520)),U_11524))
| ~ hBOOL(hAPP(hAPP(c_member(U_11522),U_11511),U_11526)) ) )
& ! [U_11525,U_11523,U_11521,U_11519,U_11517] :
( ? [U_11510] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11521,U_11517)),hAPP(hAPP(c_Product__Type_OPair(U_11521,U_11517),U_11510),U_11519)),U_11523))
& hBOOL(hAPP(hAPP(c_member(U_11521),U_11510),U_11525)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11517),U_11519),hAPP(c_Relation_OImage(U_11521,U_11517,U_11523),U_11525))) ) ),
inference(miniscope,[status(thm)],[f_3092_2]) ).
fof(f_3092_4,plain,
( ! [U_11526,U_11524,U_11522,U_11520,U_11518] :
( hBOOL(hAPP(hAPP(c_member(U_11518),U_11520),hAPP(c_Relation_OImage(U_11522,U_11518,U_11524),U_11526)))
| ! [U_11511] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11522,U_11518)),hAPP(hAPP(c_Product__Type_OPair(U_11522,U_11518),U_11511),U_11520)),U_11524))
| ~ hBOOL(hAPP(hAPP(c_member(U_11522),U_11511),U_11526)) ) )
& ! [U_11525,U_11523,U_11521,U_11519,U_11517] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11521,U_11517)),hAPP(hAPP(c_Product__Type_OPair(U_11521,U_11517),sK287(U_11525,U_11523,U_11521,U_11519,U_11517)),U_11519)),U_11523))
& hBOOL(hAPP(hAPP(c_member(U_11521),sK287(U_11525,U_11523,U_11521,U_11519,U_11517)),U_11525)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11517),U_11519),hAPP(c_Relation_OImage(U_11521,U_11517,U_11523),U_11525))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_11510,sK287(U_11525,U_11523,U_11521,U_11519,U_11517))],[f_3092_3]) ).
fof(f_3092_5,plain,
( ! [U_11519,U_11521,U_11517,U_11525,U_11523] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11521,U_11517)),hAPP(hAPP(c_Product__Type_OPair(U_11521,U_11517),sK287(U_11525,U_11523,U_11521,U_11519,U_11517)),U_11519)),U_11523))
| ~ sP870(U_11519,U_11521,U_11517,U_11525,U_11523) )
& ! [U_11519,U_11521,U_11517,U_11525,U_11523] :
( hBOOL(hAPP(hAPP(c_member(U_11521),sK287(U_11525,U_11523,U_11521,U_11519,U_11517)),U_11525))
| ~ sP870(U_11519,U_11521,U_11517,U_11525,U_11523) )
& ! [U_11526,U_11511,U_11518,U_11520,U_11524,U_11522] :
( hBOOL(hAPP(hAPP(c_member(U_11518),U_11520),hAPP(c_Relation_OImage(U_11522,U_11518,U_11524),U_11526)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11522,U_11518)),hAPP(hAPP(c_Product__Type_OPair(U_11522,U_11518),U_11511),U_11520)),U_11524))
| ~ hBOOL(hAPP(hAPP(c_member(U_11522),U_11511),U_11526)) )
& ! [U_11519,U_11521,U_11517,U_11525,U_11523] :
( sP870(U_11519,U_11521,U_11517,U_11525,U_11523)
| ~ hBOOL(hAPP(hAPP(c_member(U_11517),U_11519),hAPP(c_Relation_OImage(U_11521,U_11517,U_11523),U_11525))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP870])],[f_3092_4]) ).
cnf(f_3092_6,plain,
( sP870(U_11519,U_11521,U_11517,U_11525,U_11523)
| ~ hBOOL(hAPP(hAPP(c_member(U_11517),U_11519),hAPP(c_Relation_OImage(U_11521,U_11517,U_11523),U_11525))) ),
inference(clausify,[status(thm)],[f_3092_5]) ).
cnf(f_3092_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_11518),U_11520),hAPP(c_Relation_OImage(U_11522,U_11518,U_11524),U_11526)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11522,U_11518)),hAPP(hAPP(c_Product__Type_OPair(U_11522,U_11518),U_11511),U_11520)),U_11524))
| ~ hBOOL(hAPP(hAPP(c_member(U_11522),U_11511),U_11526)) ),
inference(clausify,[status(thm)],[f_3092_5]) ).
cnf(f_3092_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_11521),sK287(U_11525,U_11523,U_11521,U_11519,U_11517)),U_11525))
| ~ sP870(U_11519,U_11521,U_11517,U_11525,U_11523) ),
inference(clausify,[status(thm)],[f_3092_5]) ).
cnf(f_3092_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11521,U_11517)),hAPP(hAPP(c_Product__Type_OPair(U_11521,U_11517),sK287(U_11525,U_11523,U_11521,U_11519,U_11517)),U_11519)),U_11523))
| ~ sP870(U_11519,U_11521,U_11517,U_11525,U_11523) ),
inference(clausify,[status(thm)],[f_3092_5]) ).
fof(f_3093_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_Image__eq__UN]) ).
fof(f_3093_2,plain,
! [U_11530,U_11529,U_11528,U_11527] : hAPP(c_Relation_OImage(U_11527,U_11528,U_11529),U_11530) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11527,tc_fun(U_11528,tc_HOL_Obool)),U_11530),hAPP(hAPP(c_COMBB(tc_fun(U_11527,tc_HOL_Obool),tc_fun(U_11528,tc_HOL_Obool),U_11527),c_Relation_OImage(U_11527,U_11528,U_11529)),hAPP(hAPP(c_COMBC(U_11527,tc_fun(U_11527,tc_HOL_Obool),tc_fun(U_11527,tc_HOL_Obool)),c_Set_Oinsert(U_11527)),c_Orderings_Obot__class_Obot(tc_fun(U_11527,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3093_1]) ).
fof(f_3093_3,plain,
! [U_11527,U_11528,U_11529,U_11530] : hAPP(c_Relation_OImage(U_11527,U_11528,U_11529),U_11530) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11527,tc_fun(U_11528,tc_HOL_Obool)),U_11530),hAPP(hAPP(c_COMBB(tc_fun(U_11527,tc_HOL_Obool),tc_fun(U_11528,tc_HOL_Obool),U_11527),c_Relation_OImage(U_11527,U_11528,U_11529)),hAPP(hAPP(c_COMBC(U_11527,tc_fun(U_11527,tc_HOL_Obool),tc_fun(U_11527,tc_HOL_Obool)),c_Set_Oinsert(U_11527)),c_Orderings_Obot__class_Obot(tc_fun(U_11527,tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_3093_2]) ).
cnf(f_3093_4,plain,
hAPP(c_Relation_OImage(U_11527,U_11528,U_11529),U_11530) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11527,tc_fun(U_11528,tc_HOL_Obool)),U_11530),hAPP(hAPP(c_COMBB(tc_fun(U_11527,tc_HOL_Obool),tc_fun(U_11528,tc_HOL_Obool),U_11527),c_Relation_OImage(U_11527,U_11528,U_11529)),hAPP(hAPP(c_COMBC(U_11527,tc_fun(U_11527,tc_HOL_Obool),tc_fun(U_11527,tc_HOL_Obool)),c_Set_Oinsert(U_11527)),c_Orderings_Obot__class_Obot(tc_fun(U_11527,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3093_3]) ).
fof(f_3094_1,plain,
! [V_j_2,V_i_2,T_b] :
( 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))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int]) ).
fof(f_3094_2,plain,
! [U_11533,U_11532,U_11531] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_11531),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),U_11532),U_11533)),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(U_11531),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11531),U_11532)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11531),U_11533))
| ~ class_Rings_Oring__1(U_11531) ),
inference(variable_rename,[status(thm)],[f_3094_1]) ).
fof(f_3094_3,plain,
! [U_11531,U_11532,U_11533] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_11531),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),U_11532),U_11533)),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(U_11531),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11531),U_11532)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11531),U_11533))
| ~ class_Rings_Oring__1(U_11531) ),
inference(definitional_conversion,[status(esa)],[f_3094_2]) ).
cnf(f_3094_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_11531),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),U_11532),U_11533)),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(U_11531),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11531),U_11532)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11531),U_11533))
| ~ class_Rings_Oring__1(U_11531) ),
inference(clausify,[status(thm)],[f_3094_3]) ).
fof(f_3095_1,plain,
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))))),
inference(fof_nnf,[status(thm)],[fact_One__int__def]) ).
fof(f_3095_2,plain,
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))))),
inference(definitional_conversion,[status(esa)],[f_3095_1]) ).
cnf(f_3095_3,plain,
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))))),
inference(clausify,[status(thm)],[f_3095_2]) ).
fof(f_3096_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_mult]) ).
fof(f_3096_2,plain,
! [U_11537,U_11536,U_11535,U_11534] : 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),U_11534),U_11535)),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),U_11536),U_11537)),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),U_11534),U_11536)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11535),U_11537))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11534),U_11537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11535),U_11536)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3096_1]) ).
fof(f_3096_3,plain,
! [U_11534,U_11535,U_11536,U_11537] : 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),U_11534),U_11535)),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),U_11536),U_11537)),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),U_11534),U_11536)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11535),U_11537))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11534),U_11537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11535),U_11536)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_3096_2]) ).
cnf(f_3096_4,plain,
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),U_11534),U_11535)),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),U_11536),U_11537)),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),U_11534),U_11536)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11535),U_11537))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11534),U_11537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11535),U_11536)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3096_3]) ).
fof(f_3097_1,plain,
! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inverse]) ).
fof(f_3097_2,plain,
! [U_11538] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11538)) = U_11538,
inference(variable_rename,[status(thm)],[f_3097_1]) ).
fof(f_3097_3,plain,
! [U_11538] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11538)) = U_11538,
inference(definitional_conversion,[status(esa)],[f_3097_2]) ).
cnf(f_3097_4,plain,
hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11538)) = U_11538,
inference(clausify,[status(thm)],[f_3097_3]) ).
fof(f_3098_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_minus]) ).
fof(f_3098_2,plain,
! [U_11540,U_11539] : 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),U_11539),U_11540)),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),U_11540),U_11539)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3098_1]) ).
fof(f_3098_3,plain,
! [U_11539,U_11540] : 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),U_11539),U_11540)),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),U_11540),U_11539)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_3098_2]) ).
cnf(f_3098_4,plain,
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),U_11539),U_11540)),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),U_11540),U_11539)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3098_3]) ).
fof(f_3099_1,plain,
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))))),
inference(fof_nnf,[status(thm)],[fact_Zero__int__def]) ).
fof(f_3099_2,plain,
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))))),
inference(definitional_conversion,[status(esa)],[f_3099_1]) ).
cnf(f_3099_3,plain,
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))))),
inference(clausify,[status(thm)],[f_3099_2]) ).
fof(f_3100_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_int__def]) ).
fof(f_3100_2,plain,
! [U_11541] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11541) = 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),U_11541),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))))),
inference(variable_rename,[status(thm)],[f_3100_1]) ).
fof(f_3100_3,plain,
! [U_11541] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11541) = 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),U_11541),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))))),
inference(definitional_conversion,[status(esa)],[f_3100_2]) ).
cnf(f_3100_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11541) = 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),U_11541),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))))),
inference(clausify,[status(thm)],[f_3100_3]) ).
fof(f_3101_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_add]) ).
fof(f_3101_2,plain,
! [U_11545,U_11544,U_11543,U_11542] : 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),U_11542),U_11543)),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),U_11544),U_11545)),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),U_11542),U_11544)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11543),U_11545))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3101_1]) ).
fof(f_3101_3,plain,
! [U_11542,U_11543,U_11544,U_11545] : 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),U_11542),U_11543)),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),U_11544),U_11545)),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),U_11542),U_11544)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11543),U_11545))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_3101_2]) ).
cnf(f_3101_4,plain,
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),U_11542),U_11543)),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),U_11544),U_11545)),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),U_11542),U_11544)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11543),U_11545))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3101_3]) ).
fof(f_3102_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat]) ).
fof(f_3102_2,plain,
! [U_11547,U_11546] : 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),U_11546),U_11547)),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),U_11546),U_11547),
inference(variable_rename,[status(thm)],[f_3102_1]) ).
fof(f_3102_3,plain,
! [U_11546,U_11547] : 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),U_11546),U_11547)),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),U_11546),U_11547),
inference(definitional_conversion,[status(esa)],[f_3102_2]) ).
cnf(f_3102_4,plain,
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),U_11546),U_11547)),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),U_11546),U_11547),
inference(clausify,[status(thm)],[f_3102_3]) ).
fof(f_3103_1,plain,
! [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))))))),
inference(fof_nnf,[status(thm)],[fact_minus__int__def]) ).
fof(f_3103_2,plain,
! [U_11548] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11548) = 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,U_11548)),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))))))),
inference(variable_rename,[status(thm)],[f_3103_1]) ).
fof(f_3103_3,plain,
! [U_11548] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11548) = 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,U_11548)),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))))))),
inference(definitional_conversion,[status(esa)],[f_3103_2]) ).
cnf(f_3103_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11548) = 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,U_11548)),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))))))),
inference(clausify,[status(thm)],[f_3103_3]) ).
fof(f_3104_1,plain,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( ( 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)))))))
| ~ 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))) )
& ( 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)))
| ~ 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))))))) ) ),
inference(fof_nnf,[status(thm)],[fact_less]) ).
fof(f_3104_2,plain,
! [U_11552,U_11551,U_11550,U_11549] :
( ( 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),U_11549),U_11550)),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),U_11551),U_11552)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11549),U_11552)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11551),U_11550))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11549),U_11552)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11551),U_11550)))
| ~ 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),U_11549),U_11550)),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),U_11551),U_11552)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(variable_rename,[status(thm)],[f_3104_1]) ).
fof(f_3104_3,plain,
( ! [U_11560,U_11558,U_11556,U_11554] :
( 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),U_11554),U_11556)),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),U_11558),U_11560)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11554),U_11560)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11558),U_11556))) )
&